Battling Resistance to Antibiotics and Pesticides: An Economic Approach 1891853511, 9781891853517

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Battling Resistance to Antibiotics and Pesticides An Economic Approach

Edited by

Ramanan Laxminarayan

Resources for the Future Washington, DC

©2003 Resou rces for th e Fu tu re All righ ts reserved. No p art of th is p u blication m ay be rep rodu ced by an y m ean s, eith er elect ro n ic o r m ech an ical, wit h o u t p erm issio n in writ in g fro m t h e p u b lish er, excep t u n der th e con dition s given in th e followin g p aragrap h : Au th orization to p h otocop y item s for in tern al or p erson al u se, th e in tern al or p erson al u se of sp ecific clien ts, an d for edu cation al classroom u se is gran ted by Resou rces for th e Fu tu re, p rovided th at th e ap p rop riate fee is p aid directly to Cop yrigh t Clearan ce Cen ter, 222 Rosewood Drive, Dan vers, MA 01923, USA. Telep h on e (978) 750–8400; fax (978) 646–8600. Prin ted in th e Un ited States of Am erica An RFF Press book Pu blish ed by Resou rces for th e Fu tu re 1616 P Street, NW, Wash in gton , DC 20036–1400 www.rff.org Library o f Co n gress Catalo gin g-in -Publicatio n Data Bat t lin g resist an ce t o an t ib io t ics an d p est icid es : an eco n o m ic ap p ro ach / Ram an an Laxm in arayan , editor. p . ; cm . In clu des in dex. ISBN 1-891853-51-1 (h ardcover : alk. p ap er) 1. Dru g resistan ce in m icroorgan ism s. 2. Pesticide resistan ce. 3. Pesticide resistan ce—Econ om ic asp ects. [DNLM: 1. Dru g Resistan ce. 2. An tibiotics—econ om ics. 3. An tibiotics— stan dards. 4. Pesticides—econ om ics. 5. Pesticides—stan dards. W B 330 B336 2002] I. Laxm in arayan , Ram an an . QR177 .B384 2002 616'.01—dc21 2002010243 f e d c b a Th e p ap er in th is book m eets th e gu idelin es for p erm an en ce an d du rability of th e Com m it t ee o n Pro d u ct io n Gu id elin es fo r Bo o k Lo n gevit y o f t h e Co u n cil o n Lib rary Resou rces. Th e t ext o f t h is b o o k was d esign ed b y Bet sy Ku lam er an d t yp eset in St o n e Serif an d Ston e San s by Carol Levie. Th e cover was design ed by Marek An tion iak.

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ISBN 1–891853–51–1

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Resources for the Future

Directors Cath erin e G. Abbott Joan Z. Bern stein Ju lia Carabias Lillo Norm an L. Ch risten sen Jr. Jam es H. S. Coop er W. Bowm an Cu tter Joh n M. Deu tch Dod A. Fraser Kath ryn S. Fu ller Mary A. Gad e F. Hen ry Habich t II David G. Hawkin s Lawren ce H. Lin d en Lawren ce U. Lu ch in i Jim Mad d y Fran k L. Matth ews William D. Nord h au s Jam es F. O’Grad y Jr. Steven W. Percy Mark A. Pisan o Roger W. San t Robert M. Solow Josep h E. Stiglitz Ed ward L. Stroh beh n Jr.

Officers Robert E. Grad y, Chairm an Fran k E. Loy, Vice Chairm an Pau l R. Portn ey, President Ed ward F. Han d , Vice President–Finance and Adm inistration Raym on d J. Kop p , Vice President–Program s Lesli A. Creed on , Corporate Secretary and Director of Developm ent

Contents

Contributors........................................................................................................ix About This Book .................................................................................................xi Introduction: On the Economics of Resistance .................................................1 Ramanan Laxminarayan

PART I. ISSUES OF OPTIM AL M ANAGEM ENT OF RESISTANCE 1

Dynamics of Antibiotic Use: Ecological versus Interventionist Strategies To M anage Resistance to Antibiotics ......................................17 James E. Wilen and Siwa M sangi

2

Using Antibiotics When Resistance Is Renewable ....................................42 Robert Rowthorn and Gardner M . Brown

3

Value of Treatment Heterogeneity for Infectious Diseases .....................63 Ramanan Laxminarayan and M artin L. Weitzman

Commentary: To Take or Not To Take the Antibiotic? .........................................76

James N. Sanchirico Commentary: Same Infection, Same Time, Same Antibiotic? ..............................84

Stephen W. Salant

4

Pest M obility, M arket Share, and the Efficacy of Refuge Requirements for Resistance M anagement ...........................................................................94 Silvia Secchi and Bruce A. Babcock

Commentary: Need for Direct Collaboration between Economists

and Biologists ............................................................................................113 Fred Gould

• v •

vi • Contents PART II. THE IM PACT OF RESISTANCE 5

The Impact of Resistance on Antibiotic Demand in Patients with Ear Infections ..................................................................................119 David H. Howard and Kimberly J. Rask

Commentary: M easuring the Cost of Resistance ...............................................134

Ramanan Laxminarayan

6

What Can We Learn from the Economics of Pesticides? Impact Assessment of Genetically M odified Plants ...............................137 Hermann Waibel, Jan C. Zadoks, and Gerd Fleischer

Commentary: The Role of Ecosystem Complexity in Genetically

M odified Organisms ..................................................................................158 Karl Seeley

7

Elements of Economic Resistance M anagement Strategies— Empirical Evidence from Case Studies in Germany ................................161 Gerd Fleischer and Hermann Waibel

Commentary: Can We Justify Resistance M anagement Strategies

for Conventional Pesticides?.......................................................................180 Fred Gould

8

Pesticide Resistance, the Precautionary Principle, and the Regulation of Bt Corn: Real Option and Rational Option Approaches to Decisionmaking ..............................................................184 Benoît M orel, R. Scott Farrow, Felicia Wu, and Elizabeth A. Casman

9

Resistance Economics of Transgenic Crops under Uncertainty: A Real Option Approach .........................................................................214 Justus Wesseler

Commentary: Economics of Transgenic Crops and Pest Resistance:

An Epidemiological Perspective .................................................................238 Christopher A. Gilligan

PART III. THE BEHAVIOR OF FIRM S 10 An Economic M odel of a Genetic Resistance Commons: Effects of M arket Structure Applied to Biotechnology in Agriculture ...........................................................................................263 Douglas Noonan Commentary: Does the M onopolist Care about Resistance?..............................288

Carolyn Fischer

Contents • vii

11 The Interaction of Dynamic Problems and Dynamic Policies: Some Economics of Biotechnology ........................................................293 Timo Goeschl and Timothy Swanson

12 Industrial Organization and Institutional Considerations in Agricultural Pest Resistance M anagement .............................................330 Jennifer Alix and David Zilberman Commentary: Strategic Issues in Agricultural Pest Resistance M anagement .......357

R. David Simpson

Index ................................................................................................................363 About the Editor ..............................................................................................377

Contributors

Jennifer Alix, gradu ate stu den t, Dep artm en t of Agricu ltu ral an d Resou rce Econ om ics, Un iversity of Californ ia, Berkeley Bruce A. Babcock, d irect o r, Cen t er fo r Agricu lt u ral an d Ru ral Develo p m en t , an d p rofessor, Dep artm en t of Econ om ics, Iowa State Un iversity Gardner M . Brown, p rofessor, Dep artm en t of Econ om ics, Un iversity of Wash in gton Elizabeth A. Casman, research en gin eer, Dep artm en t of En gin eerin g an d Pu blic Policy Carn egie Mellon Un iversity R. Scott Farrow, p rin cip al research econ om ist, Dep artm en t of En gin eerin g an d Pu blic Policy, an d director, Cen ter for th e Stu dy an d Im p rovem en t of Regu lation , Carn egie Mellon Un iversity Carolyn Fischer, fellow, Resou rces for th e Fu tu re Gerd Fleischer, In t egrat ed Pest Man agem en t p o licy exp ert , Ru ral Develo p m en t Dep artm en t, Th e World Ban k Christopher A. Gilligan, p rofessor, Dep artm en t of Plan t Scien ces, Un iversity of Cam bridge, Un ited Kin gdom Timo Goeschl, u n iversity lectu rer, Dep artm en t of Lan d Econ om y, Un iversity of Cam bridge, Un ited Kin gdom Fred Gould, p rofessor, Dep artm en t of En tom ology, North Carolin a State Un iversity David H. Howard, assistan t p rofessor, Rollin s Sch ool of Pu blic Health , Em ory Un iversity

• ix •

x • Contributors Ramanan Laxminarayan, fellow, Resou rces for th e Fu tu re Benoît M orel, sen ior lectu rer, Dep artm en t of En gin eerin g an d Pu blic Policy, an d Dep artm en t of Ph ysics, Carn egie Mellon Un iversity Siwa M sangi, gradu ate stu den t, Dep artm en t of Agricu ltu ral an d Resou rce Econ om ics, Un iversity of Californ ia, Davis Douglas N oonan, grad u at e st u d en t , Harris Sch o o l o f Pu b lic Po licy St u d ies, Un iversity of Ch icago Kimberly J. Rask, p rofessor, Rollin s Sch ool of Pu blic Health , Em ory Un iversity Robert Rowthorn, p rofessor, Facu lty of Econ om ics an d Politics, Un iversity of Cam bridge, Un ited Kin gdom Stephen W. Salant, professor, Departm en t of Econ om ics, Un iversity of Mich igan James N. Sanchirico, fellow, Resou rces for th e Fu tu re Silvia Secchi, assist an t scien t ist , Cen t er fo r Agricu lt u ral an d Ru ral Develo p m en t, Iowa State Un iversity M artin L. Weitzman, p rofessor, Dep artm en t of Econ om ics, Harvard Un iversity Karl Seeley, assistan t p rofessor, Dep artm en t of Econ om ics, Hartwick College R. David Simpson, sen ior fellow, Resou rces for th e Fu tu re Timothy Swanson, p ro fesso r, Dep art m en t o f Eco n o m ics an d Facu lt y o f Law, Un iversity College Lon don , Un ited Kin gdom Hermann Waibel, p rofessor, In stitu te of Econ om ics in Horticu ltu re an d Agricu ltu re, Dep artm en t of Econ om ics, Un iversity of Han n over, Germ an y Justus Wesseler, assist an t p ro fesso r, En viro n m en t al Eco n o m ics an d Nat u ral Reso u rces Gro u p , So cial Scien ces Dep art m en t , Wagen in gen Un iversit y an d Research Cen ter, Th e Neth erlan ds James E. Wilen, p rofessor, Dep artm en t of Agricu ltu ral an d Resou rce Econ om ics, Un iversity of Californ ia, Davis Felicia Wu, grad u at e st u d en t , Dep art m en t o f En gin eerin g an d Pu b lic Po licy Carn egie Mellon Un iversity Jan C. Zadoks, p rofessor em eritu s, Laboratory of Ph ytop ath ology, Wagen in gen Un iversity, Th e Neth erlan ds David Zilberman, p ro fesso r, Dep art m en t o f Agricu lt u ral an d Reso u rce Eco n om ics, Un iversity of Californ ia, Berkeley

About This Book

I

n recen t decades, efforts to con trol biological organ ism s h arm fu l to h u m an s an d h u m an en terp rise h ave been con strain ed by th e growin g resistan ce of th ese organ ism s to th e con trol agen ts. Exam ples of such organ ism s in clude agricultural pests an d disease-causin g bacteria an d viruses. Organ ism s with ch aracteristics th at allow th em to su rvive th e effects of con trol agen ts are favored by Darwin ian selection . Over tim e, th ese resistan t organ ism s dom in ate organ ism s th at are su scep tible to con trol agen ts. Th e evolu tion of resistan ce is stron gly in flu en ced by th e beh avior of in d ivid u als an d in stitu tion s. In th e absen ce of suitable econ om ic in cen tives, decision m akers (such as patien ts, ph ysician s, an d growers) fail to take in to accoun t th e n egative im pact of th eir use of an tibiotics or pesticides on future social well-bein g. Battling Resistance to Antibiotics and Pesticides: An Econom ic Approach is a first attem p t to brin g togeth er a variety of approach es to th e econ om ics of resistan ce. Th e papers assem bled h ere represen t th e cuttin g edge of research in th is em ergin g field of study. Th e developm en t of bacterial resistan ce to an tibiotics is growin g to be a sign ifican t ch allen ge in m edicin e, as is in creasin g p est resistan ce to p esticides in agricu ltu re. To give bu t on e exam p le, th e p revalen ce of h igh -level p en icillin resistan ce in Streptococcus pneum oniae in th e Un ited States in creased 800-fold from 0.02% in 1987 to 16.5% in 1999. Over th e sam e p eriod , th e in crease in th e n u m ber of pest species resistan t to on e or m ore pesticides was n o less dram atic. Balan ced again st th ese dism al statistics is h ope in th e form of n ew tech n ologies su ch as p est-resistan t gen etically m odified crop s an d n ew treatm en ts for m alaria. Th e p resen t tim e affords a u n iq u e op p ortu n ity to learn from p ast experien ce to en su re th at existin g an d fu tu re produ cts are u sed wisely. • xi •

xii • About This Book

Th is book dem on strates th e ap p lication of econ om ic an alysis to m axim ize th e valu e of an tibiotics an d p esticides to society. It exam in es earlier efforts to m an age resistan ce, esp ecially in th e field of agricu ltu re, an d d iscu sses in cen tives th at in flu en ce th e beh avior of firm s en gaged in develop in g an d p rodu cin g t h ese p ro d u ct s. It sh o ws h o w an eco n o m ic ap p ro ach can n o t o n ly sh ed ligh t on h ow an tibiotics an d p esticides cou ld be better u sed bu t also can h elp stru ctu re econ om ic an d regu latory in cen tives to en su re th at in d ivid u als an d firm s act in a m an n er th at is con sisten t with societal objectives. Alth ou gh th e ch ap ters in th is book are focu sed on econ om ic an alysis, th e issu es th ey deal with are relevan t to a broad au dien ce. Detailed an alyses of th e m u lt ip le d im en sio n s o f resist an ce, lesso n s fro m p ast at t em p t s t o m an age resistan ce, an d direction s for fu tu re strategies to com bat resistan ce are asp ects of th e book th at will be u sefu l to p olicym akers. For p rofession als in th e m edical, p u b lic h ealt h , an d agricu lt u ral aren as, t h e b o o k at t em p t s t o t ran slat e som e of th e cu rren t econ om ic ap p roach es to m an agin g resistan ce in to gu id an ce for p ractition ers. 1 Econ om ists are p rovided with an overview of th e relevan t scien tific issu es as well as a variety of an alytical ap p roach es to stu d yin g th e econ om ics of resistan ce to an tibiotics an d p esticides. Th e ch ap t ers in t h is bo o k were d evelo p ed fro m p ap ers o rigin ally writ t en for a con feren ce on th e Econ om ics of Resistan ce organ ized by Resou rces for th e Fu tu re an d h eld at Airlie Hou se in Warren ton , Virgin ia, on Ap ril 5 an d 6, 2001. 2 Th e co n feren ce was h eld t o en co u rage t h e fo rm at io n o f a research co m m u n it y t o ad d ress issu es relat ed t o t h e eco n o m ics o f resist an ce. Th e ro u gh ly 70 co n feren ce p art icip an t s in clu d ed acad em ics; so cial scien ce an d m edical research ers; an d rep resen tatives from U.S. govern m en t agen cies (Food an d Dru g Ad m in istration [FDA], Cen ters for Disease Con trol an d Preven tion [CDC], En viron m en tal Protection Agen cy [EPA]), n on govern m en tal organ izat io n s, an d t h e h ealt h care, p h arm aceu t ical, an d agrib u sin ess in d u st ries. A n u m b er o f p art icip an t s were fro m co u n t ries o t h er t h an t h e Un it ed St at es, in clu d in g Can ad a, t h e Un it ed Kin gd o m , Germ an y, t h e Net h erlan d s, an d Israel. Th e wid e array o f exp ert ise fo rced in t erd iscip lin ary co m m u n icat io n t h at co n t rib u t ed t o t h e u n d erst an d in g o f wh at eco n o m ics can p ro vid e in term s of m akin g better u se of biological con trol agen ts su ch as an tibiotics an d p esticides an d for discip lin in g scien tific assu m p tion s m ade in econ om ic m odels u sed to stu d y th e evolu tion of resistan ce. Th is book reflects th e d ialogu e bet ween eco n o m ist s, m ed ical an d agricu lt u ral exp ert s, an d p o licym akers at th e m eetin g. To a read er wh o h as m an aged t o escap e a grad u at e d egree in eco n o m ics, t h e ch ap t ers in t h is b o o k m ay ap p ear, at first glan ce, t o b e fairly t ech n ical. Becau se th ese ch ap ters rep resen t som e of th e earliest efforts in th is em ergin g area, m u ch em p h asis h as been p laced on p erfectin g th e m eth od ology—a fact th at m igh t n ot be im m ediately ap p aren t to a scien tific or p olicy au dien ce. To

About This Book • xiii

m ake th ese ch ap ters accessible to a wid er au d ien ce, com m en taries written by n atu ral scien tists an d econ om ists su p p lem en t th e ch ap ter su m m aries written b y t h e au t h o rs t h em selves. Th e n ext sect io n p ro vid es an o verview o f h o w t h ese ch ap t ers fit t o get h er an d wh at in sigh t s t h ey p ro vid e. Th ese p ieces, in con ju n ction with th e in trodu ction to th e econ om ics of resistan ce in th e n ext section , attem p t to in form p olicym akers an d h ealth an d agricu ltu ral p rofessio n als o f t h e kin d s o f an alyses eco n o m ist s en gage in an d t o in d icat e t h e kin ds of an swers econ om ists m igh t p rovide in fu tu re work.3

Overview of Chapters Rath er th an divide th is book between an tibiotics an d p esticides, th e 12 ch ap ters h ave been organ ized in to th ree th em atic p arts. Part I focu ses on th e u se of econ om ic tools to ch aracterize th e efficien t u se of an tibiotics an d p esticides in th e face of resistan ce. Part II d eals with a broad array of issu es related to th e econ om ic im p act of resistan ce an d d ecision m akin g u n d er u n certain ty abou t fu tu re resistan ce. Part III exam in es in cen tives faced by com p an ies th at m ake an tibiotics an d p esticid es an d d escribes h ow regu latory in cen tives m igh t be stru ctu red for th ese in d u stries. Th e obviou s ad van tage of th is arran gem en t is t h at it em p h asizes t h e co m m o n alit y o f issu es t h at arise in t h e m ed ical an d agricu lt u ral co n t ext s an d p ro vid es t h e read er wit h in sigh t s in t o t h e issu e o f resistan ce at a broader level of abstraction . Th e t wo o p en in g ch ap t ers o f Part I b y Wilen an d Msan gi an d Ro wt h o rn an d Brown u se sim ilar ap p roach es to exten d ou r u n d erstan d in g of th e op tim al u se of an tibiotics wh en th ere is a sign ifican t fitn ess cost associated with b act erial resist an ce. In Ch ap t er 1, Wilen an d Msan gi t ackle t h e p ro b lem o f op tim al u se of a sin gle an tibiotic an d com p are strategies th at lower th e overall tran sm ission of in fection th rou gh better in fection con trol m eth od s (su ch as freq u en t h an d wash in g by n u rsin g staff) with th ose th at im p rove an tibiotic u se (su ch as t reat m en t gu id elin es an d swit ch in g p ro t o co ls). Alt h o u gh ep id em io lo gical st u d ies h ave sh o wn t h at in fect io n co n t ro l can b e rem arkab ly efficien t in con trollin g th e em ergen ce of dru g resistan ce, esp ecially in h osp ital set t in gs, t h is asp ect o f resist an ce m an agem en t h as n o t received su fficien t atten tion . By com p arin g th ese p olicies in an econ om ic fram ework, Wilen an d Msan gi are ab le t o d escrib e t h e b alan ce o f an t ib io t ic co n t ro l an d in fect io n con trol th at is econ om ically efficien t. Th e econ om ic elem en t in d eterm in in g t h is balan ce is wo rt h em p h asizin g an d can be illu st rat ed by a p ro vo cat ively ext rem e exam p le. A p o licy o f assign in g a sin gle n u rsin g st aff t o a sin gle p atien t can be very effective in con trollin g resistan ce, bu t th e costs of d oin g so wo u ld b e en o rm o u s. By u sin g an eco n o m ic m et ric, we can co m p are t h e eco n o m ic b en efit o f a p art icu lar resist an ce m an agem en t p o licy again st t h e costs of im p lem en tin g su ch a p olicy.

xiv • About This Book

Ch ap t er 2 by Ro wt h o rn an d Bro wn exam in es h o w we can m ake t h e best u se of two an tibiotics, each of wh ich is effective again st on e strain of bacteria b u t n o t again st t h e o t h er. At t h e t im e o f t reat m en t , t h e p h ysician m ay b e u n aware of th e sp ecific bacterial strain th at h e or sh e is treatin g an d ch ooses th e best p ossible treatm en t, keep in g in m in d th at a su ccessfu l treatm en t m ay cu re t h e p at ien t b u t co u ld also in crease t h e likelih o o d o f resist an ce in t h e fu tu re. Th e au th ors con clu de th at it m akes sen se to treat all p atien ts with th e an t ib io t ic t h at is effect ive again st t h e m o re p revalen t st rain , u n d er cert ain con dition s, even if th at an tibiotic is relatively m ore exp en sive. Alth ou gh on e m ay n o t n ecessarily en co u n t er t h e p ro b lem o f t wo d ru gs u sed t o t reat t wo m u t u ally exclu sive d iseases in a clin ical set t in g, t h e m o d el d evelo p ed h ere offers a fram ework an d p rovid es a p oin t of d ep artu re for m ore realistic variation s of th e p roblem . Ch ap t er 3 b y Laxm in arayan an d Weit zm an d eals wit h t h e issu e o f t reat m en t h o m o gen eit y wh en resist an ce is a p ro b lem . Th is ch ap t er u ses a fairly sim p le ap p ro ach t o sh o w t h at wh en resist an ce arises as a co n seq u en ce o f an tibiotic u se, it m ay be sh ortsigh ted to u se a sin gle an tibiotic on all p atien ts ju st b ecau se t h at an t ib io t ic ap p ears t o b e t h e m o st co st -effect ive o p t io n . In deed, it m ay be op tim al, from society’s p oin t of view, to u se differen t dru gs on d ifferen t, bu t observation ally id en tical, p atien ts an d in clu d e am on g th is m en u o f d ru gs so m e t h at m ay n o t b e co st -effect ive fro m t h e in d ivid u al p at ien t ’s p ersp ect ive. Th is resu lt h as im p o rt an t co n seq u en ces fo r h o w o n e ap p roach es an tibiotic or an tim alarial treatm en t. In Ch ap t er 4, Secch i an d Bab co ck d eal wit h t h e issu e o f o p t im al refu ge st rat egies fo r p est s wh en p est s are m o bile. A brief in t ro d u ct io n t o t h is t o p ic m ay be h elp fu l h ere. Recen t im p ro vem en t s in agricu lt u ral t ech n o lo gy h ave in clu d ed th e ad op tion of gen etically m od ified Bt crop s th at cod e for th e p rodu ction of a p rotein p rodu ced in n atu re by th e bacteriu m Bacillus thuringiensis (Bt). Th e Bt p ro t ein h as b een fo u n d t o b e an ext rem ely effect ive p est icid e wh ile bein g relatively ecologically ben ign . Sin ce 1998, EPA h as req u ired th at all farm ers gro win g Bt cro p s p lan t a cert ain p ro p o rt io n o f t h eir field s wit h n on -Bt crop s to d elay th e em ergen ce of resistan ce. Th e u n d erlyin g th eory is th at th e n on -Bt crop s wou ld p rovide a refu ge for p ests su scep tible to Bt, wh ich cou ld th en m ate with th e Bt-resistan t p ests th at wou ld in evitably arise from exp osu re of p ests to Bt toxin . Th e resu ltin g organ ism , it is argu ed , wou ld be su scep tible to Bt an d wou ld h elp redu ce th e likelih ood th at a fu lly resistan t Btresist an t p est wo u ld evo lve. Cu rren t refu ge req u irem en t s are m ad e o n t h e basis of fairly rigid assu m p tion s abou t th e d egree of m arket p en etration of Bt crop s an d of m obility of p ests. W h en m arket p en etration is assu m ed to be less th an com p lete an d p ests are assu m ed to be m obile, th en th ere is p oten tial for n on -Bt field s to op erate as n atu ral refu ges for Bt-su scep tible p ests. Secch i an d Bab co ck u se a m o d el o f evo lu t io n o f p est resist an ce t o sh o w t h at h igh p est

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m o b ilit y an d lo w m arket p en et rat io n can b e su b st it u t es in m an agin g p est resist an ce. W h en rigid assu m p t io n s su ch as 100% m arket p en et rat io n are relaxed, th ey fin d th at th e op tim al level of refu ge on Bt fields will be con siderably sm aller th an th e 20% refu ge th at is cu rren tly m an d ated . Th ese con clu sio n s are im p o rt an t co n sid erin g t h e p o ssib ilit y t h at m o re st rin gen t refu ge req u irem en ts m ay resu lt in lower com p lian ce with refu ge req u irem en ts. Part II begin s with a ch apter by Howard an d Rask th at takes on a ch allen gin g issu e in t h e eco n o m ics o f resist an ce—m easu rin g t h e eco n o m ic co st s o f resist an ce. Usin g d at a o n an t ibio t ics u sed t o t reat ear in fect io n s fro m t h e Nation al Am bu latory Medical Care Su rvey from 1980 to 1998, th e au th ors estim ate th e in crease in th e cost of an tibiotic treatm en t attribu table to in creases in bacterial resistan ce. Alth ou gh th eir approach is h am pered by a lack of data on resistan ce, th eir an alysis (wh ich u ses tim e as a proxy for in creasin g resistan ce) offers som e in sigh t in to th e order of m agn itu de of costs of resistan ce. Between 1997 an d 1998, in creases in d ru g resistan ce are estim ated to h ave raised th e cost of treatin g ear in fection s by abou t 20% ($216 m illion ). Ch ap t er 6 b y Waib el, Zad o ks, an d Fleisch er sh o ws h o w lesso n s learn ed from p ast exp erien ce with p esticides can h elp gu ide cu rren t an d fu tu re regu lation on Bt crop s. Th ey p rovid e an overview of variou s m eth od ological issu es relat ed t o em p irically assessin g t h e im p act o f p est icid es o n agricu lt u ral p ro d u ction . Fu rth er, th ey argu e th at evalu ation s of Bt tech n ology th at take in to accou n t th e resistan ce-related costs associated with th is tech n ology as well as recogn ize th e altern ative p est con trol op tion s available to farm ers are im p ortan t to en su re th at th e ben efits of th is tech n ology are n ot overestim ated. In Ch ap ter 7, Fleisch er an d Waibel evalu ate th e econ om ic im p act of p est resist an ce t o p est icid es u sin g t wo case st u d ies fro m Germ an y. In t h e first stu dy, th ey exam in e wh eth er p est con trol costs h ave been in creasin g as a con seq u en ce of p est resistan ce, takin g in to accou n t tech n ological im p rovem en ts in p esticides. Sp ecifically, th ey iden tify an econ om ic cost to p est resistan ce by lookin g at tren ds in con su m p tion of p esticides relative to oth er ch em icals on farm in p u ts. In th e secon d stu dy, th ey exam in e th e p rivate an d social costs of weed resist an ce t o at razin e. Th e sh are o f m aize is p o sit ively co rrelat ed wit h th e u se of atrazin e. Th erefore, fields th at h ave h igh sh ares of m aize reflect an im p licit willin gn ess on th e p art of farm ers to sacrifice atrazin e effectiven ess in th e fu tu re for greater sh ort-term p rofits. Atrazin e was ban n ed in 1991, p artly b ecau se o f it s en viro n m en t al im p act o f p o llu t in g gro u n d wat er so u rces. Becau se farm ers wh o u sed atrazin e m ore in ten sively before th e ban were also likely to h ave ach ieved greater p rofits in th e sh ort ru n , th e ban resu lted in a n egat ive im p act o f t h ese farm ers’ d ecisio n s o n o t h ers wh o h ad b een m o re con servative with th eir u se of h erbicides. Th e m et h o d o lo gical h u rd les faced b y t h ese an alyses are sim ilar in so m e resp ects to th ose in th e earlier ch ap ter by Howard an d Rask, illu stratin g th e

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sign ifican t advan tages in con tem p latin g an alytical m eth ods to stu dy th e econ om ic im p act of resistan ce. Th is ch ap ter also illu strates th e p roblem of extern alit ies t h at are p ervasive in t h e u se o f an y p est co n t ro l t ech n o lo gy. Fo r in stan ce, organ ic farm ers h ave u sed Bt foliar sp rays for m an y years becau se Bt sp ray is on e of th e few p est con trol tech n ologies con sidered to be n on ch em ical. With th e em beddin g of Bt toxin in n ew crop s, th e widesp read adop tion of Bt cro p s t h reat en s t h e effect iven ess o f fo liar sp rays via t h e d evelo p m en t o f resist an ce. Alt h o u gh co n ven t io n al farm ers m ay b e ab le t o swit ch t o o t h er con trol m eth od s wh en resistan ce evolves, th e n egative im p act of th eir ad op tion on organ ic farm ers m ay be m ore lon g term . Ch ap ter 8 by Morel, Farrow, Wu , an d Casm an , an d Ch ap ter 9 by Wesseler ad d ress th e p roblem of u n certain ty regard in g p est resistan ce wh en d ecid in g wh eth er to adop t gen etically m odified crop s su ch as Bt crop s described earlier. Th e likelih o o d t h at p est s will b eco m e resist an t t o t h ese n ew cro p s seem s in evitable, alth ou gh th ere is sign ifican t u n certain ty abou t h ow soon th is will h ap p en . Fo r t h is reaso n , if t h ere is a sign ifican t risk t h at p est s will q u ickly b eco m e resist an t t o t h ese n ew cro p s, t h en farm ers will wan t t o see great er im p ro vem en t s in yield wit h t h e Bt cro p (co m p ared wit h t h e co n ven t io n al, n on -Bt crop ) if th ey are to be con vin ced to switch to th e n ew tech n ology. Th e greater th e risk of p est resistan ce, or of oth er ecological p roblem s, th e greater th e im p rovem en t in Bt crop yield will h ave to be. Both of th ese ch ap ters u se t h e ap p ro ach o f real o p t io n valu e t h eo ry, an eco n o m ic t ech n iq u e u sed t o assess d ecision s m ad e u n d er u n certain ty. Sim p ly p u t, th e op tion valu e is th e econ om ic valu e of d elayin g a d ecision p en d in g th e arrival of better in form ation . Both ch ap ters u se th is ap p roach to estim ate th e h u rdle rate or th e m in im u m yield im p rovem en t afforded by th e Bt crop to m ake th e risk of adop tin g th is tech n ology worth it to th e farm er. Part III d eals wit h in cen t ives faced by p ro d u cers o f an t ibio t ics an d p est icid es. Ch ap ter 10 by Noon an takes on th e im p ortan t q u estion of h ow in cen tives faced by m on op olist p rod u cers in flu en ce th e op tim al size of refu ges to m it igat e p est resist an ce t o gen et ically m o d ified Bt cro p s. In d ivid u al farm ers wou ld n ot ch oose to adop t th ese strategies on th eir own , becau se th e costs in t erm s o f red u ced p ro fit s clearly o u t weigh t h e in d ivid u al b en efit asso ciat ed wit h lo wer p est resist an ce in t h e fu t u re. Th erefo re, EPA h as m an d at ed t h at refu ge areas be grown with n on -Bt crop so th at th e likelih ood of em ergen ce of p est resistan ce is m in im ized . Usin g a th eoretical m od el, Noon an sh ows th at m on op olistic seed p rod u cers m ay h ave a greater in cen tive for en su rin g th at growers are scru p u lou s in p lan tin g refu ges th an wou ld be th e case if th ere was a co m p et it ive su p p ly o f gen et ically m o d ified Bt seed s. Fu rt h erm o re, t h is in cen t ive m ay b e large en o u gh t o en su re an even great er level o f effo rt o n refu ges t h an is so cially o p t im al. In o t h er wo rd s, o n e wo u ld exp ect t o see refu ges bein g grown even if EPA did n ot m an date th em . Th is resu lt h as im p or-

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tan t im p lication s for p u blic p olicy becau se it in d icates th at seed com p an ies’ in cen tives m ay im p ly th at EPA regu lation s on growin g refu ge areas are u n n ecessary. Em p irical eviden ce in su p p ort of th is argu m en t wou ld m ake a stron ger case for revisitin g EPA’s efforts in th is area. In Ch ap ter 11, Goesch l an d Swan son address th e q u estion of th e u sefu ln ess of th e p aten t system for en cou ragin g th e develop m en t of n ew an tibiotics an d p est icid es wh en resist an ce is a recu rrin g p ro b lem . Th ey co m p are t h e resist an ce p ro b lem wit h ru n n in g o n a t read m ill ju st t o st ay in t h e sam e p lace. In du stry can eith er slow down th e p ace of th e treadm ill by sellin g less of th eir p ro d u ct , o r ru n fast er b y rap id ly co m in g u p wit h n ew p ro d u ct s t o rep lace o ld er p ro d u ct s m ad e o b so let e b y resist an ce. In m akin g t h is d ecisio n , firm s m u st keep in m in d two con sideration s: th eir p rodu ct cou ld be m ade obsolete b y resist an ce an d t h eir p ro d u ct co u ld b e m ad e o b so let e b y a n ew p ro d u ct in trodu ced by a com p etitor firm . Th e stan dard p aten t len gth of 17 years m ay n ot give firm s su fficien t in cen tive to care abou t resistan ce. Th is ch ap ter p oin ts to th e n eed for recogn izin g th e sh ortcom in gs of th e p aten t system in givin g firm s a greater in cen tive to care abou t resistan ce an d th e n eed to look in oth er direction s to solve th is p roblem . Ch ap t er 12 b y Alix an d Zilb erm an p ro vid es a st rikin g co n t rast t o o t h er ch ap t ers in t h is b o o k. It ch allen ges t h e n o t io n t h at resist an ce is a co n seq u en ce o f t h e o verap p licat io n o f p est icid es. Alix an d Zilb erm an review t h e co m p lex in cen t ives t h at m o t ivat e gro wers an d p est icid e firm s t o sh o w t h at u n derap p lication of p esticides m igh t be ju st as p roblem atic (by n ot killin g su fficien t n u m b ers o f p est s) as o verap p licat io n t h at co u ld lead t o in creasin g resistan ce. Overap p lication m ay n ot be a p roblem wh en th e p esticide in du stry is in vest ed in t h e efficacy o f it s p ro d u ct s, an d t h is in t u rn d ep en d s o n h o w st ro n g it s p ro p ert y righ t s are. Th e au t h o rs favo r a h o list ic view o f p est icid e m an u fact u re an d u se. Fu rt h er, t h ey p o in t o u t t h at eco n o m ic agen t s su ch as agricu ltu ral exten sion con su ltan ts an d p esticide advisors h ave an in cen tive to en cou rage op tim al p esticid e u se even if in d ivid u al growers lack th ese in cen tives. Fin ally, th ey em p h asize th e n eed for m ore em p irical stu dies on th e m u ltip le in stitu tion al an d oth er factors th at in flu en ce p esticide ch oice an d u se on th e farm an d th e role of th ese in flu en ces in bu ildin g p est resistan ce.

Final Thoughts Th e ap p lication of econ om ics to p olicy design in volves two stages. In th e first stage, econ om ic p rin cip les can p resen t th e best-case scen ario an d advise u s on wh at kin d o f p o licy will get u s t o t h at ben ch m ark o u t co m e. Fo r in st an ce, a sim p le p olicy ru le in th e case of an tibiotics m ay be th at we sh ou ld u se a variety of an tibiotics in p rop ortion s determ in ed by econ om ic costs an d th e p robab ilit y t h at b act eria will acq u ire resist an ce t o each d ru g (see Ch ap t er 3).

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Alth ou gh su ch an “op tim al” p olicy m ay n ot n ecessarily be attain able in th e real world, it h elp s u s assess oth er secon d-best p olicies again st th e ben ch m ark of a first-best p olicy. In th e secon d stage, we u se ou r u n d erstan d in g of in cen tives an d beh avior t o sp ecify h o w in d ivid u al agen t s su ch as p h ysician s o r farm ers co u ld b e in d u ced t o fo llo w t h e o p t im al p o licies o u t lin ed in t h e first st age o r at least in flu en ce beh avior su ch th at th e ou tcom e is as close to th at ach ieved by th e first -b est p o licy as p o ssib le. Th e ch allen ge o f t ran slat in g t h e eco n o m ic p rescrip tion s in to a form th at is u sefu l to p olicym akers is dau n tin g. However, by n ot takin g th is im p ortan t step , attem p ts to u n d erstan d th e p roblem of resistan ce will fall sh o rt o f ach ievin g an im p act o n p o licy. Th is b o o k is far m o re su ccessfu l at describin g th e first stage th an th e secon d. Mu ch work rem ain s to be d on e on d esign in g in cen tives to en su re th at an tibiotics an d p esticid es are u sed op tim ally. At th e tim e of writin g th is, th e econ om ics of resistan ce is an em ergin g field o f research , an d a n u m b er o f t h e ch ap t ers in t h is vo lu m e are st ill in t h e p rocess of d evelop m en t. We believe th at p u blish in g th ese p relim in ary id eas will be h elp fu l in exten d in g th e stu d y of th e econ om ics of resistan ce. Recen t con cern s abou t bioterrorism an d re-em ergin g in fection s su ch as tu bercu losis rem in d u s of th e n eed to give m ore seriou s th ou gh t to ou r arsen al of an tibiotics—m an agin g th ose th at we h ave efficien tly an d develop in g n ew on es. We h o p e t h is vo lu m e, even if it d o es n o t read ily p ro vid e co m p let e an swers t o su ch q u estion s, p rovokes ideas to p u rsu e in th is growin g an d top ical field.

Acknowledgements My forem ost d ebt is to th e con tribu tors with ou t wh ose su p p ort an d p atien ce with m u ltip le rou n ds of review, th is book wou ld h ave n ot been p ossible. I am gratefu l to Pau l Portn ey for h avin g both th e gen erosity an d foresigh t to su p p o rt t h is en d eavo r, Mike To m an fo r h is st ro n g an d u n waverin g su p p o rt o f (m ost of) m y crazy ideas at RFF, an d Su san Doyle for h er rem arkable job takin g care of th e logistics of th e RFF Con feren ce on th e Econ om ics of Resistan ce. I h ave h ad (an d con tin u e to h ave) th e ben efit of ou tstan din g an d tru ly su p p ortive co lleagu es at RFF. David Sim p so n , Caro lyn Fisch er, Jim San ch irico , Ray Kop p , Don Reism an an d Rebecca Hen derson , Em ily Aron ow, Barb Jem elkova, Kay Mu rp h y, an d Pau lin e Wiggin s d eserve p articu lar m en tion in con n ection with th is p roject. Th e vo lu m e h as also b een h elp ed b y co m m en t s p ro vid ed b y t h e p art icip an ts at th e RFF Con feren ce. Man y reviewers con tribu ted th eir tim e an d effort to h elp sh ap e th ese ch ap ters with th eir in sigh ts an d exp erien ce an d h elp ed a set o f co n feren ce p ro ceed in gs reach it s p resen t p o lish ed fo rm . I wo u ld also like to th an k David Bell, William Blain e, Eric Van Du sen , Gérard Gau d et an d

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Marc Lip sit ch fo r h elp in g m ake t h is bo o k p o ssible. I ackn o wled ge fin an cial su p p o rt fro m t h e Agen cy fo r Healt h Care Research an d Q u alit y an d t h e Nation al Cen ter for In fectiou s Disease at th e Cen ters for Disease Con trol an d Preven t io n fo r t h eir sp o n so rsh ip o f t h e wo rksh o p o n t h e Eco n o m ics o f An tim icrobial Resistan ce. Preeth a, Tejas, th e Rajaram an s an d th e oth er Laxm in arayan (m y m oth er) co n t in u e t o an ch o r m y life wit h t h eir lo ve an d ligh t . Fo r t h is I am m o st gratefu l.

RAMANAN LAXMINARAYAN W ASHINGTON , DC

Notes 1. Note th at econ om ic in tu ition is on ly p rovid ed as gu id an ce an d can n ot be su bstit u t ed fo r act u al t rials t o t est t h e m ed ical o r agricu lt u ral su it ab ilit y o f t h e p ro p o sed st rat egies. Ho wever, even at t h e level o f ab st ract io n ad o p t ed b y t h e ch ap t ers in t h is boo k, it is p ossible t o d eliver som e broad in sigh t s in t o t h e resist an ce p ro blem , wh ich will th en h ave to be tested an d op eration alized by p ractition ers. 2. Th e ch ap ters h ave u n dergon e su bstan tial revision sin ce th e m eetin g. 3. Th ere is a co m m o n m isco n cep t io n o u t sid e t h e eco n o m ics p ro fessio n t h at eco n om ics is largely abou t m easu rin g costs (an d som etim es ben efits). Alth ou gh th is is certain ly p art of wh at econ om ists do, th ese are m erely stop s on th e way to th e fin al destin at io n , wh ich is t o d esign p o licies an d in cen t ives t h at in flu en ce h u m an beh avio r. In d oin g th is, econ om ics offers p owerfu l an alytical tools an d form al ap p roach es to stu d y in cen tives faced by in dividu als an d ways of align in g th ese in cen tives with th ose of society at large.

Introduction

On the Economics of Resistance Ramanan Laxminarayan

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om e of th e m ost am azin g tech n ological ach ievem en ts of th e p ast cen tu ry h ave in vo lved su ccessfu l h u m an co n t ro l o f b io lo gical o rgan ism s. Th e in t ro d u ct io n o f an t ib io t ics in t h e early 1940s h elp ed b rin g ab o u t d ram at ic d eclin es in m ortality from in fectiou s d iseases an d h as been wid ely acclaim ed as on e of th e m ost im p ortan t advan ces in th e h istory of m edicin e. In th e field of agricu ltu re, th e u se of p esticid es, in secticid es, an d h erbicid es h elp ed brin g abou t vast in creases in food su p p ly in both d evelop ed an d d evelop in g cou n t ries. Ho wever, ever sin ce t h ese p ro d u ct s were in t ro d u ced , o u r co n t in u ed cap acity to u se th em effectively h as been ch allen ged by th e ability of bacteria an d p est s t o ad ap t , evo lve, an d escap e t h e effect o f t h ese p ro d u ct s. Clearly econ om ic an d beh avioral factors p lay an im p ortan t role in en cou ragin g th e rap id growth of resistan ce. However, ou r u n d erstan d in g of th ese factors lags far beh in d scien tific u n derstan din g of th e p roblem . Th e p u rp ose of th is in trodu ctory essay is to illu strate wh ere econ om ics m igh t be u sefu l in u n derstan din g an d d evelop in g p olicy resp on ses to th e p roblem of resistan ce an d to p rovide som e in sigh t based both on th e existin g literatu re an d m y own th ou gh ts on th e econ om ics of resistan ce. Problem s of resistan ce th at arise as a con seq u en ce of h u m an -in d u ced evolu t io n are n o t rest rict ed t o an t ib io t ics an d p est icid es alo n e. In sect s can d evelo p resist an ce t o in sect icid es, m alarial p arasit es t o an t im alarials, an d weed s t o h erb icid es. Th e co m m o n m ech an ism in all t h ese in st an ces is t h at selection p ressu re p laced by th e u se of con trol agen ts p rovid es a com p arative advan tage to th e sm all fraction of organ ism s n atu rally resistan t to th e agen ts.

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2 • Introduction: On the Economics of Resistance

Over tim e, Darwin ian selection favors th e resistan t organ ism s over th ose th at are su scep tible to th e effect of th e agen t an d ren ders th e con trol agen t in effect ive. Fro m a b eh avio ral p ersp ect ive, t h e u n d erlyin g reaso n in all t h ese in st an ces is t h at in d ivid u al act o rs su ch as p at ien t s, p h ysician s, an d farm ers m ay n ot h ave th e in cen tive to take in to accou n t th e n egative im p act of th eir u se of an tibiotics, p esticides, an d oth er con trol agen ts on th e fu tu re effectiven ess o f t h ese p ro d u ct s fo r everyo n e else. Firm s m ay h ave lim it ed in t erest in th e effectiven ess of th eir p rodu cts, an d th eir goals of m axim izin g p rofits m ay n o t n ecessarily b e co n sist en t wit h so ciet al go als o f m akin g t h e b est u se o f th ese p rodu cts.

What Role Can Economics Play? First an d forem ost, econ om ics can h elp p rovid e an estim ate of th e econ om ic co st s an d b en efit s o f an t ib io t ic o r p est icid e u se an d t h e m agn it u d e o f t h e im p act o f resist an ce. Ho wever, t h e u sefu ln ess o f eco n o m ics in st u d yin g resist an ce go es far beyo n d t h is fu n ct io n . Eco n o m ics can p lay an im p o rt an t ro le b o t h in u n d erst an d in g t h e evo lu t io n o f resist an ce an d in d evelo p in g p o licy resp o n ses t o t h e p ro b lem . Bro ad ly sp eakin g, so ciet y’s b at t le again st resist an ce t akes p lace o n t wo fro n t s. First , we n eed t o m an age o u r exist in g arsen al o f d ru gs an d an t ib io t ics carefu lly t o m axim ize t h e valu e d erived fro m t h eir u se. Seco n d , we n eed t o d evelo p (o r en co u rage t h e d evelo p m en t of) n ew d ru gs an d p esticid es to rep lace old p rod u cts th at resistan ce h as ren d ered in effect ive. Th ese t wo st rat egies are in t ricat ely lin ked . O u r effo rt s t o b et t er m an age resist an ce t o exist in g p ro d u ct s co u ld red u ce t h e ret u rn s t o in vest m en t in n ew p ro d u ct s. So , p arad o xically, t h e evo lu t io n o f resist an ce m ay create a d em an d for n ew p rod u cts th at lead s to greater research in vestm en t. Con versely, th e greater availability of n ew p rod u cts m ay in crease th e variety of p rod u cts th at we h ave available, an d th is m ay h elp u s m ake better u se of existin g p rod u cts (see Ch ap ter 3). Econ om ics h as a lon g h istory with both th e op tim al m an agem en t of n atu ral resou rces, su ch as oil, trees, an d fish eries, an d th e op tim al design of in cen tives to in flu en ce th e beh avior of in dividu als an d corp orate en tities. Con siderin g an t ib io t ic o r p est effect iven ess as a so ciet al reso u rce co u ld h elp d evise strategies to u se an tibiotics an d p esticid es in a m an n er th at ben efits society. Eco n o m ist s co u ld h elp d esign regu lat o ry an d o t h er in cen t ives t o en co u rage firm s to com e u p with n ew p rodu cts to rep lace an tibiotics an d p esticides th at are n o lon ger effective, as well as to take resistan ce in to accou n t wh en d ecid in g on strategies to m arket existin g p rodu cts. Th e existin g literatu re an d ideas for th e role th at econ om ics can p lay in addressin g th e ch allen ges of resistan ce are described in th e section s th at follow.

Introduction: On the Economics of Resistance • 3

How Big Is the Problem? We live in a wo rld in wh ich p ro b lem s t en d t o get p rio rit ized in o rd er o f d ecreasin g eco n o m ic sign ifican ce, o r so eco n o m ist s wo u ld like t o b elieve. Alth ou gh th e en orm ity of th e resistan ce p roblem m ay be self-eviden t to th ose in th e m edical an d agricu ltu ral com m u n ities wh o deal with it on a daily basis, assessin g th e econ om ic im p act is a n ecessary first step to brin gin g th e p roblem to th e atten tion of p olicym akers an d stakeh old ers. Th ere h as been som e work in th is direction , alth ou gh m u ch rem ain s to be don e. In th e m edical con text, econ om ic costs associated with an tibiotic resistan ce can be attribu ted to at least th ree factors. First, resistan t in fection s are m ore expen sive to treat; patien ts in fected with resistan t bacteria requ ire lon ger h osp italization an d face h igh er treatm en t costs th an p atien ts in fected with dru gsu scep tible strain s. Secon d , th e risk of m ortality is greater for resistan t in fection s, an d th is im p oses a cost on society. Fin ally, th e cost of in trodu cin g n ew an tibiotics to rep lace old in effective on es is in creasin g an d in volves th e com m itm en t of resou rces th at cou ld be d ep loyed to oth er p u blic h ealth research projects, su ch as developin g n ew dru gs for AIDS or can cer (Reed et al. 2001). Resist an ce co st s are rarely co n sid ered even in eco n o m ic evalu at io n s o f an tibiotic treatm en t altern atives becau se th e u n certain ty of th e im p act of cu rren t an t ibio t ic u se o n fu t u re resist an ce d im in ish es t h e im p o rt an ce o f resist an ce costs (Coast et al. 1996). Alth ou gh u n certain ty regardin g th e actu al cost of resistan ce is con siderable, som e p rojection s sh ow th at, even with con servat ive est im at es, t h e co st o f an t ib io t ic resist an ce is h igh en o u gh t o in flu en ce co st –ben efit d ecisio n s m ad e at t h e in d ivid u al p rescrip t io n level (Reed et al. 2001). Th erefore, it ap p ears th at th e cost of an tibiotic resistan ce m ay be h igh en ou gh to warran t in clu sion in cost-effectiven ess an alyses of an tibiotic treatm en ts. Th e an n u al figu re q u oted m ost often for th e econ om ic im p act of resistan ce in th e Un ited States ran ges from $350 m illion to $35 billion (at 1989 d ollar rates, Ph elp s 1989). Th ese estim ates assu m e 150 m illion p rescrip tion s are gen erat ed each year an d vary d ep en d in g o n , am o n g o t h er fact o rs, t h e rat e at wh ich resistan ce grows with resp ect to in creasin g an tibiotic u se, an d th e p robab ilit y t h at a p at ien t will d ie fo llo win g in fect io n wit h a resist an t p at h o gen (Ph elp s 1989). A m ore recen t stu dy th at m easu red th e deadweigh t loss associat ed wit h t h e lo ss o f an t ib io t ic effect iven ess relat ed t o o u t p at ien t p rescrip t io n s in t h e Un it ed St at es t o b e $378 m illio n an d as h igh as $18.6 b illio n (Elbash a 1999). A rep ort by th e Office of Tech n ology Assessm en t (OTA) to th e U.S. Con gress estim ated th e an n u al cost associated with an tibiotic resistan ce in h o sp it als, at t ribu t able t o five classes o f h o sp it al-acq u ired in fect io n s fro m six d ifferen t an t ibio t ic-resist an t bact eria, t o be at least $1.3 billio n (at 1992

4 • Introduction: On the Economics of Resistance

dollar rates) (OTA 1995). Th e Cen ters for Disease Con trol an d Preven tion estim ated th at th e cost of all h osp ital-acq u ired in fection s, in clu din g both an tibiotic-resistan t an d an tibiotic-su scep tible strain s in th eir figu res was $4.5 billion (OTA 1995). Th e lack of tim e series data on both an tim icrobial u se an d bacterial resistan ce h as m ad e it d ifficu lt to estim ate th e d ose–resp on se relation sh ip between an tim icrobial u se an d resistan ce, fu rth er com p licatin g an assessm en t of th e econ om ic costs of resistan ce. On th e p esticide fron t, accordin g to th e In secticide Resistan ce Action Com m ittee, an in d u stry-fu n d ed grou p , in secticid e resistan ce in creases th e cost of p est con trol by n early $40 m illion each year (IRAC 2002). Th is estim ate d oes n ot in clu d e th e secon d ary en viron m en tal d am ages associated with in creased p esticid e u se. On e sp ecific exam p le of crop losses associated with p est resistan ce is resist an ce t o t h e Co lo rad o p o t at o b eet le (Leptinotarso decem lineata), wh ich cost p otato p rod u cers in Mich igan $16 m illion in crop losses in 1991.

How Can We M ake the Best Use of Existing Antibiotics and Pesticides? Con siderin g th e effectiven ess of an tibiotics (or pesticides) as a n atu ral resou rce th at is m u ch th e sam e as a stock of fish or a forest can h elp u s explore ways of m akin g better u se of th is resou rce. Th e con cep t of p est su scep tibility to p esticides as a n atu ral resou rce was first in trodu ced 30 years ago (Carlson an d Castle 1972). Sin ce th en , th ere h as been sporadic in terest in applyin g th e tools of econ o m ics t o u n d erst an d in g h o w t h ese agen t s m igh t be bet t er u sed given t h at resist an ce is a likely co n seq u en ce o f u sin g t h em (Hu et h an d Regev 1974; Com in s 1977a,b; Brown an d Layton 1996; Laxm in arayan an d Brown 2001). Alth ou gh th e literatu re on p est resistan ce d ates back to th e 1970s, in terest in an tibiotic resistan ce is m ore recen t. In terest in determ in in g th e kin ds of strategies th at wou ld m axim ize th e valu e from cu rren t an tibiotics an d pesticides h as been accom p an ied by d iscu ssion s of h ow econ om ic in cen tives cou ld be u sed to in du ce in dividu als wh o u se th ese produ cts to m ake better u se of an tibiotics an d pesticides. In th e an tibiotics con text, Brown an d Layton d escribed a d yn am ic m od el of an tibiotic u se in wh ich con su m ers an d farm ers both u se an tibiotics wh ile ign orin g th e im p act of th eir u se on th e oth er grou p (1996). Th is resu lts in a greater u se of an tibiotics by both grou p s of u sers. Laxm in arayan an d Brown u sed a fram ework based on an ep id em iological m od el of in fection in wh ich an t ibio t ic effect iven ess is t reat ed as a n o n ren ewable reso u rce (2001). In t h e m od el p resen ted , bacterial resistan ce (th e con verse of effectiven ess) d evelop s as a resu lt o f select ive p ressu re o n n o n resist an t st rain s cau sed b y an t ib io t ic u se. Th eir p ap er sh ows th at th e op tim al p rop ortion an d tim in g of th e u se of available an tibiotics can be derived as a fu n ction of th e rates at wh ich bacter-

Introduction: On the Economics of Resistance • 5

ial resistan ce to each an tibiotic evolves an d on p h arm aceu tical costs of each an tibiotic. In th e agricu ltu ral econ om ics literatu re, th e Hu eth an d Regev m odel sh ows p est su scep t ibilit y t o p est icid es as a st o ck o f n o n ren ewable n at u ral reso u rce th at is p rivately costless to u se in th e sh ort ru n bu t extrem ely costly for societ y t o rep lace in t h e lo n g ru n wh en n ew p est icid es are req u ired (Hu et h an d Regev 1974). Ad o p t in g t h is ap p ro ach o f t reat in g su scep t ib ilit y as an exh au stible resou rce in a stu dy on th e op tim al m an agem en t of p est resistan ce, Co m in s fo u n d t h at t h e co st o f resist an ce is an alyt ically eq u ivalen t t o an in crease in th e cost of th e p esticide (Com in s 1977a,b, 1979). More recen tly, atten tion h as tu rn ed to th e op tim al m an agem en t of resistan ce t o n ewly in t ro d u ced Bt (Bacillus thuringiensis) cro p s, wh ich are gen et ically m odified to p rodu ce a p rotein h igh ly toxic to m an y in sect p ests. Becau se th e Bt toxin is con stan tly p resen t, u n like ch em ical p esticid es, th e strategy of m an agin g resistan ce by op tim ally tim in g ap p lication of p esticides is n o lon ger p ossible with th e n ew tech n ology. Settin g aside refu ge areas in wh ich su scep t ib le p est s can su rvive h as b een p ro p o sed t o red u ce t h e select io n p ressu re p laced on th em in th e areas wh ere th e Bt crop is grown . A n u m ber of p ap ers h ave b een writ t en o n ap p ro ach es t o d et erm in in g t h e o p t im al size o f t h ese refu gia (Hu rley et al. 1999; Hyd e et al. 1999; Livin gst o n et al. 2000; Laxm in arayan an d Sim p son 2002). From an econ om ist’s p ersp ective, con trol of h arm fu l biological organ ism s u sin g co n t ro l agen t s (e.g., an t ib io t ics, an t ivirals, fu n gicid es) is q u it e u n like oth er tech n ologies in th at it h as two sid e-effects, n eith er of wh ich is con sid ered by in dividu als wh o u se th ese agen ts an d wh o act in th eir own self in terest. In th e case of p esticid e u se, a farm er wh o u ses p esticid es effectively will kill p ests, in clu d in g som e th at cou ld oth erwise m igrate to oth er field s. However, t h e in d ivid u al farm er h as n o in cen t ive t o reco gn ize t h is p o sit ive sid eeffect of h is or h er u se of p esticides. On th e n egative side, th e u se of p esticides en gen d ers greater resistan ce in th e fu tu re. Th is effect, too, is n ot fu lly taken in to con sideration by an y in dividu al farm er u n less effects are en tirely local. If on e were to th in k abou t th is in th e con text of u sin g an tibiotics to treat bacterial in fection s or u sin g in secticides to kill in sects, th e u biq u ity of th is in cen tive p roblem d escribed h ere becom es ap p aren t. Dep en d in g on wh eth er th e valu e of th e p ositive im p act of p est red u ction is greater th an or less th an th e n egative im p act of fu tu re resistan ce, th e in dividu al farm er m ay u se p esticides to a greater or lesser exten t th an wou ld be best from a societal p ersp ective. Pu blic eco n o m ics h as a lo n g h ist o ry in d ealin g wit h ext ern alit y p ro blem s, an d t h e in sigh t s gain ed co u ld o ffer so lu t io n s t o co n fro n t in g t h e b eh avio ral issu es regardin g resistan ce. In addition to ou r n eed to u n derstan d th e in flu en ce of h u m an beh avior on t h e evo lu t io n o f resist an ce, t h ere are t h ree o t h er reaso n s fo r lo o kin g at eco -

6 • Introduction: On the Economics of Resistance

n om ic ou tcom es in addition to biological ou tcom es wh en dealin g with resistan ce. First, for an y given resistan ce m an agem en t strategy, econ om ics en ables u s to evalu ate trad eoffs between th e ben efits of u sin g th e p rod u ct tod ay an d th e fu tu re costs of resistan ce. On e m igh t ch oose to sim p ly m in im ize th e p robability th at resistan ce will arise; h owever, m in im izin g resistan ce, by itself, is a m ean in gless o bject ive an d can be acco m p lish ed by n o t u sin g an t ibio t ics o r p esticides at all. We u se th ese p rodu cts on ly becau se th ey p rovide a ben efit in term s of killin g bacteria or p ests. Th erefore, if a p articu lar resistan ce m an agem en t strategy is very effective at redu cin g resistan ce bu t in creases th e n u m ber o f p est s, it m ay n o t n ecessarily be t h e best st rat egy t o ad o p t . Mo reo ver, t h e ben efits an d costs of u sin g an tibiotics or p esticides occu r at differen t p oin ts in tim e, an d econ om ics p rovides a fram ework for m akin g in tertem p oral com p arison s of ou tcom es. We can illu strate th e im p ortan ce of econ om ics in stu d yin g th e in tertem p oral trad e-off in volved in resistan ce m an agem en t in th e con text of h osp ital in fect io n s. Th e o verall o b ject ive o f h o sp it al in fect io n co n t ro l co m m it t ees wh ich are ch arged with th e well-bein g of all p atien ts in th e h osp ital both in t h e p resen t an d in t h e fu t u re, is t o en su re t h at p at ien t s reco ver so o n an d th at bacterial resistan ce is m in im ized . Given th at th e com m ittee’s objective is t o balan ce bet ween t reat m en t o u t co m es in t h e p resen t again st t h e p o ssibility of fu tu re resistan ce, econ om ic an alysis p lays a u sefu l role in p rovid in g a m et ric fo r co m p arin g p resen t an d fu t u re b en efit s an d co st s o f an t ib io t ic treatm en t. A seco n d , relat ed ben efit o f t h e eco n o m ic way o f t h in kin g is t h at it p ro vid es a co n sist en t fram ewo rk fo r evalu at in g d ifferen t st rat egies t o m an age resistan ce, in clu din g th ose th at do n ot in volve ch an ges in h ow we u se an tibiotics. For in stan ce, sim p le p rocedu res su ch as freq u en t h an d wash in g by n u rsin g staff cou ld h elp red u ce th e p revalen ce of resistan t in fection s in h osp itals (Au st in et al. 1999). Ho wever, wit h o u t kn o win g t h e co st o f im p lem en t in g a strict h an d -wash in g p rogram , th is strategy can n ot be com p ared with on e of restrictin g th e u se of an tibiotics in th e h osp ital. Th e th ird ben efit of in trodu cin g econ om ic an alysis is th at it can alter con clu sio n s reach ed b y p u rely ep id em io lo gical m o d els, as well as en rich t h eir ap p licability to th e real world wh ere econ om ic costs p lay an im p ortan t role. Fo r in st an ce, Bo n h o effer an d co lleagu es sh o wed t h at given t wo id en t ical an tibiotics, a strategy of u sin g th e two dru gs on eq u al fraction s of th e p atien t p o p u lat io n wo u ld b e su p erio r t o o n e in wh ich at an y given t im e o n ly o n e d ru g is u sed on all p atien ts an d th e two d ru gs are p eriod ically cycled (1997). Usin g econ om ic m odels in con ju n ction with m ath em atical disease m odels, it is p ossible to d em on strate th at th eir con clu sion rests on th e assu m p tion th at both th e levels of resistan ce to th e two an tibiotics as well an tibiotic treatm en t costs are iden tical (Laxm in arayan an d Brown 2001). Th is m ay n ot be th e case

Introduction: On the Economics of Resistance • 7

in reality. Th ere are sim ilar exam p les in th e agricu ltu ral con text of com bin in g eco n o m ic an d b io lo gical m o d els t h at illu st rat e t h e valu e o f a m u lt id iscip lin ary p ersp ective on resistan ce m an agem en t strategies (Mu n ro 1997). Alt h o u gh eco n o m ic an alysis is h elp fu l in m an y ways, it s u sefu ln ess rest s critically on ou r u n derstan din g of th e evolu tion ary p rocesses th at drive resistan ce. Collaborative efforts between n atu ral an d social scien tists are likely to m ake tan gible con tribu tion s to th e p olicy p rocess.

How Can We Encourage the Development of New Antibiotics and Pesticides? To date, th ere is very little research on h ow th e in n ovation of n ew an tibiotics an d p esticides m ay be affected by th e p roblem of resistan ce. Existin g work h as eith er exp lored h ow resistan ce affects in cen tives to in n ovate or h ow m arket stru ctu re can in flu en ce h ow firm s ch oose to d evelop an d sell an tibiotics an d p est icid es. Eco n o m ic research h as sh o wn t h at research exp en d it u res b y a p h arm aceu t ical firm will in crease in resp o n se t o in creasin g resist an ce t o it s exist in g p o rt fo lio o f an t ib io t ics (Kile 1989). Fu rt h erm o re, t h is resp o n se d ep en d s o n wh et h er t h e cu rren t d ru g is m ad e b y t h is firm o r b y a rival becau se resistan ce to th e rival firm ’s d ru g can on ly in crease th e valu e of th is firm ’s existin g p ortfolio. Th eo ret ical m o d els h ave b een u sed t o illu st rat e t h e co m m o n -p ro p ert y p roblem associated with an tibiotics. Tisd ell u sed a sim p le, two-p eriod m od el in wh ich th e n u m ber of an tibiotic doses adm in istered in th e first p eriod in flu en ces treatm en t effectiven ess in th e secon d p eriod (1982). In a p olicy solu tion rem in iscen t of th e sole-own er fish ery m od el, Tisd ell p rop osed eith er regu latin g first-p eriod an tibiotic con su m p tion or gran tin g a m on op oly to sellers of an t ibio t ics t o en su re t h ey co n sid er t h e in t ert em p o ral d ep let io n o f effect iven ess. Settin g p aten t breadth op tim ally h as been su ggested as a way of solvin g th is com m on -p rop erty p roblem an d en cou ragin g firm s to take resistan ce in to con sid eration (Laxm in arayan 1999). Fin ally, oth er research ers h ave h yp oth esized th at a com p etitive m arket for an tibiotics will n ot be able to p rod u ce a variet y o f an t ibio t ics t h at is o p t im al fro m t h e st an d p o in t o f m an agin g d ru g resist an ce an d t h at sp ecial in cen t ives m ay b e n eed ed t o en co u rage firm s t o develop n ew an tibiotics (Ellison an d Hellerstein 1999). In sp ite of ou r best efforts to m an age resistan ce, an tibiotics an d p esticid es th at are cu rren tly in u se will in evitably be less effective in th e fu tu re. Econ om ics can h elp in d esign in g in cen tives to en cou rage research an d d evelop m en t of n ew p rodu cts. Policym akin g efforts to design su ch in cen tives to en cou rage in n ovation sh ou ld be gu id ed by two criteria. First, p olicies to en cou rage th e d evelop m en t of n ew an tibiotics (or p esticid es) m u st n ecessarily be con sisten t wit h o t h er p o licies t h at in flu en ce h o w firm s ch o o se t o p rice an d sell t h eir

8 • Introduction: On the Economics of Resistance

p ro d u ct s. Alt h o u gh we wan t firm s t o co m e u p wit h n ew p ro d u ct s, we also wan t t o in crease (o r at t h e very least n o t d ecrease) t h eir in cen t ives t o care abou t p rod u ct effectiven ess. Secon d , th e fu n d am en tal p olicy objective is n ot ju st to in crease in cen tives for firm s to in trodu ce any n ew an tibiotics (or p esticides) bu t to sp ecifically develop n ew p rodu cts th at are sign ifican tly differen t from existin g on es in th eir m ech an ism s of action . Th is m in im izes th e com m o n -p ro p ert y p ro blem t h at arises wh en d ifferen t firm s m ake p ro d u ct s wit h lin ked m odes of action an d, con seq u en tly, n o sin gle firm h as su fficien t in cen tive to care abou t declin in g p rodu ct effectiven ess. If we th in k of p rodu ct effect iven ess as a reso u rce, like o il fo r in st an ce, an o p t im al p o licy wo u ld be o n e th at en cou rages d ru g firm s to search for n ew “wells” of effectiven ess again st bacteria, rath er th an to drill n ew “wells” to extract existin g reserves in com p etition with oth er p rod u cers. Given th is latter criterion , stan d ard p olicy solu t io n s su ch as research in vest m en t t ax cred it s an d lo n ger p at en t len gt h m ay n ot n ecessarily solve th e p roblem . In creasin g p aten t len gth often h as been su ggested as a way of en cou ragin g in n ovation by in creasin g th e retu rn from in vestm en t (OTA 1995). In th e case of p rod u cts like an tibiotics an d p esticid es in wh ich th e rate of p rod u ct obsolescen ce is in flu en ced b y h o w firm s p rice t h eir p ro d u ct s, in creasin g p at en t len gth h as th e addition al ben efit of in creasin g th e stake th at firm s h ave in th e effectiven ess of th eir p rodu cts. However, th e len gth of th eir p aten ts lim its th e ext en t t o wh ich firm s h ave an in cen t ive t o care ab o u t t h e effect iven ess o f th eir p rod u cts. Ph arm aceu tical (an d p esticid e) firm s m ay h ave fewer reason s to care abou t th e effectiven ess of th eir d ru gs after p aten t exp iration an d are th erefore likely to extract d ru g effectiven ess at a rate greater th an is socially op tim al. Th is occu rs in m u ch th e sam e way as a logger wh o h as a fixed -term con cession on a forest will try to cu t down as m an y trees as p ossible before h is con cession exp ires, an d it is a socially u n desirable ou tcom e. Ext en d in g p at en t len gt h wo u ld give p h arm aceu t ical co m p an ies a great er in cen tive to care abou t th e effectiven ess of th eir p rod u ct over a lon ger tim e h o rizo n . Th erefo re, o n e wo u ld exp ect t h at t h ey wo u ld b e less aggressive in m arketin g th eir p rod u cts in th e in terests of p reservin g th eir p rod u ct’s effectiven ess an d en cou rage carefu l u se of th eir p rod u cts. However, all else bein g eq u al, exten d in g p aten t len gth is likely to in crease th e n u m ber of “m e-too” d ru gs th at are close su bstitu tes of existin g an tibiotics an d th at d raw on existin g stocks of effectiven ess (see Ch ap ter 11, for in stan ce). Th is wou ld en cou rage a greater degree of com p etition between firm s for th e sam e stock of effect iven ess an d , co n seq u en t ly, t o o fast a rat e o f effect iven ess exh au st io n . Th is in cen tive m ech an ism is n ot sp ecifically targeted at ou r objective of en cou ragin g t h e d evelo p m en t o f n ew d ru gs wit h in n o vat ive m o d es o f act io n t h at cou ld be effective again st organ ism s resistan t to existin g p rod u cts. Th erefore, in creasin g p aten t len gth (or even p rovid in g research in vestm en t tax cred its,

Introduction: On the Economics of Resistance • 9

fo r t h at m at t er) m ay n o t b e su fficien t t o p ro m o t e t h e d evelo p m en t o f n ew classes of an tibiotics. O t h er p o licy o p t io n s t h at h ave received at t en t io n in t h e an t ibio t ics co n text in clu de m ech an ism s to exch an ge p aten t len gth exten sion s for u se restriction s. Th e OTA rep ort on an tibiotic resistan ce su ggests th at an arran gem en t cou ld be worked ou t between th e Food an d Dru g Ad m in istration (FDA), th e Paten t Office, an d th e p h arm aceu tical firm to in crease th e p aten t len gth wh ile lim itin g th e n u m ber of u ses for wh ich th e an tibiotic m ay be u sed . However, ext en sive an alyses o f o ff-label d ru g u se h ave sh o wn t h at an t ibio t ics are n o t n ecessarily p rescrib ed fo r o n ly t h e co n d it io n s fo r wh ich t h ey received FDA ap p roval (Ch ristop h er 1993). Th erefore, su ch an agreem en t m ay n ot n ecessarily work with ou t som e way of en forcin g restriction s on an tibiotic u se. Th ese p roblem s are likely to arise in th e p esticide aren a as well. Disco u ragin g t h e p ract ice o f t reat m en t h o m o gen eit y—wh ereb y a sin gle an t ib io t ic o r a few an t ib io t ics (o r p est icid es) are wid ely u sed wh ile n ewer p rod u cts are kep t on th e sid elin es for u se on ly for resistan t in fection s—cou ld in flu en ce n ew p ro d u ct d evelo p m en t . Great em p h asis is o ft en p laced o n t h e m ost cost-effective an tibiotic or p esticid es, an d n ew p rod u cts are often kep t o n t h e sid elin es as b acku p s if t h e cu rren t ly u sed p ro d u ct fails. O n t h e o n e h an d , t h ese p o licies en su re a large m arket o f resist an t in fect io n s fo r t h e backu p d ru g on ce th e fron tlin e d ru g fails. On th e oth er h an d , th ey m ay d iscou rage m an u factu rers wh o m ay be u n willin g to take a risk based on th e cu rren t fron tlin e p rod u ct failin g an d wou ld th erefore be u n willin g to d evelop a n ew dru g. Policies th at en cou rage p rodu ct h om ogen eity sh ou ld, th erefore, be sen sitive to th eir effect on p rodu cer in cen tives. A fin al issu e is th e relative im p ortan ce of in n ovation com p ared with m easu res to m an age resistan ce to existin g an tibiotics an d p esticides. Clearly, m easu res n eed to be taken on both fron ts, bu t we n eed to h ave som e assessm en t of t h e relat ive im p o rt an ce o f t h ese t wo aven u es t o ad d ressin g t h e resist an ce p ro b lem . Recen t evid en ce su ggest s t h at n ew an t ib io t ics m ay h ave m u ch sh o rt er life sp an s co m p ared wit h d ru gs in t ro d u ced a few d ecad es ago . Th is m ay in d icate sign ifican t cross-resistan ce between old an d n ew p rod u cts. For in stan ce, estim ates of th e resistan ce-related costs of with drawin g organ op h osp h at es fro m ap p le farm in g m igh t b e t o o lo w if t h ere h ad b een sign ifican t cross-resistan ce between th e old an d n ew p esticides (Mu n ro 1997). Fin ally, th e co st s o f in t ro d u cin g n ew p est icid es h ave in creased d ram at ically wit h each gen eration of p esticid e (Ham m ock an d Son d erlu n d 1986). Th is is believed to be tru e in th e case of an tibiotics as well an d is esp ecially worrisom e becau se it h igh ligh ts th e im p ortan ce of n ot relyin g on th e arrival of tech n ological fixes to solve th e p roblem of risin g resistan ce. To th e exten t th at th ese p roblem s are widesp read, we can rely m u ch less on bein g saved by in n ovation an d will h ave to devote greater effort to con servin g

10 • Introduction: On the Economics of Resistance

ou r existin g dru gs. However, th e arrival of Bt crop s th at h ave little or n o crossresistan ce with older p esticides su ch as p yreth roids h as in dicated th at in som e in stan ces, it m ay be worth wh ile to an ticip ate a tech n ological fix.

Directions for Further Research Th e econ om ics of resistan ce is in its in itial stages of form ation . Alth ou gh th is book covers a wide swath of q u estion s, m u ch m ore work is n eeded to resp on d to th e growin g ch allen ges p osed by in creasin g resistan ce th at th reaten s to roll back advan ces m ade again st in fectiou s diseases an d agricu ltu ral p ests. A n u m ber of research issu es discu ssed in th is section are sp ecific to an tibiotics or p esticides, an d so th ey are discu ssed in th is order.

Antibiotics

Th is b o o k m akes so m e h ead way in d iscu ssin g t h e kin d s o f st rat egies t h at wo u ld m axim ize t h e eco n o m ic valu e fro m an t ib io t ics. Ho wever, m u ch rem ain s to be d on e in u n d erstan d in g th e in cen tives faced by p atien ts, p h ysician s, an d h o sp it al ad m in ist rat o rs an d in d esign in g eco n o m ic in cen t ives t o en su re t h at an t ib io t ics are u sed in acco rd an ce wit h a b est p o licy. A relat ed issu e is h ow we m igh t be able to d iscou rage in ap p rop riate u se of an tibiotics sh o rt o f act u ally reviewin g an d seco n d -gu essin g m ed ical d ecisio n s. Fro m a p h ysician ’s p ersp ective, th ere are few in cen tives to care abou t th e im p act of resist an ce an d m an y in cen t ives t o en su re t h e co n t em p o rary in d ivid u al p atien t’s well-bein g. Th e h igh cost of liability in su ran ce rein forces th e Hip p ocrat ic o at h t o d o t h e b est fo r t h e p at ien t . Th ese fact o rs m ay fu rt h er in d u ce p h ysician s to err on th e side of p rescribin g an tibiotics wh en th ey are u n n ecessary an d p rescribin g stron ger, m ore broad -sp ectru m an tibiotics th an m ay be n ecessary. Ad d ressin g th e p roblem of resistan ce m ay req u ire th at th is fu n d am en tal con trad iction between p erceived p atien t well-bein g an d societal wellbein g be resolved. Alt h o u gh t h e p u blic h as in creasin gly exp ressed co n cern abo u t t h e em ergen ce of an tibiotic-resistan t bacteria (Bard en et al. 1998), p atien ts in gen eral h ave few in cen tives to care abou t th e resistan ce extern ality. In su ran ce sh ields m an y p at ien t s fro m b ein g d irect ly resp o n sib le fo r t h e co st o f m ed ical care, fu rth er d istortin g th e tru e cost of an tibiotic treatm en t from th e p atien t’s p ersp ect ive. A large, ran d o m ized st u d y sh o wed t h at p eo p le wh o received free m edical care u sed 85% m ore an tibiotics th an th ose req u ired to p ay for at least som e p ortion of th eir m edical care (Foxm an et al. 1987). In cen tives for better u se o f an t ibio t ics m ay h ave t o be st ro n gly lin ked wit h h o w p at ien t s p ay fo r an tibiotics an d m ay call for ch an ges to in su ran ce reim bu rsem en t for an tibiotics. More research is n eeded to u n derstan d th ese lin kages.

Introduction: On the Economics of Resistance • 11

An o t h er area in wh ich p u b lic p o licy co u ld b e illu m in at ed b y m o re eco n o m ic an alysis is wh at o ft en h as been ch aract erized as in ap p ro p riat e u se o f an tibiotics for farm an im al feed. Th e scien ce of h ow th e u se of an tibiotics for growth p rom otion in an im als resu lts in resistan t in fection s in h u m an s is still in develop m en t, an d th ere is disagreem en t on th e relative im p ortan ce of th is cau sal factor wh en com p ared to in ap p rop riate u se of an tibiotics in h u m an s. Regardless, th e n eed for p u blic p olicy is eviden t. For in stan ce, th ere h as been a great d eal of con troversy su rrou n d in g FDA ap p roval of flu oroq u in olon es, an an tibiotic u sed in h u m an s th at is also ap p roved for u se in an im als. In recen t m on th s, FDA h as with drawn p erm ission for th is dru g to be m arketed for an im al u se, a m ove th at was op p osed by Bayer, on e of th e two m an u factu rers of th is dru g. FDA’s case was m ade on th e basis of a risk an alysis th at sh owed th at flu oroq u in olon e u se in an im als p osed an in creased risk of flu oroq u in olon eresistan t in fection s of Cam pylobacter pylori. However, th e m ore fu n d am en tal q u est io n is wh y firm s ch o o se t o sell an t ib io t ics as gro wt h p ro m o t ers wh en su ch u se cou ld p oten tially h arm th e d em an d for th e h u m an version of th ese an t ib io t ics. O n e p o ssib le aven u e fo r research is t o u n d erst an d h o w fact o rs su ch as t h e p at en t sco p e given t o an t ib io t ics, an d d ifferen ces in t h e FDA ap p roval p rocesses for u sin g an tibiotics in an im als as growth p rom oters an d in h u m an s as th erap eu tic agen ts cou ld in flu en ce in cen tives for p h arm aceu tical firm s with resp ect to an tibiotic resistan ce.

Pesticides

Cu rren t in terest in resistan ce in th e agricu ltu ral con text h as arisen with th e adoption of gen etically m odified crops. Gen etically m odified corn , cotton , an d soybean s th at express th e Bt protein h ave been widely adopted in U.S. agricu ltu re. Un like wh en oth er p esticides are u sed, EPA h as form u lated sp ecific ru les for growers to en su re th at resistan ce to Bt does n ot arise. Research on econ om ic in cen tives can im p rove cu rren t p olicies in at least two direction s. Th e cu rren t strategy of u sin g m an d atory refu ge areas th at are m on itored an d en forced by seed co m p an ies m ay su ffer fro m several d rawbacks. Su bst an t ial m o n it o rin g an d en forcem en t costs m ay n eed to be taken in to accou n t. Growers m ay follow on ly th e letter of th e law an d grow refu ge areas on ly in poor qu ality lan d wh ere th ey will be m u ch less effective. Also, in dividu al growers m ay ch eat an d n ot observe th e m an d ated refu ge req u irem en ts. Fin ally, th e exten t of refu ge n eeded m ay depen d on con cen tration of oth er Bt fields in th e close proxim ity (see Ch ap t er 4). So , fo r in st an ce, it m ay be m o re im p o rt an t t o en su re t h at a co t t o n farm er in Lo u isian a fo llo ws t h e refu ge req u irem en t t h an a co t t o n farm er in Ch in a, wh ere cotton fields are in terspersed with oth er crops. Th e ch allen ge, th erefore, is to d esign su itable in cen tive m ech an ism s th at en cou rage each farm er to in vest in m ore socially desirable refu ge strategies. A

12 • Introduction: On the Economics of Resistance

n u m ber of d ifferen t in cen tive m ech an ism s m ay offer altern atives to th e cu rren t m an datory refu ge prin ciple. For in stan ce, a “resistan ce u ser fee” on gen etically m o d ified seed s co u ld be levied t o fo rce gro wers t o bear t h e so cial co st associated with pest resistan ce to th ese crops. Th is u ser fee cou ld be calibrated to th e den sity of Bt crop in th e local area an d cou ld be u sed to set u p com m on refu ge areas or be u sed to pay som e farm ers to grow on ly n on -Bt crop. An oth er strategy m ay be to su bsidize seed m ixtu res th at con tain both gen etically m odified an d n o n –gen et ically m o d ified variet ies. Th e m ixed seed st rat egy is believed to be particu larly feasible in th e case of th e pin k bollworm , in wh ich larval m ovem en t is m in im al (Tabash n ik 1994). A th ird m ech an ism th at cou ld be con sidered in th is research is th e con cept of tradable refu ge perm its. Un der th is fram ework, growers wh o focu s on n on -Bt crop s wou ld receive refu ge p erm its th at cou ld th en be bou gh t by growers of Bt crops in stead of growin g th eir own refu ge areas. Th is approach is sim ilar to th e con cept of tradable pollu tion perm its in th e en viron m en tal econ om ics literatu re, an d can be applied in areas of m on ocu ltu re. A fou rth m ech an ism wou ld allow growers to p ool th eir n on Bt refu ge areas or join tly pay a sin gle farm er to grow on ly n on -Bt crop as lon g as it satisfies biological requ irem en ts for spatial proxim ity to th e Bt crop. In p u rsu in g th ese aven u es of research , m u ltid iscip lin ary efforts h ave a far greater p oten tial to yield an swers th an th ose efforts u n dertaken by n atu ral or social scien tists workin g en tirely with in th eir own dom ain s.

References Au stin , D.J., M.J. Bon ten , R.A. Wein stein , S. Slau gh ter, an d R.M. An d erson . 1999. Van co m ycin -Resist an t En t ero co cci in In t en sive-Care Ho sp it al Set t in gs: Tran sm issio n Dyn am ics, Persisten ce, an d th e Im p act of In fection Con trol Program s. Proceedings of the National Academ y of Sciences of the USA 96(12): 6908–13. Barden , L.S., S.F. Dowell, B. Sch wartz, an d C. Lackey. 1998. Cu rren t Attitu des Regardin g Use of An tim icrobial Agen ts: Resu lts from Ph ysician s’ an d Paren ts’ Focu s Grou p Discu ssion s. Clinical Pediatrics 37: 665–72. Bon h oeffer, S., M. Lip sitch , an d B.R. Levin . 1997. Evalu atin g Treatm en t Protocols to Preven t An tibiotic Resistan ce. Proceedings of the National Academ y of Sciences of the USA 94(22): 12106–11. Brown , G., an d D.F. Layton . 1996. Resistan ce Econ om ics: Social Cost an d th e Evolu tion of An tibiotic Resistan ce. Environm ent and Developm ent Econom ics 1(3): 349–55. Carlson , G., an d E.N. Castle. 1972. Econ om ics of Pest Con trol. In Control Strategies for the Future. Wash in gton , DC: Nation al Academ y of Scien ces, 79–99. Ch rist o p h er, W.L. 1993. O ff-Label Dru g Prescrip t io n : Fillin g t h e Regu lat o ry Vacu u m . Food and Drug Law Journal 48: 247–62. Coast, J., R.D. Sm ith , an d M.R. Millar. 1996. Su p erbu gs: Sh ou ld An tim icrobial Resistan ce Be In clu ded as a Cost in Econ om ic Valu ation ? Health Econom ics 5: 217–26. Co m in s, H.N. 1977a. Th e Develo p m en t o f In sect icid e Resist an ce in t h e Presen ce o f Migration . Journal of Theoretical Biology 64: 177–97.

Introduction: On the Economics of Resistance • 13 ———. 1977b. Th e Man agem en t of Pesticide Resistan ce. Journal of Theoretical Biology 65: 399–420. ———. 1979. An alytic Meth ods for Man agem en t of Pesticide Resistan ce. Journal of Theoretical Biology 77: 171–88. Elb ash a, E. 1999. Dead weigh t Lo ss o f Bact erial Resist an ce Du e t o O vert reat m en t . Un p u b lish ed rep o rt fo r t h e Cen t ers fo r Disease Co n t ro l an d Preven t io n , At lan t a, GA. Elliso n , S.F., an d J. Hellerst ein . 1999. Th e Eco n o m ics o f An t ib io t ics: An Exp lo rat o ry Stu d y. In Measuring the Prices of Medical Treatm ent, ed ited by J.E. Trip lett. Wash in gton , DC: Brookin gs In stitu tion . Fo xm an , B., R. Bu rciaga Vald ez, K.N. Lo h r, G.A. Go ld b erg, J.P. Newh o u se, an d R.H. Bro o k. 1987. Th e Effect o f Co st Sh arin g o n t h e Use o f An t ib io t ics in Am b u lat o ry Care: Resu lt s fro m a Po p u lat io n -Based Ran d o m ized Co n t ro lled Trial. Journal of Chronic Diseases 40: 429–37. Ham m ock, B.D., an d D.M. Son d erlu n d . 1986. Ch em ical Strategies for Resistan ce Man agem en t. In Pesticide Resistance: Strategies and Tactics for Managem ent, ed ited by N.R. Cou n cil. Wash in gton , DC: Nation al Academ y Press. Hu eth , D., an d U. Regev. 1974. Op tim al Agricu ltu ral Pest Man agem en t with In creasin g Pest Resistan ce. Am erican Journal of Agricultural Econom ics 56: 543–53. Hu rley, T.M., S. Secch i, B.A. Babcock, an d R. Hellm ich . 1999. Man agin g th e Risk of Eu rop ean Co rn Bo rer Resist an ce t o Tran sgen ic Co rn : An Assessm en t o f Refu ge Reco m m en dation s. Am es, IA: CARD, Iowa State Un iversity, 36. Hyde, J., M.A. Martin , P.V. Preckel, C.L. Dobbin s, an d C.R. Edwards. 1999. The Econom ics of Refuge Design for Bt Corn. Am erican Agricu ltu ral Econ om ics Association Meetin g, Nash ville, TN. IRAC (In sect icid e Resist an ce Act io n Co m m it t ee). 2002. www.p lan t p ro t ect io n .o rg/ irac (accessed Febru ary 15, 2002). Kile, J.D. 1989. Research an d Develop m en t in th e Ph arm aceu tical In du stry: Th e Im p act of Dru g Resistan ce. Doctoral dissertation . Madison , W I: Un iversity of Wiscon sin . Laxm in arayan , R. 1999. Econ om ics of An tibiotic Resistan ce. Doctoral dissertation . Seattle, WA: Un iversity of Wash in gton . Laxm in arayan , R., an d G.M. Brown . 2001. Econ om ics of An tibiotic Resistan ce: A Th eo ry o f O p t im al Use. Journal of Environm ental Econom ics and Managem ent 42(2): 183–206. Laxm in arayan , R., an d R.D. Sim p son . 2002. Refu ge Strategies for Man agin g Pest Resistan ce in Tran sgen ic Agricu ltu re. Environm ental and Resource Econom ics 22: 521–36. Livin gston , M.J., G.A. Carlson , an d P.L. Fackler. 2000. Bt Cotton Refuge Policy. Am erican Agricu ltu ral Econ om ics Association Meetin g, Tam p a Bay. Mu n ro, A. 1997. Econ om ics an d Biological Evolu tion . Environm ental and Resource Econom ics 9: 429–9. OTA (Office of Tech n ology Assessm en t). 1995. Im pact of Antibiotic-Resistant Bacteria: A Report to the U.S. Congress. Govern m en t Prin tin g Office. Wash in gton , DC: OTA. Ph elp s, C.E. 1989. Bu g/ Dru g Resist an ce: So m et im es Less Is Mo re. Medical Care 27(2): 194–203. Reed , S., S. Su llivan , an d R. Laxm in arayan . 2001. So cio eco n o m ic Issu es Relat ed t o An tibiotic Use. In Appropriate Antibiotic Use, ed ited by D.E. Low. Lon d on : Th e Royal Society of Medicin e Press, 41–6.

14 • Introduction: On the Economics of Resistance Tabash n ik, B.E. 1994. Delayin g In sect Ad ap tation to Tran sgen ic Plan ts: Seed Mixtu res an d Refu gia Recon sidered. Proceedings of the Royal Society of London, Series B 255: 7–12. Tisdell, C. 1982. Exp loitation of Tech n iq u es th at Declin e in Effectiven ess. Public Finance 37: 428–37.

PART I

Issues of Optimal M anagement of Resistance

Chapter 1

Dynamics of Antibiotic Use Ecological versus Interventionist Strategies To M anage Resistance to Antibiotics James E. Wilen and Siwa M sangi

This chapter explores som e econom ic and epidem iological im plications of alternative disease treatm ent strategies in an institutional setting such as a hospital or clinic. We m odify and generalize the integrated econom ic/ epidem iological m odel first introduced by Laxm inarayan and Brow n (2001). Laxm inarayan and Brow n adapted an epidem iological m ulticom partm ent model of treatment and infection from Bonhoeffer and others (1997), a characterization based, in turn, on early twentieth-century population models of disease transmission and infection. Laxminarayan and Brown added an economic objective function that incorporates explicit assessment of the present value of the costs and benefits of accelerated disease reduction caused by treatm ent. Laxm inarayan and Brown derived im portant qualitative conclusions about how to optim ally treat a diseased population, show ing how treatment and the corresponding buildup of antibiotic resistance are similar to the fundamental economic problems of optimally exploiting a nonrenewable resource. As Laxm inarayan and Brown argued, in a closed system , the population of individuals responsive to or susceptible to antibiotic treatment can be thought of as a resource w ith positive econom ic value. Treatm ent yields a stream of benefits associated with accelerated recovery of the diseased population, but at the sam e tim e, antibiotic resistance as a result of treatment leads to a “ draw down” of the stock of susceptibility. The optimal treatm ent decision thus m ust account for the dynam ic trade-off associated w ith im m ediate disease reduction gains and long-term future resistance buildup costs. Our chapter generalizes the Laxminarayan and Brown paper in an important way by including the possibility that there are fitness costs associated with genes that allow a disease to be resistant to antibiotic treatment. Laxminarayan and Brown ignored fitness costs to highlight the analogy with the • 17 •

18 • Chapter 1: Dynamics of Antibiotic Use nonrenewable resource problem. We show that fitness costs affect the optimal treatment regime in two major ways. First, with fitness costs it is possible that the optimal long-run treatment regime involves steady state strategies that hold resistant and susceptible populations in a symbiotic balance, more like a multispecies renewable resource problem than a nonrenewable problem. Second, with fitness costs, it is also possible that ecological (nonantibiotic) strategies that encourage susceptible bacteria to outcompete resistant bacteria are econom ically preferable to interventionist strategies involving aggressive antibiotic treatment. In the appendix, we solve the general problem explicitly, characterizing long-term steady states and approach paths in term s of fundam ental param eters. Our chapter explains the results using modified phase diagrams that characterize the results qualitatively. We also com pare the two broad kinds of treatm ent strategies, categorized as interventionist and ecological, with a numerical model.

h is ch ap ter exam in es som e of th e econ om ic im p lication s of an tibiotic u se with in a h u m an p op u lation an d illu strates th e im p lication s of relative fitn ess am on g d ifferen t d isease vectors on d ru g resistan ce in th e p op u lation . As em p h asized th rou gh ou t th is book, th e issu e of an tibiotic resistan ce is clearly on e of th e m ore im p ortan t con tem p orary world h ealth issu es. Over th e p ast few years, p h ysician s an d h ealt h care p ract it io n ers h ave co m e face t o face wit h several viru len t st rain s o f d ru g-resist an t d iseases. To n am e ju st a few, p en icillin -resist an t go n o rrh ea; van co m ycin -resist an t Staphylococcus aureus; an d th e bacterial sp ecies Enterococcus faecalis, Mycobacterium tuberculosis, an d Pseudom onas aeruginosa, are all ju st begin n in g to evad e th e reach of th e cu rren t stockp ile of an tibiotics. Th ese n ew resistan t bacteria rep resen t a clear an d p resen t d an ger to m an y in d evelop in g an d d evelop ed cou n tries alike. Mu ch acq u ired an t ib io t ic resist an ce h as co m e ab o u t as a resu lt o f m isu se b y b o t h p h ysician s an d self-m ed icatin g in d ivid u als, wh ich h as in d u ced n atu ral selection p ressu re favorin g th e su rvival of resistan t gen es with in viral an d bacterial sp ecies. Th e con seq u en t grad u al bu ild u p of d ru g resistan ce in th e p op u lation h as p u t in creasin g p ressu re on research ers to develop n ew treatm en t agen ts to keep q u ickly m u t at in g p at h o gen s in ch eck. Man y o bservers h ave su ggest ed t h at t h e large, fro n t -lo ad ed co st s o f d ru g in n o vat io n an d t h e lo n g ap p ro val lags h ave slo wed t h is p ro cess, h o wever, an d kn o wled geable in sid ers su ggest t h at n o n ew “m iracle” d ru gs are o n t h e h o rizo n wit h wid e effect iven ess t o attack th ese n ew resistan t strain s of disease. Clearly, p olicy d ecision s affectin g th e su p p ly sid e of th e p roblem will be critical to th e fu tu re of d isease con trol becau se research an d d evelop m en t at th e p h arm aceu tical level d ep en d on p aten t laws, in tellectu al p rop erty righ ts, an d tax an d su bsid y p olicies. At th e sam e tim e, p h ysician s an d h osp itals are begin n in g to p ractice n ew n otion s of d ru g-u se m an agem en t aim ed at red u c-

T

Chapter 1: Dynamics of Antibiotic Use • 19

in g th e bu ild u p of resistan ce via d em an d sid e m an agem en t. In th is ch ap ter, we exten d th e im p ortan t op tim al an tibiotic u se work by Laxm in arayan an d Brown (2001) to in clu de cases in wh ich bacterial p op u lation s can be m an aged wh en fit n ess co st s are asso ciat ed wit h resist an ce. Th e Laxm in arayan an d Brown p ap er p oses a p u rp osefu lly stark p roblem in wh ich an tibiotic u se irreversib ly d egrad es t h e st o ck o f d ru g su scep t ib ilit y. Th is fram ewo rk in t h eir m od elin g stru ctu re relies on th e assu m p tion th at n o fitn ess cost is associated with bacteria th at is resistan t to an an tibiotic d ru g. In th is ch ap ter, we in trodu ce fitn ess costs, leadin g to a system in wh ich an tibiotic effectiven ess can be m an aged t o a st ead y st at e. In o u r set t in g, an t ib io t ic effect iven ess can b e regard ed as a “ren ewable” rath er th an “n on ren ewable” resou rce, op en in g u p op p ortu n ities for in terestin g resistan ce m an agem en t trade-offs, in clu din g p ossibilities of m an agem en t with ou t u sin g an tibiotics. We con trast two d ifferen t regim es. We first discu ss th e basic ep idem iological dyn am ics u n der a n o-treatm en t p olicy, wh ich we refer to as an “ecological” p olicy. By ecological p olicy, we m ean a n o n in t erven t io n ist p o licy t h at allo ws a d isease t o p ro gress in a m an n er d ictated by th e n atu ral in teraction am on g bacteria exh ibitin g in tersp ecific an d in t rasp ecific co m p et it io n . We t h en exp lo re t h e t reat m en t o r “in t erven t io n ist ” regim e fo r wh ich t h e d isease p ro gresses in a m an n er d ictated by in tersp ecific an d in trasp ecific com p etition th at is aid ed an d altered by an tibiotic d ru g treatm en t. Fin ally, we com p are th e ou tcom es of in terven tion ist an d treatm en t regim es. Th is com p arison is th en exten d ed with a d iscu ssion of a broad er ran ge of n on d ru g treatm en t regim es as m ech an ism s for m an agin g th e p roblem of an tibiotic resistan ce.

Literature Review Most of th e literatu re th at cu rren tly exists on th e su bject of an tibiotic resistan ce is largely with in th e biological an d m ed ical scien ce literatu re. Op tim al h u m an d ru g u se h as been ad d ressed wit h in an eco n o m ic co n t ext by o n ly a h an d fu l of econ om ists. Am on g th e m ost n otable p ap ers th at h ave d ealt with t h e eco n o m ic co n sid erat io n s su rro u n d in g b io lo gical resist an ce h ave b een t h o se o f Hu et h an d Regev (1974), Bro wn an d Layt o n (1996) an d , m o st recen tly, Laxm in arayan an d Brown (2001). Th e Hu eth an d Regev paper was on e of th e first papers to exam in e th e econ om ics of resistan ce bu ildu p. Hu eth an d Regev exam in ed th e problem of pest resistan ce with in an agricu ltu ral con text an d h an d led th e p est m an agem en t problem in a very gen eral, an alytical fram ework u sin g optim al con trol th eory. Th ey co n sid ered th e o p t im al t im in g o f p est icid e ap p lication over a growin g seaso n t o m axim ize cro p p ro fit s n et o f p est co st s an d su bject t o bio lo gical eq u ation s of m otion for crop growth an d su scep tibility. Th ey con clu d ed th at th e gradu al depletion of resistan ce sh ou ld be an ticipated an d accou n ted for as

20 • Chapter 1: Dynamics of Antibiotic Use

p art o f an o p t im al d ecisio n an d t h at t h e t im in g o f p est icid e ap p licat io n is im portan t. Th e Brown an d Layton p ap er exam in ed both agricu ltu ral an d h u m an dru g u se in a very gen eral an alytical fram ework, givin g m ore atten tion to th e p rivat e versu s p u blic asp ect o f t h e p ro blem . By ju xt ap o sin g t h e d yn am ic o p t im ization p roblem of th e social p lan n er with th e m yop ic an d static op tim ization p roblem of th e p rivate an tibiotic u ser, th ey sh owed th at th e p rivate u ser treats too m u ch com pared with th e social optim u m of th e dyn am ic optim izer. Th ey also addressed th e in tergen eration al issu es th at arise with in creased resistan ce over tim e an d discu ssed th e issu e of h ow m an y people sh ou ld be treated an d wh o sh o u ld be t reat ed first . Th ese gen eral d iscu ssio n s give a go o d overview of th e im portan t issu es su rrou n din g th e socially optim al u se of dru gs in treatin g a p op u lation an d su ggest u sefu l direction s for fu rth er work. At th e sam e t im e, t h e p ap er lacks so m e o f t h e sp ecificit y t h at can be d erived fro m m ore explicit epidem iological an d econ om ic form u lation s. Th e Laxm in arayan an d Brown (2001) p ap er is am on g th e first to recast an ep id em io lo gical m o d el o f an t ib io t ic-resist an t d isease wit h in an eco n o m ic fram ework th at con sid ers th e econ om ic costs an d ben efits of treatm en t. Th e resu lt is a series of an alytical an d sim u lation resu lts th at are som etim es in con cert wit h , an d so m et im es at varian ce wit h , t rad it io n al an alysis based exclu sively o n ep id em io lo gical m o d elin g. Th e m o d el we p resen t t akes t h e Laxm in arayan an d Bro wn wo rk as a p o in t o f d ep art u re (u sin g t h eir n o t at io n wh ere p o ssible) an d gen eralizes it in several n o n t rivial d irect io n s. Th e m o st im p ortan t gen eralization is th e in corp oration of th e p ossibility th at resistan t d iseases in cu r a fit n ess co st asso ciat ed wit h t h eir abilit y t o be u n affect ed by an t ibio t ic t reat m en t . As it t u rn s o u t , t h is is a crit ically im p o rt an t feat u re o f op tim al an tibiotic treatm en t m od els, an d wh eth er fitn ess costs are in clu d ed affects th e q u alitative n atu re of th e solu tion in su rp risin g ways. Ou r secon d co n t rib u t io n is t o fo cu s o n t h e co m p ariso n o f “in t erven t io n ist ” st rat egies in volvin g an tibiotic d ru g u se an d “ecological” strategies in volvin g con trol of bacterial p op u lation s with ou t dru gs. Th e ep idem iological m odel we u se as a fou n dation for ou r an alysis is, as in t h e Laxm in arayan an d Bro wn (2001) an alysis, t h e m o d el o f in fect io n an d acq u ired resistan ce discu ssed in Bon h oeffer an d oth ers (1997). Th e Bon h oeffer m odel is a “m u lticom p artm en t” m odel of treatm en t an d in fection . Becau se it u ses a p u re ep id em iological m od el of d isease, th e Bon h oeffer p ap er d oes n ot op tim ize with an econ om ic objective fu n ction bu t in stead sim u lates th e n u m ber of u n in fected in dividu als over a given tim e h orizon u n der differen t treatm en ts. In assessin g th e efficacy of variou s p olicies, Bon h oeffer an d oth ers did n o t exp licit ly assign co st s t o eit h er t reat m en t act io n s o r illn ess, an d t h ey ign ored an y role for discou n tin g over th e p lan n in g p eriod. Laxm in arayan an d Bro wn an alyzed t h e an t ib io t ic t reat m en t p ro b lem as a d yn am ic eco n o m ic

Chapter 1: Dynamics of Antibiotic Use • 21

op tim ization p roblem with exp licit treatm en t ben efits, treatm en t costs, an d d iscou n tin g. Im p ortan tly, th e Laxm in arayan an d Brown assu m p tion of zero fitn ess costs lead s to a ch aracterization of th e p roblem for wh ich , for em p h asis, t h e “st o ck o f an t ib io t ic effect iven ess” is a d ep let ab le o r n o n ren ewab le resou rce u n eq u ivocally redu ced with an tibiotic u se. In th e m odel we develop , we relax t h is assu m p t io n t o exam in e sit u at io n s in wh ich t h e st o ck o f effectiven ess is at least p oten tially ren ewable.

Epidemiological M odel Th e m odel we u se follows directly from th e com partm en t m odel presen ted by Bon h oeffer an d oth ers (1997) for a sin gle treatm en t regim e, wh ich is based, in tu rn , on th e popu lation m odels of disease tran sm ission an d in fection dyn am ics th at date back to Kerm ack an d McKen drick (1927), Soper (1929), an d earlier st ill t o Ro ss (1911). Th e m alaria ep id em ic m o d el o f Ro ss an d t h e an t ibio t ic treatm en t m odel of Kerm ack an d McKen drick both m ake u se of th e in teraction between in fected m em bers of th e popu lation an d th ose wh o are u n in fected (or su sceptible)—h en ce th e n am e “SIS” (su sceptible → in fected → su sceptible). Th e essen t ials are cap t u red in t h e sch em at ic in Figu re 1-1, in wh ich we h ave a given en t ry rat e E in t o t h e p o p u lat io n o f u n in fect ed in d ivid u als, as well as an asso ciat ed d eat h rat e n. Th e in crease in t h e p o p u lat io n o f t h o se in fected with th e d ru g-sen sitive strain of viru s or bacteria Iw is con trolled by (a) th e rate of tran sm ission β an d th e in teraction between th ose wh o are u n in fected an d th ose wh o are alread y in fected , as well as (b) th e n atu ral recovery or clearan ce rate of th e d ru g-sen sitive strain of in fection rw Iw , in ad d ition to an y addition al recovery p rovided by treatm en t, frf (1 – s)Iw . Th e rate of ch an ge of th e p op u lation in fected with th e d ru g-resistan t strain Ir is con trolled on ly by th e tran sm ission / in teraction effect an d th e n atu ral recovery rr Ir. In ad d ition , th ere are death rates (m ) associated with th e in fected p op u lation , wh ich in co rp o rat e n at u ral as well as d isease-relat ed effect s an d cro ss-o ver effect s fro m t h e d ru g-sen sit ive t o t h e resist an t p o p u lat io n cau sed by d ru g-in d u ced acq u isit io n o f resist an ce fsrf Iw wh ere s is t h e fract io n o f t h o se t reat ed wh o acq u ire resistan ce. Th e treatm en t variable f rep resen ts th e fraction of th e p op u lation treated with th e dru g an d, as su ch , is bou n ded between 0 an d 1. A sp ecial featu re of th is kin d of m odel is th at treatm en t is assu m ed to be n on selective. Th u s it is assu m ed th at in fected in d ivid u als can be id en tified to receive treatm en t with ou t kn owin g wh eth er a sp ecific in d ivid u al h arbors th e resistan ce b act eria o r t h e su scep t ib le b act eria. Th e t ech n ical im p licat io n o f t h is assu m p t io n is t h at o n e can n o t co n t ro l t h e t wo in fect ed p o p u lat io n s sep arately; in stead, th ey are join tly con trolled in a m an n er th at reflects th eir relat ive ab u n d an ce. Treat m en t co n t ro l in t h is m o d el essen t ially in creases t h e rem issio n rat e o f t h e in d ivid u al in fect ed wit h su scep t ib le b act eria. Th e rf

22 • Chapter 1: Dynamics of Antibiotic Use

E (entry rate) n

Uninfected ( S)

Iw [ r w + f (1–s) r f ]

βSIw

r r Ir

βSIr

Sensitive ( I w )

Resistant ( Ir) fsIw r f (drug-induced resistance)

mIr (death)

mIw (death)

FIGURE 1-1. Schematic of Single Drug Treatment Regime

p aram eter rep resen ts th e additional rem ission rate of bacterial in fection over an d ab o ve t h e n at u ral reco very rat e. W h ile so m ewh at st ylized , t h is m o d el cap tu res th e essen tials of in fection d yn am ics with in a p op u lation an d len d s itself q u ite easily to an alysis, both n u m erically an d an alytically. Th e dyn am ic equation s of m otion for th e com partm en t m odel are as follows: S˙ = E − nS − βS( I w + Ir ) + rw I w + rr Ir + f (1 − s ) I w rf

(

)

I˙w = βS − m − rw − frf I w

(1)

I˙r = (βS − m − rr ) Ir + fsI w rf We follow Laxm in arayan an d Brown (2001) in sim p lifyin g th is m od el by assu m in g th at we are d ealin g with a closed p op u lation su ch as a h osp ital or region al clin ic in an isolated area. Th ese assu m p tion s are em bodied by assu m in g E = m = n = 0. Dealin g wit h a clo sed p o p u lat io n allo ws o t h er co n ven ien ces, in clu din g th e ability to n orm alize th e wh ole p op u lation so th at S + I = 1 an d th e ability to n orm alize th e p op u lation of in dividu als in fected with th e su scep t ib le b act eria st rain as a fract io n o f t h e t o t al p o p u lat io n o f in fect ed in dividu als. As Laxm in arayan an d Brown sh owed, it is th en p ossible to redu ce

Chapter 1: Dynamics of Antibiotic Use • 23

th e state variables of in terest in th e m odel to ju st two: th e total p op u lation of in fected in d ivid u als I(t) an d th e fraction of th e in fected p op u lation su scep tib le t o an t ib io t ics w(t). Becau se acq u ired resist an ce act s o n ly t o m o d ify t h e d ru g-in d u ced m ortality of su scep tible bacteria, it d oes n ot affect th e q u alitative con clu sion s; h en ce we set S = 0 also. Th ese n orm alization s an d th e resu ltan t m odified state eq u ation s are as follows: Iw I I˙ = βS − rr + (rr − rw )w − wrf f I = β − rr + w [ Δr − rf f ] I − βI 2

S + I = 1, I = I w + I r , w =

(

[

(

w˙ = w (1 − w ) Δr − frf

)]

) (

)

(2)

wh ere t h e q u an t it y Δr ≡ rr – rw is referred t o in t h e lit erat u re as t h e “fit n ess cost” of th e resistan t strain . Th is is n ot an econ om ic cost bu t rath er a biological co st t o t h e resist an t st rain t h at is reflect ed in in creased m o rt alit y in t h e absen ce of treatm en t, wh ich arises from th e p ossession of gen es th at allow it to su rvive u n der dru g treatm en t. In oth er words, a p ositive fitn ess cost m ean s th at th e resistan t strain of bacteria or viru s h as an advan tage th at allows it to su rvive in t h e p resen ce o f t h e d ru g. Bu t t h at ad van t age co m es at a su rvival cost rr > rw in th e sen se th at th e d ru g-sen sitive strain will d om in ate th e com bin ed d isease ecology in th e absen ce of treatm en t. Th is can be illu strated in th e p h ase diagram s th at follow (see Figu res 1-2, 1-3, an d 1-4). First we d escribe th e p h ase sp ace of th is d yn am ical system u n d er extrem e con trols, th at is, con trol strategies with eith er f = 0 or f = 1. A p h ase d iagram p lots th e trajectories of th e two differen tial eq u ation s th at describe th e evolu tion of th e stock of in fected in dividu als an d th e p rop ortion of recep tive in dividu als. Gen erally th e system will evolve from som e arbitrary in itial state to an eq u ilibriu m , at wh ich p oin t both stocks h ave reach ed th eir lon g-term stead y state levels. In th e absen ce of treatm en t (f = 0), we obtain th e ph ase diagram in Figu re 1-2, wh ich sh ows th e trajectories of both th e stock of in fected in dividu als an d th e stock of in dividu als receptive to an tibiotic treatm en t. Note th at in th e absen ce of treatm en t, th e equ ilibriu m is su ch th at th ere is a backgro u n d level o f in fect io n eq u al t o [(β – rw )/ β] an d t h e m ix o f bact eria is su ch t h at all are t reat able by t h e an t ibio t ic (w = 1). Co n sid er an in fect io n “even t” in wh ich th ere is an in trodu ction of in dividu als in fected with a resistan t bacterial strain . Th is is sh own by th e trajectory begin n in g with an in fection level h igh er th an th e origin al eq u ilibriu m an d a p op u lation m ix of on ly p artially recep tive bacteria w < 1. In th is case, if n o treatm en t is in itiated , th e in teraction between th e two bacterial popu lation s will allow th e bacteria receptive to dru g treatm en t to ou tcom pete th e dru g-resistan t strain , an d w will rise.

24 • Chapter 1: Dynamics of Antibiotic Use w dI/ dt = 0

w=1

dw / dt = 0

Steady state (for f = 0)

I

( β –r r)/ β

(β −r w )/β

FIGURE 1-2. Phase Space under No Treatment

At th e sam e tim e, becau se th e en tire bacteria popu lation is larger th an its n atu ral equ ilibriu m , th ere will be an excess of m ortality an d th e overall popu lation will fall. Th is is sh own in Figu re 1-2 by th e trajectory th at rises in w an d falls an d th en rises in I toward th e steady state. We call th is ou tcom e th e ou tcom e associated with an “ecological” strategy becau se it relies on n atu ral in teraction an d com p etition between th e two p op u lation s of bacteria strain s to brin g th e system back in to equ ilibriu m . For th is equ ilibriu m ou tcom e (th at in wh ich th e resistan t strain is elim in ated ) to occu r, it is n ecessary for an tibiotic-resistan t bacteria to in cu r a fitn ess cost. Th e fitn ess cost actu ally op erates as a red u ced relative su rvival rate an d is n ecessary to even tu ally elim in ate th e resistan t bacteria from th e system wh en th e n o-treatm en t option is u sed. In co n t rast , t h e p h ase d iagram fo r t h e case wit h fu ll t reat m en t (f = 1) is given in Figu re 1-3. Again , th is diagram dep icts th e join t evolu tion of th e twoeq u ation system th at describes th e p op u lation of in fected in dividu als an d th e recep tive p op u lation . We call th e fu ll treatm en t strategy th e “in terven tion ist” st rat egy, an d , as can b e seen , aft er an in fect io n even t p ert u rb at io n , a lo wer level of steady state in fection eq u al to (β – rr)/ β is ach ieved, bu t at th e cost of con vertin g th e d isease p op u lation to on e con sistin g of on ly resistan t bacteria so t h at w is d riven t o zero . Th is d ifferen t eq u ilib riu m o ccu rs b ecau se t reat m en t o ver t h e fu ll h o rizo n elim in at es t h e recep t ive bact eria an d allo ws t h e resistan t bacteria to fu lly ou tcom p ete th em in th e tran sition to eq u ilibriu m .

Chapter 1: Dynamics of Antibiotic Use • 25

w

(β−r r )/(Δr −r f)

dI/ dt = 0 dw / dt = 0

w=1

Steady state (for f = 1)

( β–r r )/ β

I

FIGURE 1-3. Phase Space under Full Treatment

As th e ph ase diagram an alysis in Figu res 1-2 an d 1-3 in dicates, two qu alitat ively d ifferen t eq u ilibria are p o ssible aft er an in fect io n even t p ert u rbat io n u n der th e u se of extrem e con trols over th e h orizon . On e, associated with wh at we call an ecological strategy, allows th e popu lation s of bacteria to com pete in an in t ersp ecific an d in t rasp ecific m an n er u n t il a (relat ively) h igh in fect io n level eq u ilibriu m is reach ed . Th e o t h er, asso ciat ed wit h an in t erven t io n ist strategy, in volves drivin g th e overall in fection level to a lower level bu t with a n ew disease popu lation of an tibiotic-resistan t bacteria. Th is is th e case em ph asized by Laxm in arayan an d Bro wn (2001), in wh ich t h e p o licy red u ces t h e depletable stock of resistan ce to zero. Im portan tly, in th e m ore gen eral m odel with fitn ess costs, th ere is an econ om ic ch oice to be m ade abou t wh ich regim e (ecological or in terven tion ist) to p u rsu e. If we con sid er th e sim p lest exam p le an d assu m e t h at t h e t reat m en t co st s o f t h e eco lo gical regim e are zero , t h en th ere is a cu toff treatm en t cost in th e in terven tion ist case th at will m ake th at strategy in ferior to followin g th e ecological strategy. In th e n ext section , we discu ss th e n atu re of th e optim al in terven tion ist strategy fu rth er. We sh ow th at th e optim al policy is n ot actu ally on e in wh ich th e optim al decision is to treat at a m axim u m rate over th e wh ole h orizon (as depicted on th e ph ase diagram in Figu re 1-4) bu t on e th at in volves a m ixed strategy of m axim u m rates an d in term ed iate rates of treatm en t. Solvin g th e op tim al treatm en t d ecision over th e h orizon of th e in terven tion ist case is a n ecessary p recu rsor to com p arin g th e ou tcom es from u sin g th e ecological or in terven tion ist strategies.

26 • Chapter 1: Dynamics of Antibiotic Use

The Economic M odel Th e m odel we u se h ere is in th e sam e sp irit as th at p resen ted in Laxm in arayan an d Bro wn (2001), bu t we h ave gen eralized it t o acco u n t fo r fit n ess co st . In addition , we m odified th e objective fu n ction to m in im ize th e discou n ted su m of treatm en t costs an d d am age costs resu ltin g from illn ess. Ad d ition al d etails an d d efin it io n s are in t h e ch ap t er ap p en d ix. Th e d yn am ic t reat m en t m o d el can be stated as follows: ∞

m in

0 ≤ f ( t ) ≤1

∫ [d I (t ) + c I (t )[f (t )]] I

0

f

(

[

e − ρt dt

])

2 I˙(t ) = β − rr + w (t ) Δr − rf f (t ) I (t ) − β( I (t )) , I ( 0 ) = I 0

s.t .

[

(

(3)

)]

w˙ (t ) = w (t ) (1 − w (t )) Δr − rf f (t ) , w ( 0 ) = w 0 Th e costs d I an d cf are th ose of in fection level in th e p op u lation an d treatm en t, resp ectively, wh ile ρ is th e d iscou n t rate. So n ow we can write ou t th e corresp on din g cu rren t valu e Ham ilton ian as

(

(

))

2 * ( •) = d I I (t ) + cf [f (t )]I (t ) + λ(t )⎡⎢ β − rr + w (t ) Δr − rf f (t ) I (t ) − β( I (t )) ⎤⎥ ⎦ ⎣ ⎤ ⎡ + µ(t ) w (t ) (1 − w (t )) Δr − rf f (t ) ⎦⎥ ⎣⎢

{

(

)}

(4)

wh ich is m in im ized in each p eriod with an ap p rop riate ch oice of th e op tim al t reat m en t rat e f *. Th ere are t wo sh ad o w p rices,λ(t) an d µ(t), co rresp o n d in g resp ectively to th e p op u lation of in fecteds I(t) an d th e p rop ortion su scep tible w(t). As is con ven tion , t m easu res con tin u ou s tim e, later su p p ressed for n otation al con ven ien ce. Becau se th is p roblem is lin ear in con trols, we n eed to isolate th e switch in g fu n ction , wh ich is as follows:

[

σ(t ) = cf I − λ(t )w (t ) I (t )rf − µ(t )(1 − w (t ))w (t )rf

]

(5)

Th is is th e coefficien t on th e treatm en t con trol, an d th e Pon tryagin op tim ality con dition s state th at f * = 0 as σ(t ) > 0 ^

f * = f as σ(t ) > 0

(6)

f * = 1 as σ(t ) < 0 W h en th e switch in g fu n ction is n egative, a m axim u m con trol th at treats th e wh ole p op u lation of in fected in d ivid u als is u sed to m in im ize th e Ham ilton ian ; wh en th e switch in g fu n ction is positive, n o con trol is warran ted. Th ese con trols correspon d to treatm en t regim es th at treat th e en tire popu lation with

Chapter 1: Dynamics of Antibiotic Use • 27

th e dru g (f * = 1), or th at treat n o on e (f * = 0), or th at treat som e possibly tim e^ varyin g fraction (f * = f (t)). W h en th e switch in g fu n ction is zero, a so-called sin gu lar con trol is in d icated . Th e com p lete solu tion to a lin ear con trol p roblem su ch as th is gen erally in volves a “syn th esized” con trol th at con sists of segm en ts of extrem e con trols, followed by segm en ts of sin gu lar con trols. In th e ^ appen dix, we solve for th e sin gu lar con trol f * = f an d th en sh ow h ow th e syn th esized con trol com bin es extrem e an d sin gu lar con trol regim es. For th e p roblem we con sider in th is ch ap ter, we p resu m e th at a closed p op u lation h as exp erien ced an in fection even t su ch th at th e in itial level of total in fect io n is at o r ab o ve t h e n at u ral eq u ilib riu m an d t h ere h as b een so m e in t ro d u ct io n o f resist an t b act erial in fect io n s. Th ese kin d s o f even t s are d ep ict ed as p ert u rbat io n s in t h e p h ase d iagram s in Figu res 1-2 an d 1-3. Fo r t h ese kin d s o f circu m st an ces, t h ere are t wo p o ssib ilit ies; each is asso ciat ed with version s of th e con trol regim es d iscu ssed earlier. On e p ossibility is th at th e op tim al con trol p olicy is a zero con trol or ecological strategy th rou gh ou t. Th e o t h er p o ssibilit y is t h at an in t erven t io n ist st rat egy is o p t im al. Th is will gen erally in volve an in itial p eriod in wh ich th e en tire in fected p op u lation is treated with an extrem e con trol f * = 1 for a p eriod, followed by a switch to a ^ sin gu lar con trol f * = f for th e rem ain in g tim e in th e h orizon . As we sh ow in th e ap p en d ix, for th e in terven tion ist strategy, th e sin gu lar con trol in volves trackin g an op tim al level of th e p op u lation of dru g-su scep tible bacteria by ad ju stin g th e con trol con tin u ou sly as th e total in fection level an d fraction su scep tible ch an ge over tim e. We sh ow th at th e followin g eq u a^ tion describes th e op tim al sin gu lar treatm en t level f . ∧

rf [ f − f ∞ ] = −{φ1 [ I ∞ ( w − w ∞ )] + φ2 [ wI ∞ − w ∞ I ] + φ3 [ w ∞ ( I ∞ − I )]}

(7)

Th e o p t im al t reat m en t level alo n g t h e sin gu lar p at h is great er t h an t h e lon g-ru n steady state valu e of th e treatm en t level f ∞ by an am ou n t related to th e differen ces between th e lon g-ru n steady state valu es of th e in fection level I∞ an d t h e fract io n su scep t ib le w ∞ an d t h e cu rren t valu es (I an d w) o f t h o se st at e variab les. Th e d ifferen ces in sid e t h e b racket s o f t h e t h ree righ t -h an d t erm s o f t h is accelerat o r fo rm u lat io n are gen erally p o sit ive, an d t h e co efficien ts φi are gen erally n egative; h en ce th e treatm en t level is at least its stead y state valu e p lu s an am ou n t over th e sin gu lar p ath . Th e lon g-run steady state values for f ∞ an d w ∞ are sh own in th e appen dix to be f∞ =

rr − rw rf

(8)

for th e op tim al lon g-ru n treatm en t rate an d w∞ =

(β + ρ − rr )cf d I rf + Δrf cf

(9)

28 • Chapter 1: Dynamics of Antibiotic Use w

dI/ dt = 0 dw / dt = 0

f = 1 regime

^

f* =f

Steady state ( f = f ∞)

( β–r r)/ β

I

FIGURE 1-4. Pseudophase Space under Transition to Singular Path of Treatment

for th e lon g-ru n fraction of th e in fected p op u lation th at rem ain s resp on sive t o d ru g t reat m en t . Th e syn t h esized o p t im al t raject o ry is sh o wn in t h e p seu dop h ase diagram in Figu re 1-4. Th e solu tion begin s with a p h ase in wh ich it is op tim al to treat th e en tire p o p u lat io n o f in fect ed in d ivid u als, in clu d in g t h o se in fect ed wit h resist an t bacteria with an extrem e con trol of f * = 1. Bu t th e cost of redu cin g th e in fection level in th e aggregate is to ch an ge th e p rop ortion of bacteria th at are su scep tible or resistan t to fu tu re treatm en t. Th is kin d of ou tcom e occu rs in th is m od el, of cou rse, p recisely becau se it is assu m ed th at it is n ot p ossible to test in d ivid u als to d eterm in e wh eth er th ey are in fected with su scep tible bacteria, an d, th erefore, a n on selective con trol is n ecessary. Th is assu m p tion is likely to h old with cu rren t d iagn ostic tech n ology becau se su scep tibility can gen erally on ly be determ in ed by cu ltu rin g bacteria sam p les, an d th at takes tim e. In th e fu t u re, m o re rap id id en t ificat io n t ech n iq u es m ay b e u sed , an d t h at wo u ld ch an ge th e n atu re of th e wh ole trade-off between in fection treatm en t an d th e d ep letion of th e stock of su scep tibility. In th e case u n d er exam in ation h ere, con trol with an extrem e con trol d rives th e su scep tible p op u lation d own an d red u ces th e total level of in fection in th e system u n til th e trajectory crosses th e isoclin e. At th at p oin t, p resu m in g th at th e extrem e con trol is still in u se,

Chapter 1: Dynamics of Antibiotic Use • 29

th e fraction su scep tible con tin u es to fall, an d th e total in fection level begin s t o rise. Th e t o t al in fect io n level rises even t u ally, even wit h su st ain ed t reat m en t , b ecau se wit h co n t in u ed an t ib io t ic t reat m en t , t h e resist an t b act eria even t u ally co m e t o d o m in at e t h e b act erial eco lo gy, an d t o t al in fect io n in creases. At som e switch p oin t th at is op tim ally d eterm in ed , th e extrem e con trol is co n vert ed in t o a sin gu lar co n t ro l in vo lvin g o n ly p art ial t reat m en t o f t h e ^ p o p u lat io n so t h at f * = f (t). W h en t h is o ccu rs, t h e t reat m en t rat e is varied con tin u ou sly accord in g to th e p rop ortion al ad ju stm en t in Eq u ation 7. Du rin g th e sin gu lar con trol p eriod , th e total in fection level begin s to rise, even t u ally reach in g t h e st ead y st at e, asym p t o t ically. In a sim ilar m an n er, t h e p o p u lat io n fract io n su scep t ib le an d t h e fract io n o f t h e t o t al p o p u lat io n t reat ed asym p t o t e t o t h eir iso clin e st ead y st at e valu es given earlier. No t e t h at t h e iso clin es in t h e t reat m en t p h ase d iagram an d t h e asso ciat ed d irect io n s o f m o t io n act u ally o n ly h o ld wit h t h e ext rem e co n t ro l in u se. W h en t h e sin gu lar co n t ro l is in o p erat io n , t ech n ically sp eakin g, t h e d ifferen t ial eq u at io n syst em b eco m es n o n au t o n o m o u s, an d a n o n au t o n o m o u s syst em can n o t b e rep resen t ed in a p h ase d iagram . At t h e sam e t im e, we can st ill p lo t t h e q u alit at ive t raject o ry o f t h e sin gu lar so lu t io n in t erm s o f t h e m o t io n im p lied fo r t h e w an d I st at e variab les, an d t h is is wh y we refer t o Figu re 1-4 as a p seu d op h ase d iagram . Several q u alit at ive ch aract erist ics o f t h e ab o ve syst em are wo rt h h igh ligh tin g. First, in con trast to th e Laxm in arayan an d Brown (2001) n on ren ewable form u lation th at assu m es n o fitn ess cost, in th is case, th ere is a lon g-ru n st ead y st at e in wh ich t h e st o ck o f an t ib io t ic resist an ce can b e co n sid ered ren ewab le. Th is st ead y st at e is m ain t ain ed b y a fract io n al t reat m en t p o licy th at keep s th e su scep tible an d resistan t bacteria in a delicate eq u ilibriu m . Th is eq u ilibriu m is ach ieved by adju stin g th e treatm en t rate so th at th e su m of th e n atu ral rate of d ecrease of su scep tible organ ism s au gm en ted by extra m ortality associated with p artial treatm en t ju st balan ces th e h igh er m ortality of th e resistan t bacteria. Secon d , th e con trol p ath is ach ieved by an in terestin g syn t h esized co n t ro l co n sist in g o f ext rem e an d sin gu lar co n t ro ls. Th e sin gu lar co n t ro l is n o t co n st an t as it is in t h e t yp ical ren ewable reso u rce m o d el, bu t in stead it is ch osen so th at th e p op u lation of su scep tible bacteria “tracks” th e d esired p ath in tran sition to an eq u ilibriu m . Th is tim e-varyin g sin gu lar p ath is a ch aracteristic of n on au ton om ou s lin ear con trol p roblem s; h ere th e eq u ation for th e stock of in fected in d ivid u als is n on au ton om ou s becau se it con tain s w(t), wh ich itself is an exp licit fu n ction of tim e. Th ird , th e syn th esized con trol m ay in volve treatm en t even beyon d th e p oin t at wh ich th e m in im u m level of in fection h as been reach ed. Th is at first seem s cou n terin tu itive: wh at is gain ed b y co n t in u in g t o p ay t reat m en t co st s aft er t h e in fect io n level h as been driven to its lowest level? Th e an swer is th at it p ays to con tin u e treatin g

30 • Chapter 1: Dynamics of Antibiotic Use

becau se t h e resu lt in g fu t u re t raject o ry o f t o t al in fect io n lies belo w t h e p at h th at wou ld oth erwise exist if, for exam p le, treatm en t stop p ed at th e level of m in im u m in fection .

A Numerical Comparison: Renewable versus Nonrenewable Cases To ch eck th ese resu lts an d to p erform com p arative dyn am ics exp erim en ts, we develop ed a discretized form of th is p roblem th at can be solved with dyn am ic p rogram m in g m eth od s. We can op tim ize th is p roblem by u sin g th e Bellm an Eq u ation , wh ich can be written as m in V ( It ) = d I It + cf It [f t ] + δV ( It +1 )

0 ≤ f t ≤1

s.t .

(

[

])

It +1 − It = β − rr + w t Δr − rf f t It − β( It ) , It = 0 = I 0

[

(

2

(10)

)]

w t +1 − w t = w t (1 − w t ) Δr − rf f t , w t = 0 = w 0 wh ere th e fun ction V(It + 1 ) gives th e carryover cost from on e period to th e n ext of th e resid u al in fection level, wh ich we also seek to m in im ize an d d iscou n t with th e factor δ = 1/ (1 + ρ). Th e optim al solu tion of th e Bellm an Equ ation in each period is eq u ivalen t to th e optim al solu tion of th e con tin u ou s tim e con trol problem for th e correspon din g periods, by Bellm an ’s Prin ciple of Optim al-

Infection/ Treatment/ Effectiveness Levels

1.2

DP Solution for Single Treatment Case ( α = 1, base parameters)

1.0 0.8 0.6 0.4 0.2

0

20

40

60

Time Periods I( t )

f(t )

w (t )

FIGURE 1-5. Behavior along Optimal Path with Fitness Cost

80

Chapter 1: Dynamics of Antibiotic Use • 31

ity. We iterate to fin d a polyn om ial approxim ation to th e value fun ction V(It + 1 ) an d th en u se it to solve th e Bellm an Eq u ation forward for each p eriod . We em p loyed a Ch ebych ev p olyn om ial ap p roxim ation algorith m to solve for th e value fun ction , wh ich was easily im plem en table in th e Gen eral Algebraic Modelin g System software package. A good discussion of approxim ation m eth ods is given by Ken n eth Judd in h is book on n um erical m eth ods (1998). Now we p resen t th e resu lts of th e dyn am ic p rogram m in g m odel for sin gle dru g u se, in th e absen ce of in du ced resistan ce effects (s = 0) an d death rate (n = 0). Fro m t h e grap h o f t h e so lu t io n , u sin g p aram et er valu es o f β = 0.6, rr = 0.3, rw = 0.15, rf = 0.3, we see t h at fo r t h e lin ear o bject ive fu n ct io n , we u lt im ately ap p roach a sin gu lar steady state, wh ere f ∞ = 0.5, an d th e in fection level asym p totes to a level of I∞ = 0.5, wh ile th at of effectiven ess rem ain s at w ∞ = 0.14. Given a fit n ess co st o f Δr = 0.15, f ∞ is bein g set in t h e st ead y st at e at a level wh ere (Δr – frf ) = 0 to h old th e two bacterial p op u lation s in balan ce. In th e stead y state, th e eq u ation of m otion for w(t) becom es station ary an d th e differen tial eq u ation for I satisfies ⎤ ⎡ β − rr = 0 .5 I˙ = ⎢⎢β − rr + w Δr − frf ⎥⎥ I − βI 2 = 0 so th at I = β   ⎥⎦ =0 ⎣⎢

)

(

as sh own in Figu re 1-5.

1.2

DP Solution for Single Drug Case ( α = 1, Rr = Rw = 0.3)

Infection/ Treatment/ Effectiveness Levels

1.0

0.8

0.6

0.4

0.2

0

20

40

60

Time Periods I(t)

f(t)

w(t)

FIGURE 1-6. Behavior along Optimal Path without Fitness Cost

80

32 • Chapter 1: Dynamics of Antibiotic Use

To con trast, we also solved for th e d yn am ically op tim al p ath for th e case u n der wh ich it is assu m ed th at th ere are n o fitn ess costs. In th is case, th e syst em is co n t ro lled at t h e ext rem es o f t h e co n st rain t set , wit h o u t a sin gu lar p ath , in typ ical “ban g-ban g” fash ion (see Figu re 1-6).

Optimal Interventionist versus Ecological Control Regimes Th e q u alitative resu lts d erived from ou r com bin ed econ om ic an d ep id em iological m od el are in in terestin g con trast to th ose typ ically d erived from p u re ep id em iological m od els. Th e d ifferen ces, of cou rse, em erge m ain ly ou t of th e fram ewo rk t h at p o ses t h e t reat m en t p ro b lem as an eco n o m ic o p t im izat io n p roblem exp ressed in term s of costs an d ben efits an d a d iscou n t rate. In ep id em io lo gy, m o st m o d elin g is d o n e wit h o u t an exp licit o p t im izat io n fram ewo rk, o ft en t o u n d erst an d im p o rt an t m ech an ism s an d t h e im p licat io n s o f variou s p aram eters an d rate con stan ts. At th e sam e tim e, p u re ep idem iological m o d els are u sed t o su p p o rt n o rm at ive co n clu sio n s abo u t t h e best co u rse o f action from am on g altern atives, u su ally with ou t m u ch exp licit d iscu ssion of th e m etric of com p arison . It is com m on , for exam p le, to con clu de th at a certain treatm en t regim e is best becau se it redu ces in ciden ce of disease th e m ost am o n g alt ern at ives. In p u re ep id em io lo gical ap p ro ach es, o u t co m es are n o t m o n et ized o r d isco u n t ed , n o r are co st s in clu d ed in a m an n er t h at lead s t o co m p u t at io n o f n et b en efit s o r easy co m p ariso n o f d ifferen t t reat m en t regim es th at in volve differen t p ath s of treatm en t an d recovery. How d o ou r n orm ative con clu sion s d erived from an in tegrated econ om ic/ epidem iological m odel differ from wh at m igh t be con clu ded with ou t th e econ om ics? To an swer th at, we first n eed to ch aracterize th e p olicy p rescrip tion t h at ep id em io lo gist s m igh t ad h ere t o wh en faced wit h t h e q u est io n , h o w sh ou ld we treat wh en treatm en t resu lts in resistan ce? An an swer th at was p u t forth n early 100 years ago by Eh rlich was “frapper fort et frapper vite,” wh ich t ran slat ed fro m t h e Fren ch m ean s “h it ‘em h ard an d h it ‘em fast ” (Eh rlich 1913). Th is sou n ds, of cou rse, very m u ch like th e first stage of an optim al lin ear p o licy in wh ich t h e p o p u lat io n is h it wit h an ext rem e co n t ro l. Th e eco n om ic resu lts d iffer in th at we h ave an an swer abou t wh en to stop treatin g, an d it is n ot wh en all of th e disease h as been elim in ated. In stead, th e econ om ically o p t im al p o licy acco u n t s fo r d im in ish in g ret u rn s t o fu rt h er t reat m en t brou gh t on by th e fact th at th e treatm en t p olicy itself ch an ges th e balan ce of su scep tible/ resistan t bacteria to su ch a degree th at fu rth er treatm en t does n ot yield n et ben efits. In terestin gly, th e optim al policy does con tin u e th e “h it ’em h ard ” treatm en t even wh en th e total in fection level is in creasin g becau se of th e dom in an ce of resistan t bacteria, bu t it even tu ally leads in to a sin gu lar con t ro l t h at brin gs t h e wh o le syst em in t o a st ead y st at e wit h a resid u al level o f eq u ilibriu m in fect io n . Th e eco n o m ic p o licy backs o ff fro m Eh rlich ’s m axim

Chapter 1: Dynamics of Antibiotic Use • 33

becau se t h e eco n o m ic p o licy acco u n t s fo r co st s an d d isco u n t s fu t u re red u ction s in disease in ciden ce. Discou n tin g p lays a role h ere in th at redu ction s in disease in ciden ce expected to occu r in th e far distan t fu tu re are discou n ted an d even t u ally d eem ed n o t wo rt h t h e cu rren t exp en ses o f co n t ro l. Th ese d ifferen ces in m o d elin g st rat egies raise age-o ld bu t st ill relevan t q u est io n s abo u t wh eth er it is m orally d efen sible to m on etize h ealth ben efits, d iscou n t fu tu re h ealth payoffs, or u se fram eworks th at force con sideration of in terperson al an d in tergen eration al trade-offs. Fin ally, an o t h er im p o rt an t q u est io n raised wit h t h e ad d it io n o f an eco n om ic fram ework is th e p olicy issu e of ch oice between two con trol regim es. In p rin cip le, in resp o n se t o an y in fect io n even t , t h e fu ll eco n o m ic d ecisio n p roblem in volves selectin g th e regim e th at m in im izes th e su m of d iscou n ted treatm en t an d illn ess dam age costs. We saw earlier th at th e op tim al in terven t io n ist st rat egy in vo lves a co m b in at io n o f ext rem e an d sin gu lar co n t ro ls, even t u ally asym p t o t in g t o so m e eq u ilibriu m level o f t reat m en t , t o t al in fection , an d fraction su scep tible. Let th e d iscou n ted valu e of th at fu lly op tim al con trol strategy be design ated as Jinterventionist an d let th e corresp on din g valu e of

w

dI/ dt = 0 for f = 0

dI/ dt = 0 for f = 1

dw / dt = 0

J* ecological

f = 1 regime

Steady state ( f = f ∞) ^

J* interventionist

f* = f

( β–r r)/ β

( β–r w )/ β

FIGURE 1-7. Hybrid Phase Space under Two Treatment Regimes

I

34 • Chapter 1: Dynamics of Antibiotic Use

t h e d isco u n t ed co n t ro l co st s fo r t h e (n o -t reat m en t ) alt ern at ive b e Jecological . Th en th e tru e social econ om ic p roblem is on e of fin din g J* = m in [ Jinterventionist , Jecological ]

(11)

Th is is dep icted in th e p h ase diagram in Figu re 1-7. In th is “h ybrid” p h ase diagram , th e dyn am ic forces dep en d on wh eth er an ecological or in terven tion ist strategy is bein g followed . If an ecological strategy is bein g p u rsu ed , th e solid an d ligh t d otted lin es d ep ict in itial n orth west m otion an d th en n orth east m otion toward th e n atu ral eq u ilibriu m at w = 1 an d I∞ = (β – rw )/ β. If an in terven tion ist strategy is bein g p u rsu ed, th e solid an d h eavy d ash ed lin es sh ow th e trajectory m otion toward th e lon g-ru n eq u ilibriu m o f w = w ∞ an d I∞ = (β – rr)/ β. Usin g t h e in t erven t io n ist st rat egy, t h e m otion is, as d iscu ssed earlier, a syn th esized con trol th at in itially m oves th e system sou th west an d th en fin ally sou th east to th e eq u ilibriu m . To verify t h at t h ere is in d eed an eco n o m ic ch o ice t o b e m ad e b et ween regim es, we exam in ed t h is co m p ariso n b et ween t h e t wo d ifferen t regim es n u m erically with ou r base case op tim ization m od el by solvin g variou s op tim izat io n p ro blem s t h at d iffer o n ly by t h e t reat m en t co st p aram et er cf . Th e p aram eters assu m ed in th e base case ru n in clu de treatm en t costs of $1.50 an d dam ages of $20. As th e treatm en t cost is in creased, th e solu tion for th e in terven tion ist strategy in volves d ifferen t syn th esized ap p roach p ath s to d ifferen t lon g-ru n eq u ilibria. In creasin g cf does n ot ch an ge th e lon g-ru n in fection level o f I∞ = (β – rr)/ β, bu t t h e lo n g-ru n valu e o f w ∞ rises. In ad d it io n , t h e p resen t valu e o f t h e d isco u n t ed t reat m en t an d d am age co st s rise, even t u ally ap p roach in g th e level associated with th e ecological strategy. As it tu rn s ou t, if t h e t reat m en t co st is in creased ab o ve ab o u t $13.50, it b eco m es o p t im al t o aban d on th e in terven tion ist strategy an d to ad op t th e ecological strategy. At th is cu toff valu e, th e cost of treatin g in fection with an in terven tion ist strategy th at red u ces th e in fection d am ages faster d oes n ot warran t th e exp en d itu res, an d it is less co st ly t o t reat t h e in fect io n even t wit h an eco lo gical so lu t io n . Th is kin d of com p arison wou ld n ot gen erally arise ou t of a p u re ep idem iological m od el becau se th e ecological solu tion wou ld be in ferior u n d er m ost sim p le n on econ om ic m etrics of com p arison .

Conclusion Th e tech n ical p art of th is ch ap ter gen eralizes p reviou s econ om ic an alyses of t h e an t ib io t ic resist an ce p ro b lem b y ad d ressin g t h e case in wh ich d isease resistan ce carries a fitn ess cost. Th is h as im p ortan t q u alitative im p lication s for econ om ically op tim al an tibiotic u se strategies. Th e first is th at it allows treatm en t t o fo llo w a p o licy t h at t reat s t h e st o ck o f an t ib io t ic effect iven ess as a

Chapter 1: Dynamics of Antibiotic Use • 35

ren ewable resou rce in con trast to th e n on ren ewable treatm en t exam in ed by Laxm in arayan an d Brown (2001). Th e op tim al treatm en t p olicy in ou r case is a syn th esized con trol in volvin g extrem e an d sin gu lar con trols. Th e sin gu lar con trol is a n on au ton om ou s con trol th at cau ses th e stock of an tibiotic effect iven ess t o t rack a m o vin g t arget o p t im al st o ck o f effect iven ess. In t h e lo n g ru n , a balan ce is ach ieved in wh ich th e bacterial p op u lation of both resistan t an d su scep t ible bact eria is h eld in a d elicat e eq u ilibriu m by cau t io u s p art ial treatm en t of th e com bin ed p op u lation s with a n on selective p olicy. Th e secon d im p ortan t featu re of th e m odel p resen ted h ere is th at it in corp orates th e p ossibility of ben ign strategies th at rely on ly on th e in terp lay between resistan t an d su scep tible bacteria. We refer to th ese as ecological strategies, bu t th ey op erate by allowin g th e n atu ral ad van tage en joyed by su scep tible bacteria to h elp th em ou tcom p ete resistan t bacteria. Th is is in con trast to in terven tion ist strategies th at give th e resistan t bacteria an ecological ad van tage by red u cin g th e effective com p etition of su scep tible bacteria. We h ave dep icted th e ecological op tion in th e sim p lest fash ion , as a n o-treatm en t strategy with n o costs relative to th e treatm en t strategy. In fact, it is probably m ore realistic to con sider ecological strategies th at also can alter key system p aram eters, su ch as th e in teraction rate β, at a cost. For exam ple, su ppose th at th ere is a baselin e in teraction rate βinterventionist associated with th e in terven tion ist regim e in volvin g aggressive treatm en t with an tibiotics but busin ess as usual in term s of oth er aspects of in fection con trol in th e h ospital or oth er in stitu tion al settin g. Su p p ose also th at th e in teraction rate for th e ecological strategy βecological can be reduced at a cost C(βinterventionist – βecological) with costs con vex in th e reduction from th e baselin e. Th en th e regim e ch oice problem in Equation 11 becom es J* = m in [ Jinterventionist , m in {Jecological − C(βinterventionist − βecological }] βecological

(12)

In th is sligh tly m ore gen eral p roblem , a su bp roblem is solved first, n am ely th e am ou n t of costs in cu rred to select an op tim al in teraction rate th at m in im izes t o t al in fect io n , t reat m en t , an d in t eract io n red u ct io n co st s. Th is is o f so m e p ract ical im p o rt an ce becau se it is, in fact , p o ssible t o ch an ge so m e o f th e p aram eters of th e p roblem th at we h ave been con siderin g im m u table, at a cost. For exam p le, Au stin an d oth ers (1999) rep ort resu lts of a h osp ital stu d y t h at t est ed h an d wash in g an d st aff co h o rt in g as m ean s o f red u cin g van com ycin -resistan t en terococci tran sm ission . Alth ou gh n o costs of th e in teract io n red u ct io n st rat egy are rep o rt ed b y Au st in an d o t h ers, p revalen ce rat es were red u ced b y h alf. Th is evid en ce su ggest s t h at t h e fu ll-b lo wn an t ib io t ic t reat m en t o p t im izat io n p ro b lem p ro b ab ly sh o u ld b e co n sid ered as o n e o f ch oice between in terven tion ist or ecological regim es bu t with each op tim ized b y o t h er syst em st rat egies in ad d it io n t o t h e fu n d am en t al ch o ices o f t reat -

36 • Chapter 1: Dynamics of Antibiotic Use

m en t rates. In an im p ortan t sen se, th is is th e valu e of brin gin g econ om ics to im p ortan t ep id em iological p olicy p roblem s; it illu m in ates im p ortan t ch oices an d trad e-offs an d sh ows h ow th ey are affected by both th e ep id em iological m ech an ism s an d th e econ om ic costs an d ben efits of p oten tial action s.

References Au st in , D. J., M. J. Bo n t en , R. A. Wein st ein , S. Slau gh t er, an d R. M. An d erso n . 1999. Van com ycin -Resistan t En terococci in In ten sive-Care Hosp ital Settin gs: Tran sm ission Dyn am ics, Persisten ce, an d th e Im p act of In fection Con trol Program s. Proceedings of the National Academ y of Sciences of the USA 96: 6908–13. Bon h oeffer, S., M. Lip sitch , an d B.R. Levin . 1997. Evalu atin g Treatm en t Protocols to Preven t An tibiotic Resistan ce. Proceedings of the National Academ y of Sciences of the USA 94(22): 12106–11. Brown , G., an d D.F. Layton . 1996. Resistan ce Econ om ics: Social Cost an d th e Evolu tion of An tibiotic Resistan ce. Environm ental and Developm ent Econom ics 1(3):349–55. Eh rlich , Pau l. 1913. Ch em o t h erap eu t ics: Scien t ific Prin cip les, Met h o d s, an d Resu lt s. Lancet ii: 445, cit ed in Levin , B., M. Lip sit ch , an d S. Bo n h o effer. 1999. Po p u lat io n Biology, Evolu tion , an d In fectiou s Disease: Con vergen ce an d Syn th esis. Science 283: 806–9. Hu eth , D., an d U. Regev. 1974. Op tim al Agricu ltu ral Pest Man agem en t with In creasin g Pest Resistan ce. Am erican Journal of Agricultural Econom ics 56: 543–53. Ju dd, Ken n eth L. 1998. Num erical Methods in Econom ics. Cam bridge, MA: MIT Press. Kerm ack, W.O., an d A.G. McKen d rick. 1927. A Con tribu tion to th e Math em atical Th eory of Ep idem ics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathem atical and Physical Character 115(772): 700–21. Laxm in arayan , R., an d G. Brown . 2001. Econ om ics of An tibiotic Resistan ce: A Th eory of Op tim al Use. Journal of Environm ental Econom ics and Managem ent 42(2): 183–206. Ross, R. 1911. The Prevention of Malaria, Secon d Edition . Lon don : Mu rray. Sop er, H.E. 1929. In terp retation of Periodicity in Disease-Prevalen ce. Journal of the Royal Statistical Society 92: 34–73.

Appendix We solve th e lin ear con trol p roblem p resen ted in th e text body in th is ap p en dix. Recall th at th e cu rren t valu ed Ham ilton ian can be written as follows:

(

(

))

2 * ( •) = d I I (t ) + cf [f (t )]I (t ) + λ(t )⎡⎢ β − rr + w (t ) Δr − rf f (t ) I (t ) − β( I (t )) ⎤⎥ ⎦ ⎣ ⎤ ⎡ + µ(t )⎢w (t ) (1 − w (t )) Δr − rf f (t ) ⎥ ⎦ ⎣

{

Recall it is assu m ed in g th e d iscou n ted m en t an d d am age treatm en t rate an d

(

)}

(A1)

th at th e objective is to m inim ize th is exp ression rep resen tsu m of treatm en t an d in fection d am age costs. Both treatco st s are assu m ed t o b e lin ear, t h e fo rm er lin ear in t h e th e latter lin ear in th e stock of in fected in d ivid u als. Th e

Chapter 1: Dynamics of Antibiotic Use • 37

t reat m en t rat e lies wit h in t h e u n it in t erval, an d t h e cu rren t valu ed sh ad o w p rices rep resen t th e m argin al con tribu tion s to th e treatm en t p rogram costs of th e stock of in fected in dividu als an d th e p rop ortion su scep tible to an tibiotics. We wou ld th u s exp ect λ(t) to be p ositive an d µ(t) to be n egative. Solvin g lin ear con trol p roblem s begin s by n otin g th at th e con trol variable en ters th e Ham ilton ian in a m an n er m u ltip lied by a coefficien t, wh ich we call th e switch in g fu n ction . Th e switch in g fu n ction σ(t) can be written as

[

σ(t ) = cf I − λ(t )w (t ) I (t )rf − µ(t )(1 − w (t ))w (t )rf

]

(A2)

so th at th e Ham ilton ian can be rewritten as 2 * ( •) = d I I (t ) + λ(t )⎡(β − rr + w (t )Δr ) I (t ) − β( I (t )) ⎤ ⎥⎦ ⎣⎢

[ {

+ µ(t ) w (t ) (1 − w (t ))Δr

[

}]

+ f (t ) cf I − λ(t )w (t ) I (t )rf − µ(t )(1 − w (t ))w (t )rf

]

(A3)

No w, t o m in im ize t h e Ham ilt o n ian in all p erio d s, t h e o p t im al t reat m en t rate con trol f * m u st be ch osen so th at f * = 0 as σ(t ) > 0 ^

f * = f as σ(t ) = 0 f * = 1 as σ(t ) < 0

(A4)

In oth er word s, wh en th e switch in g fu n ction is p ositive, it p ays to set th e co n t ro l at it s sm allest p o ssib le valu e t o m in im ize t h e Ham ilt o n ian . W h en t h e swit ch in g fu n ct io n is n egat ive, it p ays t o set t h e co n t ro l at it s largest valu e. W h en it is zero , t h e co n t ro l is a sin gu lar valu e t h at rem ain s t o b e d eterm in ed . Solvin g for th e sin gu lar valu e in volves in vestigatin g con d ition s th at m u st h old wh en th e switch in g fu n ction in Eq u ation A2 is iden tically zero for som e fin ite in terval. If th e switch in g fu n ction is zero, th en its d erivative σ⋅ (t) m u st also be zero on th e in terval. Differen tiatin g th e switch in g fu n ction in Eq u ation A2 gives u s σ˙ (t ) =

˙ − λIw˙ ] [ − λ˙ Iw − λIw ( λIwrf ) [ λIw ] [ − µ˙ w (1 − w ) − µw˙ (1 − w ) + µww˙ ] + ( µwrf ) + cf I˙ = 0 µw

(A5)

We also kn ow from th e Pon tryagin con dition s th at th e adjoin t variables m u st satisfy

38 • Chapter 1: Dynamics of Antibiotic Use

λ˙ = ρλ − {d I + λ[β(1 − I ) + w [ Δr − rf f ] − rr ]} + λβI − cf f

(A6)

an d µ˙ = ρµ − {λI[ Δr − rf f ] − µw [ Δr − rf f ] + µ(1 − w )[ Δr − rf f ]}

(A7)

⋅

⋅

Su bstitu tin g th ese an d th e state eq u ation s for w an d I in to th e exp ression for th e rate of ch an ge of th e switch in g fu n ction in Eq u ation A5 we h ave ⎡ λ˙ I˙ ⎤ ⎛ w˙ ⎞ σ˙ (t ) = − ⎢ + ⎥ ( λIwrf ) + ⎜ ⎟ − λIwrf + µw 2 rf ⎝w⎠ ⎢⎣ λ I ⎥⎦ ⎡ µ˙ w˙ ⎤ − ⎢ + ⎥ (1 − w )µwrf + cf I˙ = 0 ⎣µ w ⎦

[

] (A8)

Bu t from Eq u ation s A6 an d A7, it can be sh own th at ⎡ λ˙ I˙ ⎤ ⎡ d I + cf ⎤ ⎡ λI ⎤ ⎡ µ˙ w˙ ⎤ ⎢ + ⎥ = (ρ + βI ) − ⎢ ⎥ an d ⎢ + ⎥ = ρ − Δr – rf ⎢ − w ⎥ λ λ µ I µ w ⎥⎦ ⎢⎣ ⎣ ⎦ ⎣ ⎦ ⎦ ⎣

[

]

Su bstitu tin g th ese in to th e exp ression in A8 gives u s ⎧⎪ ⎡ d I + cf f σ˙ (t ) = ⎨−(ρ + βI ) − ⎢ λ ⎣ ⎩⎪

⎤ ⎫⎪ ⎛ w˙ ⎞ ⎥ ⎬ λIwrf + ⎜ ⎟ µwrf − cf I ⎝w⎠ ⎦ ⎭⎪

(

[

)

]

⎧⎪ ⎡ λI ⎤ ⎫⎪ − ⎨ρ − Δr − rf f ⎢ − w ⎥ ⎬(1 − w )µwrf + cf I˙ = 0 ⎪⎩ ⎣µ ⎦ ⎪⎭

[

]

(A9)

Exp an din g th is gives u s

[

] (

)

σ˙ (t ) = −ρ λIwrf + (1 − w )µwrf + d I + cf f Iwrf − βI 2 λwrf

[

+ (1 − w ) Δr − rf f

][µwr

f

]

− cf I + wrf λI − w 2 µrf + cf I˙ = 0

(A10)

Usin g Exp ression A2 for th e switch in g fu n ction , it can be sh own th at th e term s in sid e th e first bracket in Eq u ation A10 eq u al cf I. Moreover, su bstitu tin g term s from th e switch in g eq u ation d efin ition in Eq u ation A2 in to term s m u ltip lyin g (1 – w)[Δr – rf f ] in th e secon d lin e can cels th em ou t, leavin g σ˙ (t ) = −ρcf I + d I Iwrf − βI 2 λwrf + cf fIwrf + cf I˙ = 0 ⋅ Dividin g by I an d th en in sertin g th e state eq u ation for I / I gives

(A11)

Chapter 1: Dynamics of Antibiotic Use • 39

σ˙ (t ) = −ρcf + d I wrf − βIλwrf + cf β(1 − I ) − cf rr + cf w Δr = 0

(A12)

Becau se t h e swit ch in g fu n ct io n is zero alo n g t h e sin gu lar in t erval, it s first d erivat ive is also zero an d h en ce Eq u at io n A12 m u st h o ld . Bu t a co n st an t switch in g fu n ction also im p lies th at th e secon d d erivative is zero, an d h en ce we can differen tiate th e above exp ression again to get

[ ] [

d σ˙ (t ) = d I rf w˙ − βrf λwI dt

˙⎤

⎡˙

] ⎢⎢⎣ II + ww˙ + λλ ⎥⎥⎦ − βc I˙ + c w˙ Δr = 0 f

(A13)

f

Collectin g an d rearran gin g term s, we h ave d w˙ I˙ λ˙ d I rf w − βrf λwI + cf Δrw − βrf w λI + cf βI − βrf Iw λ = 0 σ˙ ] = [ dt w I λ

[

] [

] [

]

(A14)

Su bstitu tin g term s in Eq u ation A12 in to th e first term in brackets to elim in ate th e sh adow p rice an d collectin g term s leaves u s with ⎡ I˙ λ˙ ⎤ ⎡ I˙ ⎤ d ⎡ w˙ ⎤ σ˙ ] = ⎢ ⎥ ρcf − cf β(1 − I ) + cf rr − ⎢ ⎥ cf βI − ⎢ + ⎥ βrf Iw λ = 0 [ dt ⎣w ⎦ ⎢⎣ I ⎥⎦ ⎢⎣ I λ ⎥⎦

{

}

( )

(

)

(A15)

Su bstitu tin g in state an d costate eq u ation s for th e log d erivatives an d can celin g an d collectin g term s gives u s ⎡ I˙ ⎤ d ⎡ w˙ ⎤ σ˙ ] = ⎢ ⎥ ρcf − cf β(1 − I ) + cf rr − ⎢ ⎥ ρcf + 2 βIcf [ dt ⎣w ⎦ ⎢⎣ I ⎥⎦

{

}

(

)

(A16)

+ ρ2 cf − ρd I wrf − ρcf wrf f + ρβIcf = 0

Th is eq u ation m u st be satisfied alon g th e sin gu lar p ath . On ce th e state eq u a⋅ ⋅ t io n s fo r w an d I are in sert ed in t o Eq u at io n A16, t h e resu lt is an eq u at io n ^ d escribin g th e sin gu lar con trol f for th e treatm en t rate as a fu n ction of th e two state variables. Th e sin gu lar p ath th u s d erived is a n on au ton om ou s p ath ^ becau se th e op tim al treatm en t rate f (t) varies over tim e to m ake th e two state variables “t rack” t h eir o p t im al sin gu lar p at h valu es. Th is will be seen wh en th e log d erivatives of th e two costate eq u ation s are su bstitu ted in , leavin g an eq u ation describin g th e op tim al sin gu lar con trol as a feedback fu n ction of th e two state variables. Before solvin g th e fu ll solu tion for th e sin gu lar con trol at an y p oin t in tim e alon g th e sin gu lar p ath , con sid er first th e sin gu lar con trol at th e lon g-ru n eq u ilibriu m steady state. In sp ectin g Eq u ation A16 sh ows th at wh en th e system u ltim ately reach es its eq u ilibriu m , both log derivatives van -

40 • Chapter 1: Dynamics of Antibiotic Use

ish , an d th e rem ain in g p art of Eq u ation A16 d escribes con d ition s in eq u ilibriu m . In p art icu lar, we can so lve fo r t h e lo n g-ru n eq u ilibriu m valu es o f t h e con trol an d state variables f ∞, I∞, w ∞ u sin g ρ2 cf − ρd I w ∞rf − ρcf w ∞rf f ∞ + ρβI ∞ cf = 0

(A17)

wh ich can b e rearran ged t o so lve fo r t h e lo n g-ru n eq u ilib riu m valu e o f t h e sin gu lar con trol, n am ely f∞ =

β + ρ − rr d I − rf w ∞ cf

(A18)

Becau se rf f ∞ = Δr also, we can su bstitu te an d rearran ge to solve for w∞ =

(β + ρ − rr )cf

(A19)

d I rf + Δr cf

No w we are read y t o d escrib e t h e fu ll so lu t io n t o t h e sin gu lar co n t ro l at an y p oin t alon g th e sin gu lar p ath , in clu din g th e lon g-ru n steady state eq u ilibriu m . To do th is, we su bstitu te th e state eq u ation s in to Eq u ation A16 an d collect an d rearran ge term s to get

(

){

[ (

)]

}

d [σ˙ ] = Δr − rf f (1 − w ) cf ρ − β(1 − I ) + rr − wcf (ρ + 2 βI ) dt − cf (ρ + 2 βI ) β(1 − I ) − rr + rf w βId I + rf βwIcf f

(

[

)

]

(A20)

− (ρ + βI ) −ρcf + d I wrf − ρcf wrf f − βIcf wrf f = 0 By addin g an d subtractin g ρcf wΔr, we can collect term s in volvin g (Δr – rf f) to get

(Δr − rf f ){(1 − w )[cf (ρ − β(1 − I ) + rr )] − wcf (ρ + 2 βI ) + ρwcf } − cf (ρ + 2 βI )[β(1 − I ) − rr ] + βIρcf + ρ2 cf − ρw [cf Δr + d I rf ] = 0

(A21)

Makin g appropriate su bstitu tion s for com bin ation s of param eters th at describe equ ilibriu m valu es for variou s state an d con trol variables in Equ ation s A18 an d A19, we can th en write th e fu ll solu tion for th e sin gu lar con trol as

∧

rf ( f ∞ − f ) =

⎧⎪ ⎡ w − w ⎤ ⎡ ⎤⎫ ∞ + βI ⎛ w ⎞ − ⎛ I ⎞ ⎪ + β I − I ρ + 2 βI ρ⎨ρ⎢ )[ ⎢⎜ ⎥⎬ ( ∞ ] ⎥ ⎟ ⎜ ⎟ w∞ ⎦ ⎢⎣⎝ w ∞ ⎠ ⎝ I ∞ ⎠ ⎥⎦ ⎭⎪ ⎩⎪ ⎣

(A22)

(1 − w )[ρ − β( I ∞ − I )] − 2 w βI

Wh at is th e in tuition beh in d th is expression for th e sin gular con trol? Note th at in th e lon g-run equilibrium in wh ich all variables are station ary, we kn ow th at th e total level of in fected in dividu als will eq u ilibrate at I∞ = (β – rr)/ β. In ad d i-

Chapter 1: Dynamics of Antibiotic Use • 41

tion , th e equ ilibriu m valu e of th e treatm en t rate m u st be su ch th at rf f ∞ = rr – rw . Th is treatm en t rate en su res th at th e extra m ortality to th e su sceptible bacteria cau sed by th e equ ilibriu m treatm en t rate ju st brin gs in to balan ce th e su sceptible m o rt alit y rat e aft er t reat m en t wit h t h e h igh er m o rt alit y rat e o f resist an t bact eria cau sed by t h e fit n ess co st . Fin ally, t h ere is a lo n g-ru n eq u ilibriu m valu e given for th e p rop ortion of su scep tible bacteria w ∞. Usin g th ese d efin ition s in th e sin gu lar solu tion , th e solu tion for th e op tim al treatm en t rate can be seen to be a typ e of m ixed accelerator. Th at is, th e d ifferen ce between th e cu rren t optim al treatm en t rate an d its lon g-ru n equ ilibriu m valu e is related to th e differen ce between th e cu rren t fraction of su sceptible bacteria an d its lon gru n valu e (w – w ∞) an d th e differen ce between th e cu rren t an d lon g-ru n valu es of th e total in fection level (I – I∞). ⎛∧ ⎞ rf ⎜ f − f ∞ ⎟ = − φ1 I ∞ (w − w ∞ ) + φ2 [wI ∞ − w ∞ I ] + φ3 w ∞ ( I ∞ − I ) ⎝ ⎠

{ [

]

[

]}

(A23)

In th is accelerator rep resen tation , each accelerator coefficien t is a fu n ction of th e cu rren t state variables so th at φi = φi(w,I) in wh ich th e sp ecific fu n ction s are d et erm in ed b y Eq u at io n A22. Th e ad ju st m en t t o ward t h e lo n g ru n in wh ich t h e t reat m en t rat e h o ld s t h e st o ck o f t o t al in fect io n s an d su scep t ible in fect io n s co n st an t is seen as o n e in wh ich t h e gap s b et ween cu rren t an d lon g-ru n valu es of th e state variables gradu ally con verge. In su m m ary, th e op tim al in terven tion ist treatm en t p rofile associated with t h is sin gle d ru g p ro b lem is gen erally o n e in wh ich t h e en t ire p o p u lat io n is treated for a p eriod , followed by a p eriod u sin g a tim e-varyin g sin gu lar con t ro l t h at t akes t h e syst em t o a lo n g-ru n eq u ilib riu m . As we sh o wed in t h e bod y of th is ch ap ter, th is u su ally m ean s oversh ootin g th e level at wh ich th e t o t al p o p u lat io n o f in fect ed in d ivid u als is m in im ized . In p rin cip le, we can determ in e th e switch p oin t at wh ich treatm en t ch an ges from an extrem e con trol (in wh ich f = 1) to on e u sin g th e sin gu lar con trol.

Chapter 2

Using Antibiotics When Resistance Is Renewable Robert Rowthorn and Gardner M . Brown

When an antibiotic is “ correctly” prescribed to treat an infection, it can have tw o effects. In the present, it cures the patient. But used across m any patients, the practice allows the selection of more resistant organisms, thus reducing the future effectiveness of the drug not only against the strain that causes the illness under treatm ent but also against other organism s that could otherw ise be controlled by the drug. If w e do not account for this intertem poral dynam ic, w e cannot m ake socially optim al decisions about which antibiotics to use and how much of each to prescribe. This is particularly true when the evolution of resistance is fast paced. One way to address the problem is by sim ulation: different treatm ent strategies are specified, and outcomes are ranked according to some criterion. However, because so many options are possible, it is easy to miss some excellent, even optimum, outcom es. In this chapter, the optim al use of antibiotics is analyzed w ith mathematical methods developed to study other dynamic natural resource allocation problems, such as groundwater or forest resources. In the model applied here, two antibiotics are available to treat two strains of infections. Each drug is effective for only one strain. Only one drug is used per patient at a time in this model, and the doctors do not know which strain a patient has. Each cure has the same benefit. Infection and treatment dynamics follow the basic SIS (susceptible → infected → susceptible) model. The rate at which healthy people are infected by a given strain is governed by a com mon transmission coefficient. The rate at which sick people are cured in the absence of treatm ent is governed by a spontaneous recovery rate for each strain and the fraction treated. Except for the fraction of the population treated and the level of infection in the steady state (when those infected balance those cured), all other interesting results depend on both economic and epidem iological param eters. The fraction of the infected population • 42 •

Chapter 2: Using Antibiotics When Resistance Is Renewable • 43 treated by each antibiotic in the steady state varies inversely with the rate of spontaneous recovery.

b o u t t wo d ecad es aft er Flem in g d isco vered t h e m o ld fro m wh ich p en icillin is p rod u ced , th e d ru g was in trod u ced in to clin ical p ractice (Garrett 1994). Sin ce t h at t im e, t en s o f t h o u san d s o f an t ib io t ic p ro d u ct s h ave b een d evelo p ed t o su ccessfu lly t reat d iseases t h at p revio u sly h ad fat efu l co n seq u en ces. In th e Un ited States alon e at least 150 m illion cou rses of an tibiotics are p rescribed an n u ally (McCaig an d Hu gh es 1995). An n u al p rodu ction in th e Un ited States exceeds 50 m illion p ou n ds, 40% of wh ich is destin ed for an im al u se (Levy 1998). Th e su ccess of an tibiotics in treatin g d iseases en gen d ered so m u ch op tim ism th at it was easy to con clu d e, as m an y d id , th at th e con q u est of all in fectiou s diseases was im m in en t (Garrett 1994).1 Su ch op tim ism h as to be leaven ed with a down side to an tibiotic u se. W h en an tibiotics an n ih ilate dru g-su scep tible strain s, a fertile en viron m en t is left for th e d ru g-resistan t strain s to flou rish . Con cep tu ally th en , th e effectiven ess of an tibiotics (or dru g resistan ce) is a n atu ral resou rce redu ced by u se, often q u ite q u ickly. Massad an d oth ers (1993), citin g oth er literatu re, stated t h at t h e in t ro d u ct io n o f su lfo n am id e in t h e t reat m en t o f go n o rrh ea led t o m o st n ew cases cau sed b y su lfo n am id e-resist an t go n o co cci six years lat er. Mo re sp ect acu larly, t h e effect iven ess o f p en icillin in t reat in g st ap h ylo co ccicau sin g in fection s was less th en 50% after two years of exten sive clin ical u se of th e dru g (Bryson an d Szybalski 1955). A t ech n ical n egat ive ext ern alit y, m u lt ip le d ru g resist an ce, is cau sed by rep eated u se of an tibiotics. Alth ou gh m u ltip le d ru g resistan ce is m ore p revalen t in n osocom ial (h osp ital-acq u ired ) strain s (McGowan 1983; Massad et al. 1993), dru g-resistan t com m u n ity strain s, illu strated by th e recen t rise in tu bercu losis cases in th e Un ited States, are of great con cern to d isease con trol sp ecialists. It is particu larly distu rbin g th at on e stu dy fou n d m ore th an on e-h alf of th e p atien ts were in fected with a strain resistan t to on e d ru g an d abou t on et h ird were in fect ed wit h a st rain resist an t t o m o re t h an o n e d ru g. Th e in ciden ce of m u ltiple-dru g resistan ce h as m ore th an dou bled sin ce th at tim e (In stitu te of Med icin e 1992). Mu ltip le-d ru g resistan ce arisin g from d ru g u se h as at least two drawbacks. In th e case of tu bercu losis, th e disease is extrem ely con tagio u s, wh ich en h an ces t h e rat e o f in fect io n . Mo re gen erally, m u lt ip le-d ru g resist an ce in d u ced by d ru g u se can lead t o t reat m en t co st s o f $150,000 p er p atien t, an ord er of m agn itu d e h igh er th an trad ition al treatm en t costs (In stitu te of Medicin e 1992). Alth ou gh it is widely recogn ized th at an tibiotic u se cau ses in creased resistan ce, th e ep id em iologists an d biologists in th e research com m u n ity h ave n ot resp on d ed by bu ild in g op tim ization m od els. In stead , sim u lation s are con du cted on altern ative-u se p attern s. An excellen t illu stration is th e research by

A

44 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Bon h oeffer an d oth ers (1997). Th eir stu d y u sed th ree treatm en t p rotocols. In th e first protocol, both drugs were given to each in fected in dividual; in th e secon d protocol, two equal proportion s of th ose in fected were treated by two can didate drugs; an d in th e th ird protocol, all patien ts were given a sin gle drug at an y given tim e with periodic cyclin g between two drugs. Because th ese are very restrictive option s, it is un likely th at an optim um treatm en t option will be discovered , excep t fortu itou sly. Moreover, u n like econ om ists, ep id em iologists attribute th e sam e value to a successful treatm en t today as th ey do to a successful treatm en t 20 years from n ow. Th us an optim um treatm en t strategy derived from an econ om ic form u lation of th e problem n ecessarily differs from an epidem iological form ulation in wh ich th e discoun t rate is assum ed to be zero. Econ om ists in gen eral, an d n atu ral resou rce econ om ists in p articu lar, h ave been slow to recogn ize th at gain in g a better u n derstan din g of op tim al an tibiotic u se is of en orm ou s social im p ortan ce an d th at ou r can on ical m odels p rovid e u s wit h su b st an t ial co m p arat ive ad van t age in t acklin g t h e p ro b lem . Bro wn an d Layt o n (1996) lo o ked briefly at t h e t rad e-o ff bet ween an t ibio t ic u se in h u m an s an d an im als. Laxm in arayan (1999) tackles p aten t bread th for an t ib io t ics an d h as an em p irical ch ap t er o n fo recast in g resist an ce. Laxm in arayan an d Brown (2001) treat an tibiotic effectiven ess as a n on ren ewable reso u rce. In t h e fo llo win g an alysis, we t ake t h e n at u ral n ext st ep an d st u d y th e p attern of op tim al u se of two an tibiotics wh en effectiven ess (resistan ce) is a ren ewable resou rce.

Antibiotics M odel Th e m od el set ou t in th is ch ap ter con sid ers a very sim p le case. Th ere are two strain s of in fection , an d th ere are two treatm en ts, each of wh ich is effective again st o n ly o n e o f t h e st rain s an d is t o t ally in effect ive again st t h e o t h er. 2 In fect ed in d ivid u als h ave a sp o n t an eo u s reco very rat e even if t h ey are n o t t reat ed ; h o wever, t h eir reco very rat e is in creased if t h ey receive ap p ro p riat e treatm en t. In d ivid u als can on ly be in fected by on e strain at a tim e, an d th e p robability of in fection by a p articu lar strain is th e sam e for all h ealth y m em bers of th e p op u lation regardless of th eir p ast m edical h istory. In fection is n ot fatal, an d th e p op u lation is con stan t. Th e p o licy p ro b lem is t o fin d an o p t im al b alan ce b et ween t h e co st s an d ben efit s o f t reat m en t , t akin g in t o acco u n t h o w cu rren t t reat m en t d ecisio n s will affect t h e effect iven ess o f fu t u re t reat m en t o p t io n s. In t h is calcu lat io n , th e defin ition of costs is fairly obviou s. Th ey are sim p ly th e n orm al costs associated with m edical treatm en t, in p articu lar, th e cost of dru gs. Regardin g ben efits, from a p u blic stan d p oin t, wh at m atters is th e h ealth of th e p op u lation in gen eral. We assu m e th at th e overall h ealth of th e p op u lation is th e ben efit th at is weigh ed again st cost in ch oosin g th e op tim u m treatm en t strategy.

Chapter 2: Using Antibiotics When Resistance Is Renewable • 45

Th e optim um strategy depen ds on th e in form ation available to th e auth orities an d also th e econ om ic, legal, an d p olitical con strain ts u n d er wh ich th ey operate. We assum e th at th e public auth orities h ave th e followin g in form ation . Th ey kn ow all th e basic param eters of th e m odel, su ch as th e efficacy of treatm en t an d rates of sp on tan eou s recovery an d tran sm ission of in fection . From periodic sam plin g, th ey also kn ow th e prevalen ce of each strain of in fection in th e population as a wh ole, an d th ey kn ow wh o is sick. However, for reason s of tim e or expen se, it is im practical to test each sick in dividual to ascertain wh ich strain of in fection is in volved. Th us, treatm en t can n ot be tailored to th e n eeds of specific in dividuals. If on ly a fraction of th e sick in dividuals receive a particular treatm en t, th ere will be som e p atien ts for wh om th is treatm en t is wasted becau se th ey will receive a dru g for wh ich th eir strain of in fection is resistan t. Also, th ere will be oth ers wh o cou ld ben efit from th is treatm en t bu t d o n ot receive it. On e p ossibility is to ad m in ister a cocktail of both treatm en ts to all p atien ts. Th is m axim izes th e p ossibility of cu re, bu t m ay be p roh ibitively expen sive. Such difficulties are in evitable given th e lack of in form ation .

M athematical Formulation In fection s an d treatm en ts are in dexed by th e su bscrip t i = 1, 2. Each treatm en t is on ly effective again st on e strain of in fection . Patien ts wh o are in fected with st rain i an d receive t reat m en t j (≠ i), o r wh o are n o t t reat ed at all, reco ver sp o n t an eo u sly at a rat e ri, wh ich d en o t es t h e fit n ess co st o f t h e b act eria. If th ey receive th e effective treatm en t i, th eir recovery rate is eq u al to ri + αi. Th e average recovery rate for su ch p atien ts is a weigh ted su m of th ese two rates. It is eq u al to (1 – f i)ri + f i(ri + αi), wh ere f i is th e p rop ortion of p atien ts receivin g treatm en t i. Let Ii den ote th e n u m ber of in dividu als in fected with strain i an d let I = I1 + I2 . If th e total p op u lation is fixed at N, th e n u m ber of h ealth y in dividu als is eq u al to N – I. We ign ore birth s an d im m igration . In stan dard fash ion , we assu m e th at th e n u m ber of h ealth y in dividu als wh o becom e in fected wit h st rain i p er u n it o f t im e is eq u al t o βi(N – I)Ii . Th is is t h e ap p ro p riat e exp ression if in fected in dividu als are ran dom ly distribu ted am on g th e h ealth y p op u lation an d tran sm it th eir in fection via p roxim ity. Th e dyn am ics of in fection an d treatm en t sp ecified reflect th e research of Kerm ack an d McKen d rick (1927) an d are su m m arized by th e followin g differen tial eq u ation s: I˙1 = β1 ( N − I ) I1 − (r1 + f 1α1 ) I1 I˙2 = β2 ( N − I ) I 2 − (r2 + f 2 α 2 ) I 2 Su p p o se t h at t h e so cial valu e o f b ein g h ealt h y is p an d t h at t h e co st o f treatm en t i is eq u al to ci. In each case, th e u n its are m on ey p er in dividu al p er u n it of tim e. Th e flow rates of aggregate ben efits an d aggregate costs are eq u al

46 • Chapter 2: Using Antibiotics When Resistance Is Renewable

t o p(N – I) an d (c1 f 1 + c2 f 2 )I, resp ect ively. Th u s, t h e n et flo w o f ben efit s p er u n it of tim e is eq u al to p(N – I) – (c1 f 1 + c2 f 2 )I. Th e econ om ic objective is to m axim ize th e p resen t valu e of n et ben efits form ed by th e followin g in tegral, su bject to in itial con dition s, ap p rop riate con strain ts, an d th e p recedin g differen tial eq u ation s: J=

∞ − ρt

∫0

e

[ p ( N − I ) − (c f

1 1

+ c2 f 2 )dt

]

wh ere ρ is th e social discou n t rate. Note th at th is in tegral m ay n ot con verge if ρ is zero. Some Simplifications

To sim p lify th e an alysis, we n orm alize by assu m in g th at N = 1. We also m ake th e followin g su bstan tive assu m p tion s. Th e two treatm en ts are eq u ally effect ive again st t h e ap p ro p riat e in fect io n (α1 = α2 = α), an d t h e t wo st rain s are eq u ally con tagiou s (β1 = β2 = β). Fin ally, all p atien ts receive exactly on e kin d of treatm en t (f 1 + f 2 = 1). Hen ce we can write f 1 = f an d f 2 = (1 –f), an d th u s an y allo wable t reat m en t st rat egy can be fu lly d escribed by sp ecifyin g t h e t rajectory of th e sin gle con trol variable f. With th ese ad d ition al assu m p tion s, th e op tim ization p roblem is to fin d th e tim e p ath of f th at m axim izes th e in tegral J=

∞

− ρt ∫0 e ( p − AI )dt

(1)

su bject to I˙1 = [β(1 − I ) − r1 − αf ]I1 I˙2 = [β(1 − I ) − r2 − α(1 − f )]I 2

(2a) (2b)

I1 ( 0 ), I 2 ( 0 ) are given an d A = p + c1f + c2 (1 − f ) I = I1 + I 2 0 < I1 , I 2 < I I

r1 + r2 + α 2

(5)

Th ese in eq u alities im p ly th at th e rate of in fection exceeds th e fitn ess cost β > r1 , r2

(6)

If th is were n ot true, th en th e spon tan eous rates of recovery of at least on e strain would exceed th e rate of in fection , an d ultim ately th is strain would be n aturally elim in ated with out treatm en t. We can write Equation s 2a an d 2b as follows: I˙1 = [ −β( I − I *) − α( f − f *)]I1

(7a)

I˙2 = [ −β( I − I *) + α( f − f *)]I 2

(7b)

Becau se I = I1 + I2 , it follows th at I˙1 = −β( I − I * ) I + α(f − f * )( I 2 − I1 )

(8)

Also, I˙2 I˙1 − = 2 α( f − f * ) I 2 I1

(9)

Th u s I2 / I1 is con stan t if f = f *. If I = I * an d f = f *, , th en both I1 an d I2 rem ain con stan t.

Hamiltonian Conditions

Th e cu rren t valu e Ham ilton ian form ed from Eq u ation s 1, 7a, an d 7b is * = p − AI + m 1 [ −β( I − I *) − α( f − f *)]I1 + m 2 [ −β( I − I *) + α( f − f *)]I 2

(10)

48 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Th e variable A is an an alytical su bstitu tion , defin ed earlier as p + c1 f + c2 (1 – f ). An econ om ic in terp retation of th is variable is p rovid ed later in th e ch ap ter; m 1 an d m 2 are th e costate variables (sh adow p rices). Becau se ∂A/ ∂f = c1 – c2 , it follows th at ∂* = −( c1 − c2 ) I + α[m 2 I 2 − m 1 I1 ] ∂f

(11)

Th u s, for an op tim u m ⎧= 0 ⎫ ⎧< ⎫ ⎪ ⎪ ⎪ ⎪ f ⎨∈[0 ,1]⎬as − ( c1 − c2 ) I + α[m 2 I 2 − m 1 I1 ] ⎨= ⎬0 ⎪= 1 ⎪ ⎪> ⎪ ⎩ ⎭ ⎩ ⎭

(12)

Before settin g d own th e costate eq u ation s for th e Ham ilton ian Eq u ation 10, let u s first con sider th e econ om ic in terp retation of Eq u ation 12. As in oth er ren ewable resource problem s, th e costate variable m i can be in terpreted as a sh adow price. Th is variable in dicates th e m argin al ben efit to society of in creasin g th e stock of in fection i. Because in fection is h arm ful, th e sh adow price is n egative, an d –m i is th e am ou n t society is willin g to pay for treatm en t th at reduces th e stock of in fection i by on e un it. In th e presen t m odel, th ere are two differen t in fection s to con sider. As can be seen from Equation s 7a an d 7b, a ch an ge Δf in th e sh are of patien ts treated by drug 1 causes th e n um ber of peop le in fected by strain s 1 an d 2 to ch an ge by –αI1 Δf an d + αI2 Δf, resp ectively. Th e social valu e of th ese ch an ges is equ al to m 1 (–αI1 Δf ) an d m 2 (αI2 Δf ). Th eir com bin ed valu e is α(m 2 I2 – m 1 I1 ) Δf . Th e total cost of ach ievin g su ch an ou tcom e is (c1 – c2 )I Δf. W h en both an tibiotics are used, so th at variation in eith er direction is possible, th e m argin al cost of switch in g drugs m ust be exactly equal to th e social ben efit. Th us, ( c1 − c2 ) I = α[m 2 I 2 − m 1 I1 ]

(13)

Th is is m erely th e con d ition for an in terior solu tion as given in Eq u ation 12. If t h e m argin al co st o f swit ch in g t reat m en t s is d ifferen t fro m t h e so cial valu e of th e resu ltin g ch an ge in in fection stocks, th en on ly on e of th e d ru gs sh o u ld b e u sed . Fo r exam p le, if t h e co st o f swit ch in g t o an t ib io t ic 1 is less th an th e associated gain in social valu e, th en th is d ru g sh ou ld be u sed exclu sively. Th is occu rs wh en (c1 – c2 )I < α[m 2 I2 – m 1 I1 ] as sp ecified in Eq u ation 12. In th is case, f = 1, wh ich im p lies th at f 1 = 1 an d f 2 = 0. Th e costate eq u ation s of th e cu rren t valu e Ham ilton ian for i = 1 an d 2 are m˙ 1 = ρm 1 + A + m 1 [β( I − I * ) + α( f − f *)] + β[m 1 I1 + m 2 I 2 ]

(14a)

Chapter 2: Using Antibiotics When Resistance Is Renewable • 49

m˙ 2 = ρm 2 + A + m 2 [β( I − I * ) − α( f − f *)] + β[m 1 I1 + m 2 I 2 ]

(14b)

Th ese are derived by recogn izin g th at ∂I/ ∂Ii = 1 becau se I = I1 + I2 . Usin g Eq u at io n s 2a an d 2b , an d recallin g t h e d efin it io n o f A, Eq u at io n s 14a an d 14b can be written as follows ρm 1 = − p − [ c1f + c2 (1 − f )] + m˙ 1 + [m 1∂I1 / ∂I1 + m 2 ∂I 2 / ∂I1 ]

(15a)

ρm 2 = − p − [ c1 f + c2 (1 − f )] + m˙ 2 + [m 1 ∂I1 / ∂I 2 + m 2 ∂I 2 / ∂I 2 ]

(15b)

To in terpret th ese equation s, let us take Equation 15a as an exam ple. Sim ilar observation s apply to Equation 15b. Con sider an exogen ous in crease of 1 un it in I1 . Th e (n egative) sh adow p rice of th is strain of in fection is m 1 , so in fin an cial term s, th e addition al in fection is equivalen t to a n egative win dfall equal to m 1 un its of m on ey. At an in terest rate of ρ, th is win dfall would gen erate a n egative in com e stream equal to ρm 1 per period. Th us, th e left-h an d side of Equation 15a rep resen ts th e op p ortu n ity cost of ad d ition al in fection . Th e oth er sid e of th e eq u ation brin gs togeth er th e variou s con seq u en ces of th is even t. All item s are m easu red at th eir m argin al valu ation s on th e op tim u m p ath . Th e two in itial term s evaluate th e im pacts of addition al in fection on curren t levels of sickn ess an d m edical treatm en t. Both term s are n egative because extra sickn ess an d m edical treatm en t are social costs. Th e rem ain in g term s are forward lookin g. Th ey in d icate h ow an in crease in I1 affects th e fu tu re sh ad ow p rice of th is strain of in fection (“capital appreciation ”) an d th e growth rates of in fection in gen eral. Th ere is an oth er econ om ic in terp retation of th e costate eq u ation s. Rewritin g Eq u ation 14a as ρ=

m˙ 1 A − + V MP( I1 ) m1 m1

(wh ere VMP is t h e valu e o f t h e m argin al p ro d u ct ) illu st rat es t h e arb it rage p rin cip le go vern in g t h e u se o f a n at u ral reso u rce. At all t im es, t h e rat e o f retu rn on rival assets (ρ) sh ou ld eq u al th e m argin al rate of retu rn on in vestm en t in m an agin g each in fection . Th at rate h as th ree com p on en ts. Th e first term on th e righ t-h an d side is th e rate of p rice ap p reciation or dep reciation of th e asset. Th e secon d term , – A/m 1 , is th e m argin al gen eralized stock extern alit y. It cap t u res h o w t h e valu e o f t h e o b ject ive fu n ct io n , t h e n et b en efit s o f b ein g h ealt h y, ch an ges if I1 ch an ges. Th e last t erm cap t u res t h e “o wn ” real m argin al rate of retu rn on th e stock of in fection becau se V MP( I1 ) =

∂I˙1 m 2 ∂I˙2 + ∂I1 m 1 ∂I1

50 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Th u s, Eq u at io n 15a h as an in t u it ive m ean in g. Alo n g t h e o p t im u m p at h , t h e o p p o rt u n it y co st o f in fect io n is eq u al t o t h e act u al flo w o f p resen t an d fu tu re costs an d ben efits.

Interior Solution

Suppose th ere is an optim um path alon g wh ich 0 < f < 1 for an open segm en t. Let A* = p + c1f * + c2 (1 – f *). In th e appen dix we derive th e followin g equation s: 2 m 1 I1 =

+( c2 − c1 ) I 1 ⎡ * ( c2 − c1 ) I[ρ + β( I − I *)] ⎤ − ⎢A − ⎥ α β⎣ α( I 2 − I1 ) ⎦

(16a)

2 m 2 I2 =

−( c2 − c1 ) I 1 ⎡ * ( c2 − c1 ) I[ρ + β( I − I *)] ⎤ − ⎢A − ⎥ α β⎣ α( I 2 − I1 ) ⎦

(16b)

[

]

2 α[ f − f *] β( I 2 − I1 )2 I − 2 I1 I 2 ( ρ + β( I − I *)) =

−αρA* [ I 2 − I1 ] + [ I 2 − I1 ]I [ρ + β( I − I *)][ρ + βI ] ( c2 − c1 ) 2

+ β [ I 2 − I1 ]( I − I *) I 2

(17)

2

Usin g Eq u ation 17 to elim in ate f – f * from Eq u ation s 7a an d 7b, we get a p air of differen tial eq u ation s of th e form I˙1 = F1 ( I1 , I 2 ) (18) I˙2 = F2 ( I1 , I 2 ) Th is system h as a fixed p oin t at P = (I*1 , I*2 ), wh ere ⎡ (ρ + βI *)( c2 − c1 ) ⎤ * ⎥I ⎢1 − αA * ⎦ ⎣ * 1 ( )( ) + − ρ β I c c ⎡ 2 1 ⎤ * I 2* = ⎢1 + ⎥I 2⎣ αA * ⎦ I1* =

1 2

(19)

> > Becau se A* > 0, th ese eq u ation s im p ly th at I *2 =< I *1 as c2 =< c1 . In t h e st ead y st at e, t h e level o f in fect io n is h igh est fo r t h e st rain t h at is m o st exp en sive t o t reat . Th e m o re exp en sive it is t o m it igat e, t h e m o re o f a b ad t h in g p eo p le are willin g t o p u t u p wit h . Th e exact st ead y st at e level o f in fection for each strain dep en ds on th e relative costs of treatm en t, th e ben efit o f a cu re, an d t h e d isco u n t rat e—t h e rat e we are willin g t o t rad e o ff t h e valu e o f a cu re t o d ay again st t h e en su in g co st o f in creased resist an ce in t h e fu tu re. If each an tibiotic is th e sam e, th en h alf th e in fected p op u lation will be t reat ed by each an t ibio t ic, an d t h e in fect io n level is t h en t h e sam e fo r each strain . W h en th e an tibiotics are d ifferen t in cost, th e fraction of th e p op u la-

Chapter 2: Using Antibiotics When Resistance Is Renewable • 51

tion greater th an h alf treated by th e ch eap est dru g is scaled u p by th e cost differen ce between th e two an tibiotics an d th e discou n t rate an d scaled down by th e cost of in fection . Th e corresp on din g valu es for th e costate variables are m *1 an d m *2 , wh ich are bo t h eq u al t o m * = –A */ (ρ + βI *). In t h e st ead y st at e, t h e am ou n t society is willin g to p ay to redu ce th e level of in fection of each strain is th e sam e. It varies d irectly with th e d iscou n t rate an d th e rate of in fection an d in versely with th e cost of in fection . In an “au ton om ou s” p roblem of th e p resen t t yp e, an y fixed p o in t is eit h er u n st able o r is a sad d le p o in t . 3 By lin earizin g th e above eq u ation s arou n d p, it can be sh own th at, for sm all valu es of ρ, th is p oin t is an u n stable focu s (see ap p en dix). Hen ce an y m in or disp lacem en t fro m t h e st ead y st at e lead s t o an o u t ward sp iral. Sim u lat io n s in d icat e th at th e resu ltin g sp iral m ay even tu ally ap p roach a lim it cycle. Th ey also su ggest th at p is a saddle p oin t for larger valu es of ρ. Note th at th e system of d ifferen tial Eq u ation s 18 also h as a fixed p oin t at (I */ 2, I */ 2). However, as can be seen in Eq u ation s 16a an d 16b, th e associated sh adow p rices are in fin ite, an d rem ain in g at th is p oin t can n ot be op tim al.

The Singular Path

Th e system of d ifferen tial eq u ation s d iscu ssed earlier d eterm in es a fam ily of cu rves in (I1 , I2 ) sp ace. Su p p ose th at p = (I 1*, I 2*) is a sad d le p oin t. In th is case, th ere is a u n iq u e cu rve th at p asses th rou gh th e stead y state (I *1 , I *2 ) an d alon g wh ich th e direction of m ovem en t is toward th is steady state. Th is cu rve is th e sin gu lar p at h . Th e sh ap e o f t h e cu rve wh en c2 > c1 is sh o wn in Figu re 2-1. Con vergen ce toward th e steady state is asym p totic. In th e cou rse of tim e, th e p ace o f ch an ge slo ws d o wn , b u t t h e st ead y st at e is n ever act u ally reach ed . Alo n g t h e sin gu lar p at h , f is ch o sen acco rd in g t o Eq u at io n 17, an d t h e sh adow p rices m 1 an d m 2 are given by Eq u ation s 16a an d 16b. Th ey con verge to a com m on valu e m *.

Optimum Solution

Det erm in in g t h e o p t im u m so lu t io n in t h e p resen t m o d el is n o t st raigh t fo rward. Th ere are two m ain p roblem s. Th e first is to fin d a solu tion th at satisfies t h e Ham ilt o n ian co n d it io n s. Th is is esp ecially d ifficu lt wh en ρ is sm all, b ecau se so m e o f t h e o p t im u m p at h s m ay t h en co n t ain sp irals an d even a lim it cycle. Th e seco n d p ro blem arises becau se o u r Ham ilt o n ian is n o t co n cave in t h e st at e variab les, an d t h e st an d ard su fficien cy t h eo rem s o f Man gasarian or Arrow an d Ku rz do n ot ap p ly. Th u s, even if we can fin d a solu tion satisfyin g th e n ecessary Ham ilton ian con dition s, th is m ay n ot gu aran tee th at t h e so lu t io n is o p t im al. Th ere m ay be o t h er so lu t io n s t h at also sat isfy t h ese con dition s. 4

52 • Chapter 2: Using Antibiotics When Resistance Is Renewable

1.00 parameter values: p = 1. c1 = 0.1, c2 = 0.35 ρ = 0.01, α = 2, β = 1.5, r 1 = 0.1, r 2 = 0.2

0.90 0.80

Infection 2 ( I 2)

0.70 0.60 0.50 0.40 0.30

( I1* , I2* )

0.20 0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Infection 1 ( I 1) FIGURE 2-1. The Singular Path

Desp ite con siderable effort, th ese difficu lties so far h ave p reven ted u s from fin din g a defin itive an swer to th e op tim ization p roblem . Sim u lation s in dicate th at over a variety of p aram eter valu es, p = (I1*, I2*) is an op tim al p oin t. If th e system h ap p en s to be at th is p oin t, it is op tim al to rem ain th ere by keep in g f eq u al to f *. If th e system is n ot at th is p oin t, op tim al beh avior dep en ds on th e size o f ρ relat ive t o o t h er p aram et ers. W h en ρ is sm all, t h e syst em is h igh ly n on lin ear, an d we h ave n o clear in tu ition abou t th e n atu re of th e op tim u m solu tion . Th e situ ation is m u ch sim p ler wh en ρ is large en ou gh to en su re th at p is a sad d lep oin t. In th is case, th ere is a sin gu lar p ath th at con verges to th e fixed p o in t , an d we p ro p o se t h e fo llo win g so lu t io n t o t h e o p t im izat io n p ro blem . For p oin ts already on th e sin gu lar p ath , we ch oose f accordin g to Eq u ation 17, wh ich takes u s alon g th is p ath toward th e stead y state. For oth er p oin ts, we ch oose th e valu e of f wh ich leads as q u ickly as p ossible to th e sin gu lar p ath . If (I1 , I2 ) lies ab o ve t h e sin gu lar p at h , we t ake f = 0, t h ereb y en su rin g t h at all p atien ts receive th e treatm en t th at is effective again st in fection 2. Th is cau ses I2 to fall rap id ly u n til we even tu ally h it th e sin gu lar p ath . If (I1 , I2 ) lies below th e sin gu lar p ath , we take f = 1, th ereby en su rin g th at all p atien ts receive th e

Chapter 2: Using Antibiotics When Resistance Is Renewable • 53

t reat m en t t h at is effect ive again st in fect io n 1. Th is cau ses I2 t o fall rap id ly u n til on ce again we h it th e sin gu lar p ath . In eith er case, h avin g reach ed th e sin gu lar p ath , we stay on it an d con verge toward th e steady state. Th is is illu strated in Figu re 2-2. In t h e st ead y st at e, relat ive t reat m en t levels n at u rally d ep en d o n relat ive sp on tan eou s recovery rates. To m ain tain con stan t relative in fection rates for each st rain , t h e fract io n o f p at ien t s t reat ed wit h d ru g 1 m u st be as fo llo ws:

f *=

α + (r2 − r1 ) 2α

(4)

Th u s, oth er th in gs bein g equ al, th e greater th e spon tan eou s recovery rate of a particu lar strain is, th e sm aller th e fraction of patien ts treated with th e dru g effective again st th is strain is. In th e steady state, dru g th erapy is th erefore con cen trated on strain s th at h ave th e lowest rate of spon tan eou s recovery. No m at t er wh at t h e in it ial st art in g p o in t , we h ave a ru le t o d et erm in e wh ich trajectory to follow. Th is trajectory takes u s as rap idly as p ossible to th e sin gu lar p at h , an d wh en t h is p at h is reach ed , we rem ain o n it t o co n verge asym p totically to th e steady state. Ch oosin g th e ap p rop riate in itial valu es for th e sh adow p rices m 1 an d m 2 , we fin d th at all of th e n ecessary con dition s for

1.00 parameter values: p = 1. c1 = 0.1, c2 = 0.35 ρ = 0.01, α = 2, β = 1.5, r 1 = 0.1, r 2 = 0.2

0.90 0.80

Infection 2 ( I 2)

0.70 0.60 f=0

0.50 0.40 0.30

( I1*, I2 *)

0.20 f=1

0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

Infection 1 ( I 1) FIGURE 2-2. Optimal Paths

0.70

0.80

0.90

1.00

54 • Chapter 2: Using Antibiotics When Resistance Is Renewable

an op tim u m are satisfied. In th e p resen t case, th ese n ecessary con dition s m ay n ot be su fficien t for an op tim u m becau se th e Ham ilton ian is n ot con cave in th e state variables. It is th eoretically p ossible, alth ou gh u n likely, th at ou r p rop osed solu tion is n ot op tim al. Very m an y sim u lation s, n ot rep orted h ere, su ggest th at ou r solu tion is in fact op tim al.

Conclusion Startin g from an arbitrary p osition , su p p ose th e op tim u m treatm en t strategy is fo llo wed . Th e resu lt in g p at h co n verges t o t h e lo n g-ru n st ead y st at e wh en th e treatm en ts are u sed in p rop ortion s f * an d 1 – f *, wh ich are in d ep en d en t o f t h e co st s o f t reat m en t , c1 an d c2 , b u t d ep en d o n ly o n t h e sp o n t an eo u s recovery rates, r1 an d r2 , an d th e effectiven ess of treatm en t α. Th e steady state st o ck o f in fect io n is h igh er, n o t su rp risin gly, fo r t h e st rain wit h t h e h igh est m argin al treatm en t cost. However, th e n egative sh adow p rices (m 1 an d m 2 ) are th e sam e for each stock of in fection . Th is is becau se we assu m e th at th e ben efit s o f cu re an d t h e co n t agio n p aram et ers (β1 an d β2 ) are t h e sam e fo r each strain of in fection . For p oin ts on th e sin gu lar p ath du rin g th e tran sition to th e stead y state, th e op tim u m treatm en t p rop ortion s d ep en d on both econ om ic an d ep idem iological p aram eters. For oth er p oin ts, th e op tim u m strategy is to reach th e sin gu lar solu tion as fast as p ossible by settin g f = 0 or 1, as req u ired. Th e resu ltin g p ath is con ven tion ally kn own as th e m ost rap id ap p roach p ath . In sp ect io n o f t h e cu rren t valu e Ham ilt o n ian (Eq u at io n 10) warn s u s o f t h is case becau se it is lin ear in th e con trol variable f. Th e solu tion to th e op tim ization p roblem was su bstan tially sim p lified by assu m in g t h at every in fect ed p erso n received so m e fo rm o f t reat m en t . Th is m ay be u n realistic. Ten s of m illion s of p eop le in th e Un ited States today h ave n o h ealth in su ran ce, an d som e fraction of th em will go u n treated if in fected. We also assu m ed t h at , ap art fro m a u n ifo rm d isco u n t fact o r, go o d h ealt h is valu ed u n iform ly across in d ivid u als. If th is assu m p tion is m od ified , th e op tim u m solu tion m ay be su ch th at som e p eop le are d en ied treatm en t tod ay to treat th ose willin g or able to p ay m ore tom orrow. Ou r an alysis assu m ed th at p at ien t s are n o t given an t ib io t ic co ckt ails m ad e u p o f m o re t h an o n e d ru g. Th is assu m p tion m ay ru le ou t strategies th at are su p erior to th ose exam in ed h ere. Fin ally, both d ru gs were assu m ed to be available at an y tim e, th u s p reclu din g con sideration of op tim al cyclin g.

References Ben h abib, J., an d K. Nish im u ra. 1979. Th e Hop f Bifu rcation an d th e Existen ce an d Stability of Closed Orbits in Mu ltisector Mod els of Op tim al Econ om ic Growth . Journal of Econom ic Theory 27: 421–44.

Chapter 2: Using Antibiotics When Resistance Is Renewable • 55 Bon h oeffer, S., M. Lip sitch , an d B. Levin . 1997. Evalu atin g Treatm en t Protocols to Preven t An tibiotic Resistan ce. Proceedings of the National Academ y of Sciences of the USA 94: 12106–11. Brown , G., an d D.F. Layton . 1996. Resistan ce Econ om ics: Social Cost an d th e Evolu tion of An tibiotic Resistan ce. Environm ent and Developm ent Econom ics 1(3): 349–55. Bryso n , V., an d W. Szyb alski. 1955. Micro b ial Dru g Resist an ce. Advanced Genetics 7: 1–46. Garrett, L. 1994. The Com ing Plague: Newly Em erging Diseases in a W orld Out of Balance. New York: Pen gu in Books. In stitu te of Med icin e. 1992. Em erging Infections: Microbial Threats to Health in the United States. Wash in gton , DC: Nation al Academ y Press. Kerm ack, W.O., an d A.G. McKen d rick. 1927. A Con tribu tion to th e Math em atical Th eory of Ep idem ics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathem atical and Physical Character 115(772): 700–21. Laxm in arayan , R. 1999. Econ om ics of An tibiotic Resistan ce. Doctoral dissertation . Seattle, WA: Un iversity of Wash in gton . Laxm in arayan , R., an d G.M. Brown . 2001. Econ om ics of An tibiotic Resistan ce: A Th eory of Op tim al Use. Journal of Environm ental Econom ics and Managem ent 42(2): 183–206. Leon ard , D., an d N. Van Lon g. 1992. Optim al Control Theory and Static Optim ization in Econom ics. Cam bridge, U.K.: Cam bridge Un iversity Press. Levy, S.B. 1998. Th e Ch allen ge o f An t ib io t ic Resist an ce. Scientific Am erican 278(3): 46–53. Massad, E., S. Lu n dberg, an d H.M. Yan g. 1993. Modelin g an d Sim u latin g th e Evolu tion o f Resist an ce again st An t ib io t ics. International Journal of Biom edical Com puting 33: 65–81. McCaig, L.F., an d J. M. Hu gh es. 1995. Tren ds in An tim icrobial Dru g Prescribin g Am on g Office-Based Ph ysician s in th e Un ited States. Journal of the Am erican Medical Association 273(3): 214–19. McGowan , J.E., Jr. 1983. An tim icrobial Resistan ce in Hosp ital Organ ism s an d Its Relation to An tibiotic Use. Reviews of Infectious Diseases 5(6): 1033–48. Ryder, H.E., Jr., an d G.M. Heal. 1973. Op tim al Growth with In tertem p orally Dep en den t Preferen ces. Review of Econom ic Studies 40: 1–31. Skiba, A.K. 1978. Op tim al Growth with a Con vex–Con cave Produ ction Fu n ction . Econom etrica 46(3): 527–39. Tep p er, B.S. 1969. Microbial Resistan ce to Dru gs. In Biology of Population: The Biological Basis of Public Health, edited by B.K. Sladen an d F.B. Ban g. New York: Am erican Elsevier Pu blish in g Co.

Appendix Eq u ation s 14a an d 14b can be written as follows: I˙1 + β(m 1 I1 + m 2 I 2 ) I1 I˙ m˙ 2 = ρm 2 + A − m 2 2 + β(m 1 I1 + m 2 I 2 ) I2

m˙ 1 = ρm 1 + A − m 1

(A1)

56 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Becau se d(m i Ii )/ dt = m˙ i Ii + m i I˙i, th e eq u ation s for Eq u ation A1 can be written d (m 1 I1 )

[ [

]

= ρ m 1 + A + β(m 1 I1 + m 2 I 2 ) I1 dt d( m 2 I 2 ) = ρ m 2 + A + β(m 1 I1 + m 2 I 2 ) I 2 dt

(A2)

]

Su btractin g yields d (m 2 I 2 − m 1 I1 ) dt

[

] ( I2 − I1 )

= ρ(m 2 I 2 − m 1 I1 ) + A + β(m 1 I1 + m 2 I 2 )

(A3)

Interior Solutions

Con sid er a p ath for wh ich th e switch in g eq u ality in Eq u ation 12 h old s con tin u ou sly. With in th is segm en t, m 2 I 2 − m 1 I1 = −

(c2 − c1 ) I

(A4a)

α

Becau se th is eq u ality h old s th rou gh ou t th e segm en t, we can d ifferen tiate to obtain d (m 2 I 2 − m 1 I1 ) −(c2 − c1 ) I˙ = α dt Usin g Eq u ation 8, it follows from Eq u ation A1 to Eq u ation A3 th at ρ(c2 − c1 ) I

[

]

+ A + β (m 1 I1 + m 2 I 2 ) ( I 2 − I1 ) α ⎛c −c ⎞ = −⎜ 2 1 ⎟ −β( I − I * ) I + α(f − f * )( I 2 − I1 ) ⎝ α ⎠ −

[

]

(A4b)

Defin e A* = p + c1 f * + c2 (1 – f *) Th en A + (c2 – c1 )(f – f *) = A*, an d we can write Eq u ation A4b as follows −ρ(c2 − c1 ) I α

+ A * ( I 2 − I1 ) + β(m 1 I1 + m 2 I 2 )( I 2 − I1 ) −

Th u s m 1 I1 + m 2 I 2 = −

[

(c2 − c1 ) β I − I * I = 0 ) ( α

]⎞⎟

1 ⎛ * (c2 − c1 ) I ρ + β( I − I * ) ⎜A − β ⎜⎝ α( I 2 − I1 )

⎟ ⎠

(A5)

Chapter 2: Using Antibiotics When Resistance Is Renewable • 57

From Eq u ation s A4 an d A5 we obtain

2 m 1 I1 =

+(c2 − c1 ) I α

−

[

]⎞⎟

[

]

1 ⎛ * (c2 − c1 ) I ρ + β( I − I * ) ⎜A − β ⎜⎝ α ( I 2 − I1 )

⎟ ⎠

(c2 − c1 ) I ρ + β( I − I * ) − (c2 − c1 ) I 1 ⎛ − ⎜ A* − 2 m 2 I2 = α β ⎜⎝ α( I 2 − I1 )

(A6)

⎞ ⎟ ⎟ ⎠

From Eq u ation A5, n otin g th at I = I1 + I2 an d I˙ = I˙1 + I˙2 , it follows th at αβ

(c2 − c1 )

( I 2 − I1 )2

= ( I 2 − I1 )

2

d dt

d (m 1 I1 + m 2 I 2 ) dt

[

]I ⎞⎟

⎛ ρ + β( I − I * ) ⎜ ⎜ ( I 2 − I1 ) ⎝

[

⎟ ⎠

] [

][

= ( I 2 − I1 ) ρ + β( I − I * ) + βI I˙ − ρ + β( I − I * ) I I˙2 − I˙1

[ ]( [ ]) = [ρ + β( I − I * )](2 I I˙ − 2 I I˙ ) + βI ( I − I ) I˙

]

(A7)

= ρ + β( I − I * ) ( I 2 − I1 ) I˙ − I I˙2 − I˙1 + βI ( I 2 − I1 ) I˙ 2 1

1 2

2

1

⎛ I˙ I˙ ⎞ = −2 ρ + β( I − I * ) I1 I 2 ⎜ 2 − 1 ⎟ + βI ( I 2 − I1 ) I˙ ⎝ I 2 I1 ⎠

[

]

Th is can be written as follows αβ 2 d (m 1 I1 + m 2 I 2 ) I 2 − I1 ) ( dt (c2 − c1 )

[

] [

] = α[f − f * ]⎡⎢β( I − I ) I − 4 I I [ρ + β( I − I * )]⎤⎥ − β ( I ⎦ ⎣

= –4 α ρ + β( I − I * ) I1 I 2 ( f − f *) + βI ( I 2 − I1 ) − β( I − I * ) I + α(f − f * )( I 2 − I1 ) 2

2

1

2

1 2

2

− I1 )( I − I * ) I 2

(A8)

Notin g th at I = I1 + I2 an d u sin g Eq u ation s A2 an d A5, it can be sh own th at d (m 1 I1 + m 2 I 2 ) dt

= (ρ + βI )(m 1 I1 + m 2 I 2 ) + AI ρA * =− + ( A − A* )I β (ρ + βI )(c2 − c1 ) I ρ + β( I − I * ) + αβ( I 2 − I1 ) ρA * =− − (c2 − c1 )(f − f * ) I β (ρ + βI )(c2 − c1 ) I ρ + β( I − I * ) + αβ( I 2 − I1 )

[

]

[

]

(A9)

58 • Chapter 2: Using Antibiotics When Resistance Is Renewable

From Eq u ation s A5 an d A9 it follows th at

[

]

2 α(f − f * )⎛⎝ β( I 2 − I1 ) I − 4 I1 I 2 ρ + β( I − I * ) ⎞⎠ − β2 ( I 2 − I1 )( I − I * ) I 2

=

⎡ * ⎤ −αβ ( I2 − I1 )2 ⎢ ρAβ + (c2 − c1 )(f − f * ) I ⎥ c2 − c1 ⎣ ⎦ + ( I 2 − I1 ) I ρ + β( I − I * ) (ρ + βI )

[

]

wh ich can be written as

[

]

2 2 α(f − f * )⎛⎝ β( I 2 − I1 ) I − 2 I1 I 2 ρ + β( I − I * ) ⎞⎠

−αρA * ( I 2 − I1 )

2

=

(c2 − c1 )

[

]

+ ( I 2 − I1 ) I ρ + β( I − I * ) (ρ + βI ) + β2 ( I 2 − I1 )( I − I * ) I 2

(A10)

Becau se I = I1 + I2 , th is determ in es f as a fu n ction of I1 an d I2 . Determination of I *1 and I *2

Su p p ose f = f * an d I = I *. Eq u ation A10 is th en satisfied if eith er I1 = I2 = I */ 2 or −

αρA * ( I 2 − I1 ) c2 − c1

+ ρI * (ρ + βI * ) = 0

(A11)

Th e p oin t I1 = I2 = I */ 2 can n ot be a station ary solu tion to th e op tim ization p ro b lem b ecau se t h e asso ciat ed sh ad o w p rices m 1 an d m 2 are in fin it e (see Eq u ation A6). From Eq u ation A10, I 2 − I1 =

(ρ + βI * )(c2 − c1 ) I * αA *

Becau se I1 + I2 = I *, it follows th at I1 = I *1 an d I2 = I *2 wh ere 1 ⎡ (ρ + βI * )(c2 − c1 ) ⎤ ⎥I * ⎢1 − αA * 2 ⎢⎣ ⎥⎦ * ⎡ (ρ + βI )(c2 − c1 ) ⎤ I * 1 I 2* = ⎢1 + ⎥ αA * 2 ⎢⎣ ⎥⎦

I1* =

Becau se A* > 0, it follows th at I *2 > I *1 wh en c2 > c1 .

(A12)

Chapter 2: Using Antibiotics When Resistance Is Renewable • 59

Linear Approximation

Let g =f −f * z 1 = I1 − I1* (A13)

z 2 = I 2 − I 2* z = I − I* Th en I = z + I*

(

I 2 − I1 = (z 2 − z 1 ) + I 2* − I1*

)

(A14)

From Eq u ation s 7a an d 7b in th e text

(

)

(A15a)

(

)

(A15b)

dz 1 = ( −βz − αg ) I1* + z 1 dt

dz 2 = ( −βz + αg ) I 2* + z 2 dt

To in vestigate th e beh avior of (I 1 , I2 ) arou n d (I *1 , I *2 ), we in vestigate th e beh avior of (z 1, z 2 ) aroun d (0, 0). To th is en d, we express th e righ t-h an d side of th e above equation s as lin ear fun ction s of z 1 an d z 2 , ign orin g h igh er-order term s. Let u s first co n sid er Eq u at io n A10. Usin g Eq u at io n s A13 an d A14 an d eq u atin g first-order term s, we obtain

(

)

2 ⎛ ⎞ 2 αg ⎜ β I 2* − I1* I * −2 ρI1* I 2* ⎟ ⎝ ⎠

=−

(

2 αρA * (z 2 − z 1 ) I 2* − I1*

c2 − c1 + (z 2 − z 1 ) I * ρ(ρ + βI * )

)

( ) + ( I * − I * ) I * βz (ρ + βI * ) + ( I * − I * ) I * ρβz + β ( I * − I * )zI * ⎛ −2 αA * I * − I * ( ) + I * (ρ + βI * )⎞⎟ + z ( I * − I* )(ρ + βI * )(ρ + 2 βI *) = (z − z )ρ⎜ + I 2* − I1* z ρ(ρ + βI * ) 2

1

2

1

2

2

2

2

2

1

⎜ ⎝

1

1

(c2 − c1 )

(

)

⎟ ⎠

2

1

= −(z 2 − z 1 )ρ(ρ + βI * ) I * + z I 2* − I1* (ρ + βI * )(ρ + 2 βI * )

(A16)

60 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Usin g Eq u ation A16 we can elim in ate g from Eq u ation s A15a an d A15b. Let

)

(

2 ⎛ ⎞ J = 2 ⎜ β I 2* − I1* I * − 2 ρI1* I 2* ⎟ ⎝ ⎠

K= L=

−ρ(ρ + βI * ) I *

(

J

)

I 2* − I1* (ρ + βI * )(ρ + 2 βI * ) J

Th en Eq u ation A16 can be written as αg = K(z 2 − z 1 ) + Lz

(A17)

Hen ce, lin earizin g Eq u ation A15a, we obtain

[ ] = [ −( L + β)z − K(z − z )]I* = [ −( L + β)(z + z ) − K(z − z )]I * = [[( K − L) − β]z − [( K + L) + β]z ]I *

dz1 = −βz − K(z 2 − z 1 ) − Lz I1* dt 2

1

1

(A18a)

1

2

2

1

1

1

2

1

Likewise, from Eq u ation A15b, we obtain dz 2 = −βz + K(z 2 − z 1 ) + Lz I 2* dt

[ ] = [( L − β)z + K(z − z )]I * = [( L − β)(z + z ) + K(z − z )]I * = [ −[( K − L) + β]z + [( K + L) − β]z ]I * 2

1

1

2

2

2

1

1

(A18b)

2

2

2

In m atrix n otation ⎡ dz 1 ⎤ ⎢ dt ⎥ ⎡z 1 ⎤ ⎥ = D⎢ ⎥ ⎢ ⎢ dz 2 ⎥ ⎣z 2 ⎦ ⎢⎣ dt ⎥⎦ wh ere

[

]

[( K + L) + β]I * ⎤⎥ ] [( K + L) − β]I * ⎥⎦

⎡ ( K − L) − β I * − 1 D=⎢ ⎢− ( K − L + β I * ) 2 ⎣

[

1

2

Note th at D = −4 βKI1* I 2*

(

)

TrD = L I 2* − I1* + ( K − β) I *

(A19)

Chapter 2: Using Antibiotics When Resistance Is Renewable • 61

Th e eigen valu es of D satisfy th e ch aracteristic eq u ation λ2 − λtrD + D = 0 Hen ce th e roots λ1 an d λ2 are given by trD ±

λi =

(trD )2 − 4 D 2

From Eq u ation A19, it follows th at

( ) = ( I * − I * ) (ρ + βI * )(ρ + 2 βI * )

JtrD = I 2* − I1* JL + I * JK − βI * J 2

2

1

− ρI * (ρ + βI * ) 2

(

)

2 ⎤ ⎡ − 2 βI * ⎢β I 2* − I1* I * −2 ρI1* I 2* ⎥ ⎦ ⎣ 2⎤ 2 ⎡ = I 2* − I1* ρ2 + 3βρI * − ρI * ⎢ρI * +β I 2* − I1* ⎥ ⎦ ⎣ 2 2 ⎡ ⎤ = ρ2 ⎢ I 2* − I1* − I *2 ⎥ + 2 βρ I 2* − I1* I * ⎣ ⎦

)[

(

(

(

]

(

)

(

)

)

)

2

= −4 I1* I 2*ρ2 + 2 βρ I 2* − I1* I *

(

)

2 ⎤ ⎡ = 2 ρ⎢β I 2* − I1* I * − 2 ρI1* I 2* ⎥ ⎦ ⎣ = ρJ

Th u s trD = ρ > 0

(A20)

For sm all ρ, it is clear from Eq u ation A12 th at J > 0, an d h en ce K < 0, an d |D| > 0. Moreover, (trD)2 is of order ρ2 an d |D| is of order ρ. Th u s, for sm all ρ, th e discrim in an t (trD)2 – 4|D| is ap p roxim ately eq u al to –4|D| an d is th erefore n egative. Th is im p lies th at th e roots λ1 an d λ2 are com p lex con ju gates of th e form θ + φ i an d θ – φ i wh ere 2θ = tr D = ρ > 0. Th u s, in th e vicin ity of (I *1 , I *2 ), every p ath is an exp losive sp iral. Th e sm allest d isp lacem en t from th is stead y state will gen erate a sp iral m otion ou tward.

62 • Chapter 2: Using Antibiotics When Resistance Is Renewable

Notes 1. Often op tim ism abou t th e h ealin g p ower of an tibiotics is m isgu id ed . Ph ysician s ro u t in ely p rescribe an t ibio t ics fo r sit u at io n s in wh ich an t ibio t ics can n o t be effect ive. Levy rep orts circu m stan ces wh en m ore th an 80% of th e p h ysician s sam p led h ad p rescribed an tibiotics “again st th eir better ju d gm en t.” On e-th ird of th e an n u al ou tp atien t p rescrip tion s for an tibiotics are believed to be u n n ecessary (Levy 1998). 2. Dru gs are, in gen eral, d ifferen tially effective again st d ifferen t typ es of in fection . O n e d ru g m ay b e q u it e effect ive again st cert ain t yp es o f in fect io n s b u t in effect ive again st oth er in fection s. We con sid er a h igh ly sim p lified case in wh ich th ere on ly two dru gs an d two varian ts of a certain in fection . Each dru g is effective again st on e varian t bu t totally in effective again st th e oth er varian t. Th is assu m p tion sim p lifies th e exp osition with ou t sacrificin g an yth in g fu n d am en tal. Ou r an alysis can be easily m od ified to cover th e m ore realistic case in wh ich each dru g is to som e exten t effective again st both varian ts of th e in fection . 3. See Leon ard an d Van Lon g (1992, 294–5). 4. Th ese d ifficu lties are illu strated in Skiba (1978), wh o p resen ts a m od el in wh ich th ere are m an y differen t solu tion s th at satisfy th e Ham ilton ian con dition s an d in wh ich an op tim al p ath m ay be a sp iral. Ryd er an d Heal (1973) an d Ben h abib an d Nish im u ra (1979) p resen t m odels in wh ich op tim al p ath s m ay h ave a lim it cycle.

Chapter 3

Value of Treatment Heterogeneity for Infectious Diseases Ramanan Laxminarayan and M artin L. Weitzman

Treatment homogeneity is valued in the medical profession. Uniform treatment guidelines are often used to ensure that all physicians prescribe a safe, efficacious, and cost-effective drug in treating a m edical condition. How ever, such a policy may be undesirable when drug resistance is endogenous. In the case of infectious diseases, selection pressure im posed by the use of any single drug (antibiotic, antiviral, or antimalarial) sooner or later leads to the evolution of resistance (by bacteria, viruses, or parasites) to that drug. In this chapter, we show that a “ mixed strategy” of multiple drug use is generally desirable and analytically characterize the conditions under which this strategy is optimal.

rom an econ om ist’s p ersp ective, th e treatm en t of in fectiou s diseases is fu n d am en tally d ifferen t from th e treatm en t of n on in fectiou s con d ition s su ch as arth ritis, cardiovascu lar disease, or can cer. Un like th e case of n on in fectiou s or ch ron ic diseases, two social extern alities—on e p ositive an d th e oth er n egat ive—in h eren t ly ch aract erize t h e t reat m en t o f in fect io u s d iseases. Take t h e case of an tibiotics (alth ou gh th e situ ation can be gen eralized to an tivirals an d an t im alarials as well). O n t h e o n e h an d , an t ib io t ic t reat m en t cu res t h e p atien t, th ereby p reven tin g th e d isease from bein g tran sm itted to oth er in d ivid u als. On th e oth er h an d , d ru g treatm en t selects in favor of h arm fu l m u tation s or organ ism s th at are resistan t to th e dru g, in creasin g th e likelih ood th at th e dru g will be less effective in th e fu tu re. Becau se th e in dividu al p atien t fails to take in to accou n t eith er of th ese extern alities wh en d ecid in g to seek treatm en t , a Pigo vian t ax o r su b sid y o f t reat m en t co u ld in p rin cip le co rrect fo r

F

• 63 •

64 • Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases

extern ality (dep en din g on wh eth er its im p act on overall social welfare is n egative or p ositive). 1 Th e extern ality p roblem im p licit in th e decision on wh eth er to seek treatm en t for in fectiou s diseases h as been well docu m en ted in earlier work (Ph ilip so n 2000). In t h is ch ap t er, we ext en d t h is lit erat u re t o lo o k at ext ern alit ies arisin g from th e choice of d ru g treatm en t on ce th e d ecision to treat h as been m ad e. Th e d egree of h om ogen eity in th e ch oice of d ru g treatm en ts for in fect io u s d iseases is rem arkab le. Fo r in st an ce, in 1997, n early 60 p ercen t o f all cases of acu te ear in fection s (a com m on con d ition in you n g ch ild ren ) in th e Un ited States were treated with am oxicillin . In fact, am oxicillin accou n ted for 35 p ercen t of all an tibiotics u sed by p h ysician s, an d th e five m ost com m on ly u sed an tibiotics u sed accou n ted for 72% of all an tibiotics u sed by p h ysician s in th is cou n try. Th is d egree of h om ogen eity h as been witn essed even in th e develop in g world. In m ost African cou n tries, ch loroq u in e was th e m ost com m o n ly u sed d ru g t o t reat m alaria fo r m an y years. In fact , in so m e m alariaen d em ic co u n t ries, it was even m ixed in wit h co m m o n salt t o en su re wid esp read an d u n iform m alarial p rop h ylaxis. Th ere are reason s wh y u n iform ity of treatm en t is freq u en tly en cou n tered . In m an y d evelop in g cou n tries, all d ru g p rocu rem en t is cen tralized an d con t ro lled b y t h e go vern m en t . Th erefo re, t h e go vern m en t d et erm in es wh ich d ru gs sh o u ld b e even allo wed in t o t h e co u n t ry, t h ereb y in flu en cin g t h e ch oice of treatm en t. In develop ed cou n tries su ch as th e Un ited States, clin ical t reat m en t gu id elin es fo r co m m u n it y-level in fect io n s are t yp ically issu ed by n ation al p u blic h ealth bod ies, su ch as th e Am erican Association of Ped iatrics an d th e Cen ters for Disease Con trol an d Preven tion . In ad d ition , in d ivid u al h osp itals both set an d follow treatm en t gu id elin es on th e basis of th e ad vice of th e h osp ital’s in fection -con trol com m ittee. Th e ch oice of dru g treatm en t is, all oth er th in gs bein g eq u al, often m ad e on th e basis of th e p rin cip le kn own as cost-effectiven ess (Wein stein an d Fin eberg 1980). In sim p le term s, th e dru g wit h t h e sm allest rat io o f t reat m en t co st t o effect iven ess is t h e d ru g o f first ch o ice fo r all p at ien t s. In ad d it io n , in d ivid u al p at ien t s act in g in t h eir o wn self-in terest ten d to p refer th e m ost cost-effective dru g op tion . Th ere are go o d reaso n s wh y su ch h o m o gen eit y is act ively p ro m o t ed am o n g t h e m ed ical p ro fessio n . Clin ical gu id elin es an d n at io n al t reat m en t p o licy reco m m en d at io n s p ro vid e gu id an ce t o in d ivid u al p h ysician s o n wh ich d ru gs are to be u sed for first-lin e treatm en t, wh ich d ru gs are to be u sed fo r seco n d -lin e t reat m en t sh o u ld t h e first -lin e t reat m en t fail, an d wh ich d ru gs are to be u sed in case of com p lication s. By sp ecifyin g treatm en t in th e form of sim p le u n iform d ecision ru les, n ation al p olicies are p articu larly u sefu l in en su rin g safe an d accu rate m ed ical treatm en t wh ile relievin g th e p h ysician of som e of th e bu rd en of m ed ical d ecision m akin g. 2 Followin g u n iform gu id elin es red u ces th e liability associated with m ed ical error for p h ysician s.

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 65

Ho wever, as t h is ch ap t er d em o n st rat es, sign ifican t d isad van t ages m ay b e associated with p rom otin g a sin gle d ru g as th e first-lin e treatm en t for a given con d ition . Th e st art in g p o in t o f t h is ch ap t er is t h e o b servat io n t h at , t o t h e ext en t th at m ost p atien ts in a region or cou n try are treated with th e sam e dru g for a given in fect io u s d isease, t h e u se o f a sin gle d ru g p laces “excessively” h igh select io n p ressu re o n o rgan ism s t h at are su scep t ib le t o t h at p art icu lar d ru g an d in creases th e likelih ood th at a resistan t strain will evolve an d p roliferate. As resist an ce t o t h e reco m m en d ed first -lin e d ru g b u ild s u p , t h at d ru g is rep laced by an altern ative th at is u sed u n til resistan ce to th is secon d dru g also in creases, an d so on in su ccession . Th e m ain m essage of th is ch ap ter is th at th e op tim al solu tion m ay th erefore be to u se n ot ju st a single dru g th rou gh ou t th e p op u lation as first-lin e agen t, bu t to p rescribe a variety of dru gs, ran dom ized over p atien ts, to en su re in ordin ate selection p ressu re is n ot p laced on an y sin gle dru g or class of dru gs. Th is ch ap ter also in directly addresses th e q u estion of wh eth er m ore exp en sive, h igh ly effective dru gs sh ou ld be kep t on th e sidelin es for u se in th e even t of seriou s, resistan t in fection s or wh eth er th ey sh ou ld be d ep loyed alon gsid e less effective agen ts on th e fron tlin es again st in fectiou s d iseases. Th e ben efit of h avin g an effective d ru g available as backu p sh ou ld all else fail can n ot be d isregard ed , n o r sh o u ld t h e m o re effect ive d ru g’s abilit y t o relieve select io n p ressu re o n t h e first -lin e d ru g b e ign o red (wh en t h e effect ive d ru g is also u sed ).3 W h at, th en , is th e op tim al solu tion ? Th e an swer, as it often h ap p en s, lies som ewh ere between th e black an d th e wh ite—it m ay be to u se m ore effective dru gs in both roles. Th e p ro blem is n o t d efin in g t h e ext en t t o wh ich t h e m o re effect ive d ru g sh ou ld be u sed bu t rath er describin g a stan dard p olicy based on gu idelin es for first-lin e treatm en t in th is situ ation . As th e sim p le m od el of th is ch ap ter will sh ow, it is gen erally m ore d esirable to u se less exp en sive agen ts on a greater fract io n o f p at ien t s an d m o re exp en sive agen t s o n a sm aller fract io n —righ t fro m t h e begin n in g—all else bein g eq u al. In t h is sen se, t h e co n cep t o f u n ifo rm gu id elin es m ay b e fu n d am en t ally flawed in t h e p resen ce o f en d o gen ou sly gen erated resistan ce. Of cou rse, it is d ifficu lt to sp ecify th ese “m ixed p olicy” fraction s in th e form of a stan d ard , u n iform , gu id elin es-based p olicy. For in stan ce, in a geograp h ically isolated area, it m ay be op tim al for th e sin gle fam ily p ractition er servin g th ese areas to p rescribe a wid e array of an tibiotics (on ly in cases in wh ich th ey are req u ired, of cou rse) so th at selection p ressu re on n o sin gle an tibiotic is allowed to bu ild u p . Clearly, th ere are p ractical difficu lties of doin g so. Th e sin gle m ost im p ortan t difficu lty is th at it m akes sen se fro m t h e in d ivid u al p h ysician ’s p ersp ect ive t o d o wh at everyo n e else in t h e cou n try is doin g an d to p rescribe th e m ost com m on ly u sed an tibiotic. Herein lies th e in trin sic extern ality issu e related to d ru g p rescribin g. Ph ysician s h ave

66 • Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases

an in cen tive to p rescribe in con cordan ce with th e rest of th e m edical com m u n ity in th e in terest of, if n oth in g else, red u cin g th eir liability in m alp ractice claim s. Of cou rse p atien ts are p u t at ease with a sin gle, u n ified decisive ch oice. Bu t su ch con cordan ce in creases th e selective p ressu re on th e dru g of com m on ch oice. Gu id elin es th at p ick ou t a sin gle d ru g for su ch targeted , n ation wid e u se m ay th erefore be exacerbatin g selection p ressu re on th at sin gle d ru g to a degree th at is socially u n desirable. Th e em ph asis placed on u sin g a sin gle dru g m ay occu r even in th e absen ce of u n iform treatm en t gu idelin es. Decen tralized decision m akers (i.e., in dividu al ph ysician s or patien ts) m ay n ot take in to accou n t th e risk in volved in prescribin g a sin gle dru g repeatedly for a com m on con dition su ch as an ear in fection . Th e in d ivid u al p h ysician ’s en co u ragem en t o f t h e d evelo p m en t o f resist an t organ ism s globally wh en ever h e or sh e d ecid es to u se th at d ru g rep resen ts a n egative extern ality. Th is extern ality rem ain s u n corrected becau se th e in dividu al p h ysician bears on ly a n egligible fraction of th e total bu rden of resistan ce th at h e or sh e m ay be placin g on oth ers with every treatm en t decision . Th e problem of excessive selection pressu re arisin g from th e u se of a sin gle d ru g occu rs n ot on ly in cou n tries wh ere p h ysician s are th e p rim ary sou rce of treatm en ts but also in coun tries wh ere th e disease is h om e treated, as is th e case with m alaria in Africa. Here too, p atien ts wou ld p refer to be treated with th e m ost cost-effective drug available to th em . However, from a societal perspective, it m ay be op tim al to u se oth er dru gs th at are n ot cost-effective from th e in divid u al p atien t’s p ersp ective. Th e q u estion th en is h ow p atien ts m igh t be p ersuaded to use th ese oth er drugs even if it is n ot in th eir self-in terest to do so. On e m igh t argu e th at th e logical exten sion of th e strategy to treat differen t p at ien t s wit h d ifferen t d ru gs is t o t reat in d ivid u al p at ien t s wit h m o re t h an o n e d ru g. Su ch a st rat egy is alread y st an d ard p ract ice fo r t h e t reat m en t o f h u m an im m u n od eficien cy viru s an d tu bercu losis. In each of th ese cases, th e u n d erlyin g p rin cip le is t h at t h e p ro b ab ilit y o f a m u lt igen ic resist an ce in a m icrobe is m u ch lower th an th e p robability of a gen etic m u tation con ferrin g resistan ce to on e dru g. Usin g two dru gs en su res th at each dru g exercises a p rotective effect over th e oth er. However, with th e argu m en t u sed for d ru g com bin ation s, resistan ce to a dru g is exogenous. Th e reason in g we follow in develop in g th e argu m en t for u sin g a wider variety of dru gs as first-lin e agen ts ru n s alo n g sim ilar lin es, as d o o u r p o licy p rescrip t io n s, excep t t h at in o u r case, dru g resistan ce develop s endogenously as an evolu tion ary reaction to excessive u sage. Th e solu tion to th e p roblem of en d ogen ou sly growin g d ru g resistan ce th en m ay be to exten d th e com bin ation treatm en t con cep t to a com m u n ity level. Fu rt h er, ro u t in ely u sin g t wo an t ib io t ics o n a sin gle p at ien t m ay b e u n d esirable for m ed ical reason s. 4 Th e altern ative is to treat d ifferen t p atien ts su fferin g from th e sam e in fectiou s disease with differen t dru gs, a p rescrip tion t h at is d ifficu lt t o im p lem en t u sin g a gu id elin es-based p o licy. In an y even t ,

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 67

th is ch ap ter con cen trates on th is case—of treatin g d ifferen t p atien ts with th e sam e in fectiou s d isease with d ifferen t d ru gs—in th e con text of en d ogen ou sly in du ced disease. We fu lly recogn ize th at to sim p lify th e com p lex task of m ed ical d ecision m akin g to fit in to th e bou n d aries of th eoretical econ om ic an alysis is to issu e an o p en in vit at io n fo r crit icism . Th e co n st rain t s im p o sed b y t h e d egree o f abstraction in develop in g th e argu m en ts in th is ch ap ter—or th e sp ecific ap p licab ilit y o f t h e resu lt s—can n o t b e o verst at ed . Th is ch ap t er ad d resses o n ly p ro b lem s asso ciat ed wit h gu id elin es t h at reco m m en d o n e kin d o f d ru g p er p atien t as first-lin e th erap y an d does n ot refer to gu idelin es th at p rom ote ju diciou s d ru g u se, safe d oses, overall safety, an d so forth . We are n ot su ggestin g th e u se of com bin ation s of d ru gs on in d ivid u al p atien ts bu t rath er a strategy o f t reat in g d ifferen t p at ien t s wit h d ifferen t d ru gs. Th is p rin cip le, kn o wn as an tibiotic h eterogen eity, is begin n in g to en ter th e set of op tion s bein g con sidered by m edical p rofession als. However, it ru n s fu n dam en tally cou n ter to th e lo n g-h eld b elief in t h e m ed ical p ro fessio n o f t h e exist en ce o f a “b est t reat m en t” for a disease an d th e deep ly felt n eed for u n iform ity in dru g treatm en t. Gu id elin es t h at p ro m o t e u n ifo rm it y in t h e ch o ice o f d ru g fo r t reat in g in fectiou s diseases m ay be in h eren tly self-defeatin g becau se u sin g th e greatest variety of dru gs decreases th e likelih ood th at m icrobes will acq u ire an d m ain tain resistan ce to an y sin gle class of dru gs. Th e sin gle m ost im p ortan t m essage of th is ch ap ter is th at, from a societal p ersp ective, it m ay even be desirable to t reat so m e p at ien t s wit h m o re exp en sive d ru gs even wh ile it is in d ivid u ally su bo p t im al t o d o so . Th e p recise fract io n o f p at ien t s t h at sh o u ld be t reat ed with th ese m ore effective dru gs can be determ in ed u sin g fairly straigh tforward criteria, wh ich we dem on strate in th e section s th at follow.

M odel of Endogenous Resistance Th is section p resen ts ou r “core m od el” of en d ogen ou sly gen erated resistan ce to dru g th erap ies. It goes with ou t sayin g th at su ch a m odel m u st of n ecessity be form u lated at a very h igh level of abstraction . Neverth eless, as will becom e clear, it is little sh ort of am azin g h ow m u ch an alytical in sigh t em erges from even su ch a sim p le form u lation . Let th ere be available m p ossible dru g th erap ies (in dexed i = 1,2,…,m ), each of wh ich m ay be u sed to cou n ter som e p articu lar d isease. For an alytical sim p licit y, we im agin e t h at everyo n e in t h e p o p u lat io n is t reat ed wit h exact ly on e com p lete treatm en t d ose of on e of th e d ru gs. Critical to ou r an alysis are th e ideas th at we are allowin g a “m ixed strategy” of differen t dru gs to be u sed o n d ifferen t p eo p le an d t h at t h e m o d el sh o u ld t ell u s wh en t h is st rat egy is op tim al rath er th an exclu d in g it a p riori. Let x i rep resen t th e fraction of th e p op u lation treated with dru g i, wh ere

68 • Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases m

∑ xi =1

(1)

0 ≤ xi ≤ 1

(2)

i=1

an d

Let th e cost (in clu sive of c n on -d ru g treatm en t costs) of d ru g i (p er u n it of p op u lation ) be given by ci > 0

(3)

Resistan ce to dru g i by th e u n derlyin g p ath ogen is assu m ed to be a Poisson p rocess with in ten sity p aram eter θi > 0

(4)

wh ere θi is a (very sm all-valu ed ) p aram eter rep resen tin g th e p robability th at resistan ce to d ru g i will d evelop en d ogen ou sly (p resu m ably by m u tation ) in th e p ath ogen in an y on e p erson treated by th at dru g. (Here we refer to endogenously acquired resistan ce, wh ich develop s sp on tan eou sly by Poisson m u tation in th e p ath ogen in a p atien ts bein g treated u sin g th e dru g, as op p osed to epidem ic resist an ce b y t h e p at h o gen , wh ich resu lt s fro m in fect io n b y a d ru gresistan t p ath ogen from an oth er p erson treated by th at sam e dru g.) W h en a fract io n x i are t reat ed b y d ru g i, t h e p ro b ab ilit y t h at a resist an t strain em erges is (to a first-order ap p roxim ation ) θi xi

(5)

If su ch a resistan t strain em erges, it will p u t at risk of ep id em ic resistan ce all x i p eop le treated by dru g i. Let th e social loss per person of bein g p laced “at risk” by resistan ce d evelop in g in th e d ru g by wh ich th ey are bein g treated be den oted L >0

(6)

Th en , co m b in in g Eq u at io n s 5 wit h 6, t h e exp ect ed so cial lo ss per person o f bein g p u t “at risk” by dru g i is L[θi x i ]

(7)

wh ereas t h e total exp ect ed so cial lo ss fro m b ein g p u t “at risk” b y b ein g exp osed to p ath ogen s th at are resistan t to dru g i is

[ Lxi ][θi x i ]

(8)

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 69

In o t h er wo rd s, we assu m e t h at it t akes t im e t o ch an ge t h ese t reat m en t fraction s an d th at in d ivid u als wh o con tin u e to be treated with d ru g i after a resistan t strain h as em erged are at risk for treatm en t failu re. Let Ni ≡

1

(9)

θi

b e t h e average n u m b er o f p eo p le t h at can b e exp ect ed t o u se d ru g i b efo re resist an ce set s in . Th en t h e t o t al exp ect ed so cial lo ss Exp ressio n 8 can b e rewritten as Lx i2

(10)

Ni Th e optim al drug com bination problem in th is m odel is on e of m in im izin g m

⎡

L

⎤

∑ ⎢⎣ci x i + N i x i2 ⎥⎦

(11)

i =1

su bject to m

∑ xi = 1

(12)

i =1

an d 0 ≤ xi ≤ 1

(13)

Characterizing the Optimal Drug Combination Th e effectiven ess of all dru gs is assu m ed to be iden tical. With ou t loss of gen erality, su p p ose th e dru gs are arrayed from least to m ost exp en sive, so th at c1 ≤ c2 ≤  ≤ cn

(14)

It is q u ite obviou s th at it will n ever be op tim al to u se (to p rescribe p ositive am ou n ts of) a m ore exp en sive dru g wh ile n ot u sin g (p rescribe zero am ou n t of) a less exp en sive d ru g. To see beyon d th is wh at is th e form of an op tim al p olicy, an d wh at it dep en ds on , let u s begin by an alyzin g in fu ll detail th e situ ation for two dru gs (m = 2). Th ere are t wo p o ssible so lu t io n s—an in t erio r so lu t io n an d a co rn er so lu tion of th e form x 1 = 1, x 2 = 0. Th e latter corresp on ds to th e n ecessary an d su fficien t first-order corn er con dition c2 ≥ c1 +

2L N1

(15)

70 • Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases

From Eq u ation 15, we m ay say th at a “m ixed” in terior solu tion u sin g both dru gs is op tim al if an d on ly if th e followin g con dition is m et:

(c2 − c1 )N 1 ≤ 2 L

(16)

W h at is th e in tu ition beh in d Con d ition 16? Th e p recise econ om ic con d it io n u n d er wh ich it is o p t im al t o in clu d e d ru g 2 in o u r m en u is t h at t h e in crease in co st asso ciat ed wit h t reat in g wit h t h e m o re exp en sive d ru g in p lace o f t h e ch eap er d ru g is less t h an o r eq u al t o t h e exp ect ed ben efit fro m u sin g two dru gs in p lace of on e. Th e term on th e righ t-h an d side, 2L/ N 1 , rep resen ts th e m argin al exp ected social cost p er p erson associated with treatin g an oth er p atien t with d ru g 1. As lon g as th e in creased treatm en t cost of u sin g d ru g 2 in p lace of d ru g 1 is less th an th e exp ected in crease in cost associated wit h en d o gen o u sly gen erat ed resist an ce if d ru g 1 were t o b e u sed , it m akes econ om ic sen se to u se dru g 2. Next , co n sid er t h e m o re gen eral case in wh ich m is an arb it rary p o sit ive in teger (larger th an two). Th e first-order con dition for a fu lly in terior solu tion is th e existen ce of a p ositive m u ltip lier λ, wh ich is d u al to Eq u ation 12, th at satisfies for p ositive x i th e con dition s ci +

2 Lx i =λ Ni

(17)

Th e m u ltip lier λ can th erefore be in terp reted as th e “u ser cost” of an y dru g bein g u sed in th e m en u . Th erefore, for an y dru g i th at is bein g u sed, th e total u ser co st eq u als t h e su m o f t h e t reat m en t co st ci an d t h e resist an ce co st (2x i/ N i)L, in wh ich t h e resist an ce co st eq u als t h e m argin al p ro b ab ilit y o f in d u cin g a resist an t in fect io n wit h an o t h er t reat m en t m u lt ip lied b y L, t h e associated social cost of in d u cin g resistan ce in th e p op u lation . Alth ou gh th e treatm en t costs of dru gs in ou r op tim al m en u can vary greatly, th eir u ser cost is id en t ical. In o t h er wo rd s, if t wo d ru gs are in clu d ed in o u r o p t im al m en u an d on e costs less th an th e oth er, th en th e resistan ce cost of th e ch eap er dru g m u st exceed th at of th e m ore exp en sive dru g so th at th e u ser cost of th e two dru gs is iden tical. Th e resistan ce cost of a dru g is, of cou rse, a fu n ction of th e fraction of th e p op u lation bein g treated with th at dru g, an d a h igh treatm en t fraction im p lies a larger resistan ce cost. Th e ast u t e read er m ay h ave gu essed wh ere we are h ead ed . Th e o p t im al decision ru le is to u se th e lowest cost dru g(s) first, as stan dard econ om ic in tu ition wou ld d ictate. W h at is n ot so stan d ard , h owever, is th e form in wh ich th ese costs arise. In addition to th e treatm en t cost th at th e in dividu al p atien t faces, th ere is an ad d ition al cost associated with th e in creased p robability of d ru g resist an ce asso ciat ed wit h each u se o f t h e d ru g. Th is resist an ce co st is en d o gen o u sly d et erm in ed by t h e fract io n o f t h e in fect ed p o p u lat io n t h at is

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 71

ad m in ist ered t h e d ru g in q u est io n . Th erefo re, t h e o p t im al m en u d esign is su ch th at th e su m of treatm en t an d resistan ce costs of all dru gs on th e m en u is iden tical, th u s en su rin g th at som e dru gs m ay fin d th eir way in to th is m en u even if t h ey are n o t t h e least exp en sive fro m a t reat m en t co st p ersp ect ive. Makin g u se of Eq u ation 17, Con dition 12 can be rewritten as m

λ=

∑ ck N k k =1 m

2L

+

∑Nk k =1

m

∑N k

(18)

k =1

Th e n ext st ep is t o d et erm in e t h e o p t im al u ser co st fo r a given set o f d ru gs th at are available to th e social p lan n er (n ot ju st th ose th at will be in clu ded on t h e m en u ). Th e o p t im al u ser co st can be exp ressed as t h e su m o f t h e resist an ce p robability weigh ted average cost of all available dru gs an d th e exp ected m argin al cost of treatm en t failu re associated with an y sin gle treatm en t wh en all available dru gs are bein g u sed. Co m b in in g Eq u at io n s 18 an d 17, t h e “in t erio rn ess” co n d it io n x i > 0 is eq u ivalen t to th e con dition ci ≤ λ, or eq u ivalen tly, x i = (λ − ci)

Ni L

(19)

wh ich is t h e ap p ro p riat e gen eralizat io n o f Eq u at io n 16. Fro m an eco n o m ic p ersp ect ive, it is o p t im al t o in clu d e an y d ru g i in t h e m en u o f t h e d ru gs so lon g as th e cost of th e dru g is less th an or eq u al to th e ben ch m ark u ser cost λ. It is n ow in tu itively clear wh at is an easy-to-ap p ly m yop ic algorith m for determ in in g op tim al d ru g u se. Su p p ose by in d u ction it is kn own th at an op tim al solu tion in clu d es a p ositive u se of all d ru gs j wh ere j < i for som e i. Th e n ext q u estion to ask is wh eth er it is addition ally op tim al to u se dru g i at a p ositive level. Th e an swer is “yes” if an d on ly if

∑ (c i − c j ) N j < 2 L

(20)

jNk

(22)

In oth er words, th e valu e of N i by itself does n ot determ in e wh eth er a dru g will be in clu ded in an op tim al p rogram . However, N i does determ in e th e fract io n o f p at ien t s wh o sh o u ld b e t reat ed wit h d ru g i, as is d em o n st rat ed b y rewritin g Eq u ation 17 as xi = ( λ − ci)

Ni L

(23)

From Eq u ation s 17 an d 18, for an y two dru gs j an d k bein g u sed in p ositive am ou n ts, we can write xj xk

=

(2 L + ∑ ci N i − c j ∑ N i ) N j (2 L + ∑ ci N i − ck ∑ N i ) N k

(24)

We h ave alread y n o t ed t h at t h e p aram et er N i d o es n o t ever in vert t h e o rd er in w h ich a d ru g i is in clu d ed in t h e o verall d ru g m en u . H o w ever, fro m Eq u at io n 24, t h e average u sefu l lifet im e p aram et ers {N i} co u ld resu lt in a relat ively less co st -effect ive d ru g b ein g u sed o n a larger fract io n o f p at ien t s, su ch t h at x k > x j even w h ile ck > cj , so lo n g as N j is su fficien t ly larger t h an N k . Referrin g back to Exp ression 14, if on e were to follow th e tradition al m edical co st -effect iven ess crit erio n , o n e wo u ld first u se o n ly d ru g 1, t h en lat er switch to dru g 2 wh en resistan ce evolved to dru g 1, an d so on . However, m ovin g seq u en tially in strict order of in creasin g cost-effectiven ess ratios an d treatin g all p atien ts with th e sam e d ru g at th e sam e tim e can be m yop ically in effect ive wh en ever acco u n t is t aken o f t h e in escap ab le fact t h at im m u n it y is en dogen ou s—as we h ave ju st sh own . In fact, it is n ot even op tim al to u se th e m ost cost-effective d ru g on th e largest n u m ber of p atien ts. W h en resistan ce evo lves en d o gen o u sly, a p aram et er rep resen t in g t h e average n u m b er o f p atien ts wh o m u st be treated before resistan ce ap p ears determ in es (alon g with dru g costs) th e op tim al in ten sity of dru g u sage.

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 73

Discussion Th e extern ality problem associated with th e treatm en t of in fectiou s diseases— on e th at is related to a treatm en t’s d u al p rop erties of red u cin g con tagion an d lim itin g drug resistan ce—h as a reduced-form structure th at is extrem ely fam iliar to an y econ om ist. Extern alities are a com m on problem , wh eth er th ey are related to h igh way con gestion or air p ollu tion , an d cop iou s econ om ics p ap ers h ave dealt with th ese issues. Always, a n egative extern ality calls for usin g less of th e privately optim al good an d m ore of th e privately m ore expen sive altern atives. Wh at is un usual about drug resistan ce is th at th is problem h as n ot been widely recogn ized as a social extern ality—possibly of en orm ou s con sequ en ce. Followin g th is lin e of th in kin g, we arrived at sim p le criteria for ch oosin g an op tim al an tibiotic policy, wh ich con trasts sh arply with th e con clu sion of th e stan dard con ven tion al h ealth econ om ists’ in dividualistic cost-effectiven ess an alysis. Un der th e stan dard cost-effectiven ess ap p roach , th e econ om ic criteria m ost com m on ly u sed in offerin g an econ om ic p ersp ective on th e op tim al ch oice of first-lin e treatm en t is th at th e d ru g with th e lowest ratio of cost to effectiven ess is select ed as t h e p rim ary o r first -lin e d ru g. W h en t h is crit erio n is fo llowed, it ign ores th e p ossibly large n egative extern ality of overu sin g a p articu lar d ru g. A large n u m b er o f p ap ers in t h e m ed ical lit erat u re u se t h e p rivate-cost ap p roach to d eterm in e th e “op tim al” treatm en t for a com m u n icable disease. Bu t th e very n atu re of a com m u n icable disease m ean s th ere is a p o t en t ially large ext ern alit y asso ciat ed wit h d ru g t reat m en t s. Th e st an d ard m ed ical ap p roach fails to recogn ize th e extern ality p roblem associated with t h e u n ifo rm u se o f a sin gle d ru g. Th e ext ern alit y h ere is sim ilar t o t h e o n e en cou n tered in agricu ltu re in wh ich all farm ers decide to grow a sin gle “op tim al” crop , th ereby en cou ragin g th e evolu tion of p ests th at can wip e ou t th e en t ire m o n o cu lt u re. Alt h o u gh in t h e agricu lt u ral co n t ext , t h e so lu t io n is t o gro w d ifferen t variet ies d isp ersed sp at ially, in t h e m ed ical co n t ext , t h e t ru e op tim al solu tion is an alogou sly to u se a “m ixed” variety of dru gs in fraction s th at are p rop ortion al to th eir in dividu al cost-effectiven ess. Th ere are m an y in st an ces in wh ich we co u ld m o ve fro m a p o licy o f a n at io n ally reco m m en d ed t reat m en t t o a p o licy in wh ich lo cal d o ct o rs h ave m ore con trol over th e dru g p rescribed. So th e recom m en ded p olicy ch an ge is from on e of active p rom otion of treatm en t h eterogen eity to a m ore decen tralized ap p roach to d ecision m akin g. Su ch a strategy wou ld raise m u ch con cern over th e lack of a “n ation al strategy” to com bat a disease su ch as m alaria even if su ch a co o rd in at ed st rat egy wo u ld h ast en t h e d ay wh en t h e p rescrib ed gu idelin e treatm en t wou ld becom e in effective. With ou t a d ou bt, th ere m ay be p ractical p roblem s with u sin g a variety of dru gs at th e h ealth care settin g for a sin gle in fectiou s con dition . For in stan ce, a p h ysician m ay h ave to exp lain to in d ivid u al p atien ts wh y th ey are gettin g

74 • Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases

d ifferen t d ru gs. Th e sp ecific t reat m en t given by d ifferen t d o ct o rs will d iffer d ep en d in g o n t h eir (d ifferen t ) assessm en t s o f p ro b ab ilit y weigh t s. Th is is p oten tially p roblem atic becau se p atien ts typ ically look to d octors to resolve u n certain ty by p rescribin g th e “sin gle best” treatm en t. Herein lies th e dilem m a. We h ave boxed ou rselves in to a p articu lar way of reason in g th at th ere is a “best” treatm en t for an ailm en t, on e th at is attribu table to th e fact th at we are n ot u sed to h avin g an y extern alities in m ed icin e. Th e sin gle best treatm en t ap p roach works well for n on in fectiou s con d ition s bu t breaks d own bad ly for in fectiou s d iseases, in wh ich sign ifican t n egative ext ern alit ies are likely t o be p resen t in t h e fo rm o f en d o gen o u sly gen erat ed d ru g resistan ce. On ce we becom e aware of th e n atu re of th is p articu lar extern ality as on e th at req u ires th e p h ysician to also con sid er society’s best in terest s, wh ile d et erm in in g wh at is in t h e b est in t erest o f t h e p at ien t , t h en an o p t im al st rat egy m ay well in vo lve a m ixt u re o f less exp en sive an d m o reexp en sive dru g th erap ies. Drug resistance is endogenous. Th e cu rren t st rat egy h as b een t o wait fo r resistan ce to evolve before bein g su rp rised each tim e it ap p ears, as if it were an ad h o c p ro blem req u irin g so m e q u ick fix. Eco n o m ist s can co n t ribu t e t o t h e form u lation of strategies th at wou ld in tern alize th e cost of en dogen ou sly gen erated resistan ce in to th e p rocess of treatm en t d ecision m akin g. Th is ch ap ter tries to take a first step in su ch a direction .

References Ph ilip son , T. 2000. Econ om ic Ep idem iology. In Handbook of Health Econom ics, edited by A.J. Cu lyer an d J.P. Newh ou se. New York: Elsevier, 1762–99. Wein stein , M.C., an d H.V. Fin eberg. 1980. Clinical Decision Analysis. Ph ilad elp h ia, PA: W.B. Sau n ders Com p an y.

Notes 1. It is u sefu l t o co n t rast appropriate d ru g t reat m en t (o r t reat m en t fo r a b act erial in fection th at is likely to be cu red faster becau se of th at treatm en t) with inappropriate dru g treatm en t (wh ich does n ot cu re th e p atien t an y faster th an if th at treatm en t were n o t u sed ). An exam p le o f ap p ro p riat e d ru g t reat m en t is t h e u se o f an t ibio t ics t o cu re bacterial in fection s; an exam p le of in ap p rop riate d ru g treatm en t is p rescribin g an tibio t ics fo r viral in fect io n s. Ap p ro p riat e d ru g t reat m en t b en efit s b o t h t h e in d ivid u al p atien t an d society, wh ereas in ap p rop riate d ru g treatm en t ben efits n eith er th e p atien t n or society. Alth ou gh in ap p rop riate d ru g treatm en t is a sign ifican t factor in th e growin g resistan ce of m icrobes to dru gs, th is ch ap ter focu ses exclu sively on op tim al p olicies related to ap p rop riate d ru g treatm en t. In p ractice, ap p rop riate d ru g treatm en t often is lin ked to a gu id elin es-typ e p olicy u n d er wh ich p h ysician s are exp ected to ad h ere u n iform ly to a p redeterm in ed seq u en ce of dru gs to be u sed for treatm en t.

Chapter 3: Value of Treatment Heterogeneity for Infectious Diseases • 75 2. Nat io n al p o licies are esp ecially u sefu l in co u n t ries in wh ich t h e p rim ary h ealt h care p ro vid er is t yp ically a h ealt h care wo rker wit h lim it ed t rain in g. In co u n t ries in wh ich go vern m en t -ru n p u b lic h ealt h facilit ies are t h e p rim ary so u rces o f d ru gs, n ation al p olicies d eterm in e wh ich d ru gs are available at d ifferen t levels of th e h ealth care system . For in stan ce, a secon d-lin e dru g m ay on ly be available at a h osp ital an d n ot at a p rim ary care clin ic. 3. An im p ortan t argu m en t again st keep in g n ewer, m ore effective d ru gs on th e sid elin es as b acku p s is t h at su ch a p o licy t en d s t o lo wer t h e in cen t ive fo r d ru g firm s t o develop n ew dru gs th at m ay n ot be u sed exten sively du rin g th e life of th eir p aten t p rotection . 4. Th ese m edical reason s m ay in clu de u n desirable side-effects from u sin g two dru gs, m ore com p licated dosage regim en s, an d econ om ic costs.

Commentary

To Take or Not To Take the Antibiotic? James N. Sanchirico

I

m u st adm it th at wh en I got sick in th e past, m y on ly th ou gh ts were on h ow to get better an d h ow to get better soon er. An d if th at in clu ded takin g an tibiotics, th en th at is wh at I did. After readin g Ch apters 1 an d 2, wh at before was alm o st an in st in ct ive d ecisio n h as n o w beco m e m o re co m p licat ed an d in volves n ot ju st m y private ben efits an d costs, bu t also society’s. W h at are th e p rivate ben efit an d costs? If p rescribed ap p rop riately, an tibio t ics will t reat m y in fect io n an d in m an y cases get m e b ack o n m y feet so o n er. An t ib io t ics also red u ce t h e risks t h at t h e in fect io n will lead t o m o re serio u s h ealt h p ro b lem s in t h e fu t u re. Acco rd in g t o Web MD (h ttp :/ / www.webm d .com ), an tibiotics are th e treatm en t of ch oice for strep tococcal strain s, an d if left u n treated , strep th roat can lead to rh eu m atic fever (m ostly in ch ild ren ) or in flam m ation of th e kid n eys. As far as th e costs, th ere is t h e co st o f p u rch asin g t h e an t ib io t ics an d t h e o p p o rt u n it y co st s t h at in clu d e t im e sp en t o n d o ct o r visit s an d in creased su scep t ib ilit y t o o t h er in fection s wh ile takin g th e an tibiotic. W h at are th e social ben efits an d costs? A reassu rin g fact is th at treatin g m y in fection with an an tibiotic is also good for society. By takin g an an tibiotic, fo r in st an ce, I can b e slo win g d o wn , elim in at in g, o r b o t h , t h e sp read o f an in fection in m y com m u n ity. 1 Un fortu n ately, every tim e I decide to u se an tibio t ics, I am in creasin g t h e p ro b ab ilit y t h at a p art icu lar b act erial st rain will b eco m e resist an t t o t h e an t ib io t ic. In o t h er wo rd s, m y d ecisio n t o u se t h e an tibiotic tod ay h as a cost in term s of red u ced effectiven ess th at is born e in th e fu tu re by both cu rren t an d fu tu re gen eration s. 2 W h at is also u n settlin g is t h at b ecau se resist an ce can sp read fro m o n e b act eriu m t o an o t h er (cro ss• 76 •

Commentary: To Take or Not To Take the Antibiotic? • 77

resistan ce), it is p ossible th at each u se of on e an tibiotic can lead to m ore th an on e bacteriu m becom in g resistan t. W h at are th e im p lication s of th e p rivate an d social ben efits an d costs on th e level of an tibiotic u se? If in d ivid u als on ly weigh th e p rivate ben efits an d co st s wh en d ecid in g t o u se an t ib io t ics, t h en t h eir co n su m p t io n will b e less th an wh at is op tim al for society. In oth er word s, I wou ld n ot be takin g in to accou n t th at an tibiotics will redu ce th e sp read of in fection in th e com m u n ity. However, an tibiotic u se cou ld exceed som e socially op tim al level if th e costs o f red u ced effect iven ess are n o t t aken in t o acco u n t . 3 Man y argu e t h at t h e overp rescrip tion of an tibiotics in cases in wh ich th ey are in ap p rop riate, su ch as viral in fect io n s, is evid en ce t h at in d ivid u als (b o t h t h o se wh o are ill an d t h o se wh o p rescrib e t h e t reat m en t ) are n o t t akin g in t o acco u n t t h e so cial costs associated with an tibiotic u se. How sh ou ld society balan ce th e p ositive an d n egative trade-offs associated wit h t reat in g b act erial in fect io n s wit h an t ib io t ics? An d o n wh at eco n o m ic an d ep id em io lo gical fact o rs sh o u ld su ch an o p t im al p o licy be based ? Th ese are th e q u estion s th at both ch ap ters ad d ress u sin g stylized m od els th at cap tu re con dition s likely to exist in a rem ote h osp ital. Th e ch ap ters assu m e th at a social p lan n er (e.g., h osp ital ad m in istrator) is given th e task of d eterm in in g t h e o p t im al st rat egy t o t reat b act erial in fect io n (s) o ver t im e b y t akin g in t o accou n t both th e p ositive an d n egative extern alities of an tibiotic u se. Both ch ap ters fram e th e p roblem u sin g a related an d well-develop ed literatu re on th e exp loitation of ren ewable (e.g., fish , trees) n atu ral resou rces. Th ey also exten d th e Laxm in arayan an d Brown (2001) an alysis on th e econ om ics o f an t ib io t ic resist an ce b y t akin g in t o acco u n t t h e case in wh ich t h ere is a n on zero fitn ess cost of resistan ce. Th e fitn ess cost of resistan ce is th e evolu tion ary d isad van tage p laced on resistan t strain s relative to su scep tible strain s in th e absen ce of an tibiotics. Th e ch ap ters differ in th e n u m ber of an tibiotics availab le fo r u se an d t h e n u m b er o f b act erial st rain s: Wilen an d Msan gi (Ch ap ter 1) an d Brown an d Rowth orn (Ch ap ter 2) illu strate th e socially op tim al treatm en t for th e case with on e an d two dru gs, resp ectively. W h ile t h e u n d erlyin g eco n o m ic, ep id em io lo gical, an d in st it u t io n al assu m p t io n s o f t h e an alyses are n o t likely t o h o ld in p ract ice, t h e st ylized m odels do h igh ligh t th e econ om ic an d p u blic h ealth in tertem p oral trade-offs associated with u sin g an tibiotics. Th e ch ap ters also illu strate th e in sigh ts th at econ om ic an alysis can brin g to th e p u blic h ealth debate on an tibiotic u se.

Disease Ecology Th e ch ap t ers are b ased o n t h e SIS (su scep t ib le → in fect ed → su scep t ib le) m o d el o f in fect io n an d t reat m en t at t rib u t ed t o Kerm ack an d McKen d rick (1927). Th e m odel with an d with ou t treatm en t is illu strated in th e Wilen an d

78 • Commentary: To Take or Not To Take the Antibiotic?

Msan gi ch ap ter u sin g p h ase diagram s to describe th e differen t dyn am ic traject o ries. Becau se so m e p eo p le m igh t n o t b e fam iliar wit h p h ase d iagram s o r com p letely clear on h ow resistan ce develop s over tim e, I will elaborate fu rth er on th e disease ecology as m odeled in th ese ch ap ters.4 To fram e th e discu ssion , I will u se a form of Eq u ation 1 fou n d in Wilen an d Msan gi’s d iscu ssio n (Ch ap t er 1) (n o t at io n an d variab le d efin it io n s fo llo w d irect ly). Ap p lyin g all o f t h e sam e assu m p t io n s an d su b st it u t in g in S =1 – I an d I = Iw + Ir, I get dI w = β(1 − I w ) I w − rw I w − βI w I r − rf I w f dt dI r = β(1 − I r ) I r − rr I r − βI w I r dt

(1)

(2)

Note th at th is system of eq u ation s is also th e sp ecial case of th e Rowth orn an d Brown m od el with f 2 = 0. Th ese d ifferen tial eq u ation s rep resen t th e in stan tan eo u s rat e o f ch an ge o f resist an t an d su scep t ib le b act erial st rain s. In o t h er words, th e eq u ation s p rovide stru ctu re to exp lain h ow th e levels of th ese bacteria ch an ge from on e p eriod to th e n ext. For exam p le, if each strain is in d ep en d en t o f t h e o t h er, t h e first t erm [β(1 – Ii )Ii wit h i = w, r] in d icat es t h at it wo u ld gro w t o a p o p u lat io n o f 1 in t h e lo n g ru n (st ead y st at e, wh ich is defin ed wh ere dIi /dt = 0). If we in clu de th e secon d term , wh ich is th e n atu ral m ortality rate of th e two strain s, th en th e p op u lation s wou ld grow to 1 – ri/ β. Th is is th e p oin t at wh ich growth is directly offset by death s an d th e p op u lation level rem ain s stable over tim e. Th e d isease eco lo gy is su ch t h at t h e resist an t an d su scep t ib le b act erial strain s are n ot in d ep en d en t, an d , in fact, th ey com p ete again st on e an oth er. Th is com p etition is rep resen ted by th e th ird term , βIw Ir. Th e com p etition is essen tially th e battle of th e weakest, becau se th e strain th at dies off th e fastest lo ses. Fo r in st an ce, if t h e n at u ral m o rt alit y rat e o f t h e resist an t st rain (rr) is great er t h an t h e su scep t ib le st rain (rw ), t h en in t h e lo n g ru n wit h o u t t reat m en t (f = 0), t h e o n ly st rain t h at wo u ld p ersevere is t h e su scep t ible o n e. In oth er word s, if we d o n ot u se an tibiotics, th en th e resistan t strain wou ld go extin ct. Th e “do-n oth in g” strategy is wh at Wilen an d Msan gi h ave called th e ecological strategy. Th e differen ce between th e n atu ral m ortality rates is called fitn ess cost (Δr = rr – rw ), wh ich as Wilen an d Msan gi discu ss, is solely a biological cost. W h at h ap p en s t o t h e d isease eco lo gy wh en we u se an t ibio t ics (f > 0)? Operation ally, th is m ean s th at th e fou rth term in Equ ation 1 is positive (rf Iw f ). Th e con sequ en ce of th is is th at it sh ifts th e relative advan tage from th e su sceptible strain to th e resistan t strain as it in creases th e m ortality rate of th e su sceptible strain . All else bein g equ al, th e lower th e level of th e su sceptible strain in

Commentary: To Take or Not To Take the Antibiotic? • 79

existen ce, th e less com petition th e resistan t strain h as. Th erefore, th e m ore we treat with an tibiotics, th e easier we are m akin g it for th e resistan t bacteria to su rvive. As th e level of th e resistan t strain in creases, for exam ple, from treatin g all in d ivid u als (f = 1), t h e m o re resist an ce bu ild s an d t h e less effect ive t h e an tibiotic becom es.5 In th e lim it, th erefore, all in fected people wou ld be takin g th e an tibiotic, bu t it wou ld be h avin g n o effect on th e in fection . Th is story is fou n d in Wilen an d Msan gi’s Figu re 1-3.

The Case of One Antibiotic and One Infection

As m en t io n ed p revio u sly, Wilen an d Msan gi co n sid ered t h e case in wh ich th ere is on ly on e an tibiotic. Th e social p lan n er is assu m ed to ch oose th e op tim al tim e p ath of treatm en t su ch th at discou n ted p resen t valu e of costs (dam age an d treatm en t) is m in im ized. With on e an tibiotic, th e p lan n er can eith er d ecid e to u se it (in terven tion ist strategy) or n ot u se it (ecological strategy) in an y given p eriod. In t h is set t in g, t h e o p t im al st rat egy is t o t reat t h e en t ire p o p u lat io n in itially an d th en at som e p oin t begin to treat on ly a fraction of th e p op u lation . Over tim e, th e fraction treated decreases, wh ich m ain tain s th e effectiven ess of t h e an t ib io t ic lo n ger. Even t u ally, t h e fract io n o f t h e p o p u lat io n t reat ed ap p ro ach es t h e lo n g-ru n so lu t io n in wh ich t h e level o f effect iven ess an d in fect io n rem ain co n st an t . Th is so lu t io n is d ep ict ed in Wilen an d Msan gi’s Figu re 1-4. W h ile th e lon g-ru n level of in fection is in d ep en d en t of econ om ic p aram et ers, t h e o p t im al level o f effect iven ess d ep en d s o n t h e co st s o f t reat m en t . In p art icu lar, o n e t reat s less wh en co st s are h igh er. Th erefo re, t h e h igh er th e cost of treatm en t, th e h igh er th e level of effectiven ess (an d lower levels of resistan ce) in th e lon g ru n , everyth in g else bein g eq u al. Wilen an d Msan gi p rovid e a n ice d iscu ssion on h ow th eir form u lation of th e m od el an d th eir resu lts d iffer from th ose u sed in ep id em iology to stu d y differen t an tibiotic treatm en t strategies (Bon h oeffer et al. 1997). For exam p le, t h e au t h o rs fin d t h at t h e st rat egy o f t reat in g t h e en t ire p o p u lat io n in it ially (illu st rat ed n u m erically in t h eir Figu re 1-5) is co n sist en t wit h t h e “h it ‘em h ard an d h it ‘em fast” ru le of th u m b. Accordin g to th e au th ors, th eir op tim al st rat egy d iffers fro m t h e ru le o f t h u m b b ecau se it st o p s t reat in g t h e en t ire p op u lation before th e disease is elim in ated. W h y is t h ere a d ifferen ce b et w een t h e eco n o m ic an d ep id em io lo gical st rat egies? As t h e au t h o rs m en t io n , t h e eco n o m ic p o licy t akes in t o acco u n t bo t h t h e co st s t o d ay t o t reat an d t h e in creasin g co st s asso ciat ed wit h fu t u re t reat m en t becau se co n t in u in g t o t reat at h igh levels bu ild s u p resist an ce. So h o w w ill a p u b lic h ealt h o fficial kn o w w h en t o st o p t reat in g w it h t h e an t ibio t ic? Th is is a d ifficu lt q u est io n , an d o n e t h at I believe is n o t sat isfact o rily ad d ressed in t h eir an alysis. I su sp ect t h at t h e o m issio n is d u e t o t h e

80 • Commentary: To Take or Not To Take the Antibiotic?

fact t h at t h ere is n o sim p le an alo g t o t h e ep id em io lo gical ru le o f t h u m b t o h elp gu id e t h e d ecisio n . In fact , t h e t im e t o st o p t reat m en t d ep en d s n o t ju st o n t h e p art icu lar d isease eco lo gy, in it ial levels o f in fect io n , co st s o f t reat m en t , an d t h e d isco u n t rat e bu t also o n relat ive levels an d in t erp lay am o n g t h ese fact o rs. 6

The Case of Two Antibiotics and Two Strains

Ro wt h o rn an d Bro wn gen eralized t h e Wilen an d Msan gi m o d el t o t h e case with two an tibiotics an d two typ es of in fection . Th e gen eralization , h owever, com es at th e cost of in creasin g com p lexity, th e im p lication s of wh ich are well d etailed in th e ch ap ter. Two sim p lifyin g assu m p tion s are th at each an tibiotic is on ly effective again st on e typ e of in fection an d th at all in fected in dividu als are t reat ed wit h o n ly o n e an t ib io t ic. 7 By m akin g t h ese assu m p t io n s, t h e au th ors h ave ru led ou t th e ecologist strategy of Wilen an d Msan gi as well as th e p ossibility of treatin g with an an tibiotic cocktail. Th e au th ors also assu m e th at doctors do n ot h ave en ou gh in form ation on wh ich typ e of in fection th e p atien t h as (it is eith er n ot feasible or too costly to test th e p atien ts) to determ in e wh ich an t ib io t ic will b e effect ive. Th erefo re, so m e fract io n o f t h o se u sin g an an tibiotic will n ot get better. If th ey d o get better, it is n ot becau se th ey are takin g th e an tibiotic. Th e social p lan n er is assu m ed to kn ow th e level of each in fection in th e closed p op u lation . Un like th e Wilen an d Msan gi form u lation wh ose objective fu n ction is to m in im ize costs, th e objective fu n ction of th e Rowth orn an d Brown m od el is t o m axim ize t h e d isco u n t ed p resen t valu e o f n et b en efit s. Net b en efit s are defin ed as th e social valu e of bein g h ealth y tim es th e n u m ber of h ealth y in divid u als less t h e co st s o f t reat in g in fect io n s wit h b o t h an t ib io t ics. Q u alit atively, th e objectives are th e sam e. 8 Havin g said th at, th ere are su btle im p ort an t d ifferen ces b et ween t h e t wo fram ewo rks. Fo r exam p le, t h e Wilen an d Msan gi op tim al solu tion is essen tially a cost-effective strategy, wh ich does n ot n ecessarily in clu d e valu in g p u b lic h ealt h . Th e ap p ro ach b y Ro wt h o rn an d Bro wn assu m es t h at t h ere is so m e co n st an t so cial valu e o f b ein g h ealt h y across in d ivid u als in th e closed p op u lation an d across gen eration s. W h eth er su ch a valu e exists an d can be m easu red an d wh eth er it is m orally d efen sible is u n clear. In th e en d, both m odelin g fram eworks are n ot im m u n e to em bedd in g ju d gm en t s o n t h ese issu es an d bo th raise im p ortan t q u estion s on h ow so ciet y m igh t wan t t o t h in k ab o u t valu in g p u b lic h ealt h t o d ay an d in t h e fu tu re. Th e Ro wt h o rn an d Bro wn m o d el h as t wo st at e eq u at io n s (t wo levels o f in fect io n ) an d t wo co n t ro ls (t wo an t ib io t ic t reat m en t rat es), wh ich are red u ced to on e with th e assu m p tion th at all in fected in d ivid u als are treated (f 1 = 1 – f 2 ). It is p ossible th at each strain of in fection h as its own tran sm ission

Commentary: To Take or Not To Take the Antibiotic? • 81

rate, n atu ral m ortality, m ortality in d u ced by treatm en t, an d so forth . Allowin g for all th is h eterogen eity in th e m od el, h owever, m akes it d ifficu lt to d isen tan gle wh at is cau sed by wh at. In th e en d, th e au th ors assu m e m ost of th is h eterogen eity away an d focu s on econ om ic differen ces in th e treatm en t costs of th e two an tibiotics. Th ey fin d t h at t h e relat ive levels o f in fect io n in t h e lo n g ru n d ep en d o n th e cost of treatm en t (ci), ben efit of a cu re (p), d iscou n t rate (ρ), n atu ral m ortality rates (ri), effectiven ess of th e treatm en ts (α), an d con tagion rate of th e diseases (β). Th e fraction treated with each an tibiotic dep en ds on ly on th e disease ecolo gy (fit n ess co st an d effect iven ess o f t h e t reat m en t s). Everyt h in g else bein g eq u al, t h e in fect io n wit h t h e h igh est co st o f t reat m en t is m o st p revalen t in th e lon g ru n . Th e au th ors’ in terp retation of th is resu lt is th at p eop le are m ore toleran t of a bad th in g th e m ore exp en sive it is to m itigate. Th is resu lt is con sisten t with Wilen an d Msan gi, wh o fou n d th at th e h igh er th e cost of treatm en t, th e h igh er th e level of effectiven ess. W h at are t h e q u alit at ive ch aract erist ics o f t h e o p t im al u se o f an t ib io t ics o ver t im e? Like t h e Wilen an d Msan gi ch ap t er, t h ere is n o clo sed fo rm d yn am ic solu tion im p lyin g th at th e au th ors m u st u se n u m erical m eth od s to so lve fo r p o ssib le o p t im al so lu t io n s. Ro wt h o rn an d Bro wn fo u n d t h at t h e p lan n er in itially sh ou ld u se exclu sively th e an tibiotic th at is effective again st th e strain th at is m ost p revalen t. However, if th is an tibiotic is also th e m ore exp en sive on e, th en it is n ot clear th at th is rem ain s th e op tim al strategy. Of cou rse, it wou ld n ever m ake sen se to em p loy th e m ore exp en sive an tibiotic if th e oth er typ e of in fection was m ore p revalen t (th e p lan n er wou ld be sim p ly th rowin g m on ey an d an tibiotics away). At som e p oin t, it becom es ad van tageou s to em p loy both an tibiotics sim u ltan eou sly, bu t as th e au th ors m en tion , it is n ot clear h ow th e p aram eters affect th is switch in g tim e.

Discussion Th ese ch ap t ers h ave raised so m e im p o rt an t eco n o m ic an d ep id em io lo gical issu es associated with an tibiotic resistan ce. Th e two ch ap ters em p loy op tim al con trol fram eworks as th e m ean s to u n d erstan d h ow a social p lan n er m igh t b alan ce t h e so cial an d p rivat e b en efit s an d co st s o ver t im e. Th e b alan ce is fou n d wh en th e (m argin al) retu rn s to treatin g on e m ore in dividu al today are eq u al to th e (m argin al) costs of in creased resistan ce born e in th e fu tu re. Mo re im p o rt an t t h an t h e p art icu lar resu lt s, wh ich are b ased o n assu m p t io n s t h at are n o t likely t o ap p ly t o m an y set t in gs, are t h e d ifferen t p o licy im p lication s th at com e ou t of m od els th at take in to accou n t both econ om ic an d ep id em io lo gical fact o rs. Fo r exam p le, t h e co st s o f t reat m en t affect n o t o n ly t h e am o u n t o f p o p u lat io n t reat ed in an y p erio d b u t also t h e d evelo p -

82 • Commentary: To Take or Not To Take the Antibiotic?

m en t of resistan ce over tim e. To n atu ral resou rce econ om ists, th e differen ce is n ot su rp risin g becau se th ere is a lon g h istory of an alyses com bin in g biological an d eco n o m ic fact o rs t h at d erive d ifferen t co n clu sio n s t h an t h o se d erived on ly from biological m od els. In th e cu rren t p u blic h ealth d ebate, h owever, it ap p ears th at th ese typ es of m odels an d strategies are n ot bein g con sidered an d as su ch , th e q u alitative n atu re of th e fin din gs are p robably m ore su rp risin g to th at au dien ce. Alt h o u gh each ch ap t er set s o u t t o ch aract erize t h e o p t im al u se o f an t ibiotics, wh ile takin g in to accou n t resistan ce costs, n eith er ad d resses h ow th ese co n t ro l st rat egies m igh t be im p lem en t ed . Fo r exam p le, in n o n -h o sp it al set tin gs, h ow can p olicym akers p rovide th e correct sign als su ch th at p rivate in dividu als an d th ose wh o p rescribe th e an tibiotics do wh at is in th e best in terest of society? An d h ow d oes th e cu rren t h ealth care system im p ed e or facilitate th e ability of p olicym akers in su ch an en deavor? Nor do th e ch ap ters exp lain h ow th e resistan t strain com es to be (e.g., is it becau se p atien ts d o n ot com p lete th eir fu ll cou rse of an tibiotics?). Fin ally, both ch ap ters take th e stock of an tibiotics as fixed , bu t th ere are critical feed backs between th e d em an d for an tibiotics an d th e su p p ly of n ew an tibiotics, wh ich m igh t m itigate or d elay th e develop m en t of resistan ce in ou r cu rren t stock.

References An d erson , R.M., an d R.M. May. 1991. Infectious Diseases of Hum ans: Dynam ics and Control. Oxford, U.K.: Oxford Un iversity Press. Bon h oeffer, S., M. Lip sitch , an d B.R. Levin . 1997. Evalu atin g Treatm en t Protocols to Preven t An tibiotic Resistan ce. Proceedings of the National Academ y of Sciences of the USA 94(22): 12106–11. The Econom ist. 2001. Th e Lin e of Least Resistan ce. May 5, 71–2. Ellison , S.F., an d J.K. Hellerstein . 1999. Th e Econ om ics of An tibiotics: An Exp loratory Stu d y. In Measuring the Prices of Medical Treatm ents, ed ited by J.E. Trip lett. Wash in gton , DC: Brookin gs In stitu tion , 118–43. Laxm in arayan , R., an d G.M. Brown . 2001. Econ om ics of An tibiotic Resistan ce: A Th eory of Op tim al Use. Journal of Environm ental Econom ics and Managem ent, 42(2): 183–206. Kerm ack, W.O., an d A.G. McKen d rick. 1927. A Con tribu tion to th e Math em atical Th eory of Ep idem ics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathem atical and Physical Character 115(772): 700–21.

Notes 1. Th is is wh at econ om ists call a p ositive extern ality. An extern ality exists wh en th e welfare of on e in dividu al dep en ds n ot on ly on h is or h er action s bu t also on th e action s of oth er in dividu als wh o are ou t of h is or h er con trol. Oth er (p ositive extern alities) ben efits in clu d e both a red u ction in th e p robability th at th e in fection will lead to fu rth er

Commentary: To Take or Not To Take the Antibiotic? • 83 m ed ical co m p licat io n s req u irin g m o re co st ly t reat m en t s an d a p o t en t ial red u ct io n in th e n u m ber of days ou t of work. 2. Th is is wh at econ om ists call a n egative extern ality. 3. See Ellison an d Hellerstein (1999) for th e p oten tial im p lication s of th ese ben efits an d co st s o n t h e p rice o f an t ibio t ics an d in cen t ives fo r research an d d evelo p m en t o f n ew an tibiotics. 4. See An derson an d May (1991), Bon h oeffer et al. (1997), an d The Econom ist (2001) for m ore in form ation on disease ecology an d h ow resistan ce develop s. 5. Th e disease ecology m odels u sed in both ch ap ters do n ot take in to accou n t crossresistan ce. 6. Th e discou n t rate reflects a social rate of tim e p referen ce wh ere a p ositive discou n t rate im p lies th at fu tu re ben efit an d costs associated with treatm en t are valu ed less by th e social p lan n er th an th ose in cu rred tod ay, all else bein g eq u al. A zero d iscou n t rate corresp on ds to th e case in wh ich all ben efits an d costs are weigh ed eq u ally, irresp ective of wh en th ey occu r. 7. Th e assu m p t io n s regard in g t h e d isease eco lo gy are essen t ially t h e sam e in bo t h ch ap ters. 8. To illu strate th is, first rewrite th e total social valu e of bein g h ealth y as pN – pI an d n ote th at becau se th e p op u lation size is exogen ou s, it does n ot affect th e m argin al decision ru les fou n d in th e n ecessary an d su fficien t con dition s for an op tim al solu tion . Th e on ly factor th at affects th e op tim al solu tion is –pI, wh ich is th e red u ction in th e total valu e of h ealth (pN) cau sed by in fection in th e society. In oth er word s, it is th e cost to so ciet y asso ciat ed wit h t h e level o f in fect io n , wh ich is d II in t h e Wilen an d Msan gi ch ap ter.

Commentary

Same Infection, Same Time, Same Antibiotic? Stephen W. Salant

R

owth orn an d Brown (Ch ap ter 2) an d Laxm in arayan an d Weitzm an (Ch ap ter 3) ch aracterize th e socially op tim al way to treat on e kin d of bacterial in fection in a p op u lation wh en m u ltip le an tibiotics are available. Th e first of th ese form u lation s is static, wh ereas th e secon d is dyn am ic. In both form u lation s, ch oosin g th e an tibiotic best su ited for each p atien t in isolation is n ot so cially o p t im al b ecau se su ch a p o licy d isregard s t h e effect s su ch a ch o ice im p o ses o n t h ird p art ies. W h en t h e t h ird -p art y effect s o f su ch ch o ices are taken fu lly in to accou n t, it often tu rn s ou t—for d ifferen t reason s in th e two fo rm u lat io n s—t o be o p t im al t o t reat t h e sam e t yp e o f in fect io n in d ifferen t in dividu als at th e sam e tim e with differen t an tibiotics. Neith er ch ap ter con siders th e p ractical difficu lties of im p lem en tin g su ch a p olicy. On e of th ese an tibiotics will typ ically be less costly for th e in d ivid u al p at ien t t h an t h e o t h er if p riced at m argin al co st . Th ere is n o d iscu ssio n o f h o w p at ien t s can be in d u ced o r co m p elled t o t ake t h e an t ibio t ic t h at is n o t t h e best t reat m en t fo r t h eir illn ess fo r t h e sake o f an o n ym o u s t h ird p art ies. Nor is th ere an y discu ssion of h ow in su ran ce coverage an d m arket p ower distort from m argin al costs th e p rices th at p resu m ably stron gly in flu en ce an tibiotic ch oices in d ecen tralized settin gs. Th e exclu sive focu s of both ch ap ters is on th e socially op tim al p olicy—n ot its im p lem en tation .

The Static Analysis of Laxminarayan and Weitzman Laxm in arayan an d Weitzm an h ave p rovided u s with a sh ort, th ou gh t-p rovokin g an alysis o n t h e o p t im al way t o t reat a sin gle kin d o f bact erial in fect io n • 84 •

Commentary: Same Infection, Same Time, Same Antibiotic? • 85

afflict in g a gro u p o f p at ien t s wh en several an t ib io t ics exist , each o f wh ich cou ld cu re a p atien t at a differen t cost. Accordin g to th e au th ors, cu rren t m edical p ractice in volves treatin g p atien ts u n iform ly with th e sam e an tibiotic— th e ch eap est available after fu ll accou n t is taken of th e bacteria’s su scep tibility to each d ru g. If in creasin g resistan ce to th is first-lin e an tibiotic su bseq u en tly ren ders a secon d-lin e an tibiotic th e least exp en sive op tion , th e recom m en dat io n is t h en revised , an d t h e seco n d -lin e t reat m en t is u sed u n ifo rm ly o n all u n t reat ed p at ien t s. Th is p o licy lead s t o t h e u se o f several an t ib io t ics, wit h each u sed to su ch an exten t th at th e cost p er cu re is eq u alized . Th is so-called “u n ifo rm t reat m en t p o licy” m ay seem t h e sen sible way t o cu re t h e gro u p at least aggregat e co st . Bu t Laxm in arayan an d Weit zm an exp lain wh y it is n o t an d wh at p olicy is best with in th eir stylized form u lation . To u n d erstan d Laxm in arayan an d Weitzm an ’s critiq u e of cu rren t p ractice an d th eir p rop osed altern ative, fam iliarity with th e h igh way con gestion an alo gy u n d erlyin g t h eir an alysis is h elp fu l. Th e m o d el o f h igh way co n gest io n ap p eared in t h e first ed it io n o f Pigo u ’s Econom ics of W elfare (1920, 194). Fo r Laxm in arayan an d Weit zm an ’s an alo gy t o wo rk, each veh icle m u st b e assu m ed t o t ran sp o rt a sin gle m o t o rist . Su p p o se a gro u p o f m o t o rist s (t h e cou n terp art of th e p atien ts) desires to get from a com m on origin (th e in fected st at e) t o a co m m o n d est in at io n (t h e cu red st at e) b y an y o f a set o f ro u t es (an t ib io t ic t reat m en t s) co n n ect in g t h ese t wo p o in t s. Su p p o se t h at t h e t im e req u ired to get to th e destin ation dep en ds on th e rou te taken (ju st as th e cost p er cu re dep en ds on th e an tibiotic) becau se of variation s in “exogen ou s” factors su ch as th e len gth an d th e n u m ber of lan es of each rou te (th e cou n terp art to th e in h eren t attribu tes of each an tibiotic) as well as in su ch “en dogen ou s” factors as ad d ition al m in u tes of d elay cau sed by con gestion (th e cou n terp art of th e addition al cost p er cu re cau sed by in du ced resistan ce). Does th e p olicy of (a) directin g all m otorists to th e fastest rou te (th e least-cost an tibiotic)—takin g fu ll acco u n t o f t h e cu rren t level o f co n gest io n o n each ro u t e—an d (b ) ch an gin g th at recom m en d ation if an oth er rou te becom es th e fastest—m in im ize aggregat e h o u rs sp en t en ro u t e t o t h e d est in at io n ? Su ch a p o licy will resu lt in th e m otorists bein g allocated am on g th e variou s rou tes in su ch a way th at th e travel tim e on every rou te is eq u alized. Th e h igh way an alogy exp oses th e logical flaw in th e “u n iform treatm en t” p olicy. Un der th at p olicy, fu ll accou n t is taken of th e cu rren t delays cau sed by th e con gestion alon g each rou te. Bu t no account is taken of th e fact th at th e p o licy b ein g co n sid ered will affect t h e co n gest io n an d h en ce t h e d elays o n each ro u t e. Failu re t o t ake t h ese co n seq u en ces in t o acco u n t co n st it u t es t h e flaw in t h e u n ifo rm t reat m en t p o licy—wh et h er ap p lied t o h igh way co n gestion or to an tibiotic resistan ce. Gran t ed , t h e d elay im p o sed b y o n e ad d it io n al m o t o rist o n t h e first -lin e ro u t e m ay seem in co n seq u en t ial—say, 0.01 m in u t es (0.6 seco n d s) p er

86 • Commentary: Same Infection, Same Time, Same Antibiotic?

m o t o rist . Bu t if 10,000 o t h er m o t o rist s are o n t h at sam e ro u t e, t h e d elay im p osed on everyon e ad d s u p : th e resu ltin g aggregate in crease in travel tim e wou ld in th at case be (0.01)(10,000) = 100 m in u tes (1 h ou r an d 40 m in u tes)! Co n seq u en t ly, as lo n g as t h e fast est seco n d -lin e ro u t e t akes fewer t h an 100 m in u tes lon ger th an th e con gested first-lin e rou te, aggregate travel tim e cou ld be red u ced by req u irin g t h e ad d it io n al m o t o rist t o u se t h e fast est untraveled rou te. Su p p ose th at in th e absen ce of an y con gestion on th e oth er rou tes, th e best of th em takes 60 m in u tes lon ger th an th e first-lin e rou te wh en it is con gested with 10,000 cars. Th en 40 m in u tes in aggregate travel tim e is saved by d irectin g th at ad d ition al m otorist to th e slower rou te. Note th e trad eoff: on e m otorist h as to sp en d an extra h ou r in h is or h er car on th e secon d-lin e rou te so t h at each o f 10,000 m o t o rist s avo id s a 0.6-seco n d d elay t h at wo u ld b e cau sed if h e or sh e in stead took th e first-lin e rou te. In deed, a further redu ction in aggregat e t ravel t im e co u ld h ave b een ach ieved if so m e o f t h ese 10,000 m otorists h ad been assign ed to th e secon d-lin e rou te. Th e op tim al solu tion ch aracterized by Laxm in arayan an d Weitzm an takes th is lin e of argu m en t to its logical con clu sion an d ap p lies it n ot to h igh way co n gest io n b u t in st ead t o an t ib io t ic resist an ce. Wit h o u t lo ss o f gen eralit y, label th e ch eap est an tibiotic in th e absen ce of an y in du ced resistan ce “an tibiotic 1,” th e n ext ch eap est “an tibiotic 2,” an d so forth . In th eir solu tion , a design ated n u m ber of p atien ts are treated with an tibiotic 1, a d ifferen t n u m ber are treated with an tibiotic 2, an d so forth in su ch a way th at (a) every p atien t is treated (an d cu red) u sin g som e an tibiotic an d (b) n o reassign m en t of on e or m ore p atien t(s) to differen t an tibiotics wou ld redu ce th e aggregate cost of cu rin g everyon e. A m ore form al com p arison of th e two p olicies is p resen ted in th e ap p en dix to th is com m en tary. Th e op tim al solu tion h as several strikin g ch aracteristics. If som e an tibiotics th at cou ld cu re th e d isease are n ot u sed becau se of th eir cost, th ere will be a “bou n d ary” an tibiotic k su ch th at every an tibiotic 1, 2, …, k is u sed to som e ext en t , an d n o n e o f t h e rem ain in g an t ib io t ics are u sed at all. Th e ran ge o f an t ib io t ics u sed will b e at least as wide as in t h e u n ifo rm t reat m en t p o licy. Th u s, if th e op tim al solu tion wou ld u se an tibiotics 1, …, k, th e u n iform p olicy wou ld u se 1, …, j wh ere j ≤ k. How read ily th e given bacteria d evelop resistan ce to each of th e unused an tibiotics h as n o effect on th e op tim al solu tion . Bu t t h eir su scep t ib ilit y t o t h e k an t ib io t ics t h at are u sed does in flu en ce t h e n u m b er o f p at ien t s assign ed t o each o f t h ese an t ib io t ics. Th e sim p lest case o ccu rs wh en t h e k an t ib io t ics are equally su scep t ib le t o resist an ce—t h at is, wh en addin g a given n u m ber of p atien ts to any of th e k u sed an tibiotics raises it s co st p er cu re b ecau se o f t h e in d u ced resist an ce b y t h e sam e am o u n t p er ad d ition al p atien t. In th at case, th e op tim al solu tion in volves p u ttin g m ore p eo p le o n an t ib io t ic 1 t h an o n an t ib io t ic 2, m o re o n an t ib io t ic 2 t h an o n an tibiotic 3, an d so forth .

Commentary: Same Infection, Same Time, Same Antibiotic? • 87

Bu t th e op tim al solu tion h as on e trou blin g ch aracteristic th at we cau gh t a glim p se of in th e n u m erical exam p le—it creates arbitrary d istin ction s am on g id en tical p eop le an d treats th em d ifferen tially. Ju st as everyon e travelin g on t h e first -lin e ro u t e in t h e o p t im al so lu t io n get s t o t h e co m m o n d est in at io n faster th an everyon e travelin g on th e secon d -lin e rou te, so everyon e treated u sin g an tibiotic i in cu rs a sm aller cost to be cu red th an everyon e treated with an tibiotic i + 1 (wh ere i + 1 ≤ k). Som e p eop le m igh t fin d th e p rop osed solu tion in eq u itable. Bu t eq u ity aside, it p oses two p ractical difficu lties. First, p atien ts u sin g a m ore exp en sive an tibiotic wh en oth ers in th e sam e situ ation are bein g cu red at less exp en se with a d ifferen t an tibiotic are ap t to dem and th at th eir p h ysician s p rescribe th e ch eap er dru g for th em . If th e p h ysician s refu se, t h e p at ien t s m ay t h reat en t o su e o r t o swit ch d o ct o rs. It is n o t clear to m e th at p h ysician s cu rren tly u n willin g to rein in p aren ts dem an din g an tibiotics for th eir ch ild ren ’s viral ear in fection s can be relied on to en force th e arbitrary discrim in ation in h eren t in th e cost-m in im izin g p olicy. Bu t assu m e every p h ysician in a given h osp ital or a given state acq u ired th e n ecessary backbo n e t o d o exact ly wh at t h e o p t im al p o licy calls fo r—t o p rescribe fo r so m e su bgro u p o f p at ien t s wh o wo u ld h ave received t h e first -lin e d ru g, t h e seco n d -lin e d ru g in st ead . As a resu lt , resist an ce t o t h e seco n d -lin e d ru g wou ld in crease an d ach ievin g a cu re with it wou ld becom e m ore costly th an with th e first-lin e dru g. Even if p atien ts with in th e ju risdiction of a given h osp ital or state cou ld be coerced to settle for th e secon d-lin e dru g desp ite its h igh er co st , p at ien t s m erely visit in g t h e ju risd ict io n wh o m igh t o t h erwise h ave taken th e secon d -lin e d ru g wou ld n ow strictly p refer th e first-lin e d ru g as less costly. In th eory, for every p atien t we force to take th e secon d-lin e dru g in stead of th e first-lin e d ru g, th ere will be on e p atien t we can n ot force wh o will swit ch fro m t h e seco n d -lin e d ru g t o t h e first -lin e d ru g. Th is o ffset t in g beh avio r st o p s o n ly wh en t h ere rem ain n o p at ien t s o u t sid e o u r ju risd ict io n on th e secon d -lin e d ru g. On ly th en will ou r p rop osed reform h ave an y effect on th e aggregate costs of treatin g th e p atien ts u n der ou r con trol. In sh ort, for th e p olicy to h ave ben eficial effects, a su fficien t p ortion of th e p atien ts with th e in fection h as to be u n der ou r con trol.

The Dynamic Analysis of Rowthorn and Brown W h ereas t h e Laxm in arayan an d Weit zm an ch ap t er is b ased o n t h e eco n o m ist ’s st at ic m o d el o f h igh way co n gest io n fro m Pigo u (1920), Ro wt h o rn Brown ’s ch ap ter is based on th e ep id em iologist’s d yn am ic m od el of in fection fro m Kerm ack an d McKen d rick (1927). In t h eir fo rm u lat io n , t h ere are t wo an tibiotics an d two strain s of th e in fection . As a sim p lification , an tibiotic 1 is assu m ed to h ave n o effect on strain 2, an d an tibiotic 2 is assu m ed to be sim ilarly in effective again st strain 1. Again st strain i (i = 1, 2), on e cou rse of an tibi-

88 • Commentary: Same Infection, Same Time, Same Antibiotic?

otic i su cceeds in th e fraction ai of th e cases. Let ci den ote th e cost of a 14-day cou rse of an tibiotic i. Su p p ose it is kn own th at I1 p eop le h ave strain 1 an d I2 p eo p le h ave st rain 2, bu t it is t o o co st ly t o id en t ify t h e st rain in fect in g an y given p atien t. Let I d en ote th e aggregate n u m ber of p eop le in fected with th e two strain s: I = I1 + I2 . Hen ce, th e p robability th at a p erson will be cu red if h e or sh e takes an tibiotic i for 14 days is th e p rodu ct of (a) th e p robability th at h e or sh e h as strain i (Ii/ I) an d (b) th e p robability th at th e an tibiotic will be su ccessfu l, given th at th e p erson h as strain i. If a p erson p laces m on etary valu e P on bein g cu red, th en h e or sh e will strictly p refer an tibiotic 1 if (P)(a1 )( I1 / I) – c1 > (P)(a 2 )(I2 / I) – c2 an d will weakly p refer an tibiotic 2 oth erwise. Notice th at th is decision ru le takes n o accou n t of th e con tagion rates of th e two strain s or th e n u m ber of h ealth y p eop le wh o m igh t p oten tially becom e in fected . Su ch in form ation is irrelevan t to th e ch oice of wh at is th e best treatm en t for an y given in d ivid u al p atien t, bu t it is obviou sly cen tral to h ow h e or sh e sh ou ld b e t reat ed if t h e go al is in st ead t o p ro m o t e t h e welfare o f t h e so ciet y as a wh ole. Rowth orn an d Brown n ever discu ss th is decision ru le, bu t it seem s p ertin en t to m en tion as th e cou n terp art to Laxm in arayan an d Weitzm an ’s u n iform treatm en t p olicy. Both p olicies take in to accou n t cu rren t levels of resistan ce, bu t n eith er takes in to accou n t th e con seq u en ces for th ird p arties of an in dividu al’s ch oice of an tibiotic. Th e th ird p arties affected in Rowth orn an d Brown ’s form u lation are n ot, as with Laxm in arayan an d Weitzm an , oth er in dividu als su fferin g from th e sam e disease at th e sam e tim e (th e oth er m otorists cu rren tly on th e sam e roadway). Fo r t h e m o st p art , t h e t h ird p art ies will b e t h o se in fect ed in t h e fu t u re b y eith er th e in d ivid u al wh o is n ow bein g treated or by th ose h e or sh e in fects. Th e co re o f t h e Ro wt h o rn –Bro wn ’s m o d el is a p air o f d ifferen t ial eq u at io n s describin g th e evolu tion in con tin u ou s tim e of th e n u m ber of p eop le in fected with th e two strain s (th e two “state variables”), given th e fraction of in fected p eo p le t reat ed wit h each an t ib io t ic o ver t im e (t h e t wo “co n t ro l variab les”) an d exogen ou s p aram eters describin g rates of con tagion , th e size of th e en tire p o p u lat io n , an d so fo rt h . To sim p lify t h eir t h eo ret ical an alysis, t h e au t h o rs exclu d ed fro m co n sid erat io n co n t ro l st rat egies in wh ich (a) so m e in fect ed p atien ts receive n eith er an tibiotic or (b) som e receive both an tibiotics at on ce. Th is red u ces th e n u m ber of con trol variables to on e: th e fraction of in fected p atien ts treated with an tibiotic 1 (th e fraction u sin g an tibiotic 2 can th en be in ferred as th e com p lem en t). Given th is d escrip tive core m od el, th e au th ors u se Pon tryagin ’s m axim u m p rin cip le to dedu ce a set of first-order con dition s th at m u st n ecessarily h old if t h e d isco u n t ed in t egral o f t h e excess o f b en efit s o ver co st s is m axim ized . An alysis of th e p roblem tu rn s ou t to be tricky for a variety of reason s well docu m en ted in th e ch ap ter. Th e p h ase p ortrait u sed to describe th e op tim al solu tion h igh ligh ts th e evolu tion of th e two state variables bu t, to th ose u n fam il-

Commentary: Same Infection, Same Time, Same Antibiotic? • 89

iar with su ch d iagram s, p robably obscu res th e op tim al tim e p ath of th e con t ro l variab le(s). Dep en d in g o n t h e n u m b er o f p eo p le in fect ed b y t h e t wo strain s in itially, it is socially op tim al to p rescribe th e sam e an tibiotic for everyon e du rin g a fin ite tim e in terval an d th en to begin u sin g th e oth er an tibiotic on som e fraction of th e in fected p atien ts. W h et h er su ch a m o d el is fo rm u lat ed in co n t in u o u s o r in d iscret e t im e is largely a m atter of taste. I h ave a m in or p referen ce for a discrete-tim e form u lation becau se it is easier to exp lain to n on sp ecialists an d to sim u late. It m ay be h elp fu l, t h erefo re, t o refo rm u lat e t h e d yn am ic syst em in d iscret e t im e su ch th at each p eriod con sists of 14 days, th e len gth of on e cou rse of an an tibiotic. Th e core of th e m odel wou ld th en be a p air of differen ce eq u ation s. As a n ewcom er to th e area of an tibiotic resistan ce, I d o n ot kn ow wh at progress h as been m ade sin ce 1927 in n u m erically im plem en tin g th e discretetim e cou n terp art to th e Kerm ack–McKen d rick m od el. Bu t I can well im agin e th at som e distin gu ish ed econ om ists are very kn owledgeable abou t th e em pirical im plem en tation of th is m odel (at least for som e in fection s an d som e sets of an tibiotics), just as oth ers are well in form ed about dyn am ic optim ization . On e p roblem is gettin g p ractition ers from d ifferen t d iscip lin es to com m u n icate effectively. I wou ld th in k an accessible, u ser-frien d ly sim u lation m od el th at could be m an ipulated on lin e or in an electron ic worksh eet would facilitate such com m u n ication . On e con strain ed op tim ization p ackage (Solver) is stan d ard eq u ip m en t in m ost Microsoft Excel version s1 an d greatly en h an ced version s can seam lessly rep lace th e stan d ard p ackage with in Excel at reason able p rices (h ttp :/ / www.fron tsys.com / ). Rowth orn an d Brown em p h asized th at th e dyn am ic problem th ey an alyzed resem bles th ose th at arise in resource econ om ics. How dyn am ic resource problem s of approxim ately th e sam e com plexity as Rowth orn an d Brown ’s can be solved an d p resen ted to n on sp ecialists u sin g Excel’s Solver is well-illu strated th rou gh ou t Jon Con rad ’s 1999 u n d ergrad u ate textbook, Resource Econom ics. But wh eth er it be a can n ed program like Solver or on e specially tailored to th e problem , such a user-frien dly tool th at perm its calcu lation of th e op tim al p rogram on lin e or on on e’s p erson al com p u ter wou ld facilitate d ialogu e between th e scien tists an d social scien tists. Th e scien tists h ave a com parative advan tage in ch oosin g th e appropriate dyn am ic system an d calibratin g it em p irically. Th ey m ay con clu d e th at th e Kerm ack–McKen d rick d yn am ic system sh ou ld reflect u n certain ty or sh ou ld be oth erwise m od ified . Th e social scien tists, in turn , h ave a com parative advan tage in n um erically solvin g th e dyn am ic optim ization problem specified by th e scien tists, ascertain in g th at th e op tim u m h as been p rop erly iden tified 2 an d u sin g dyn am ic op tim ization th eory (a) to explain th e in tuition for th e optim al strategy an d (b) to illum in ate its sen sitivity to perturbation s in th e specification . Besides th e p rom otion of dialogu e an d collaboration , su ch sim u lation exercises can m ake t wo o t h er im p o rt an t co n t ribu t io n s. First , t h ey elim in at e t h e

90 • Commentary: Same Infection, Same Time, Same Antibiotic?

n eed to exclu de a p riori strategies, wh ich , for som e sets of p aram eters of in terest , m ay in clu d e t h e act u al o p t im u m . Fo r exam p le, as sim p lificat io n s, Rowth orn an d Brown exclu ded strategies in wh ich som e p atien ts receive both an tibiotics sim u ltan eou sly or som e p atien ts receive n eith er dru g. Th e sim u lation sh ou ld be flexible en ou gh to in clu de all p ossible strategies. 3 Th ere is a fin al an d d ecisive reason for con sid erin g su ch sim u lation m od els. Th e socially op tim al p olicy worked ou t in each ch ap ter d iffers from cu rren t p ractice. Th is tells u s on ly th at som e im p rovem en t is p ossible. Bu t it tells u s n o t h in g wh at so ever ab o u t t h e m agnitude o f t h e p o t en t ial im p ro vem en t . Clearly, th ere is n o p oin t in aban d on in g cu rren t p ractice to ach ieve a m in u scu le im p ro vem en t . A carefu lly calib rat ed sim u lat io n can clarify wh et h er im p ro vem en t s o f sign ifican t m agn it u d e are ach ievab le. If t h ey are, it m ay n on eth eless be p ossible to cap tu re m u ch of th at p oten tial gain u sin g a strategy sim p ler th an th e fu lly op tim al on e—say, in Rowth orn an d Brown ’s case, by u sin g th e best of th e sim p ler strategies in wh ich everyon e is treated at an y given tim e with th e sam e d ru g. A calibrated sim u lation can clarify th is issu e as well.

References Con rad, J. Resource Econom ics. 1999. Cam bridge, U.K.: Cam bridge Un iversity Press. Kerm ack, W., an d A.G. McKen drick. 1927. A Con tribu tion to th e Math em atical Th eory of Ep idem ics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathem atical and Physical Character 115(772): 700–21. Myerson , R. 1981. Op tim al Au ction Design . Mathem atics of Operations Research 6: 58–73. Pigou , A.C. 1920. Econom ics of W elfare. Lon don : Macm illan .

Appendix to the Laxminarayan and Weitzman M odel Su p p ose th ere are w– in fected in dividu als an d m an tibiotics th at can be u sed to t reat t h em . In t h e ab sen ce o f resist an ce, an t ib io t ic i (i = 1, … , m ) can cu re som eon e at cost C i. In dex th e an tibiotics so th at C i < C i + 1 . If Y i in dividu als are assign ed d ru g i, t h e co st in creases by siY i becau se o f t h e in d u ced resist an ce. Hen ce, th e aggregate cost of treatin g Y i in d ivid u als with an tibiotic i is Y i(C i + siY i). Defin e average cost (AC i)(th e cost p er p erson treated with an tibiotic i) as ACi (Yi ) =

Yi (Ci + siYi ) Yi

= Ci + siYi

Defin e m argin al co st (MC i) (t h e in crease in t h e aggregat e co st o f t reat in g p atien ts with an tibiotic i wh en an addition al p erson is given dru g i) as MCi (Yi ) =

d Yi (Ci + siY ) + Ci + 2 siYi dYi

Commentary: Same Infection, Same Time, Same Antibiotic? • 91

Let th e su p erscrip t u d en ote th e u n iform treatm en t p olicy an d th e su p erscrip t o d en o t e t h e o p t im al p o licy. Th en t h e fo llo win g co n d it io n s u n iq u ely d efin e t h e n u m ber o f p at ien t s t akin g each an t ibio t ic u n d er t h e t wo p o licies (as well as j, k, λ, an d γ): Un der th e u n iform treatm en t p olicy

∑ Yiu = w

(1)

i

Yiu > 0 an d ACi Yiu = γ for i = 1, , j

( )

(2)

Yiu = 0 an d ACi (0 ) ≥ γ for i = j + 1,, m

(3)

Un der th e op tim al p olicy

∑ Yio = w

(4)

i

Yio > 0 an d MCi Yio = λ for i = 1,, k

( )

(5)

Yio = 0 an d MCi (0 ) ≥ λ for i = k + 1,, m

(6)

Becau se MC i(Y i) > AC i(Y i) for Y i > 0, λ > γ. A solu tion in wh ich j = k = 2 is illu st rat ed in Figu re A-1 (fo r sim p licit y, d rawn wit h s1 = s 2 ). In t h e u n ifo rm treatm en t p olicy, th e average cost p er p atien t is eq u alized (at γ, th e h eigh t of t h e lo wer h o rizo n t al lin e in t h e figu re). Th e h o rizo n t al co m p o n en t s o f t h e in t ersect io n o f t h at lin e wit h AC 1 an d AC 2 in d icat e t h e n u m b er o f p at ien t s u u assign ed d ru g 1 (Y 1 ) an d d ru g 2 (Y 2 ), resp ect ively, u n d er t h e u n ifo rm t reat m en t p olicy. Sim ilarly, in t h e o p t im al p o licy, t h e m arginal cost o f ad d in g an o t h er p at ien t t o eit h er an t ibio t ic is eq u alized (at λ, t h e h eigh t o f t h e h igh er h o rizon tal lin e). Th e h orizon tal com p on en ts of th e in tersection of th at lin e with 0 MC 1 an d MC 2 in d icate th e n u m ber of p atien ts assign ed d ru g 1 (Y 1 ) an d d ru g 0 2 (Y 2 ), resp ectively u n d er th e op tim al p olicy. As d rawn , λ (an d h en ce γ) p ass ben eath C 3 (an d h en ce ben eath C 4 ,…,C n ); h en ce, j = k = 2. It is p ossible, h owever, to d evise cases in wh ich th e op tim al p olicy u ses a broad er assortm en t of an tibiotics (j < k). As th e grap h reflects, if th e op tim al p olicy rep laces th e u n iform treatm en t p olicy, som e of th e p atien ts wh o wou ld h ave taken d ru g 1 are given d ru g 2, becau se th is cau ses in creased resistan ce to d ru g 2 an d red u ced 0 0 resistan ce to d ru g 1, AC 1 (Y l ) < AC 2 (Y 2 ) u n d er th e op tim al p olicy.

AC3

M C2 C3 AC2

M C1

λ

AC1

γ

Cost disadvantage in the optimal solution

C2

C1

o

Y1

Panel (a)

u

Y1

u

Y2

o

Y2

Panel (b)

FIGURE A-1. Average and M arginal Costs under Uniform and Optimal Treatment Policies

Panel (c)

92 • Commentary: Same Infection, Same Time, Same Antibiotic?

M C3

Commentary: Same Infection, Same Time, Same Antibiotic? • 93

Notes 1. Look u n der Tools an d click on Add-In s to load Solver. If th e Solver p ackage is n ot availab le u n d er Ad d -In s, lo ad it fro m t h e p ro gram d isks o r co n su lt wit h yo u r syst em adm in istrator. 2. W h en u sin g Solver on dyn am ic p roblem s, for exam p le, I always in clu de a colu m n to verify th at th e strategy th e p rogram locates as op tim al satisfies th e n ecessary con d ition s for a m axim u m in every p eriod. 3. Man y u n exp ected solu tion s in op tim ization or eq u ilibriu m p roblem s h ave been id en tified d u rin g a com p u terized sim u lation . My own work on losses from h orizon tal m ergers (an eq u ilibriu m p roblem ) an d on th e social an d p rivate advan tages of creatin g asym m etries in two-stage gam es (an op tim ization p roblem ) grew ou t of com p u terized sim u lation s. Th e exam p le in Myerson (1981) of a seller facin g bu yers of u n kn own bu t correlated typ es wh o, by cleverly exp loitin g th e correlation between th em , can always extract th eir entire su rp lu s was also first id en tified by a com p u ter sim u lation . In all of th ese exam p les, th e su rp risin g resu lt wou ld h ave been m issed if th e com p u ter-assisted search was artificially restricted to th e class th e research er th ou gh t a p riori wou ld con tain th e solu tion .

Chapter 4

Pest M obility, M arket Share, and the Efficacy of Refuge Requirements for Resistance M anagement Silvia Secchi and Bruce A. Babcock

Bt crops, the first generation of agricultural biotechnology, have been widely adopted in the United States. There are concerns about the possible development of resistance to Bt by the targeted pests; therefore, the U.S. Environm ental Protection Agency has m andated the use of refuges. Refuges are portions of the field in which non-Bt seed is planted. This practice allows the interbreeding of pests and slows resistance. The current policy is based on the assumption that the market share of Bt crops is 100%. How ever, if m arket penetration is low er, pest m obility can substantially alter the efficacy of refuges. When pests are mobile, untreated fields serve as “ natural refuge” because pests from untreated fields can move to treated fields. The importance of natural refuges depends on pest mobility and market penetration. High mobility and low market penetration increase substitution possibilities betw een m andatory and natural refuges because the pests—and their genetic m akeup—behave like a com m on property resource among farmers and there are high levels of externalities. We focus on the im pact of m arket penetration and pest m obility on resistance buildup to improve the effectiveness of the current policy and to identify the level of m arket penetration at w hich natural refuges becom e ineffective. We use a simulation model to mimic the behavior of profit-maxim izing farm ers on nine adjacent Bt and non-Bt corn fields for 15 years. Farm ers planting the non-Bt corn use econom ic thresholds to decide w hether to apply a non- Bt pesticide. A random elem ent is introduced to m im ic the real variability of the pest population from year to year. The mobility of the pest is parameterized by the percentage of the pest population on a field that moves to neighboring fields.

• 94 •

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 95 We find that farmers using traditional hybrids have a higher pest population, which is highly susceptible to Bt. The negative externality produced by the net influx of these pests into the Bt fields is small, and it is more than offset by the positive impact that the susceptible pests have on delaying resistance buildup. Furtherm ore, the num ber of pests m oving into the non- Bt fields is low and does not cause significant damage. We also find that resistance does not spread from the Bt to the non-Bt fields, and that lack of complete market penetration significantly reduces the buildup of resistance on Bt fields unless m obility is very low. This suggests that the current policy is only optim al if m arket penetration is com plete or mobility is close to zero.

T

h e u se of agricu ltu ral biotech n ologies h as been in creasin g dram atically in th e Un ited States sin ce th e m id -1990s. Am on g th e m ost su ccessfu l crop s are Bt p lan t-p esticides, wh ich are en gin eered to exp ress th e Bacillus thuringiensis (Bt) δ-en d otoxin s an d target th e Eu rop ean corn borer (ECB). Bt p esticid es h ave lo n g been u sed in sp ray fo rm by o rgan ic an d in t egrat ed p est m an agem en t farm ers, an d th eir effectiven ess an d safety are well establish ed. Th e U.S. En viron m en tal Protection Agen cy (EPA) req u ires farm ers wh o wan t to grow Bt corn an d cotton to follow resistan ce m an agem en t p lan s to slow resistan ce to t h e Bt t o xin s b ecau se o rgan ic farm ers an d en viro n m en t al gro u p s are co n cern ed ab o u t t h e p o ssib le d evelo p m en t o f resist an ce t o Bt b y t h e t arget ed p ests. Moreover, EPA is in terested in resistan ce issu es becau se of th e p rovision s of th e Federal In secticide, Fu n gicide, an d Roden ticide Act an d th e Food Qu ality Protection Act. Becau se of th ese acts, th e agen cy is reassessin g th e en viron m en tal an d h u m an h ealth im p acts of p esticid es th at h ave lon g been on th e m arket, su ch as th e organ op h osp h ates. Som e of th ese old er p rod u cts m ay be with drawn from th e m arket, an d EPA is con cern ed abou t th e lon g-term viabilit y o f alt ern at ive, m o re en viro n m en t ally frien d ly p ro d u ct s su ch as t h e Bt crop s (see for in stan ce EPA 1998a). Sp ecifically, th e EPA resistan ce m an agem en t p lan con sists of a com bin ation o f m an d at o ry refu ges an d h igh d o ses. Refu ges are p o rt io n s o f t h e field in wh ich n o n -Bt seed is so wn an d Bt in sect icid es are n o t sp rayed t o allo w t h e in terbreedin g of p ests su scep tible to Bt with resistan t p ests. Th is in terbreedin g slo ws resist an ce b u ild u p . Refu ges are co u p led wit h h igh d o ses o f t h e t o xin exp ressed by th e p lan ts th rou gh ou t th e season an d in all th e p lan t tissu es so on ly th e few resistan t p ests su rvive on Bt crop s. Th e u se o f u n t reat ed areas as refu ges fo r su scep t ib le p est s is n o t a n o vel id ea. It h as b een an alyzed b y en t o m o lo gist s at t h e t h eo ret ical level (Georgh iou an d Taylor 1977; Cap rio 1998), an d it h as been advocated in p ractice as a strategy to slow th e resistan ce to acaricid es u sed to con trol th e twosp o t t ed sp id er m it e in p ear o rch ard s (Cro ft an d Du n ley 1993), im id aclo p rid

96 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

ap p lied t o su p p ress t h e Co lo rad o p o t at o b eet le in p o t at o es (Dively et al. 1998), an d foliar ap p lication s of Bt u sed to con trol th e diam on dback m oth in cab b age cu lt ivat io n s (Perez et al. 1997). Th e gen et ic u n d erp in n in g o f t h e h igh -d o se refu ge st rat egy is t h at t h e resist an ce t o t h e p est icid e fo llo ws t h e Hard y-Wein berg p rin cip le (Hartl an d Clark 1989). Th is m ean s th at resistan ce is given by a sin gle, n on -sex lin ked gen e with two alleles, so th at th e p est p op u lat io n is co m p o sed o f h o m o zygo t e-su scep t ible (SS), h et ero zygo t e (RS), an d h om ozygote-resistan t (RR) in dividu als. Th e m ajority of th e p est p op u lation is su scep tible to th e p esticide becau se th e resistan ce gen e R is rare an d recessive. Th erefore, m ost p ests are SS typ e. In ad d ition , p esticid es also con trol RS-typ e p ests. Becau se th e Bt crop s are h igh dose, all bu t th e RR-typ e p ests, an d p ossibly a sm all m in ority of th e RS-typ e p ests, are killed. Th e refu ge works in slowin g resist an ce b ecau se t h e sm all n u m b er o f resist an t su rvivo rs fro m t h e Bt field s m at e wit h t h e (m o st ly SS t yp e) p est s fro m t h e refu ge, so t h at t h e o ffsp rin g is SR typ e. EPA’s cu rren t refu ge req u irem en ts for Bt crop s are based on th e assu m p tion th at th e m arket sh are of th e Bt seed is 100%. Th is is eq u ivalen t to assu m in g p est m o b ilit y d o es n o t cau se p est m an agem en t ext ern alit ies. In gen eral, t h o u gh , p est m an agem en t ext ern alit ies o ccu r b ecau se farm ers wh o d o n o t con trol a p articu lar p est will h ave h igh er p est p op u lation s th an th ose wh o do. Th e m ovem en t of th ese p ests from th e field s of n on con trollin g farm ers in to th e fields of con trollin g farm ers creates two extern alities. A n egative extern ality is created becau se d am agin g p ests travel from u n con trolled field s to con trolled field s, cau sin g d am age on th e con trolled field s. However, th is m ovem en t also creates a p ositive extern ality with resp ect to resistan ce m an agem en t becau se th ose p ests th at m ove will be m ore su scep tible to th e con trol p ractice. Th e tim e dim en sion is very im p ortan t to both th ese typ es of extern alities. Th e effects of differen tial p est p ressu re m ay be felt with in a growin g season or gen eration of p ests1 if th e p ests cau se dam age after th ey m ove. Bu t, p erh ap s m ore im p ortan tly, th ese effects take p lace from on e gen eration or growin g season to t h e n ext . In ad d it io n , t h e ext ern alit ies cau sed b y d ifferen t ial resist an ce freq u en cies are in h eren tly d yn am ic becau se th e sp read of resistan ce takes p lace from on e gen eration to th e n ext. If all farm ers u se th e sam e p est con trol p ractices an d in all oth er ways are iden tical, th en th e extern al costs an d ben efits of p ests m ovin g from field A to field B are offset by th e costs an d ben efits of p ests th at m ove from field B to field A. Th at is, 100% m arket p en et rat io n im p lies t h at n o ext ern alit ies are p resen t , an d t h e an alysis o f o p t im al resist an ce m an agem en t st rat egies can p ro ceed u n d er t h is assu m p t io n (see fo r exam p le Hu rley et al. 1999). Pest m o b ilit y can su b st an t ially alt er t h e efficacy o f u sin g refu ge as a resist an ce m an agem en t st rat egy wh en m arket p en et rat io n o f t h e resist an ce-in d u cin g co n t ro l st rat egy is less t h an 100%. W h en p est s are m o b ile, u n t reat ed field s

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 97

can serve as “n atu ral refu ge” becau se p ests from u n treated fields can m ove to treated field s. Th e ability of n atu ral refu ge to su bstitu te for regu latory refu ge d ep en d s o n bo t h p est m o bilit y an d m arket p en et rat io n . High m o bilit y an d low m arket p en etration clearly sh ou ld in crease su bstitu tion p ossibilities. Bu t it is n ot certain if n atu ral refu ge can serve as a su bstitu te if m arket p en etration is say, 50%, an d p est m obility is sm all. EPA im p licitly ackn owled ges th at p est m obility is a cru cial com p on en t of th e Bt resistan ce q u estion becau se th e very ration ale of EPA’s regu latory effort is b ased o n t h e p o ssib ilit y t h at , b ecau se o f p est m o b ilit y, resist an ce m ay sp read , m akin g t h e Bt u sed as a sp ray in o rgan ic farm in g in effect ive (EPA 1998a). Th e sam e p o p u lat io n b io lo gy p ro cesses b eh in d t h e in -field refu ge strategy ap p ly to th e field-to-field case. EPA an d en tom ologists, in fact, refer to field s p lan t ed wit h n o n -Bt h yb rid s as u n st ru ct u red o r m arket -d riven refu ge (see for in stan ce EPA 1998b). Figures 4-1 an d 4-2 sh ow th e level of Bt corn m arket pen etration in 1999 by coun ty for th e Un ited States. Clearly, m arket pen etration is quite variable across region s, ran gin g from less th an 10% to m ore th an 50% of th e corn acreage. Th is variability suggests th e n eed to an alyze in m ore detail th e im portan ce of m arket p en etration in th e d evelop m en t of resistan ce. On th e on e h an d , th e p en etration of th e Bt tech n ology cou ld rem ain lim ited , an d th e p resen ce of u n stru ctu red refu ge m igh t be en ou gh to gu aran tee th at resistan ce n ever becom es a con cern . Th is is a distin ct possibility, given th e Japan ese an d European position on gen etically m od ified organ ism s (GMOs): a Eu rop ean or Jap an ese ban on GMO im ports would h ave a dram atic im pact on th e adoption of Bt crops in th e Un ited States. On th e oth er h an d, th e ben efits of Bt corn cou ld prom pt rapid, widespread adoption . In th e an alysis th at follows, we do n ot specify th e forces drivin g m arket pen etration . Besides th e beh avior of export m arkets, oth er factors th at h ave th e p oten tial to in flu en ce th e p lan tin g decision s of farm ers are Farm Bill p rovision s, th e relative p ricin g of th e Bt seed , an d th e role of bun dlin g. 2 Moreover, plan tin g decision s always depen d on th e local ch aracteristics of th e farm system , su ch as th e h istory of corn borer in festation s. Ou r an alysis focuses on th e im pact of m arket pen etration on resistan ce an d th e role of p est m obility in d eterm in in g th e size of th e extern alities to im p rove th e effectiven ess of resistan ce m an agem en t p olicy. In p articu lar, id en tification of th e th resh old m arket p en etration for wh ich th e u n stru ctu red refu ge becom es in effective cou ld p rom p t regu latory au th orities to m on itor refu ge com p lian ce m ore closely or to in crease th e level of refuge recom m en ded in a region . Th e issu es con sid ered in th is ch ap ter are likely to becom e m ore cen tral to p o licym akers b ecau se t h e in d u st ry is d evelo p in g n ew gen et ically m o d ified cro p s t h at will b e act ive again st b o t h t h e co rn ro o t wo rm an d t h e ECB an d b ecau se in t erest is gro win g in d evelo p in g resist an ce m an agem en t p lan s fo r cu rren t p esticides so as to exten d th eir life.

10–19% 20–29% 30–39% 40–49% 50–59%

FIGURE 4-1. U.S. Distribution of Bt Corn Notes: Th e figu re rep resen ts th e p ercen tage of total corn acreage p lan ted to Bt corn h ybrids in cou n ties in wh ich m ore th an 50,000 acres of corn were p lan ted. Source: Bt corn in du stry sales data com p iled by FSI, In c. 1999.

02-Laxminarayan 11/11/02 4:19 PM Page 98

0–9%

98 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

% Bt Corn

10–19% 20–29% 30–39% 40–49% 50–59%

FIGURE 4-2. Distribution of Bt Corn—Central Corn Belt Notes: Th e figu re rep resen ts th e p ercen tage of total corn acreage p lan ted with Bt corn h ybrids in Cen tral Corn Belt cou n ties in wh ich m ore th an 50,000 total acres of corn were p lan ted. Source: Bt corn in du stry sales data com p iled by FSI, In c. 1999.

02-Laxminarayan 11/11/02 4:19 PM Page 99

0–9%

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 99

% Bt Corn

100 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

To stu dy th e effects of p est m obility an d in com p lete m arket p en etration on p est resist an ce, we d evelo p ed a d yn am ic farm p ro d u ct io n m o d el an d u sed sim u lation resu lts to an alyze th e in terp lay between th e extern alities created by p est m obility an d th e m an agem en t of resistan ce at differen t levels of m arket p en et rat io n an d p est m o b ilit y. O u r an alysis fo cu ses o n Bt co rn an d t h e ECB. O u r o b ject ive was t o d et erm in e t h e effect o f p est m o b ilit y o n t h e b u ild u p o f resist an ce. A recen t st u d y su ggest ed t h at ECB m o b ilit y is h igh er t h an p revio u sly assu m ed (Sh o wers et al. 2000), b u t given t h e in su fficien t am ou n t of eviden ce, th e followin g m odel an alyzes th e p roblem at variou s levels of p est m obility. We ap p lied th e m odel to th e case of corn p rodu ction an d u sed a grid o f n in e field s t h at can be so wn wit h t h e Bt seed o r wit h a t rad ition al corn h ybrid. Th e m odel was develop ed alon g th e m eth odological lin es o f Lazaru s an d Dixo n (1984) an d Hu rley an d o t h ers (fo rt h co m in g). Lazaru s an d Dixon u sed a n on lin ear p rogram m in g m odel to com bin e both com m on p rop erty resou rce issu es with exp licit gen etics for th e corn rootworm , wh ereas Hu rley an d o t h ers exam in ed t h e eco n o m ic valu e o f m ech an ism s t o slo w resist an ce bu ild u p fo r Bt cro p s. O u r an alysis also fo llo wed a lin e o f research begu n in th e 1970s (Taylor an d Hadley 1975; Hu eth an d Regev 1974; Regev et al. 1976, 1983) t h at t reat s su scep t ib ilit y t o a p est icid e as a n o n ren ewab le resou rce. We bu ilt on th ese stu d ies by m ain tain in g th e key assu m p tion th at su scep tibility is n on ren ewable. Th is m ean s th at n o fitn ess costs are associated with resistan ce: resistan t p ests h ave th e sam e rep rod u ctive p oten tial an d su rvival cap acity as su scep tible on es.

Our M odel Ou r m odel bu ilds on Hu rley an d oth ers (forth com in g). It is based on p est p op u lat io n d yn am ics t h at allo w t h e d irect m easu rem en t o f resist an ce d evelo p m en t followin g th e Hard y-Wein berg p rin cip le d escribed in th e in trod u ction . Th e o n ly d ifferen ce fro m t h e gen et ics o f t h e p est p o p u lat io n in t h e Hu rley an d o t h ers m o d el is t h at a ran d o m elem en t is in t ro d u ced t o m im ic t h e real variab ilit y o f t h e p est p o p u lat io n fro m year t o year. ECB p o p u lat io n s are h igh ly variab le, an d it is d ifficu lt t o accu rat ely p red ict co rn b o rer p ressu re fro m t h e p revio u s year’s p est p o p u lat io n size. Also , ad d in g a st o ch ast ic elem en t p reven ts a collap se in th e ECB p op u lation in th e field with ou t su dden ly in creasin g th e p op u lation size beyon d reason . Determ in istic m od els ten d to exh ibit su ch a lon g-term collap se of th e p est p op u lation , a p h en om en on th at m ost observers th in k is u n realistic. Each year, t h e in it ial p est p o p u lat io n size o n t h e n o n -Bt field s is d rawn from a u n iform ran dom distribu tion . Th e stoch astic sh ock does n ot affect th e gen et ic m akeu p o f t h e p est p o p u lat io n becau se it rep resen t s en viro n m en t al co n d it io n s su ch as weat h er an d am o u n t o f rain fall. Th e ran d o m n u m b er is

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 101

th e sam e for all th e fields con sidered, reflectin g th e fact th at atm osp h eric con dition s are likely to be sim ilar across adjacen t fields. On th e Bt fields, th e size of th e in itial p op u lation eq u als su rvivors from th e p reviou s year p lu s a fraction of th e sam e p op u lation sh ock th at affects th e n on -Bt fields. Scalin g down t h e sh o ck in creases t h e realism o f t h e sim u lat io n resu lt s in t wo ways. First , sim u lated ECB p op u lation s on th e Bt field s ten d to be sm aller th an th ose in th e n on -Bt fields. Th is allows resistan ce to Bt to actu ally occu r.3 Secon d, farm ers treatin g with tradition al sp rays on th e n on -Bt fields will be u n able to drive th e p est p op u lation s to extin ction becau se of th e larger p op u lation sh ocks. Th e p est p op u lation an alyzed h as two gen eration s p er year (bivoltin e), bu t t h e m o d el is gen eralizab le t o u n ivo lt in e o r m u lt ivo lt in e p o p u lat io n s. Mo re gen erally, t h is fram ewo rk is easily ap p licab le t o all p est s t h at exh ib it so m e degree of m obility, ran gin g from in sects to weeds an d fu n gi, an d to crop s th at su ffer dam age from a com m on p est p op u lation .4 Th e m o d el is b ased o n n in e co rn field s, so m e o f wh ich —always t h e sam e 5 —are p lan t ed wit h Bt co rn . Fo llo win g O n st ad an d Gu se (1999) an d Mason an d oth ers (1996), th e dam age fu n ction of th e ECB is lin ear, bu t differen tiated, across gen eration s. First-gen eration ECBs cau se m ore dam age to corn becau se th ey attack it at an earlier stage of develop m en t wh en th e p lan t stalk can wit h st an d less d am age. Th e farm er p lan t in g t h e n o n -Bt co rn h as t h e ch oice of ap p lyin g a n on -Bt based p esticide for both th e first- an d secon d-gen eration p ests. Th e cost of ap p lyin g th e ch em ical in p u t is fixed , an d th e p esticid e h as a m axim u m efficacy bou n d th at is set at variou s levels ran gin g from 70% t o 90%. Th e reaso n fo r an alyzin g vario u s levels o f efficacy is t h at t h e level o f efficacy o f t h e sp rayed p est icid e d et erm in es t h e effect ive size o f t h e u n st ru ct u red refu ge: fo r a given level o f m arket p en et rat io n , t h e h igh er t h e efficacy of th e sp ray, th e lower th e effective level of u n stru ctu red refu ge. Also, t h e effect iven ess o f sp rays h as been in creasin g in t h e recen t p ast , so t h at at th is tim e, efficacy can reach 90% in op tim al con dition s (Hellm ich 1998). Th e d ecisio n t o sp ray is b ased o n eco n o m ic t h resh o ld s d escrib ed in Maso n an d oth ers (1996); th e th resh old s d ep en d on th e level of d am age of th e p est, th e co st s o f sp rayin g, an d , o f co u rse, t h e effect iven ess o f t h e p est icid e. As we n oted earlier, th e p est p op u lation m odeled is in th e h igh ran ge becau se th is is m ostly th e case in location s wh ere sign ifican t acreage of Bt corn is p lan ted. Bt farm ers p lan t corn an d refu ge, wh ich is left u n sp rayed . Th e refu ge size co n sid ered is 20% o f t h e field , wh ich is co n sist en t wit h cu rren t EPA regu lation . Followin g Hu rley an d oth ers (forth com in g), th is p rop ortion of th e field is con stan t th rou gh ou t th e tim e h orizon . Th e yearly p rofit p er acre for th e Bt farm er is given by

{ [

] }

[

]

(1 − θ) pY 1 − ( EG1 N G1 + EG 2 N G 2 ) − β + θpY 1 − ( EG1 N G1 + EG 2 N G 2 ) − C

(1)

102 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

wh ere 6 θ = p rop ortion of refu ge, h ere 20% p = real corn p rice p er bu sh el at 1992 p rices, $2.35 Y = p est-free average yield, 130 bu sh els p er acre N G1 an d N G2 = n u m ber of p ests p er p lan t, first an d secon d gen eration s EG1 an d EG2 = dam age p er p est p er p lan t, EG1 = 0.05 an d EG2 = 0.024 C = costs of p rodu ction n et of th e sp rayin g p rice, $185 p er acre β = Bt p rem iu m , $10 p er acre We assu m e th ere are n o p rice or yield differen tials between th e Bt corn an d th e h ybrid p lan ted in th e refu ge. Becau se th e d am age fu n ction is lin ear, an d m atin g is ran dom , we can rewrite Eq u ation 1 as

[

]

pY 1 − ( EG1 N G1 + EG 2 N G 2 ) − C − (1 − θ)β

(2)

Th e n on -Bt farm er m axim izes

[

]

pY 1 − EG1 N G1 (1 − αS1 ) − EG 2 N G 2 (1 − αS2 ) − C − χ(S1 + S2 ) s.t. α ∈[0 . 7 , 0 . 8 , 0 . 9 ] an d S1 , S2 ∈ {0 ,1}

(3)

wh ere χ = cost of th e sp ray ap p lication , $14 p er acre S1 = n on -Bt sp ray ap p lication for first-gen eration ECB S2 = n on -Bt sp ray ap p lication for secon d-gen eration ECB α = m axim u m efficacy of th e n on -Bt sp ray Th e sizes of th e in itial p est p op u lation in th e Bt an d n on -Bt field s in each seaso n are calibrat ed t o en su re t h at sp rayin g o ccu rs regu larly in t h e n o n -Bt fields th rou gh ou t th e 15 years con sidered an d th at th e p est p op u lation in th e Bt field s can reach t h e sm all size n ecessary fo r resist an ce t o d evelo p in t h e absen ce of m obility bu t d oes n ot collap se an d can in crease again on ce resistan ce is establish ed. Th e in itial p est p op u lation in th e n on -Bt fields each year is given by N G1 (t) = ε an d ε ∼ U[0, 0.1]

(4)

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 103

Th e in itial p est p op u lation in th e Bt fields each year is given by th e su rvivin g secon d-gen eration p ests, SG2 , p lu s th e stoch astic elem en t e scaled by a factor φ N G1 (t) = SG2 (t – 1)+ φe φ = 0.000001 an d ε ~U[0, 0.1]

(5)

Th e p resen ce of th e p reviou s year’s su rvivors in th e d eterm in ation of th e in itial p est p op u lation for th e n ext season gu aran tees th at th e p est p op u lation n u m bers in th e Bt fields can in crease on ce resistan ce is establish ed. Th e sh ock, com m on to Bt an d n on -Bt fields, gu aran tees th at th e p op u lation does n ot collap se, wh ereas t h e scalin g fact o r φ en su res t h at , at first , t h e p est p o p u lat io n n u m bers decrease en ou gh for resistan ce to develop . Th e in t raseaso n p o p u lat io n d yn am ics, t h at is, t h e relat io n sh ip b et ween first an d secon d gen eration , are th e sam e as in Hu rley an d oth ers (forth com in g) an d is detailed in On stad an d Gu se (1999). Th e ap p roach is based on den sity-dep en den t su rvival of th e corn borers. Th is sim u lates th e fact th at com p etition cau ses a redu ction in su rvival as th e den sity of corn borers in creases so th at th e growth fu n ction of th e p ests follows a logistic cu rve. Eq u ation s 1 an d 3 in corp orate th e effects of th e p op u lation d yn am ics an d th e im p act of ch an ges in th e p est’s gen etic m akeu p . Ch an ges in N G1 an d N G2 can be th e d irect resu lt of ch an ges in th e p est p op u lation ’s size or, in d irectly, can b e cau sed b y variat io n s in t h e gen et ic freq u en cy o f resist an t p est s. As resistan ce in creases, th ere is a decrease in th e effectiven ess of th e Bt toxin s so th at m ore p ests su rvive an d d am age th e crop . Becau se ou r focu s is resistan ce to Bt, we will assu m e th at resistan ce to th e sp ray p esticides u sed by th e farm ers p lan tin g con ven tion al h ybrid s d oes n ot d evelop . Th is wou ld be th e case, for in stan ce, if farm ers rotated p esticid es with d ifferen t m od es of action . Th e rate of in terest u sed for calcu latin g th e n et p resen t valu e of p rodu ction is 4%. As n o t ed earlier, t h e t im e h o rizo n u sed is 15 years, wh ich is a co n servat ive estim ate of th e tim e in wh ich backstop tech n ologies will becom e available. Th e m o b ilit y o f t h e p est is p aram et erized b y t h e p ercen t age o f t h e p est p op u lation on a field th at m oves to n eigh borin g field s an d th en breed s with t h e lo cal p o p u lat io n . Here we u se t h ree levels o f p est m o b ilit y: 1 p est p er 10,000, 1 p est p er 100,000, or 1 p est p er 1,000,000 will leave th e field . Note th at su ch low m obility will ten d to give con servative resu lts in term s of resistan ce d evelo p m en t (sim u lat ed resist an ce levels will likely b e o verst at ed )

104 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

b ecau se lo w m o b ilit y will lim it t h e in flu x o f su scep t ib le p est s in t o t h e Bt fields. Th is form of effective p est m obility is d e facto a red u ced form em bod yin g two kin d s of variables: th e first is th e p est m obility p rop er, as d eterm in ed by b io lo gical an d en viro n m en t al fact o rs, an d t h e seco n d is t h e farm size. Th e larger th e field , th e less likely p ests are to create an extern ality by m igratin g from on e farm to th e n ext, as th ey ten d to live an d m ate with in th e p erim eter o f t h e field . Co n sist en t wit h field evid en ce, o n ly first -gen erat io n ECBs are m odeled as m ovin g ou tside th e field. 7 We assu m e t h at p est s will m o ve o n ly t o ad jacen t field s. We also assu m e th at th e grid of n in e field s exam in ed is rep resen tative of a larger p rod u ction regio n t h at fo llo ws t h e sam e p ro d u ct io n p ract ices as t h o se d escribed in t h is grid . More sp ecifically, th is en tails th at th e p rod u ction ch aracteristics of th e n in e field s exam in ed are m irro red in t h e n eigh bo rin g n in e field gro u p s. An exam p le is given in Figu re 4-3, in wh ich th e gray area in th e cen ter is th e field actu ally an alyzed in th e sim u lation s.

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FIGURE 4-3. Example of the Spatial Grid Used in the M odel Note: Th e darker areas in th e Bt fields rep resen t refu ges.

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Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 105

Th is form ulation h as th e advan tage th at th e position in g of fields in th e grid becom es irrelevan t, an d th e on ly variable th at affects resu lts is h ow m an y Bt fields th ere are in th e grid, wh ich allows u s to con cen trate on m arket pen etration . Th e m odel is program m ed in Matlab’s sim ulation en viron m en t, Sim ulin k. Each 15-year scen ario is rep licated 100 tim es. It is im p ortan t to n ote th at th e cost of p esticid e ap p lication p er acre for th e n on -Bt field s rep resen ts on ly th e d irect cost. It d oes n ot in clu d e th e tim e th at th e farm er sp en d s scou tin g for pests to determ in e th e pest population levels. Th erefore, th e results presen ted in th e n ext section will gen erally un derestim ate th e ben efits of Bt corn .

Results Resu lts for th e baselin e case of zero m obility corresp on d to th e zero an d fu llm arket p en etration cases. If all farm ers p lan t n on -Bt h ybrids, n o resistan ce to Bt will occu r an d p rofits will be determ in ed by th e efficacy of th e sp rayed p esticid es an d th e m od alities of th eir ap p lication s. If, h owever, all farm ers p lan t Bt corn , th e evolu tion of resistan ce will follow th e sam e p ath as if on ly on e farm er were p lan tin g Bt, actin g in an isolated en viron m en t. In th e baselin e case of n o p est m obility, th e n et p resen t valu e p er acre of p lan t in g Bt co rn fo r 15 years is $1,300.85. Th ere is lit t le variab ilit y in t h e retu rn s across th e sim u lation ru n s becau se Bt toxin s are extrem ely effective in killin g ECB, an d th e p op u lation d oes n ot h ave tim e to recover in th e 15-year tim e h orizon con sid ered . Th e average p rop ortion of fin al freq u en cy of resistan ce alleles is 0.76, with a stan d ard d eviation of 0.29. Th erefore, on average, at th e en d of th e 15-year tim e h orizon , resistan ce alleles accou n t for 76% of th e total, im p lyin g th at resistan ce d oes in d eed occu r with zero m obility an d 20% refu ge. Th is resu lt is con sisten t with p reviou s fin din gs (see, for exam p le, Hu rley et al. forth com in g). As for th e farm ers p lan tin g a n on -Bt h ybrid , th eir p rofits will dep en d on th e effectiven ess of th e p esticide th ey h ave at th eir disp o sal an d o n t h e p est p o p u lat io n d yn am ics. Tab le 4-1 sh o ws h o w p ro fit s in crease as t h e p est icid e efficacy go es u p . Fo r an y given p est icid e efficacy, p rofits are always h igh er for th e lower p est p op u lation becau se th e p op u lation cau ses less dam age an d req u ires fewer p esticide ap p lication s. TABLE 4-1. Average Net Present Value of Non-Bt Profits per Acre with Zero M obility Pesticide efficacy (percentage of pest population killed) 70 80 90

Dollars $1,122.80 (27.96) $1,161.62 (24.04) $1,213.72 (13.37)

Note: Stan dard deviation s across sim u lation ru n s are in p aren th eses.

106 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

Th e effect of an in crease in p esticid e efficacy is twofold . First, th e n u m ber o f ap p licat io n s t o co n t ro l first -gen erat io n co rn bo rers in creases becau se t h e cost of ap p lication is th e sam e bu t its p rodu ctivity is h igh er. Secon d, th e n u m b er o f p est icid e ap p licat io n s t o co n t ro l seco n d -gen erat io n co rn b o rers go es down as th e first ap p lication ’s level of con trol in creases. Tab le 4-2 rep o rt s t h e average n u m b ers o f t im es t h at sp rayin g o ccu rs fo r first- an d secon d -gen eration borers in th e 15-year tim e fram e. For in stan ce, a farm er wh o h as at h is o r h er d isp o sal a p est icid e wit h an 80% efficacy will sp ray on average 7.6 years ou t of 15 for first-gen eration borers an d 9.2 years ou t of 15 for secon d-gen eration borers. Th e resu lts rep orted in Table 4-2 illu strate th at th e average p est p op u lation s u sed in th e sim u lation s were set at a h igh level. Th is ch oice is m otivated by two con sid eration s. First, Bt ad op tion rates are likely to be h igh er wh ere corn borer p ressu re is in ten se becau se th e tech n ology is m ore valu able to farm ers. If th e farm er h ad n ot ad op ted Bt, h e or sh e wou ld h ave h ad to sp ray very freq u en tly, th erefore retu rn s wou ld h ave been su bstan tially lower. Secon d , in term s of th e d evelop m en t of resistan ce, lower p est p op u lation s are n ot likely to exh ibit a su bstan tially differen t beh avior becau se th e p est p op u lation will be lower in both th e Bt an d n on -Bt fields. Th e in trod u ction of m obility h as little effect on th e p rofits of th e Bt farm ers. Th e reason for th is is th at th e corn borers m ovin g in to th e Bt field from th e n on -Bt field s ten d to be su scep tible to th e Bt toxin so th e p ests are killed off an d are n ot able to cau se an y dam age. Th u s th e size of th e n egative extern ality cau sed by th e p ests n ot killed on th e Bt fields is n early zero. Sim ilarly, for th e n on -Bt farm ers, p rofits are u n affected by ch an ges in th e level o f m arket p en et rat io n fo r all levels o f m o b ilit y co n sid ered . Ret u rn s d ep en d o n ly o n t h e efficacy o f t h e p est icid es t h at farm ers h ave at t h eir d isp osal. Th e reason resides in th e m u ch lower p est p op u lation den sities th at are fou n d in th e Bt field s, th e relatively low levels of m obility con sid ered in th e sim u lation s, an d th e fact th at th e sp ray p esticid es h ave a m od e of action d ifferen t from Bt so th ey can easily kill th e few resistan t p ests m ovin g ou t of th e Bt field s. Th u s t h e size o f t h e n egat ive ext ern alit y cau sed by su rvivin g p est s m ovin g from Bt fields to n on -Bt fields is also n early zero.

TABLE 4-2. Average Number of Pesticide Applications for the Non-Bt Farmers Pesticide efficacy (percentage of pest population killed) 70 80 90

First-generation 6.7 (1.9) 7.6 (1.8) 8.6 (1.8)

Note: Stan dard deviation s across sim u lation ru n s are in p aren th eses.

Second-generation 12.5 (1.3) 9.2 (1.8) 4.5 (1.8)

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 107

As for resistan ce, with 20% refu ge in th e Bt field s, th ere are n o ch an ges to th e gen etic m akeu p of th e p est p op u lation in th e n on -Bt fields. Th is in dicates th at th e sp read of foci of resistan ce ou tside th e Bt fields m igh t becom e a con cern on ly for very h igh levels of m arket p en etration an d low com p lian ce to t h e refu ge reco m m en d at io n s. Th is d o es n o t im p ly t h at n o resist an ce will d evelop in th e Bt field s. As we will see n ext, th is is n ot gen erally th e case. It does h owever m ean th at resistan ce is p robably goin g to be con tain ed in th e Bt field s becau se very few resist an t co rn bo rers will m o ve o u t o f t h e field . Th e sm all n u m ber th at m ove to th e n on -Bt areas will eith er m ate with su scep tible in sects or be killed by th e ap p lication s of sp ray p esticid es. Th is su ggests th at th e size of th e n egative extern ality cau sed by m ovem en t of resistan t ECB from Bt fields to n on -Bt fields is also sm all. In th e Bt field s, resistan ce cou ld very well d evelop d ep en d in g on th e level of m arket p en etration , th e efficacy of th e p esticid e u sed in th e n on -Bt areas, an d th e level of m obility an d of p est p op u lation p ressu res. Sp ecifically, lower levels of m obility cau se m ore resistan ce to develop becau se of th e isolation of resistan t p ests. Figu re 4-4 sh ows th at resistan ce is n ot an issu e for p est m obility levels greater th an 1 in 100,000 p ests m ovin g ou t of a field . High er levels of m obility in trodu ce en ou gh su scep tible p ests in to th e Bt fields to dilu te th e resist an ce gen es. Th at is, wh en m o b ilit y is h igh , n at u ral refu ge cau sed b y in co m p let e m arket p en et rat io n o f t h e t ech n o lo gy is ext rem ely effect ive in lim itin g th e bu ild u p of resistan ce on Bt field s. Th is su ggests th at th e op tim al level of regu latory refu ge cou ld be su bstan tially lower wh en m arket p en etration is low th an wh en it is h igh . Resistan ce on Bt fields cou ld becom e a con cern if m obility is very low an d m arket p en etration is h igh . As Figu re 4-4 illu strates, for very low m obility, th e fin al freq u en cy of resistan ce wou ld be h igh er th an 0.1 for m arket p en etration levels greater th an 60%. It is im p ortan t to n ote th at n eith er m arket p en etration n or p esticide efficacy p lay a role in th e develop m en t of resistan ce for th e h igh er levels o f m o b ilit y: t h e ab so lu t e n u m b er o f p est s leavin g t h e n o n -Bt field s is always h igh en ou gh to gu aran tee th at resistan ce d oes n ot take h old . Th e p rop ortion of resistan t alleles stays low irresp ective of th e level of m arket p en etration an d p esticid e efficacy for th e h igh est levels of m obility. Even m ore in terestin gly, stan d ard d eviation s are very low, an d th e fin al freq u en cy of resistan ce is well below 0.01 in all th e sim u lation ru n s. Th in gs are n ot su bstan tially differen t if m obility decreases to 0.001%, with two excep tion s. Stan dard deviation s in crease for th e h igh est level of m arket p en etration , an d th ere is a p ositive, if low, p robability th at th e fin al freq u en cy of resistan ce m igh t be h igh . If p esticid e efficacy is 70%, th e p robability th at th e fin al freq u en cy of resistan ce exceeds 0.1 is 0.0025. Bo t h p est icid e efficacy an d m arket p en et rat io n p lay a ro le in t h e lo west level of m obility an alyzed h ere. Figu re 4-4 in dicates th at, if th e Bt tech n ology

108 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

Final Proportion of Resistance

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is u sed in h alf o f t h e field s o r so , resist an ce will in crease su bst an t ially. Varian ces are very h igh as well, an d th ey ten d to in crease as m arket p en etration in creases. Also, at th is very low level of m obility, lower p esticid e efficacy will m argin ally in crease t h e d evelo p m en t o f resist an ce, at lo w levels o f m arket p en etration , above th e levels sh own in Figu re 4-4. Th e reason is th at th e lower efficacy of th e p esticid e will brin g abou t h igh er n u m bers of su scep tible corn borers m ovin g in to th e Bt field s. As th ey m ate with resistan t corn borers, th e n u m ber of h eterozygotes in creases. As discu ssed earlier, th ese resu lts are m u ch less worrisom e th an th ey m igh t ap p ear at first sigh t wh en we take in to accou n t th at th e very sm all p op u lation size will en su re th at th e resistan ce is n ot tran sm itted to th e n on -Bt fields. Th e few resistan t p ests escap in g from th e Bt fields will eith er m ate with su scep tible p ests or be killed off by th e p esticides u sed by th e n on -Bt farm ers, wh ich h ave a m o d e o f act io n d ifferen t fro m Bt. Th is u n d ersco res t h e im p o rt an ce o f t h e assu m p tion we m ade th at th e farm ers p lan tin g tradition al h ybrids do n ot u se a Bt-based sp ray. If t h e n o n -Bt areas were sp rayed wit h a Bt-based p est icid e, resistan ce m igh t well sp read from th e tran sgen ic p lan ted fields.

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 109

Conclusion In gen eral, in th e case of Bt corn , th e n et ou tcom e of th e p resen ce of extern alities d iscu ssed in th e in trod u ction is clear. Farm ers u sin g trad ition al h ybrid s h ave a h igh er p est p o p u lat io n t h at is h igh ly su scep t ible t o Bt. Th e n egat ive extern ality p rodu ced by th e n et in flu x of th ese p ests in to th e Bt fields is sm all. An d it is m o re t h an o ffset b y t h e p o sit ive im p act t h at t h e su scep t ib le p est s h ave on d elayin g resistan ce bu ild u p . Fu rth erm ore, th e n u m ber of p ests m ovin g in to th e n on -Bt field s is very low an d d oes n ot cau se sign ifican t d am age. Th e sim u lation resu lts in d icate som e p aram eter levels at wh ich th e sp read o f resist an ce m igh t b eco m e a co n cern . First , t h e resu lt s are fairly ro b u st — resistan ce d oes n ot sp read from th e Bt to th e n on -Bt field s, at least in th e 15year tim e h orizon con sidered h ere. Th is is an im p ortan t resu lt becau se it su ggest s t h at even if fo ci o f resist an ce d evelo p , t h ey will b e co n t ain ed b y t h e h igh er p o p u lat io n p ressu re in ad jacen t field s: t h e h igh d o se co n cep t d o es in deed work. Secon d, for th e two h igh er levels of m obility con sidered—wh ich are still very con servative in term s of h ow m an y corn borers will m ove from field to field —th e Bt field s th em selves d o n ot becom e sign ifican tly resistan t. In ad d ition , for th e levels of m obility con sid ered , lack of com p lete m arket p en etration of Bt corn sign ifican tly red u ces th e bu ild u p of resistan ce on Bt fields. Th is suggests th at th e optim al level of refuge on Bt fields is likely con siderably lower th an th e 20% level set by cu rren t regu lation s. Th is su ggests th at th e 20% refu ge is p robably on ly op tim al if m arket p en etration is com p lete or m obility is zero—wh ich are exactly th e scen arios con sidered by previous an alyses th at were con sulted wh en EPA decided on th e 20% refuge level. To p u t t h e m o b ilit y p aram et ers in t o p ersp ect ive, let u s co n sid er so m e o f th e resu lts of th e Sh owers an d oth ers (2000) p ap er m en tion ed in th e in trodu ction . Accordin g to th e U.S. Dep artm en t of Agricu ltu re (USDA 1999), th e average farm size in th e Un ited States in 1997 was 436 acres or 1.744 sq u are kilom eters. If we sim p listically assu m e th at th e farm s are sq u are, th ey will h ave a side of abou t 1,321 m eters. Sh owers an d oth ers in 1986 released 283,436 adu lt corn borers at th e begin n in g of th e growin g season . 8 Th ey set u p trap s at 200, 800, an d 3,200 m eters from th e release site. At th e 3,200-m eter distan ce, th ey retrieved 35 corn borers, or 0.012% of th e in sects th at h ad been released . Of cou rse, cau tion is n ecessary in th e u se of th ese data. For in stan ce, th e Sh owers exp erim en t set u p t h e t rap s t o ret rieve t h e co rn b o rers in h ab it at s d ifferen t from corn : in th e sp ecific case m en tion ed h ere, th ey were th ree com bin ation s of brom e, alfalfa, gian t foxtail, an d a creek. Sh owers rep orts th at h abitat was a sign ifican t fact o r in d et erm in in g t h e n u m b er o f co rn b o rers ret rieved . Th is in dicates th at corn -from -corn m ovem en ts m igh t h ave differen t ch aracteristics fro m t h e o n es Sh o wers an d o t h ers rep o rt ed in 2000. Th e d irect io n o f fligh t also seem s to be sign ifican t, an d th is su ggests th at th e disp ersal m igh t n ot be

110 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements

as h o m o gen eo u s as t h e sim u lat io n s h ave assu m ed . Desp it e t h ese caveat s, h owever, th e Sh owers resu lts in d icate th at th e levels of m obility u sed in th e scen arios discu ssed earlier are likely to be lower th an th ey actu ally are. Market p en et rat io n p lays a ro le at t h e lo west level o f m o bilit y. In su ch a scen ario, h avin g m ore th an 50% of th e field s p lan ted with Bt corn m igh t be p ro blem at ic. In gen eral, t h e resu lt s o n t h e freq u en cy o f resist an ce in t h e Bt field s are h igh ly d ep en d en t on th e level of p est m obility. Th is p oin ts ou t th e im p o rt an ce o f co llect in g m o re in fo rm at io n o n t h e ch aract erist ics o f t h e m o vem en t o f t h e ECB. Th e sim u lat io n s p resen t ed h ere su ggest o t h er q u est io n s fo r fu t u re research . First , t h e grid size co u ld b e in creased t o an alyze wh eth er scale p lays a role in th e sp read of resistan ce. In p articu lar, in all th e cases p resen ted h ere, th e Bt fields were con tigu ou s to at least on e n on -Bt field. A fin er grid co u ld allo w t h e exp lo rat io n o f t h e case o f a less-t h an -co m p let e m arket p en et rat io n wit h Bt field s bein g co m p let ely su rro u n d ed by Bt field s. Secon d , if m obility is very low, th e assu m p tion of ran d om m atin g is likely to becom e less rep resen tative of th e beh avior of th e p est p op u lation : th e n u m ber of corn borers in th e Bt fields is very low, so it m igh t h ap p en th at th e resistan t borers su rvivin g in th e Bt p ortion of th e fields will ten d to m ate am on g th em selves, as will th e su scep tible borers livin g in th e refu ge. Th erefore, th e p ossibility of n on ran dom m atin g in th e Bt fields sh ou ld be taken in to accou n t, an d its im p act on resistan ce develop m en t sh ou ld be exam in ed. Th ird, th e sim u lation s su ggest th at com p lian ce to th e refu ge recom m en d ation s m igh t be critical t o t h e p reservat io n o f su scep t ib ilit y. Th e in t ro d u ct io n o f a co m p lian ce fu n ct io n co u ld in crease t h e sign ifican ce o f t h e m o d el’s resu lt s. Also , m o re work is n eed ed on th e d eterm in an ts of m arket p en etration . In p articu lar, th e role of exp ort m arkets beh avior an d h istorical corn borer in festation s in determ in in g p lan tin g decision s n eeds to be fu rth er in vestigated. Th ese issu es seem to h ave been th e m ain in flu en ces beh in d th e recen t tren ds of Bt corn acreage (USDA 2001). Fin ally, th e resu lts also su ggest th at, u n d er certain circu m stan ces, trad able refu ges m igh t be u sed to com p en sate farm ers p lan tin g trad ition al h ybrid s for th e p ositive extern ality th ey p rovide to farm ers p lan tin g Bt crop s. 9 So far, EPA h as focu sed on in -field refu ges, wh ich , as we n oted earlier, m igh t be p roblem atic from th e stan d p oin t of com p lian ce. Trad able refu ges m igh t be a su p erior p olicy if p est m obility is h igh an d m arket p en etration is low.

References Cap rio, M.A. 1998. Evalu atin g Resistan ce Man agem en t Strategies for Mu ltip le Toxin s in th e Presen ce of Extern al Refu ges. Journal of Econom ic Entom ology 91(5): 1021–31. Croft, B.A., an d J.E. Du n ley. 1993. Habitat Pattern s an d Pesticide Resistan ce. In Evolution of Insect Pests: Patterns of Variation, edited by K.C. Kim an d R.A. McPh eron . New York: Joh n Wiley an d Son s.

Chapter 4: Pest M obility, M arket Share, and Refuge Requirements • 111 Dively, G.P., P.A. Fo llet t , J.J. Lin d u ska, an d G.K. Ro d erick. 1998. Use o f Im id aclo p rid Treated Row Mixtu res for Colorado Potato Beetle (Coleop tera: Ch rysom elidae) Man agem en t. Journal of Econom ic Entom ology 91(2): 376–87. Geo rgh io u , G.P., an d C.E. Taylo r. 1977. O p erat io n al In flu en ces in t h e Evo lu t io n o f In secticide Resistan ce. Journal of Econom ic Entom ology 70(3): 319–23. Hartl, D.L., an d A.G. Clark. 1989. Principles of Population Genetics, Secon d Ed ition . Su n derlan d, MA: Sin au er Associates. Hellm ich , R.L. 1998. Person al com m u n ication with th e au th ors, Decem ber 8. Hu eth , D., an d U. Regev. 1974. Op tim al Agricu ltu ral Pest Man agem en t with In creasin g Pest Resistan ce. Am erican Journal of Agricultural Econom ics 56: 543–51. Hu rley, T.M., B.A. Babco ck, an d R.L. Hellm ich . Fo rt h co m in g. Bio t ech n o lo gy an d Pest Resistan ce: An Econ om ic Assessm en t of Refu ges. Journal of Agricultural and Resource Econom ics. Hu rley, T.M., S. Secch i, B.A. Babcock, an d R.L. Hellm ich . 1999. Managing the Risk of European Corn Borer Resistance to Transgenic Corn: An Assessm ent of Refuge Recom m endations. St aff Rep o rt 99-SR88. Am es, IA: Cen t er fo r Agricu lt u ral an d Ru ral Develo p m en t, Iowa State Un iversity. Lazaru s, W.F., an d B.L. Dixon . 1984. Agricu ltu ral Pests as Com m on Prop erty: Con trol of th e Corn Rootworm . Am erican Journal of Agricultural Econom ics 66: 456–65. Mason , C.E., M.E. Rice, D.D. Calvin , J.W. Van Du yn , W.B. Sh owers, W.D. Hu tch in son , J.F. Witkowski, R.A. Higgin s, D.A. On stad, an d G.P. Dively. 1996. European Corn Borer Ecology and Managem ent. No rt h Cen t ral Regio n al Ext en sio n , Pu b licat io n No . 327. Am es, IA: Iowa State Un iversity. On stad, D.W., an d C.A. Guse. 1999. Econom ic Analysis of Transgenic Maize and Nontransgenic Refuges for Managing European Corn Borer (Lepidoptera: Pyralidae). Un p u blish ed rep ort. Ch am paign , IL: Cen ter for Econ om ic En tom ology, Illin ois Natural History Survey. Peck, S.L., F. Go u ld , an d S.P. Elln er. 1999. Sp read o f Resist an ce in Sp at ially Ext en d ed Regio n s o f Tran sgen ic Co t t o n : Im p licat io n s fo r Man agem en t o f Heliothis virescens (Lep idop tera: Noctu idae). Journal of Econom ic Entom ology 92(1): 1–16. Perez, C.J., A.M. Sh elton , an d R.T. Rou sh . 1997. Man agin g Diam on d back Moth (Lep idop tera: Plu tellidae) Resistan ce to Foliar Ap p lication s of Bacillus thuringiensis: Testin g Strategies in Field Cages. Journal of Econom ic Entom ology 90(6): 1462–70. Regev, U., A.P. Gu tierrez, an d G. Fed er. 1976. Pests as a Com m on Prop erty Resou rce: A Case Stu d y of Alfalfa Weevil Con trol. Am erican Journal of Agricultural Econom ics 58: 186–97. Regev, U., H. Sh alit, an d A.P. Gu tierrez. 1983. On th e Op tim al Allocation of Pesticid es with In creasin g Resistan ce: Th e Case of th e Alfalfa Weevil. Journal of Environm ental Econom ics and Managem ent 10: 86–100. Sh o wers, W.B., R.L. Hellm ich , M.E. Derrick-Ro b in so n , an d W.H. Hen d rix III. 2000. Aggregation and Dispersal Behavior of Marked and Released European Corn Borer (Lepidoptera: Cram bidae) Adults. Un p u b lish ed rep o rt . Am es, IA: Co rn In sect s an d Cro p Gen et ics Research Un it , USDA-ARS an d Dep art m en t o f En t o m o lo gy, Io wa Agricu ltu re an d Hom e Econ om ics Exp erim en t Station , Iowa State Un iversity. Taylor, C.R., an d J.C. Hadley. 1975. In secticide Resistan ce an d th e Evalu ation of Con trol Strategies for an In sect Pop u lation . The Canadian Entom ologist 107: 237–42. USDA (U.S. Dep art m en t o f Agricu lt u re). 1999. Farm s an d Lan d in Farm s—Fin al Est im at es 1993–1997. St at ist ical Bu llet in N. 955. (accessed Au gu st 25, 2000).

112 • Chapter 4: Pest M obility, M arket Share, and Refuge Requirements ———. Eco n o m ic Research Service. 2001. Agricu lt u ral Bio t ech n o lo gy: Ad o p t io n o f Biotech n ology an d Its Produ ction Im p acts. Briefin g Room . (accessed Novem ber 15, 2001). U.S. EPA (En viro n m en t al Pro t ect io n Agen cy). 1998a. T he Environm ental Protection Agency’s W hite Paper on Bt Plant-Pesticide Resistance Managem ent. Wash in gt o n , DC: U.S. EPA. ———. 1998b . Pest icid e Fact Sh eet Au gu st 17. (accessed October 30, 1999).

Notes 1. Som e p ests, su ch as th e Eu rop ean corn borer, can h ave on e to fou r gen eration s in each growin g season . 2. Bu n dlin g wou ld occu r, for exam p le, if th e seed p rodu cers sold a su p erior seed on ly in a Bt fo rm . Farm ers wan t in g t o t ake ad van t age o f su ch a p ro d u ct wo u ld h ave n o ch oice bu t to p lan t a Bt crop . 3. It is essen t ial t h at p o p u lat io n s d eclin e t o fairly sm all n u m b ers fo r resist an ce t o becom e p revalen t becau se th e in itial freq u en cy of th e resistan ce gen e is very low to start with . As th e p est p op u lation size declin es, su scep tible p ests (an d th eir gen es) will all be killed by th e p esticid e. Th is n atu ral selection p ressu re allows th e resistan t p ests to take over. 4. For in stan ce, th e m odel cou ld be ap p lied to corn an d cotton , wh ich are both ECB h osts. 5. Th is ap p ears to be a n on trivial q u estion wh en an alyzin g resistan ce d evelop m en t (see Peck et al. 1999). 6. For th e sp ecific valu es see Mason an d oth ers (1996,) On stad an d Gu se (1999), an d Hu rley an d oth ers (forth com in g). 7. Th e reaso n fo r t h is ap p ears t o b e t h at seco n d -gen erat io n p est s h ave less o f an in cen tive to leave th eir corn field, becau se th e corn is at a later develop m en t stage an d p rovides a better h abitat. 8. Sh o wers an d o t h ers (2000) also released —an d recap t u red —co rn b o rers fu rt h er in t o t h e gro win g seaso n . Ho wever, t h e n u m ber o f co rn bo rers ret rieved at a d ist an ce greater th an on e kilom eter was always lower in th e secon d release, in dicatin g th at corn borers ten d to m ove fu rth er away at th e begin n in g of th e season . 9. We are gratefu l to David Sim p son for p oin tin g th is ou t to u s.

Commentary

Need for Direct Collaboration between Economists and Biologists Fred Gould

Ch ap t er 4 by Secch i an d Babco ck rein fo rces t h e n eed fo r in t erd iscip lin ary in teraction in solvin g agricu ltu ral p roblem s. As a biologist, I assu m e th at th e econ om ic assu m ption s of Secch i an d Babcock are appropriate an d con cen trate on th e ecological an d agricu ltu ral assu m p tion s of th eir m od el. In th is regard , two m ajor assu m ption s abou t in sects an d farm ers in th eir ch apter stan d ou t as p roblem atic. Th e assu m p tion of zero or very low levels of m ovem en t of corn bo rers am o n g co rn field s co n t rast s wit h t h e view o f en t o m o lo gist s. Th e assu m p tion th at farm ers will p lan t Bt corn in th e sam e field s year after year an d plan t n on -Bt corn in th e sam e fields year after year is especially u n likely if m o vem en t o f t h e Eu ro p ean co rn bo rer is even t h ree o rd ers o f m agn it u d e h igh er th an assu m ed by Secch i an d Babcock. Th e reason in g h ere is relatively st raigh t fo rward . Befo re a farm er ever p lan t s Bt co rn , let u s assu m e t h ere are 1,000 corn borers per acre in all fields. If th e farm er plan ts n on -Bt corn in field A du rin g year 1, on average, th e den sity of corn borers from th at field th at will in fest it in year 2 is abou t 1,000 per acre (assu m in g th at region al pest den sities are n ot in a lon g-term p h ase of in crease or d eclin e). If field B is p lan ted with h igh -dose Bt corn in year 1, th e n u m ber of corn borers from th at field th at are expected to in fest it in year 2 is fewer th an 1 per acre becau se of th e h igh efficacy of th e toxin . If 1 ou t of every 100 corn borers from field A m oves to field B, th ere will be abou t 990 corn borers per acre in field A an d fewer th an 11 per acre in field B. In No rt h Caro lin a, an d I assu m e in Io wa t o o , a farm er faced with th is situ ation wou ld m ost likely decide to rotate corn varieties in year 2, p lan tin g Bt corn in field A wh ere th ere were lots of corn borers, an d p lan tin g n on -Bt corn in field B wh ere th ere were very few pests. • 113 •

114 • Commentary: Need for Direct Collaboration

Th e assu m p t io n o f t h e m o d el t h at t h e farm er d o es n o t ro t at e field s between Bt an d n on -Bt seem s in correct, bu t th e real q u estion is wh eth er th is in co rrect assu m p t io n h as an y co n seq u en ces o n t h e rat e o f resist an ce evo lu tion . Secch i an d Babcock in d icate th ey are aware th at Peck an d oth ers (1999) h ave p u b lish ed resu lt s in d icat in g t h at t h is issu e o f ro t at io n “ap p ears t o b e n on -trivial,” so th e logic in n ot addressin g th e issu e is n ot clear. Fu rth erm ore, t h e in sect m o d eled by Peck an d o t h ers h as a m u ch h igh er rat e o f in t erfield m ovem en t th an assu m ed by Secch i an d Babcock for corn borers, an d th at differen ce m in im izes th e im p act on resistan ce d evelop m en t of ch oosin g n ot to rotate field s. Gou ld (1986) m od eled Hessian fly ad ap tation to con ven tion ally bred , in secticid al wh eat cu ltivars. Th is in sect h as m obility m ore com p arable to th e m obility of corn borers th an th e system m odeled by Peck an d oth ers. In th e Hessian fly work, I assu m ed eith er 1% in terfield m ovem en t or 10% in terfield in sect m ovem en t an d a h igh in itial resistan ce freq u en cy of 0.1 or 0.2. I ran t h e m o d el wit h an d wit h o u t ro t at io n o f field s b et ween t h e p lan t in g o f wh eat t h at was t o xic an d n o n t o xic t o Hessian fly. Th e sim u lat io n s t h at in clu d ed field rotation resu lted in rap id evolu tion of Hessian fly strain s with t o leran ce o f t h e t o xic wh eat . W h en field s were n o t ro t at ed an d in it ial gen e freq u en cy was 0.1, th e rate of in crease in resistan ce freq u en cy was rap id for th e first few gen eration s in th e toxic crop , bu t th en th e resistan ce freq u en cy in th e toxic crop declin ed an d alm ost stabilized at a low, n on p roblem atic freq u en cy (becau se of recessiven ess). At lower in itial gen e freq u en cies, th e stabilized freq u en cy is exp ected to be even lower. Th e d ifferen ce in o u t co m e relat ed t o farm er b eh avio r was d ram at ic, an d th e resistan ce d yn am ics in th e n on rotation sim u lation s were n on lin ear. It is, th erefore, u sefu l to at least p resen t a sim p lified d escrip tion of th e p op u lation an d gen etic d yn am ics in th e n on rotated case. In th e first year, th e toxic an d n on toxic fields start with iden tical Hessian fly den sity. After th e first year, th e in sect d en sit y in t h e t o xic field s d im in ish es b ecau se ap p ro xim at ely 96% o f t h e su scep t ible Hessian flies are killed . By t h e seco n d year, t h e freq u en cy o f resist an t in sect s in t h e t o xic field s in creases d ram at ically, b u t t h ere are n o t en ou gh of th em to cau se sign ifican t dam age. In th e n on toxic wh eat field, th e p op u lation size of su scep tible in sects in creases stead ily. By th e th ird year, th e d en sity of Hessian flies in th e n on toxic wh eat is m ore th an 100 tim es h igh er t h an in t h e t o xic wh eat field , so m o vem en t o f 10% o f t h e in sect s fro m t h e n o n t o xic t o t h e t o xic wh eat can ju st ab o u t swam p o u t t h e few resist an t in sects in th e toxic crop . Th is lowers th e overall freq u en cy of resistan t in sects an d begin s a lon g selection p h ase in wh ich th e resistan ce freq u en cy in creases at an alm ost im p ercep tible rate. Th e agron om ic p roblem with th is ap p roach is t h at t h e field s t h at are always p lan t ed t o Hessian fly-su scep t ib le wh eat are exp ect ed t o d evelo p very h igh d en sit ies o f t h e p est s, an d t h at co u ld cau se m ajor yield loss.

Commentary: Need for Direct Collaboration • 115

For th e Eu rop ean corn borer, it is gen erally assu m ed th at th e Bt resistan ce gen e freq u en cy (An dow et al. 2000) is m u ch lower th an assu m ed in th e Hessian fly m odel (abou t 0.001 or 0.0001). With low rates of in terfield m ovem en t of adu lt corn borers an d with ou t rotation , th e in terp lay of p op u lation dyn am ics an d p o p u lat io n gen et ics is exp ect ed t o st ym ie p est ad ap t at io n . If Secch i an d Babcock ch an ged th e assu m p tion s in th eir m odel su ch th at corn farm ers p lan t Bt corn in th e field s exp ected to h ave h igh d en sities, th ey wou ld get a differen t ou tp u t. Befo re an y fu t u re wo rk is d o n e o n Bt/ n o n -Bt ro t at io n , t h e rat es u sed fo r in t erfield m o vem en t o f co rn b o rers sh o u ld b e reassessed b ecau se t h is t o o co u ld h ave a m ajo r im p act o n t h e m o d el o u t p u t . W h ile we will n ever h ave p erfect kn owledge of th e rates of m ovem en t, we already kn ow th at th e m ovem en t is m ore th an zero. Farm ers kn ow th at wh en a field p reviou sly p lan ted wit h Bt co rn is p lan t ed wit h n o n -Bt co rn in t h e fo llo win g year, t h e in fest at io n s are m u ch h igh er t h an wo u ld b e exp ect ed if o n ly o ffsp rin g fro m co rn borers th at d evelop ed in th at field in th e p ast year were in festin g th e n ewly p lan ted field. Secch i an d Babco ck ju st ify t h eir u se o f very lo w rat es o f in t erfield m o vem en t on th e basis of resu lts of an u n p u blish ed rep ort by Sh owers an d oth ers (2000). Th ey cit e t h is st u d y as cap t u rin g o n ly 0.012% o f t h e art ificially released corn borer adu lts at 3,200 m eters from th e release site. Th is n u m ber is p resen t ed as an abso lu t e p aram et er, as if 99.998% o f t h e in sect s m o ved less th an th is d istan ce. I d o n ot h ave access to th e cited p u blication . However, if th is research was con du cted like oth er in sect release, recap tu re stu dies, on ly a sm all fract io n o f t h e released in sect s is ever reco vered . Th erefo re, it is n o t ap p rop riate to u se calcu lation s based on th e n u m ber of in sects released . Fu rt h erm o re, as t h e d ist an ce fro m t h e p o in t o f release in creases, t h e sam p lin g d evices b eco m e effect ive o ver a sm aller an d sm aller p ercen t age o f t h e area wh ere th e in sects cou ld be m ovin g (i.e., as th e trap distan ce from th e p oin t of release in creases, th e circu m feren ce of th e circu lar area wh ere in sects cou ld be in creases p ro p o rt io n at ely as 6.28 t im es t h e d ist an ce. Th erefo re, t h e cap t u re rat e also m u st be ad ju st ed fo r t h e fract io n o f t h e area at a d ist an ce o f 3,200 m eters th at was sam p led (Sou th wood 1978). Th e st at em en t t h at d irect in t erd iscip lin ary in t eract io n s are n eed ed t o ad d ress m o st real-wo rld p ro blem s h as been rep eat ed t h o u san d s o f t im es, so th ere is certain ly n oth in g n ew in statin g it on e m ore tim e. However, th e Secch i an d Bab co ck wo rk serves as a rem in d er o f t h e im p o rt an ce o f t h is co m m en t . Wit h o u t d irect in p u t fro m b io lo gist s, eco n o m ist s m ay m ake n aïve assu m p tion s. Had biologists written th is p ap er, th e resu lt m ay h ave been n o m ore u sefu l becau se th e econ om ic asp ects wou ld p robably h ave been n aïve. If both biologists an d econ om ists h ad an eq u al voice in develop in g th is m odel, it wou ld h ave been m u ch m ore u sefu l.

116 • Commentary: Need for Direct Collaboration

References An d ow, D.A., D.M. Olson , R.L. Hellm ich , D.N. Alstad , an d W.D. Hu tch ison . 2000. Freq u en cy of Resistan ce to Bacillus thuringiensis Toxin Cry1Ab in an Iowa Pop u lation of Eu rop ean Corn Borer (Lep id op tera: Cram bid ae). Journal of Econom ic Entom ology 93: 26–30. Go u ld , F. 1986. Sim u lat io n Mo d els fo r Pred ict in g Du rabilit y o f In sect -Resist an t Germ Plasm : Hessian Fly (Dip tera: Cecid om yiid ae)-Resistan t Win ter W h eat. Environm ental Entom ology 15: 11–23. Peck, S., F. Go u ld , an d S.P. Elln er. 1999. Sp read o f Resist an ce in Sp at ially Ext en d ed Regio n s o f Tran sgen ic Co t t o n : Im p licat io n s fo r Man agem en t o f Heliothis virescens (Lep idop tera: Noctu idae). Journal of Econom ic Entom ology 92: 1–16. Sh owers, W.B., R.L. Hellm ich , M.E., an d W.H. Hen drix III. 2000. Aggregation and Dispersal Behavior of Marked and Released European Corn Borer (Lepidoptera: Cram bidae) Adults. Un p u b lish ed rep o rt . Am es, IA: Co rn In sect s an d Cro p Gen et ics Research Un it, USDA-ARS an d Dep artm en t of En tom ology, Iowa Agricu ltu re an d Hom e Econ om ics Exp erim en t Station , Iowa State Un iversity. Sou th wood, T.R.E. 1978. Ecological Methods, Secon d Edition . Lon don : Ch ap m an & Hall.

PART II

The Impact of Resistance

Chapter 5

The Impact of Resistance on Antibiotic Demand in Patients with Ear Infections David H. Howard and Kimberly J. Rask

It is w idely recognized that patterns of antim icrobial use affect prevailing rates of resistance. Less often noted is that, in som e cases, resistance w ill affect prescribing patterns. The first relationship is driven by the biological process of natural selection, the second is driven by physicians’ rational behavioral responses to a changing environm ent. When presented w ith a patient, a physician must estimate for every available antibiotic the probability that the patient’s infection will be cured by the drug. These probabilities will depend on a number of factors, one of which is the rate of resistance to each antibiotic prevailing in the surrounding com m unity. The higher the rate of resistance to a particular antibiotic is, the lower the ex ante probability that it will be effective. All else being equal, the physician will choose the antibiotic associated with the highest probability of cure. Resistance affects physicians’ drug choice via these probabilities; once the rate of resistance to a particular antibiotic reaches a critical level, physicians will cease to use it, instead prescribing its closest substitute. The purpose of this chapter is to m easure em pirically the im pact of resistance on physicians’ drug choice. Documenting the relationship between resistance and drug choice is important because the drugs to w hich m any pathogens have developed resistance are typically the least expensive antibiotics. Therefore, increasing levels of resistance will increase drug spending. The dat a used t o est im at e t he relat ionship com e from a physician office visit-level survey spanning the period 1980 to 1998. They consist of 6,928 observations on patients younger than 18 years of age w ith a diagnosis of ot it is m edia w ho received a prescript ion for 1 of 18 ant ibiot ics.

• 119 •

120 • Chapter 5: The Impact of Resistance on Antibiotic Demand We use a conditional logit m odel to estim ate m arket shares for each drug as a funct ion of drug at t ribut es such as price. We com bine t hese at t ributes w ith a tim e trend variable and interpret these tim e–attribute interact ions as m easuring t he im pact of resist ance levels (w hich are not observed) on physicians’ drug choice. Using t hese result s, w e sim ulat e w hat m arket shares w ould have been in 1997 and 1998 had resist ance levels rem ained at 1990 levels by rest rict ing t he t im e–at t ribut e coefficients to zero. By m ultiplying the m arket share for each drug by its price and t hen sum m ing over drugs, w e est im at e w hat t ot al spending w ould have been. Com paring this figure w ith actual spending, w e conclude that resist ance, by inducing physicians t o sw it ch t o m ore expensive ant ibiotics, increased annual antibiotic spending for initial otitis m edia visits by about 20% in 1997 and 1998. Alt hough t his figure is only a very rough approxim at ion, it show s t hat w hen m easuring t he burden of ant im icrobial resist ance, it is im port ant t o consider t he im pact of resist ance on drug choice and spending.

O

ver t h e last 20 years, u se o f an d sp en d in g o n n ew an t ib io t ics h as in creased . Th is t ren d is o f in t erest t o p o licym akers fo r several reaso n s. First , an t ib io t ics, o n e o f t h e m o st freq u en t ly p rescrib ed d ru g classes in t h e ou tp atien t settin g, are a n atu ral target for cost-cu ttin g efforts. Th e cost differen ce between n ew an d old an tibiotics is su bstan tial, an d th ere is con cern th at p h ysician s an d p at ien t s are n o t su fficien t ly p rice sen sit ive (Berm an et al. 1997; Foxm an et al. 1987; Reed et al. 2002). Secon d , an d m ore im p ortan tly, th e u se of n ewer, m ore p owerfu l an tibiotics is both a cau se an d con seq u en ce of in creasin g an tim icrobial resistan ce. Th e u se of an an tibiotic kills off on ly b act eria su scep t ib le t o t h e an t ib io t ic, leavin g resist an t b act eria in it s wake. New broad-sp ectru m an tibiotics, wh ich ten d to be effective again st m an y differen t b act erial sp ecies, m ay co n t rib u t e t o t h e m o re rap id d evelo p m en t o f resistan ce. At th e sam e tim e, th e u se of n ew an tibiotics m ay be a con seq u en ce o f resist an ce if t h eir ad o p t io n is m o t ivat ed b y p h ysician s’ b elief t h at o ld an tibiotics will n ot be effective. In th is ch ap ter, we estim ate a d iscrete ch oice m od el of p h ysician s’ an tibio t ic ch o ice fo r ch ild ren wit h ear in fect io n s. O u r d at a were t aken fro m an office-visit level su rvey an d sp an th e p eriod 1980 to 1998, wh ich allowed u s to observe h ow p rescribin g tren d s h ave ch an ged over tim e. We ch ose to look at ear in fection , or otitis m edia, becau se it is on e of th e m ost com m on reason s ap art from regu lar ch ecku p s for p h ysician office visits by ch ildren . Resistan ce to an tibiotics am on g th e m icroorgan ism s th at cau se ear in fection s in ch ildren h as in creased in th e last decade. In Streptococcus pneum oniae, wh ich cau ses u p to 50% of ear in fection s, p en icillin resistan ce was fou n d in fewer th an 10% of isolates in 1988 bu t m ore th an 50% of isolates in 1998 (Jacobs 2000).

Chapter 5: The Impact of Resistance on Antibiotic Demand • 121

Previo u s eco n o m ic research o n an t im icro b ial resist an ce h as h igh ligh t ed t h e n egat ive ext ern alit y asso ciat ed wit h an t ib io t ic u se, d ecreased fu t u re an t ib io t ic effect iven ess (Elliso n an d Hellerst ein 1999; Bro wn an d Layt o n 1996), an d derived op tim al-u se p olicies an alogou s to op tim al extraction p olicies for a n atu ral resou rce (Goesch l an d Swan son 2000; Laxm in arayan 2001; Laxm in arayan an d Weit zm an [Ch ap t er 3]; Wilen an d Msan gi [Ch ap t er 1]). Laxm in arayan sh ows, for exam p le, th at p eriod ically rem ovin g an an tibiotic from u se, a p olicy kn own as “cyclin g,” is op tim al on ly u n d er a restrictive set o f assu m p t io n s ab o u t h o sp it als’ co st s. Go esch l an d Swan so n an d Laxm in irayan an d Weitzm an sh ow th at gen erally it is op tim al to u se a n u m ber of differen t an tibiotics sim u ltan eou sly, with th e u se of a p articu lar an tibiotic determ in ed b y it s effect iven ess an d p rice (see Laxm in arayan an d Weit zm an , Ch ap ter 3). We view ou r stu d y as com p lem en tary to th ese efforts. As lon g as we h ave in clu d ed p olicy-relevan t variables, th e estim ates p resen ted h ere can be u sed to design p rogram s to ach ieve th e an tibiotic u se levels recom m en ded by th eory. An u n resolved q u estion in th e econ om ic an d m ed ical literatu re on resistan ce, an d on e of in terest to p olicym akers, is wh at is th e econ om ic im p act of resist an ce? Mu ch o f t h e lit erat u re d iscu sses t h e co st in t erm s o f ad verse even t s (see, fo r exam p le, Co ast et al. 1996), an d p at ien t d eat h b ecau se o f resist an ce in h o sp it als, t h o u gh rare, h as b een d o cu m en t ed at a n u m b er o f in stitu tion s. In ou tp atien t settin gs, organ ism s rem ain su scep tible to at least a few an tibiotics (alth ou gh th ey m ay even tu ally becom e resistan t), an d severe co m p licat io n s cau sed b y u n reso lved ear in fect io n are in freq u en t . 1 Th e p revailin g resistan ce levels in a com m u n ity m ay in flu en ce p h ysician s’ ch oices of in it ial an t ibio t ic t h erap y an d h en ce co st s. Resist an ce in d u ces a sh ift t o ward n ewer an tibiotics, th e in crem en tal cost of wh ich m ay be attribu ted to resistan ce aft er co n t ro llin g fo r t h eir m o re favo rab le d o sin g an d sid e-effect p rofiles. 2 Figu re 5-1 sh ows th at p er-p rescrip tion sp en d in g on an tibiotics u sed to treat ear in fection s in ch ild ren grew from $13 to m ore th an $20 (in 1996 d ollars) between 1980 an d 1998. We u se d em an d estim ates to sim u late h ow m u ch of th e growth in th e u se of n ew an tibiotics was cau sed by in creases in resistan ce. Ou r stu dy adds to an d bu ilds on th e growin g body of literatu re on p h arm aceu t ical d em an d an d m arket s. A n u m b er o f st u d ies h ave in vest igat ed t h e im p act of p rice, ad vertisin g, an d p ast u se on p h ysician s’ ch oice of an tibiotic (Bern d t et al. 1995; Elliso n et al. 1997; Rizzo 1999). Th e Elliso n an d o t h ers stu d y is m ost relevan t to ou rs becau se it focu ses on a sp ecific class of an tibiotic, cep h alosp orin s. Ou r stu d y d iffers from th eirs in th at we d efin e th e m arket by in dication rath er th an an tibiotic class. We also observe in dividu al ch aracteristics, wh ich allows u s to estim ate th e im p act of p h ysician sp ecialty on p rice sen sitivity.

122 • Chapter 5: The Impact of Resistance on Antibiotic Demand

30

25

Dollars

20

15

10

5

0

80

82

84

86

88

90

92

94

96

98

Year FIGURE 5-1. Average Spending per Prescription

Choice M odel Th e decision m aker in ou r ch oice m odel is th e p h ysician . We do n ot dwell on th e divergen ce between p h ysician s’ in cen tives an d p atien ts’ u tility h ere, bu t it is worth m en tion in g th at an tibiotic p rescribin g an d p h ysician visit tim e m ay be su bst it u t es in p ro d u ct io n . Th u s, reim bu rsem en t arran gem en t s will in flu en ce p h ysician s’ ch oice between writin g an an tibiotic p rescrip tion an d watch fu lly waitin g. In ad d ition , sh ou ld p h ysician s d ecid e to p rescribe, th eir ch oice o f an t ibio t ic fro m am o n g t h e available d ru gs will be affect ed by reim bu rsem en t arran gem en ts (i.e., th e m ore p owerfu l th e an tibiotic, th e lower th e p robab ilit y t h at t h e p at ien t will req u ire a fo llo w-u p visit ). We p lan t o exam in e th ese issu es in fu tu re work. We estim ate a m ixed m u ltin om ial logit m odel of p rodu ct ch oice. Write th e u tility V of p h ysician i from an tibiotic j as Vij = γRij + α ′pij + β′xij + εij

(1)

wh ere γ rep resen t s t h e co efficien t o n t h e resist an ce t erm , α an d β rep resen t th e coefficien ts on th e oth er in dep en den t variables, R ∈[0,1] is th e p h ysician ’s

Chapter 5: The Impact of Resistance on Antibiotic Demand • 123

exp ect at io n t h at t h e in fect io n is resist an t t o d ru g j, p ij is t h e p rice o f d ru g j in t eract ed wit h in d ivid u al ch aract erist ics (in clu d in g t h e d at e o n wh ich t h e in dividu al is m akin g th e ch oice), x ij are dru g attribu tes oth er th an p rice in teract ed wit h in d ivid u al ch aract erist ics, an d εij is an id en t ically in d ep en d en t ly d ist ribu t ed erro r t erm . No t e t h at t h e p revailin g level o f resist an ce varies by p lace an d tim e, so R is su bscrip ted by i. Let yij be an du m m y variable in dicatin g if dru g j was ch osen by in dividu al i iden tically in dep en den tly distribu ted.

{

y ij = 1 if Vij = m ax V1i ,...,ViJ

}

(2)

wh ere Rj′ = R1 j ,..., RNj

[ ] p ′ = [ p ,..., p ] x ′ = [ x ,..., x ] j

1j

j

1j

Nj

Nj

θ = {γ , α, β} an d is th e vector of coefficien ts of in d ep en d en t variables Th e dem an d D for dru g j is D( Rj , p j , x j ; θ) =

∑i w ij yij

(3)

wh ere w i is a sam ple weigh t. Th e im pact of resistan ce on drug treatm en t costs is

∑ j [ p j D( Rj , p j , x j ;

]

θ) − p j D ( 0 , p j , x j ; θ)

(4)

Here, th e first term in th e brackets is actu al d em an d , an d th e secon d term is wh at dru g sp en din g wou ld be if resistan ce levels were 0 for all dem an ders.

Empirical M odel We wan t to estim ate Eq u ation 4. We observe D(Rj, pj, x j; θ), wh ich is sim p ly th e em p irical d em an d for each d ru g, bu t we d o n ot observe D(0, pj, x j; θ). To calcu late wh at d em an d for each d ru g wou ld be in th e absen ce of resistan ce, we est im at e a d iscret e ch o ice m o d el o f an t ib io t ic d em an d . Becau se we assu m e th at u tility is lin ear in p aram eters, we ign ore th e m argin al im p act of resist an ce o n u t ilit y γ becau se it is m u lt ip lied by 0 an d d ro p s o u t o f Exp ression 1 wh en calcu latin g D(0, pj, x j ; θ). We can n ot sim p ly ign ore th e im p act of resist an ce o n p h ysician s’ d ru g ch o ice, h o wever, b ecau se d o in g so wo u ld im p art bias t o t h e co efficien t s o n t h e rem ain in g, o bservable p ro d u ct at t ribu tes. Ou r ad m itted ly cru d e ap p roach to th is p roblem is to take ad van tage of t h e fact t h at resist an ce was n o t wid esp read d u rin g t h e early p erio d co vered b y o u r d at a; su rveillan ce reco rd s in d icat e t h at resist an ce am o n g t h e p ath ogen s cau sin g ear in fection s was fairly low an d stable before 1990, after wh ich it began to rise stead ily. We com bin e p rod u ct attribu tes pj an d x j with

124 • Chapter 5: The Impact of Resistance on Antibiotic Demand

d u m m y variables eq u al to zero for d ru gs p rescribed before 1990 an d eq u al to th e n u m ber of years after 1990 for d ru gs p rescribed after 1990. For exam p le, t h e p rice–t im e in t eract io n t erm fo r a p rescrip t io n issu ed in 199X is p j × m ax{199X – 1990,0}. Assu m in g th at p h ysician s’ u n d erlyin g p referen ces h ave n ot ch an ged over tim e, th e coefficien ts on th ese variables will eq u al th e bias o n t h e p ro d u ct at t rib u t e co efficien t s cau sed b y t h e o m issio n o f resist an ce, an d t h e u n in t eract ed co efficien t s will rep resen t p h ysician s’ “t ru e” p referen ces for variou s p rod u ct attribu tes. To est im at e D(0, p j, x j; θ) we first est im at e Eq u at io n 1 an d t h en co m p u t e Eq u ation s 2 an d 3 for th e p ost-1996 p ortion of th e d ata, restrictin g th e coefficien t s o n t h e t im e-at t ribu t e in t eract io n s t o be zero . Th u s we o bt ain an est im ate of wh at d em an d for variou s an tibiotics wou ld h ave been in years 1997 an d 1998 in th e absen ce of in creased resistan ce, con trollin g for th e su p erior o b servab le at t rib u t es o f t h e n ewer, m o re exp en sive d ru gs. Usin g t h ese d em an d estim ates to com p u te Eq u ation 4, we m easu re th e m argin al cost of in creases in resistan ce after 1980, ign orin g th e cost of resistan ce th at d evelop ed p rior to th at tim e. Th e action s of dru g com p an ies with resp ect to p rice levels an d n ew p rodu ct in t ro d u ct io n s d ep en d o n p revailin g resist an ce levels, an d t h e fo rm u la in Eq u at io n 4 m ay m isst at e t h e t ru e im p act o f resist an ce. At o n e ext rem e, t h e in t ro d u ct io n o f n ew an t ib io t ics m ay b e m o t ivat ed b y resist an ce t o o ld er agen ts. If th is is th e case, th en Eq u ation 4 sign ifican tly u n derstates th e im p act of resistan ce on costs. At th e oth er extrem e, all of th e n ew p rodu cts cu rren tly on th e m arket wou ld h ave been in trod u ced in th e absen ce of resistan ce, bu t th eir p rices wou ld be lower becau se th e older an tibiotics wou ld be better su bstitu tes. If th is is th e case, th en th e form u la overstates th e costs of resistan ce.3 Wish in g t o err o n t h e co n servat ive sid e, we co m p u t ed Eq u at io n 4 fo r t h e years 1997 an d 1998 u sin g 1990 p rices o r, fo r d ru gs in t ro d u ced aft er 1990, th eir p rices du rin g th eir first year on th e m arket. We assu m ed (con servatively) t h at all su b seq u en t p rice in creases were cau sed b y in creases in resist an ce rath er th an oth er factors. We est im at e Eq u at io n 1 u sin g a ran d o m -p aram et ers m u lt in o m ial lo git m odel (see Brown ston e an d Train 1999), wh ich assu m es th at th e taste p aram eters are ran d om ly d istribu ted in th e p op u lation . Un like a con ven tion al con d it io n al lo git m o d el, t h e ran d o m -p aram et ers sp ecificat io n relaxes t h e in d ep en den ce of irrelevan t altern atives p rop erty, bu t, u n like a m u ltin om ial p robit m o d el, it d o es n o t en t ail est im at io n o f an u n rest rict ed varian ce–co varian ce m atrix eith er. Let µr be th e rth ran dom draw from a distribu tion an d write th e taste p aram eter on attribu te k as a fu n ction of th is d raw β kr = b k + sk µ kr . Th en u tility for in dividu al i an d p rodu ct j (n ow in clu din g p rice in x ij) is V ijr = b ′xij +

∑k sk µr x kij + εij rk

(5)

Chapter 5: The Impact of Resistance on Antibiotic Demand • 125

Th e b k ’s are m ean co efficien t s, an d t h e sk ’s are sp read co efficien t s. If we assu m e th at th e eij’s follow an extrem e valu e distribu tion , th en , after algebraic m an ip u lation (see Mad d ala 1983, 60–1), th e sim u lated p robability th at in d ividu al i ch ooses dru g j, SPij, can be written as SPij =

1 R

∑r

( ) ∑ ( ) exp V ij j

(6)

exp V ij

an d th e log-likelih ood is LL(θ) =

∑i ∑j yij log SPij

(7)

We est im at e t h e m o d el u sin g a sim u lat ed m axim u m likelih o o d ro u t in e (McFadden an d Train 2000).4

The Data Ou r m ain d ata sou rce was th e Nation al Am bu latory Med ical Care Su rvey (NAMCS). For selected years before 1989 an d every year between 1989 an d 1998, th e Nation al Cen ter for Health Statistics d rew a sam p le of office-based p h ysician s from th e m aster files of th e Am erican Medical Association an d th e Am erican Osteop ath ic Association . Selected p h ysician s were asked to record in form ation on a subsam ple of office visits occurrin g durin g a ran dom ly ch osen week (differen t ph ysician s were assign ed differen t weeks, so data were recorded th rou gh ou t th e year). Som e q u estion s were n ot asked in all years, m akin g it im possible to in clude som e poten tially in terestin g patien t ch aracteristics, but at th e very least, respon den ts recorded in form ation on patien t diagn oses, patien t dem ograph ics, basic ph ysician ch aracteristics, an d drugs prescribed. From th e NAMCS for 1980, 1981, 1985, an d 1989 to 1998, we selected as ou r in itial sam p le all p atien ts you n ger th an 18 years of age with a diagn osis of otitis m edia, as lon g as th at diagn osis was listed before an y m en tion of a diagn o sis fo r a resp irat o ry p ro b lem (NAMCS allo ws p h ysician s t o reco rd u p t o t h ree d iagn o ses). Th is last st ep was t aken so we co u ld be reaso n ably cert ain th at an y an tibiotic received was for otitis m edia rath er th an an oth er p roblem . From th e m ed ical literatu re, we com p iled a list of m ed ication s com m on ly p rescribed fo r o t it is m ed ia. We t h en n arro wed t h e sam p le by select in g o n ly p atien ts wh o received on e of th e 18 d ru gs from th is list for wh ich at least 25 p at ien t s in t h e sam p le h ad received p rescrip t io n s. Th e 18 d ru gs acco u n t fo r m ore th an 99% of all an tibiotic p rescrip tion s in th e sam p le. Ap p roxim ately 30% of otitis m edia p atien ts do n ot receive an an tibiotic. Th is p ercen tage h as rem ain ed co n st an t o ver t im e, an d we o m it t ed t h ese in d ivid u als fro m o u r an alysis.

126 • Chapter 5: The Impact of Resistance on Antibiotic Demand

In fo rm at io n o n d ru g ch aract erist ics o t h er t h an p rice was t aken fro m an an tibiotic gu id e (Gilbert et al. 2000). Th e variable “p rice” m easu res th e total cost to th e in su rer an d p atien t of a p rescrip tion . We calcu lated m ean cost p er p rescrip tion from th e 1996 Med ical Exp en d itu re Pan el Su rvey (MEPS) h ou seh old com p on en t. 5 We con stru cted a p rice in d ex for each d ru g u sin g p er-p ill p rices rep o rt ed in Gilb ert an d o t h ers an d t h e Red Book (Med ical Eco n o m ics Data 1981; 1985). Usin g th e p rice in dex, we in flated or discou n ted th e cost for each d ru g (fro m MEPS) t o t h e ap p ro p riat e year. Th ese d at a an d t h e NAMCS data were com bin ed to form a dataset con tain in g in dividu al- an d ch oice-sp ecific attribu tes. Variables are su m m arized in Table 5-1. Th e d ru g at t ribu t e called “bro ad sp ect ru m ” d eserves a brief exp lan at io n . Th ree b act erial sp ecies cau se o t it is m ed ia: S. pneum oniae, Hem ophilus influenzae, an d Moraxhella catarrhalis. S. pneum oniae is by far t h e m o st co m m o n , acco u n t in g fo r u p t o 50% o f o t it is m ed ia cases. A n arro w-sp ect ru m an t ibio t ic, as we h ave d efin ed it , is act ive again st o n ly S. pneum oniae (in it s n on resistan t form ). A broad-sp ectru m an tibiotic, by con trast, can kill all th ree bacterial sp ecies (in th eir n on resistan t form s). Widesp read adm in istration of a b ro ad -sp ect ru m an t ib io t ic lead s t o resist an ce in H. influenzae an d M. catarrhalis, 6 wh ereas ad m in istration of a n arrow-sp ectru m an tibiotic d oes n ot affect th e evolu tion ary p ath of th ese sp ecies. In ad d ition to d u m m y variables in d icatin g each d ru g’s class, we in clu d ed in all m od els a d u m m y variable eq u al to on e if th e d ru g is am oxicillin . More

Table 5-1. Variable Descriptions (sample size 6,928) Variable

Mean

Drug characteristics Price Doses GI u p set Rash Broad sp ectru m

16.46 28.57 5.73 0.80 0.46

Am oxicillin Pen icillin

0.54 0.58

Cep h alosp orin

0.19

Interaction term s In fan t Sp ecialist

0.40 0.13

No. m eds Year

1.52 2.06

Description Price of regim en Doses p er regim en Rate of gastroin testin al u p set (1–16) Eq u als 1 if rash is a freq u en t side-effect Eq u als 1 if an tibiotic is active again st M. catarrhalis Eq u als 1 if th e dru g is am oxicillin Eq u als 1 if th e dru g is a m em ber of th e p en icillin class Eq u als 1 if th e dru g is a m em ber of th e cep h alosp orin class Patien t is less th an two years of age Ph ysician is an otolaryn gologist or oth er sp ecialist Nu m ber of m edication s p rescribed at th e visit Nu m ber of years after 1990

Chapter 5: The Impact of Resistance on Antibiotic Demand • 127

t h an 40% o f t h e p at ien t s in o u r sam p le received a p rescrip t io n fo r am o xicillin , an d we fou n d th at in clu d in g an am oxicillin d u m m y greatly in creased t h e p red ict ive p o wer o f t h e m o d el. Am o xicillin is t h e st an d ard “first -lin e” th erap y recom m en d by treatm en t gu id elin es (see, for exam p le, Gilbert et al. 2000), an d t h ese m ay exert an in d ep en d en t effect o n p h ysician s’ an t ibio t ic ch oices th at is bein g cap tu red by th e coefficien t on th is variable. Ou r d ata h ave a n u m ber of lim itation s. Th ere is a great d eal of d ru g p rice disp ersion , an d we did n ot observe if th e p rescrip tion was filled with a gen eric o r bran d ed versio n . Th u s, t h e p rices we assign ed t o each d ru g m ay m isst at e actu al costs faced by in dividu als. We also did n ot observe q u an tity p rescribed. Alth ou gh regim en s are fairly stan d ard ized , on e resp on se to an tibiotic resistan ce h as b een t o in crease d o sages t o t reat b act eria wit h in t erm ed iat e-level resistan ce. In oth er cases, p h ysician s m ay decrease th e du ration of th erap y to m in im ize th e selective p ressu re on m icroorgan ism s. We d o n ot h ave d ata on ad vertisin g an d d etailin g exp en d itu res an d , in sofar as we kn o w, n o su ch d at a exist go in g back t o 1980. Ho wever, even if we d id h ave th ese d ata, it is n ot clear th at we wou ld wan t to in clu d e th em . Th e abilit y t o t reat resist an t bact eria is a st ro n g sellin g p o in t o f t h e n ewer d ru gs an d is exp licitly m en tion ed in som e p rin t advertisem en ts. If th e claim s related to resistan ce in dru g advertisem en ts or detailin g activities m otivate p h ysician s to switch d ru gs, th en we wou ld wan t to attribu te th e ch an ge in beh avior to resistan ce, n ot advertisin g or detailin g.

Estimation and Results Table 5-2 disp lays p aram eter estim ates. Th e first colu m n p resen ts resu lts from a stan dard con dition al logit m odel, an d th e secon d an d th ird colu m n s p resen t resu lts from a m ixed m u ltin om ial logit m odel. No t e t h at each o f t h e d ru g at t ribu t es excep t d ru g class in t eract s wit h t h e followin g in d ivid u al ch aracteristics: an in fan t p atien t, a sp ecialist p h ysician , n u m ber o f p rescrip t io n s received by t h e p at ien t (a cru d e m easu re o f d isease severity), an d year. In teractin g p atien t ch aracteristics with d ru g class in d icators p rodu ced u n stable estim ates. We com bin ed a n u m ber of oth er in dividu al at t rib u t es wit h d ru g at t rib u t es in o u r in it ial est im at es, su ch as regio n , b u t n o n e were co n sist en t ly sign ifican t . So m e o f t h e m o st in t erest in g in d ivid u al at t ribu t es, in su ran ce so u rce fo r exam p le, were n o t rep o rt ed in every year o f th e su rvey. Based o n t h e sp ecificat io n t est o u t lin ed in Th eo rem 2 o f McFad d en an d Train (2000), we rejected th e h yp oth esis th at con dition al an d m ixed m u ltin om ial m o d els are eq u ivalen t . Th u s, we b ased o u r sim u lat io n s o n t h e m ixed m u lt in o m ial est im at es. Th e eco n o m et ric lit erat u re p ro vid es lit t le gu id an ce regardin g wh ich or h ow m an y of th e coefficien ts in th e m ixed logit sh ou ld be

128 • Chapter 5: The Impact of Resistance on Antibiotic Demand TABLE 5-2. Conditional and M ixed Logit Results Conditional logit

Mixed logit b

Price × In fan t × Sp ecialist × No. m eds. × Year Doses × In fan t × Sp ecialist × No. m eds. × Year GI upset × In fan t × Sp ecialist × No. m eds. × Year Rash × In fan t × Sp ecialist × No. m eds. × Year Broad spectrum × In fan t × Sp ecialist × No. m eds. × Year Am oxicillin Pen icillin class Cep h alosp orin class Sam p le size Log-likelih ood

–0.042 –0.005 0.012 0.001 0.004 –0.019 –0.001 0.021 0.007 –0.002 –0.113 0.003 –0.018 0.025 0.001 –0.739 0.007 –0.133 –0.158 0.166 0.119 0.351 0.327 –0.067 –0.053 2.655 –0.884 –0.596 6,928 13,908

SE (0.004)* (0.003) (0.004)* (0.002) (0.001)* (0.007)* (0.005) (0.007)* (0.004)* (0.001) (0.011)* (0.008) (0.011) (0.005) (0.002)* (0.171)* (0.106) (0.137) (0.068)* (0.021)* (0.121) (0.084)* (0.125)* (0.057) (0.018)* (0.070)* (0.088)* (0.099)*

b –0.174 0.011 0.046 –0.003 0.015 –0.018 –0.013 0.016 0.009 –0.004 –0.122 0.022 0.003 0.016 0.014 –1.038 0.020 –0.175 –0.139 0.058 1.281 0.224 0.181 –0.077 –0.134 2.916 –0.700 –0.243 6,928 13,200

SE

S

(0.011)* 0.365 (0.007) (0.009)* (0.004) (0.001)* (0.009) –0.059 (0.006)* (0.008)* (0.004)* (0.001)* (0.014)* (0.009)* (0.012) (0.006)* (0.002)* (0.178)* (0.110) (0.142) (0.071)* (0.022)* (0.168)* (0.091)* (0.134) (0.061) (0.019)* (0.092)* (0.095)* –0.045 (0.117)* 0.382

SE (0.015)*

(0.051)

(3.089) (2.405)

* Sign ifican t at 95% level of con fiden ce.

allo wed t o vary, so o u r ch o ices in t h is m at t er were so m ewh at ad h o c. We fou n d th at, in exp licably, som e com bin ation s of ran dom coefficien ts p rodu ced p aram eter estim ates th at rose with ou t bou n d . 7 Takin g th ese restriction s in to accou n t, we allowed th e coefficien ts on p rice, p ills p er regim en , an d dru g class to vary. Sim p ly allowin g th e coefficien ts on th e d ru g class in d icators to vary rep licat ed a n est ed lo git m o d el. Allo win g t h e co efficien t s o n p rice an d p ills p er regim en t o vary, wh ich fu rt h er relaxed t h e in d ep en d en ce o f irrelevan t altern atives axiom , cou n ts for h eterogen eity in th e dru g p rices an d in su ran ce arran gem en ts faced by p atien ts an d th e work sch ed u les of p atien ts’ p aren ts. We assign ed trian gle distribu tion s on th e in terval [–1,1] to th e µk ’s. Th e m odel

Chapter 5: The Impact of Resistance on Antibiotic Demand • 129

was estim ated via sim u lated m axim u m likelih ood u sin g 150 Halton d raws of µk for each k. 8 Tu rn in g o u r at t en t io n n o w t o t h e p aram et er est im at es fro m t h e m ixed m u ltin om ial logit m odel, all of th e coefficien ts on th e first six dru g attribu tes were of th e exp ected sign , an d five were sign ifican t at th e 5% level. Th e coefficien ts on th e dru g class in dicators were also sign ifican t at con ven tion al levels. Th e fin d in g th at p rice was n egatively an d sign ifican tly related to d em an d is in t erest in g in an d o f it self. So m e research ers wo rry t h at b ecau se m ed ical exp en ses are covered by in su ran ce, p h ysician s h ave n o in cen tive to con sid er p rice wh en p rescribin g d ru gs. Clearly th is is n ot th e case, alth ou gh we fou n d in an o t h er m o d el in wh ich p rice was in t eract ed wit h in su ran ce t yp e (n o t sh own ) th at p h ysician s of in su red p atien ts were less sen sitive to p rice. All six of th e attribute–year in teraction s were sign ifican t, an d five h ad a differen t sign from th eir correspon din g level coefficien t. To un derstan d th is result, con sider th e coefficien t on th e price–year in teraction , wh ich was positive. On e possible in terpretation is th at ph ysician s h ave becom e less sen sitive to price, an u n likely occu rren ce in ligh t of th e growth of m an aged care (see, for exam p le, Wein er et al. 1991). An oth er in terpretation , an d th e on e we prefer, is th at ph ysician s’ price sen sitivity is un ch an ged or possibly even greater, but resistan ce h as in duced th em to substitute toward m ore expen sive drugs, wh ich , because of th e om ission of resistan ce as an observed drug ch aracteristic, was reflected as a positive coefficien t on th e price–year in teraction . Of course oth er tren ds m ay affect p h ysician s’ an d p atien ts’ p referen ces over an tibiotic attribu tes. However, a n u m ber of th ese can be ru led ou t based on th e p attern of coefficien ts. For exam ple, ph ysician s m ay be m ore likely to prescribe broad-spectru m dru gs for ch ild ren wh ose m oth ers work. Yet th e n egative coefficien t on th e sp ectru m year in teraction in dicates th at th e in crease in th e n u m ber of workin g m oth ers h as n ot h ad a sign ifican t im pact on an tibiotic prescribin g tren ds. Of th e five sp read coefficien ts, on ly th e on e for p rice is sign ifican t at th e 5% level. Th e fact th at th e sp read coefficien t is greater th an th e m ean coefficien t im p lies th at abou t 10% of th e sam p le derives p ositive u tility from h igh er p rices. Alth ou gh th is is an u n fortu n ate by-p rod u ct of assu m in g th at th e µk ’s can take on n egative valu es, ou r m arket sh are p red iction s (see Figu re 5-2) are close en ou gh to actu al m arket sh ares th at we do n ot believe th is is a su bstan tial liability in term s of p redictin g beh avior. 9

Resistance and Empiric Substitution Befo re co m p u t in g Eq u at io n 4, we valid at ed t h e m o d el b y co m p arin g p red icted an d actu al m arket sh ares. Figu re 5-2 d isp lays actu al m arket sh ares (th e ^ bars) an d p redicted m arket sh ares, D(Rj, pj, x j; θ), as well as th e 95% con fiden ce in tervals based on 100 bootstrap ru n s.

130 • Chapter 5: The Impact of Resistance on Antibiotic Demand

A sin gle sim ulation run en tails (a) drawin g th e bk’s an d sk’s from th eir respective d istribu tion s, (b) d rawin g µr’s from trian gle d istribu tion s, (c) d rawin g εij’s from in dep en den t logistic distribu tion s, (d) com p u tin g u tility levels for Eq u ation 1, an d (e) com putin g Equation 2 an d th en Equation 3 to calculate m arket sh ares. Con sid erin g th at we h ave 18 d ifferen t m arket sh ares to p red ict, th e m odel does a tolerably good job. Th e con fiden ce in tervals aroun d th e m ean s of th e p red icted m arket sh ares are q u ite wid e becau se of th e ran d om p aram eter specification . Som e of th e m ean s are off by qu ite a bit too, bu t oth ers are very close to actual m arket sh ares (for exam ple, for trim eth oprim -sulfam eth oxazole). We calcu lated th at th e average sp en d in g p er p rescrip tion for an tibiotics to t reat n ew cases o f o t it is m ed ia d u rin g 1997 an d 1998 was $18.41. O u r p red ict ed p er-p rescrip t io n co st is $19.20 (95% co n fid en ce in t erval: $17.08, $21.39). We est im at ed b y rest rict in g t h e co efficien t s o n t h e year–at t rib u t e in teraction s to be zero th at in th e absen ce of resistan ce, th e p er-p rescrip tion cost wou ld be on ly $15.05 (95% con fiden ce in terval: $13.66, $17.03).

TM P/ SM X Sulfisox. Eryth/ Sulf. Erythro. Clarithro. Azithro. Loracarbef Cephalexin Cef. Axetil Cefprozil Cef. Proxetil Cefixime Cefadroxil Cefaclor Penicillin Ampicillin Amox/ Clav Amoxicillin 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

M arket Share Figure 5-2. Actual and Predicted M arket Share Notes: Th e bars represen t actu al m arket sh ares. TMP/ SMX = trim eth oprim / su lfam eth oxazole, Su lfisox. = su lfisoxazole, Eryth / Su lf. = eryth rom ycin / su lfisoxazole, Eryth ro. = eryth rom ycin , Clarith ro. = clarith rom ycin , Azith ro. = azith rom ycin , Cef. Axetil = cefu roxim e axetil, Cef. Protexil = cefp od oxim e p rotexil, an d Am ox/ Clav = am oxicillin clavu lan ate.

Chapter 5: The Impact of Resistance on Antibiotic Demand • 131

Mu ltip lyin g th e differen ce between th e actu al p er p rescrip tion cost an d th e sim u lated p er-p rescrip tion cost by th e total n u m ber of p rescrip tion s for otitis m ed ia p er year—abou t 12 m illion —yield s an estim ate of th e im p act of resistan ce on an tibiotic costs: ($18.01 – $15.09) × 12,000,000 ≈ $40,000,000. Th u s we con clu d ed th at resistan ce in creases total sp en d in g on an tibiotics to treat n ew ep isodes of ear in fection (abou t $216 m illion ) by abou t 20%.

Conclusion In creasin g th e resistan ce of m icroorgan ism s to com m on ly prescribed an tibiotics h as led clin ician s, biologists, an d even som e econ om ists to call for p olicies restrictin g an tibiotic use. However, th ere is n ot m uch in form ation on th e scope of th e problem , especially in outpatien t settin gs. Previous efforts to estim ate th e im pact of resistan ce h ave focused on m easurin g patien t m orbidity an d m ortality. Th ese estim ates un derstate th e cost of resistan ce to th e exten t th at th ey fail to take accou n t of th e im p act of resistan ce on p h ysician s’ an tibiotic ch oices. Th e greater th e prevalen ce of resistan ce is, th e m ore likely ph ysician s are to use expen sive an tibiotics. Based on th is prin ciple, our “back-of-th e-en velope” sim ulation s sh ow th at resistan ce in creases an tibiotic costs for ear in fection by $35 m illion an n u ally. Th is is n ot to say th at th is en tire cost is a deadweigh t loss— resistan ce is a n atu ral con sequ en ce of th e selective pressu res brou gh t abou t by an tibiotic u se. Neverth eless, th e size of th e figu re su ggests th at th ere m ay be large return s to efforts to slow th e developm en t of resistan ce.

Acknowledgements We th an k Joh n McGowan , Ern ie Bern dt, sem in ar p articip an ts at th e Econ om ics o f Resist an ce co n feren ce sp o n so red b y Reso u rces fo r t h e Fu t u re, an d an an on ym ou s reviewer for com m en ts an d h elp fu l su ggestion s.

References Berm an , S., P.J. Byrn s, J. Bon d y, P.J. Sm ith , an d D. Lezzotte. 1997. Otitis Med ia-Related An tibiotic Prescribin g Pattern s, Ou tcom es, an d Exp en ditu res in a Pediatric Medicaid Pop u lation . Pediatrics 100(4): 585–92. Bern d t, E.R., L.T. Bu i, D.H. Reiley, an d G.L. Urban . 1995. In form ation , Marketin g, an d Pricin g in th e U.S. An ti-Ulcer Dru g Market. Am erican Econom ic Review 85(2): 100–5. Brown , G., an d D.F. Layton . 1996. Resistan ce Econ om ics: Social Cost an d th e Evolu tion of An tibiotic Resistan ce. Environm ent and Developm ent Econom ics 1(3): 349–55. Brown ston e, D., an d K. Train . 1999. Forecastin g New Produ ct Pen etration with Flexible Su bstitu tion Pattern s. Journal of Econom etrics 89(1): 109–29. Coast, J., R.D. Sm ith , an d M.R. Millar. 1996. Su p erbu gs: Sh ou ld An tim icrobial Resistan ce Be In clu ded as a Cost in Econ om ic Evalu ation ? Health Econom ics 5: 217–26.

132 • Chapter 5: The Impact of Resistance on Antibiotic Demand Cu lp ep p er, L., an d J. Fro o m . 1997. Ro u t in e An t im icro b ial Treat m en t o f Acu t e O t it is Media: Is It Necessary? Journal of the Am erican Medical Association 278(20): 1643–5. Ellison , S.F., I. Cockbu rn , Z. Grilich es, an d J. Hau sm an . 1997. Ch aracteristics of Dem an d for Ph arm aceu tical Produ cts: An Exam in ation of Fou r Cep h alosp orin s. RAND Journal of Econom ics 28(3): 426–46. Ellison , S.F., an d J.K. Hellerstein . 1999. Th e Econ om ics of An tibiotics: An Exp loratory Stu d y. In Measuring the Prices of Medical Treatm ents, ed ited by J.E. Trip lett. Wash in gton , DC: Brookin gs In stitu tion , 118–51. Fo xm an , B., R. Bu rciaga Vald ez, K.N. Lo h r, G.A. Go ld b erg, J.P. Newh o u se, an d R.H. Bro o k. 1987. Th e Effect o f Co st Sh arin g o n t h e Use o f An t ib io t ics in Am b u lat o ry Care: Resu lt s fro m a Po p u lat io n -Based Ran d o m ized Co n t ro lled Trial. Journal of Chronic Diseases 40: 429–37. Gilbert, D.N., R.C. Moellerin g, an d M.A. San de. 2000. The Sanford Guide to Antim icrobial Therapy. Hyde Park, VT: An tim icrobial Th erap y, In c. Goesch l, T., an d T. Swan son . 2000. Lost Horizon s: Th e In teraction of IPR System s an d Resistan ce Man agem en t. Pap er p resen ted at In tern ation al Worksh op on An tibiotic Resistan ce: Global Policies an d Op tion s. Febru ary 2000, Cam bridge, MA. Jacobs, M.R. 2000. In creasin g An tibiotic Resistan ce am on g Otitis Med ia Path ogen s an d Th eir Su scep tibility to Oral Agen ts Based on Ph arm acodyn am ic Param eters. Pediatric Infectious Disease Journal 19(5): S47–56. Laxm in arayan , R. 2001. Bact erial Resist an ce an d t h e O p t im al Use o f An t ib io t ics. Resou rces for th e Fu tu re discu ssion p ap er 01–23. Wash in gton , DC: Resou rces for th e Fu tu re. Mad d ala, G.S. 1983. Lim ited-Dependent and Qualitative Variables in Econom etrics. Cam bridge, U.K.: Cam bridge Un iversity Press. McFadden , D., an d K. Train . 2000. Mixed MNL Models for Discrete Resp on se. Journal of Applied Econom etrics 15(5): 447–70. Med ical Econ om ics Data, In c. 1981. Red Book. Mon tvale, NJ: Med ical Econ om ics Data. ———. 1985. Red Book. Mon tvale, NJ: Medical Econ om ics Data. Ph ilip son , T. 2000. Econ om ic Ep idem iology. In Handbook of Health Econom ics, edited by A.J. Cu lyer an d J.P. Newh ou se. New York: Elsevier, 1762–99. Reed , S.D., R. Laxm in arayan , D.J. Black, an d S.D. Su llivan . 2002. Econ om ic Issu es an d An tibiotic Resistan ce in th e Com m u n ity. Annals of Pharm acotherapy 36: 148–54. Revelt, D., an d K. Train . 1998. Mixed Logit with Rep eated Ch oices: Hou seh olds’ Ch oices of Ap p lian ce Efficien cy Level. Review of Econom ics and Statistics 80(4): 647–57. Rizzo, J.A. 1999. Ad vertisin g an d Com p etition in th e Eth ical Ph arm aceu tical In d u stry: Th e Case of An tih yp erten sive Dru gs. Journal of Law and Econom ics 42(1): 89–116. Ru u d, P. 1996. Approxim ation and Sim ulation of the Multinom ial Probit Model: An Analysis of Covariance Matrix Estim ation. Un p u blish ed rep ort. Berkeley, CA: Un iversity of Californ ia. Train , K. 1999. Halt o n Seq u en ces fo r Mixed Lo git . Un p u blish ed rep o rt . Berkeley, CA: Un iversity of Californ ia. Wein er, J.P., A. Lyles, D.M. Stein wach s, an d K.C. Hall. 1991. Im p act of Man aged Care on Prescrip tion Dru g Use. Health Affairs 10: 140–54.

Chapter 5: The Impact of Resistance on Antibiotic Demand • 133

Notes 1. In d eed , t h e m ajo rit y o f ear in fect io n s reso lve wit h o u t t h erap y, an d so m e research ers (alth ou gh n ot th ose h old in g scream in g in fan ts) h ave q u estion ed th e ben efits of an tibiotic th erap y in n ew cases (Cu lp ep p er an d Froom 1997). 2. See Ph ilip son (2000) for an excellen t d iscu ssion of wh y trad ition al cost-of-illn ess m easu res u n derstate th e bu rden of in fectiou s diseases. 3. Margin al reven u e is n egat ive ab o ve p ro fit m axim izin g p rices, so u sin g p rices ab o ve t h e p ro fit m axim izin g p rices t o ap p ro xim at e d em an d levels in t h e ab sen ce o f resist an ce wo u ld u n d erest im at e t o t al reven u e (an d t h u s m ake t h e d ifferen ce bet ween reven u e wit h resist an ce an d est im at ed reven u e in t h e ab sen ce o f resist an ce ap p ear greater). 4. Mat lab p ro gram s fo r m ixed m u lt in o m ial lo git m o d els can be d o wn lo ad ed fro m David Howard’s website (www.sp h .em ory.edu / ~dh h owar). 5. Th ese co st s reflect t ran sact io n rat h er t h an list p rices b u t m ay n o t t ake in t o accou n t m an u factu rer rebates. 6. H. influenzae an d M. catarrhalis h ave “in n ate” as op p osed to “acq u ired” resistan ce to n arrow-sp ectru m an tibiotics. 7. Ru u d (1996) fou n d th at m odels in wh ich all coefficien ts were allowed to vary p rodu ced u n stable p aram eter estim ates. 8. Train (1999) fo u n d t h at t h e u se o f Halt o n d raws red u ced sim u lat io n erro r in m ixed m u ltin om ial logit m odels. 9. To avo id t h is p ro blem , Revelt an d Train (1999) su ggest ed rest rict in g t h e sp read coefficien t on p rice to be zero (i.e., n ot allowin g th e p rice p aram eter to vary in th e p op u lation ). Based on ou r con versation s with clin ician s an d ou r in itial resu lts, we believe it is im p ortan t to allow p rice to vary, given th at we d o n ot in clu d e m easu res of p atien ts’ in com e or in su ran ce coverage. An oth er op tion is to assu m e th at th e m ean coefficien t on p rice h as a beta d istribu tion . Th e p aram eters of th is d istribu tion can be d ifficu lt to iden tify, h owever.

Commentary

M easuring the Cost of Resistance Ramanan Laxminarayan

A

n im p ortan t em p irical ch allen ge in th e econ om ics of resistan ce h as been th e m easu rem en t of th e cost of resistan ce. Alth ou gh th ere is wid esp read agreem en t t h at resist an ce p laces an eco n o m ic bu rd en o n so ciet y, n o bo d y is q u ite su re h ow large th is bu rden m igh t be. Earlier efforts to q u an tify th e social welfare lo sses asso ciat ed wit h b act erial resist an ce t o an t ib io t ics arrived at a ran ge th at varied from $300 m illion to $30 billion dep en din g on factors su ch as th e valu e attribu ted to lost h u m an lives (Ph elp s 1989). A 1999 stu d y estim ated th at th e deadweigh t loss associated with th e loss of an tim icrobial effect iven ess asso ciat ed wit h o u t p at ien t p rescrip t io n s in t h e Un it ed St at es was $378 m illion an d p ossibly as h igh as $18.6 billion (Elbash a 1999). Mo re recen t effo rt s t o m easu re t h e co st o f resist an ce in h o sp it al set t in gs h ave focu sed on m easu rin g d ifferen ces in th e cost of treatin g resistan t in fection s an d su scep tible in fection s (Howard et al. 2001). However, th is is a d ifficu lt em p irical p roblem con fou n ded by th e reality th at sicker p atien ts are m ore likely to h ave lon ger h osp ital stays an d th erefore are m ore likely to con tract a resist an t in fect io n . Co n versely, p at ien t s wit h resist an t in fect io n s are m o re likely to h ave lon ger h osp ital stays an d to be sicker. Th is bidirection al cau sality is p roblem atic an d con fou n ds efforts to m easu re th e in crease in th e cost of h osp ital stays attribu table to a resistan t in fection . Th e in creased cost of h osp it al st ays at t rib u t ab le t o resist an t in fect io n s m ay b e im p o rt an t t o h o sp it al ad m in ist rat o rs. Ho wever, t h e eco n o m ic im p act o f t h is in crease m ay b e less im p ortan t to society th an th e econ om ic bu rden p laced on h ealth care system s of n eed in g to p eriod ically m ove to m ore effective an d exp en sive an tibiotics. In fection s th at were on ce treatable u sin g p en icillin , wh ich costs p en n ies, n ow • 134 •

Commentary: M easuring the Cost of Resistance • 135

req u ire an tibiotics th at cost h u n dreds of dollars. With ou t a dou bt, th e an tibiotics in u se today are m ore p owerfu l an d m u ch m ore exp en sive th an th e older d ru gs u sed a few d ecad es ago. Fu rth erm ore, it is certain ly tru e th at th e in trod u ction of n ew an tibiotics h as been n ecessitated by growin g bacterial resistan ce t o o ld er d ru gs. W h at is n o t clear is p recisely wh at p ro p o rt io n o f t h e in crease in th e d ru g cost of treatin g in fection s h as been cau sed by in creasin g dru g resistan ce an d wh at p rop ortion is attribu table to th e fact th at n ew dru gs h ave o t h er d esirab le p ro p ert ies, su ch as m o re co n ven ien t d o sin g an d fewer sid e effect s. Th e em p irical ch allen ges facin g su ch an eco n o m ic assessm en t sh ou ld n ot be u n derestim ated. David Howard an d Kim berly Rask review d ata on an tibiotics u sed to treat ear in fection s from th e Nation al Am bu latory Med ical Care Su rvey from 1980 t o 1998 t o est im at e t h e in crease in t h e co st o f an t ibio t ic t reat m en t t h at is at t ribu t able t o in creases in bact erial resist an ce. Alt h o u gh t h eir ap p ro ach is h am p ered by a lack o f d at a o n resist an ce, t h eir an alysis (wh ich u ses a t im e proxy for resistan ce) offers som e in sigh t in to th e order of m agn itu de of costs of resistan ce. Th ey fin d th at between 1997 an d 1998, in creases in dru g resistan ce raised th e cost of treatin g ear in fection s by abou t 20% ($216 m illion ). Su ch an estim ate is u sefu l to p olicym akers for at least two reason s. It p rovid es som e id ea of th e m agn itu d e of th e resistan ce p roblem before in vestin g resou rces in addition al research an d su rveillan ce. Moreover, th is estim ate p rovides an u p p er bou n d on th e likely resistan ce-related costs of u sin g an tibiotics in oth er u ses, su ch as for growth p rom otion in an im al feed. W h ile th is is n ot n ecessarily a p ro blem wit h an t ibio t ics u sed t o t reat ear in fect io n s, a sim ilar est im at e o f t h e resist an ce-relat ed co st s o f salm o n ella in fect io n s co u ld , fo r in stan ce, p rovide an idea of th e order of m agn itu de of econ om ic cost of u sin g flu oroq u in olon es for growth p rom otion . A few d rawbacks in th is an alysis cou ld be ad d ressed in fu tu re work in th is area. First , lackin g an exp licit m easu re o f resist an ce, o n e is n o t su re if t h e in crease is becau se of in creases in resistan ce or becau se of im p roved attribu tes o f t h e d ru g. Alt h o u gh t h e au t h o rs read ily ackn o wled ge t h is p ro b lem , t h e m et h o d t h ey u sed t o co rrect fo r t h e p ro b lem —u sin g a t im e d u m m y—m ay h ave p roblem s becau se of th e stron g con tem p oran eou s correlation between oth er attribu tes an d tim e (Nelson an d Kan g 1994). Secon d, m easu rin g th e cost of resistan ce by itself m ay h ave less m ean in g th an m easu rin g th e net cost of an t ib io t ic u se. An t ib io t ic u se b rin gs b o t h b en efit s (b y cu rin g in fect io n s) as well as costs (by in creasin g bacterial resistan ce). Howard an d Rask’s estim ates lo o k o n ly at t h e co st sid e an d o ffer n o gu id an ce o n t h e m agn it u d e o f d ead weigh t lo sses asso ciat ed wit h resist an ce wh en t h e ben efit s o f an t ibio t ics are taken in to con sid eration . Fin ally, th ere h as been a large in crease in th e n u m b er o f an t ib io t ic p rescrip t io n s o ver t h e years. Bet ween 1980 an d 1996, t h e n u m ber of an tibiotic doses p rescribed by office-based p h ysician s in creased by

136 • Commentary: M easuring the Cost of Resistance

44.2%, wh ereas th e in crease between 1992 an d 1996 was 12.7% (McCaig an d Hu gh es 1995). Som e p rop ortion of th is in crease is also attribu table to in creasin g resistan ce an d n eeds to be con sidered. W h at kin d of an alysis m igh t on e look for to correct som e th ese p roblem s? Adm ittedly, estim atin g th e societal ben efits of an tibiotic u se (in term s of faster recovery of p atien ts as well as red u ced p robability th at th e in fection will be tran sm itted to an oth er u n in fected in dividu al) is p roblem atic. However, it m ay be p ossible to arrive at m ore accu rate estim ates of in creases in an tibiotic costs attribu table to in creases in resistan ce. On e way of d oin g th is is by u sin g d ata o n an t ibio t ic u se an d resist an ce fro m d ifferen t regio n s. Bet t er d at a o n d ru g resistan ce are becom in g m ore wid ely available an d cou ld be u sed for su ch an an alysis. All else b ein g eq u al, o n e wo u ld exp ect average co st o f an t ib io t ic treatm en t to be greater in areas wh ere resistan ce to old er d ru gs was relatively greater. Alth ou gh su ch an exercise wou ld be valu able in evalu atin g th e cost of resistan ce in a com m u n ity settin g, a m ore m odest effort m igh t focu s on ju st a h o sp it al set t in g wh ere resist an ce can b e m easu red m o re accu rat ely an d t h e dyn am ics of in fection an d th e evolu tion of resistan ce better u n derstood.

References Elbash a, E. 1999. Deadweight Loss of Bacterial Resistance Due to Overtreatm ent. Un p u blish ed rep ort. Atlan ta, GA: Cen ters for Disease Con trol an d Preven tion , 1–53. Howard, D., R. Cordell, J.E. McGown , R.M. Packard, R.D. Scott II, an d S.L. Solom on , for th e Worksh op Grou p . 2001. Measu rin g th e Econ om ic Costs of An tim icrobial Resistan ce in Hosp ital Settin gs: Su m m ary of th e Cen ters for Disease Con trol an d Preven tion Em ory Worksh op . Clinical Infectious Diseases 33: 1573–8. McCaig, L.F., an d J.M. Hu gh es. 1995. Tren d s in An tim icrobial Dru g Prescribin g am on g Office-Based Ph ysician s in th e Un ited States. Journal of the Am erican Medical Association 273(3): 214–9. Nelson , C., an d H. Kan g. 1994. Pitfalls in th e Use of Tim e as an Exp lan atory Variable in Regression . Journal of Business and Econom ic Statistics 2(1): 73–82. Ph elp s, C.E. 1989. Bu g/ Dru g Resist an ce: So m et im es Less Is Mo re. Medical Care 27(2): 194–203.

Chapter 6

What Can We Learn from the Economics of Pesticides? Impact Assessment of Genetically M odified Plants Hermann Waibel, Jan C. Zadoks, and Gerd Fleischer

Genetically m odified plants represent a new technology widely applied for crop protection purposes (approximately 50 million hectares in 2001). The introduction of this crop protection technology is remarkably parallel to the introduction of chemical pesticides some 50 years earlier. Both technologies require intensive regulation, can produce negative externalities, and are com ponents of integrated pest m anagem ent. Therefore, the econom ic analysis of genetically m odified organism s can draw from som e m ethodological advances achieved through econom ic studies of pesticides. We review the lessons learned from the econom ics of chem ical pesticides and investigate the extent to which these can be applied to genetically modified organisms used as crop protection agents and have actually been applied in recent economic analysis of biotechnology. We draw the lessons from a review of the literature on the economics of pesticides use. We find three m ajor advancem ents in the m ethodology of pesticide productivity assessm ents: (a) the treatm ent of pesticides not as directly productive inputs, such as fertilizers; (b) a better of understanding of producers’ risk preferences with respect to pesticide use; and (c) the treatment of pest susceptibility as a natural resource. We explore the extent to w hich these three concepts show up in the studies of the econom ics of genetically m odified resistant varieties. Our review suggests that they are not well covered. However, the reasons for this gap are not identified in our chapter. Instead, w e present an outline for a conceptual fram ework of how concepts that have em erged from the eco-

• 137 •

138 • Chapter 6: What Can We Learn from the Economics of Pesticides? nomics of pesticide use can be applied to genetically modified organisms. In this outline, we emphasize two aspects: the measurement of the benefits of genetically m odified organism s relative to a realistic reference system and the m easurem ent of one m ajor externality that can be expected w ith the diffusion of genetically m odified organism s (w hich is the developm ent of pest resistance buildup). We describe the use of stochastic sim ulation approach as a m ethodology to deal with the uncertainty arising from such processes. In this context, we discuss some possibilities and problems of collecting data for conducting further econom ic analysis of genetically m odified organisms that should also be feasible under the conditions of developing countries.

W

h en syn t h et ic p est icid es were in t ro d u ced 50 years ago , great exp ect at io n s were raised . In it ially t h ere h ave b een sim ilar, h igh ly o p t im ist ic statem en ts on gen etically m odified organ ism s (GMOs) th at as yet h ave m ostly n ew crop p rotection traits. However, crop p rotection scien tists gen erally h ave becom e m ore realistic in th eir exp ectation s. Alth ou gh th e d iscu ssion on th e risks an d th e econ om ically op tim al level of syn th etic p esticide u se h as n ot yet com e to a con clu sion , GMOs h ave raised con cern s in m an y p arts of civil society, esp ecially in Eu rop e. Th ere are obviou s p arallels between th e in trodu ction of p esticides an d th e “GMO revolu tion ” in crop p rotection . Th e n egative extern alities of p esticide u se were su bject to seriou s criticism , m ain ly stim u lated by th e p u blication of Rach el Carson ’s Silent Spring in 1962 an d b y t h e assessm en t o f Pim en t el an d o t h ers (1986, 1993). Pro p o n en t s o f GMO s see t h ese p lan t s as t h e m o st p ro m isin g way t o escap e t h e p est icid e treadm ill an d as a n ecessity to overcom e th e world’s food p roblem . For exam p le, The Econom ist (1999) warn ed p olicym akers again st slowin g th e d evelop m en t o f GMO s in resp o n se t o p u b lic p an ic ab o u t p erceived h ealt h risks, p oin tin g to th eir econ om ic ben efits for agricu ltu re. Scien tists tod ay m ay be in a better p osition to carefu lly p lan th e in trod u ction of GMOs if th ey d raw on th e exp erien ce gain ed in crop p rotection from th e in trodu ction of ch em ical p esticides (Zadoks an d Waibel 2000). Both tech n ologies were rap id ly in trod u ced by m u ltin ation al com p an ies. Both q u ickly dom in ated th e scien tific debate an d reach ed h igh adop tion rates am on g farm ers. Zadoks an d Waibel con clu ded th at th e h istory of p esticides p rovides som e warn in gs relevan t to th e fu tu re of GMOs: (a) h igh p esticid e u sage is cou n terp rod u ctive becau se fu n d am en tal agroecological p rin cip les are n eglected , (b) th e tech n ology req u ires in ten sive regu lation an d h as n on eth eless m an y extern al effects th at redu ce its n et social ben efit, (c) early estim ates of ben efits from p esticides were overop tim istic, an d (d) in ten sive u se of p esticides m ade farm ers d ep en d en t o n t h em an d farm ers lo st o t h er im p o rt an t p est m an agem en t op tion s.

Chapter 6: What Can We Learn from the Economics of Pesticides? • 139

Th e lesso n s fro m t h e p est icid e st o ry are u sefu l t o b et t er u n d erst an d t h e p olitical econ om y of th e in trod u ction of th e GMO tech n ology. More im p ort an t ly, t h e t h eo ret ical an d m et h o d o lo gical in sigh t s t h at eco n o m ist s gain ed over th e p ast 30 years wh en stu d yin g th e effects of p esticid es p rovid e a baselin e from wh ich sim ilar stu dies on GMOs can take off. Becau se scien tists so far lack th e p rocedu res to fu lly u n derstan d th e ecological an d h u m an h ealth risks associated with GMOs, it is esp ecially im p ortan t th at th e ben efits of th is tech n ology be th orou gh ly stu d ied by ap p lyin g ap p rop riate m eth od ological tools.

Productivity M easurement Th e m eth odology u sed for th e econ om ic assessm en t of p esticide p rodu ctivity h as m ade im p ortan t advan cem en ts over th e last decades. In itially, econ om ists treated p esticid es in a con ven tion al p rod u ction fu n ction fram ework, th at is, assu m in g th em to be yield -in creasin g factors like n itrogen fertilizer. Usin g a Cobb–Dou glas (C–D) fu n ction fram ework, Headley (1968) estim ated th e m argin al p rodu ctivity of aggregated p esticide u se in U.S. agricu ltu re for th e p eriod 1955 to 1963. He fou n d th e m argin al valu e of a $1.00 exp en ditu re for ch em ical p esticides to be ap p roxim ately 4 US$, con clu din g th at addition al n et ben efit s co u ld b e ach ieved b y ap p lyin g m o re p est icid es. Th e figu re d erived in Headley’s an alysis h as been widely cited an d dom in ated th e debate in th e follo win g d ecad es. Th e p ro d u ct ivit y effect s o f p est icid es were o verest im at ed becau se n eith er th e level of p ests n or th e effect of oth er d am age con trol factors (e.g., agron om ic p ractices) were con sidered. Lich t en berg an d Zilberm an (1986) were am o n g t h e first t o p o in t o u t t h e m eth od ological p roblem s of ap p lyin g a stan d ard p rod u ction fu n ction fram ework to p esticides. Th ey p rovided a th eoretical exp lan ation as to wh y p rodu ction fu n ction sp ecification s, wh ich ign ore th e d am age red u ction ch aracterist ics o f p est icid es an d t reat t h em as d irect ly yield -in creasin g in p u t s, can overestim ate m argin al p esticid e p rod u ctivity. Th e (a) m issp ecification of th e p rodu ction relation sh ip s, (b) th e om ission of p est p op u lation levels an d oth er en viron m en tal factors, an d (c) th e u se of p esticid e exp en d itu re as a variable in stead of th e total costs of abatem en t in p reviou s an alyses ascribes p rodu ctivity effects to p esticides th at in reality are cau sed by oth er factors. As a rem edy, Lich ten berg an d Zilberm an su ggested m od ifyin g th e con ven tion al (logarith m ic) sp ecification of th e Cobb–Dou glas p rodu ction fu n ction : ln Q = α + βln Z + γ ln X wh ere α is a con stan t term , γ an d β are coefficien ts of in d ep en d en t variables, an d agricu ltu ral ou tp u t Q is a fu n ction of Z p rod u ctive in p u ts an d X p esticid e in p u t s. Th ey in co rp o rat e an abat em en t fu n ct io n G(X ) sh o win g t h e p ro p o r-

140 • Chapter 6: What Can We Learn from the Economics of Pesticides?

t io n o f t h e d est ru ct ive cap acit y o f t h e d am agin g agen t elim in at ed b y t h e ap p lication of a level of con trol agen t X , th at is, p esticid es. Th ey sh owed th at th e m argin al p rod u ct (m argin al effectiven ess) of th e d am age con trol agen t in th e abatem en t fu n ction sp ecification G(X ) d eclin ed faster th an th e m argin al p ro d u ct o f p est icid es in t h e Co b b –Do u glas fu n ct io n (1/ X ) wit h a co n st an t elasticity. Em p irical st u d ies ap p lyin g t h e Lich t en b erg an d Zilb erm an fram ewo rk h ave co n firm ed t h eir h yp o t h esis. Fo r exam p le, Bab co ck an d o t h ers (1992) com p ared th e m argin al p rod u ct d erived from a con ven tion al Cobb–Dou glas fu n ction with a d am age con trol sp ecification u sin g d ata from North Carolin a ap p le p ro d u cers. At t h e average fu n gicid e ap p licat io n rat e, t h e C–D resu lt s exceed ed t h e d am age fu n ct io n est im at e by a fact o r o f alm o st 10. In clu d in g st at e variables in t h eir p ro d u ct io n p ro cess m o d el, Blackwell an d Pago u lat o s (1992) su ggested th at ign orin g n atu ral abatem en t factors m igh t overestim ate t h e m argin al p ro d u ct ivit y o f p est icid es. Ch am b ers an d Lich t en b erg (1994) ap p lied a d u al rep resen tation of th e Lich ten berg an d Zilberm an d am age con t ro l sp ecificat io n t o an aggregat e U.S. agricu lt u re d at a set . Th ey co n clu d ed t h at t h e aggregat e p est d am age in U.S. agricu lt u re was lo wer t h an p revio u s est im at es su ggest ed . Th eir m o d el also h in t s at t h e im p o rt an t d ist in ct io n between p esticid es as sin gle d am age con trol agen ts an d total d am age abatem en t. Th e lon g-ru n p rice elasticity of p esticid es was fou n d to be on th e ord er o f –1.5, wh ile t h e elast icit y o f ab at em en t su b ject t o t h e p rices o f all o t h er in p u t factors was fou n d to be con sisten tly less th an –0.1, su ggestin g th at th e con tribu tion of p esticid es to th e econ om ic ou tcom e of p est con trol is overestim ated . However, it was also sh own th at th e ch oice of th e fu n ction al form in flu en ces th e con clu sion with regard to p esticid e p rod u ctivity. For exam p le, Carrasco-Tau ber an d Moffitt (1992) u sed th e Lich ten berg–Zilberm an fram ework t o an alyze 1987 cro ss-sect io n al d at a. Th ey co m p ared t h e co n ven t io n al C–D fu n ct io n wit h t h ree d ifferen t sp ecificat io n s o f t h e ab at em en t fu n ct io n (Weib u ll, lo gist ic, an d exp o n en t ial). Th e exp o n en t ial fo rm in t h e d am age co n t ro l sp ecificat io n sh o wed a m argin al p ro d u ct ivit y o f p est icid es o f less th an u n ity su ggestin g p esticid e overu se, wh ereas all oth er fu n ction al sp ecificat io n s sh o wed resu lt s sim ilar t o t h o se fo u n d by Head ley (1968). Alt h o u gh t h e exp o n en t ial fo rm is co m m o n ly u sed in p est icid e kill fu n ct io n s (e.g., Regev et al. 1976), t h ere is n o t h eo ret ical basis fo r ch o o sin g o n e fu n ct io n al form over th e oth er. O verwh elm in gly, h o wever, resu lt s fro m ap p lyin g t h e d am age abat em en t fu n ct io n co n firm n o t o n ly t h e resu lt s o f farm -level eco n o m ic st u d ies (e.g., Webst er et al. 1999) bu t also t h o se o f n u m ero u s casu al o bservat io n s o f p est m an agem en t sp ecialist s t h at p est icid es are m o re likely t o b e o veru sed t h an u n deru sed.

Chapter 6: What Can We Learn from the Economics of Pesticides? • 141

Risk Reduction Excessive p est icid e u se co m m o n ly is rat io n alized by t h e argu m en t t h at t h e excess of th e m argin al cost over th e exp ected valu e of th e m argin al p rod u ct co u ld be in t erp ret ed as a risk p rem iu m p aid by risk-averse p ro d u cers (Fed er 1979; Tisd ell et al. 1984; An t le 1988). Risk red u ct io n was believed t o be t h e farm er’s m ain m otivation in ap p lyin g p esticid es (Reich eld erfer 1981). From a com p reh en sive literatu re review, Pan n ell (1991) con clu ded th at th e n et effect of risk on optim al pesticide u se m igh t be m in im al. He poin ted ou t th at u n certain ty abou t som e variables su ch as pest den sity an d pest m ortality does in fact lead t o h igh er p est icid e u se u n d er risk aversio n , wh ereas fact o rs like o u t p u t price an d yield lead to lower pesticide levels if u n certain ty is con sidered. In h is an alysis o f Califo rn ian co t t o n p ro d u ct io n , Hu rd (1994) fo u n d n o em p irical su p p ort for th e th eory th at p esticides redu ce risk or th at in tegrated p est m an agem en t (IPM) is a risky t ech n o lo gy. Th e co n clu sio n fo u n d in t h e st u d y o f Sah a an d o t h ers (1997) t h at in fact p est icid es m ay be risk in creasin g is su p ported by oth er stu dies (Horowitz an d Lich ten berg 1993; Regev et al. 1997). Con trary to th e in terp retation d erived from th e exp ected u tility con cep t, th ese con clu sion s are ch allen ged by th e h ypoth esis provided th rou gh prospect th eory (Kah n em an an d Tversky 1979). Both exp erim en tally an d in real-world decision m akin g, even portfolio m an agers in th e bu sin ess world ten d to weigh lo sses su bst an t ially m o re t h an o bject ively co m m en su rat e gain s (Kah n em an an d Tversky 2000). Th e d ecision m aker’s u tility fu n ction , th erefore, seem s to d ifferen tiate between gain an d loss. W h ile d ecision m akers are risk averse in a gain sit u at io n t h ey m ay beco m e risk t akers in a lo ss sit u at io n . Hen ce lo ssaverse farm ers will beh ave in co n sist en t ly, t h at is, t h ey ap p ly p est icid es alth ou gh th is strategy is risk in efficien t. Em p irical eviden ce for su ch beh avior is provided by th e stu dy of Rola an d Pin gali (1993) on th e econ om ics of in secticide u se in Asian rice p rodu ction . In th eir com p arison of fou r in sect con trol strategies, depen din g on th e m odel, th e expected m on etary valu e, an d th e certain ty eq u ivalen t of “n atu ral con trol” exceed ed th ose of farm ers’ in secticid e u se p ractice. In an y case, certain ty eq u ivalen ts exceed ed exp ected m on etary valu es, in d icatin g risk-takin g beh avior. Hen ce, p rosp ect th eory cou ld p rovid e an explan ation for con tin u ou sly h igh levels of in secticide u se in Asian rice produ ction in spite of eviden ce th at th is strategy is n ot econ om ical. Regard less of th e beh avioral assu m p tion s for d ecision m akin g in p est m an agem en t an d p esticide u se, earlier con clu sion s in econ om ic literatu re th at p est icid es are risk-red u cin g in p u t s is su bject t o rest rict ive assu m p t io n s. Hen ce, th ere are few reason s to attribu te ad d ition al ben efits to p esticid es becau se of th eir risk-redu cin g effects. Risk redu ction is on e of th e argu m en ts u sed to ju stify th e in trod u ction of GMO s. Th u s, sou n d econ om ic an alysis is n eed ed to exam in e th e h yp oth esis th at tran sgen ic varieties do in deed p ossess risk-redu c-

142 • Chapter 6: What Can We Learn from the Economics of Pesticides?

in g p rop erties th at cou ld be ad d ed to th eir assu m ed p rod u ctivity-en h an cin g ben efits. Su ch an alysis also m u st in clu de th e beh avioral im p lication s for decision m akin g by sm all-scale farm ers faced with p rosp ects exp ressed in “th e lan gu age of loss,” wh ich is often u sed by p esticid e ad vertisem en ts, esp ecially in develop in g cou n tries.

Interaction with Natural Resources Decrease in p ro d u ct ivit y o ccu rs o ver t im e as a resu lt o f bio lo gical p ro cesses kn own as resistan ce to p esticid es an d p est resu rgen ce. Agricu ltu ral p rod u cers will ad ju st th eir p ractices to th is p rod u ctivity d eclin e. For in stan ce, p esticid e dem an d in creases with risin g levels of resistan ce (Carlson 1977). However, th e react io n o f t h e p ro d u cer t o in crease t h e rat e o f an in p u t fact o r wh o se m argin al p ro d u ct ivit y d eclin es is co n t rad ict o ry t o eco n o m ic rat io n ale wh en ap p lyin g a co n ven t io n al p ro d u ct io n fu n ct io n fram ewo rk. Fo llo win g t h e Lich t en b erg an d Zilb erm an (1986) fram ewo rk, resist an ce (R) can b e in t ro du ced in to th e abatem en t fu n ction : G (X , R) Lich ten berg an d Zilberm an (1986) sh owed th at in fact th e m argin al effectiven ess fu n ction is sh ifted to th e left, im p lyin g a h igh er op tim al d ose com p ared with a situ ation with ou t resistan ce or m akin g th e sh ift to a n ew, m ore effective, an d probably m ore costly ch em ical produ ct econ om ically n ecessary. From th e n atu ral resou rce econ om ics p oin t of view, resistan ce m ean s th e loss of th e biological capital, th at is, pest su sceptibility to th e pesticide (Hu eth an d Regev 1974). Fleisch er (1998a) h as estim ated th e p resen t valu e of th e costs of resistan ce to th e h erbicide atrazin e in Germ an m aize produ ction . Takin g a low d isco u n t rat e t o reflect t h e irreversibilit y o f resist an ce d evelo p m en t , t h e resou rce costs are in th e ran ge of abou t 4,600 DM to 6,000 DM per h ectare. Th e n egative side-effects of th e loss of ben eficial organ ism s in p articu lar on th e ecosystem can ch an ge th e m argin al p rod u ctivity of p esticid es over tim e. Ben eficial organ ism s act as n atu ral d am age con trol agen ts in th e abatem en t fu n ction . In p rin cip le, th ey are available to growers as a u biq u itou s com m on p rop erty resou rce. Th e econ om ic effect of a red u ction in n u m bers of ben eficial organ ism s or a ch an ge in th eir sp ecies com p osition is an even m ore com p lex issu e th an th e p rocess of p esticide resistan ce. Alth ou gh th e em ergen ce of resistan ce req u ires adju stm en ts in th e dose level or p rom p ts th e switch to n ew an d u su ally m ore exp en sive ch em icals, th e d ep letion of ben eficial organ ism s gen erally leads to a dep en den ce on ch em ical p lan t p rotection . Th e p h en om en on of p ath d ep en d en ce was first in trod u ced to th e field of p est m an agem en t by Cowan an d Gu n by (1996). Th ey p oin ted ou t th at self-

Chapter 6: What Can We Learn from the Economics of Pesticides? • 143

rein fo rcin g m ech an ism s, su ch as n et wo rk ext ern alit ies fro m ad o p t io n an d in creasin g ret u rn s t o scale, keep cro p p in g syst em s o n a p est icid e p at h alt h o u gh m o re eco n o m ical alt ern at ives are availab le. To d ay’s p est icid e u se m ay n ot on ly p red eterm in e fu tu re p esticid e u se bu t also artificially stim u late th e in trod u ction of GMOs. It th u s m ay lower th e p rofitability of altern ative strategies su ch as IPM in th e fu tu re. Co n cep t u ally, t h e effect o f in creasin g d ep en d en ce o n p est icid es is illu strated in Figu res 6-1a an d 6-1b. Figu re 6-1a sh ows th e con ven tion al fertilizer p rod u ction fu n ction with p esticid e u se as a d iscrete ch oice. Th e sh ift in th e yield/ reven u e cu rve is th e resu lt of p esticide ap p lication . Th e cost of p esticides is th e in tercep t of th e fertilizer cost cu rve. Hen ce, n et ben efits of p esticide u se eq u ate to th e differen ce in th e reven u e cu rve (ΔR) less p esticide (Cp) an d addition al fertilizer costs (ΔCf). High er p est p ressu re as a resu lt of p esticide ap p lication in p rior p eriod s will m ake th e reven u e cu rves d rift ap art. Yield s an d reven u es in t h e “wit h o u t p est icid e” sit u at io n d ro p becau se o f h igh er cro p lo ss co m p ared wit h t h e in it ial st art in g p o in t (Figu re 6-1a) wh ereas agricu lt u ral yield Y s m ay go u p as a resu lt of varietal im p rovem en t (Figu re 6-1b). As lon g as t h e d ivergen ce o f t h e reven u e cu rves is larger t h an t h e in crease in co st s, p esticides ap p ear to becom e m ore p rofitable over tim e. Th e p rocess com es to an en d wh en th e cu rren t crop p in g system becom es less p rofitable th an an altern ative, p resu m ably less p esticide-in ten sive system . Fro m a p rivat e p ro d u cer’s p o in t o f view, a ch an ge in t h e cro p p in g syst em is n ot econ om ical before th at p oin t is reach ed . By th en , th e resou rce d ep letion p ro cess is o n go in g, an d t h e farm er h as beco m e d ep en d en t o n p est icid e u se. Th is dep en den cy is sh own as an in crease in th e m argin al p rodu ct of p esticides relative to oth er in p u t factors wh en takin g th e farm er’s p oin t of view with in t h e fram ewo rk o f a p art ial an alysis. Un d er a reso u rce eco n o m ic fram ewo rk, th is ad d ition al “ben efit” is actu ally an exp ression of th e d ep letion of n atu ral resou rces an d th u s m u st be in terp reted as costs. Bo t h su scep t ib ilit y o f p est s t o ward p est icid es an d t h e st o ck o f b en eficial o rgan ism s are co m m o n -p ro p ert y reso u rces. Th erefo re, in d ivid u al p ro d u cers do n ot p erceive th eir action s to h ave m u ch in flu en ce on th ese resou rces, an d, as a resu lt , t h ey o p erat e wit h in a m yo p ic o p t im izat io n fram ewo rk. Co n seq u en t ly, an ext ern alit y is p ro d u ced wit h an “o ff-t im e n at u re,” t h at is, t h e extern ality effect is felt on ly in th e fu tu re, n ot in th e p eriod wh en it is cau sed. Th e d ep let io n o f t h ese t wo reso u rces n evert h eless h as im p licat io n s fo r t h e assessm en t o f p est icid e p ro d u ct ivit y an d co n seq u en t ly m u st b e t aken in t o accou n t wh en estim atin g ben efits. Alth ou gh resistan ce m ain ly affects th e factor X (i.e., p esticid e u se) in th e d am age con trol fu n ction , th e effect of p esticid es o n b en eficial o rgan ism s affect s t h e p o t en t ial cro p d am age. In o t h er word s, th e cost of resistan ce is sh own as th e am ou n t farm ers sp en d on d am age abat em en t . Th ese co st s wo u ld be in t ern alized 1 if t h e sect o r is t reat ed as

(b)

Ys Cp

Cp

Y1

ΔR

Yns

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ΔCf

Y1 +f

Revenue Cost

Revenue Cost

Ys

ΔR Yns

ΔCf Y0 Cp Cp

Cp F0

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Fertilizer

FIGURE 6-1. (a) Costs and Revenues of Pesticide Use in t 0 (b) Costs and Revenues of Pesticide Use in t 1.

+f

144 • Chapter 6: What Can We Learn from the Economics of Pesticides?

(a)

Chapter 6: What Can We Learn from the Economics of Pesticides? • 145

o n e firm , ign o rin g sp read effect s cau sed b y co m m o n access. Th e effect o f a red u ced st o ck o f ben eficial o rgan ism s is an o verest im at io n o f t h e ben efit o f p est icid es b ecau se t h e p ro b ab ilit y o f p est at t ack an d t h e exp ect ed level o f in festation are risin g. In th is con text, it is n o su rp rise th at, an alyzin g p esticide t rials fro m agricu lt u ral research , 2 O erke an d o t h ers (1994) fo u n d t h at cro p losses for eigh t m ajor crop s h ave in creased in relative term s over tim e.3 Th e n atu re of cu rren t GMOs with disease- an d p est-resistan t traits su ggests t h at t h e sam e p rin cip les t h at are u sed in m easu rin g p est icid e p ro d u ct ivit y sh ou ld be ap p licable to GMOs. Th is im p lies, first, th at p est-resistan t traits in tran sgen ic varieties m u st be treated as dam age con trol agen ts an d n ot as yieldin creasin g in p u ts. After all, u sin g Bacillus thuringiensis (Bt) gen es is like m akin g a p esticid e in sid e th e p lan t in stead of p lacin g it th ere in d irectly as with syst em ic p est icid es. Seco n d , wh et h er GMO s d o in d eed p o ssess risk-red u cin g p rop erties or are even risk in creasin g wh en com p ared with altern ative p lan t p rotection tech n ologies n eeds to be exam in ed. Th e largely u n kn own ecological an d h u m an h ealt h im p licat io n s an d t h e gro win g in flu en ce o f co n su m er reaction s to p olicy decision s abou t GMOs, also in develop in g cou n tries (Paarlb erg 2000), len d so m e su p p o rt t o t h e lat t er h yp o t h esis. Th ird , t h e n at u ral resou rce effects of a large-scale in trod u ction of tran sgen ic crop s m u st be cap tu red in econ om ic an alysis. Ecological effects su ch as th e develop m en t of n ew b io t yp es t h at o verco m e t h e resist an ce t rait s, o u t cro ssin g o f gen es, an d in tertem p oral carryover effects of tran sgen ic crop residu es can resu lt in sign ifican t dam age abatem en t or p reven tion costs.

Recent Economic Studies of GM Os Trad ition ally, econ om ists h ave m easu red th e im p act of tech n ological ch an ge in agricu lt u re b y u sin g t h e p erfect m arket m o d el. Th e in n o vat io n , aft er bein g ad op ted by farm ers, lowers th e m argin al costs of p rod u ction an d lead s t o a sh ift in su p p ly. Dep en d in g o n t h e d em an d elast icit y o f t h e p ro d u ct fo r wh ich t h e in n o vat io n is in t ro d u ced , t h e p rice o f t h e p ro d u ct will d ecrease (Figu re 6-2). Th e m o re elast ic t h e d em an d is, t h e m o re t h e b en efit s go t o p ro d u cers as in d icat ed b y area “ebcd – p 0 aep 1 ” wh ile t h e welfare o f co n su m ers is in creased by area p0 abp1 . If dem an d is com p letely elastic, as is th e case wh en th e world m arket p rice of a com m odity is n ot affected by th e su p p ly (sm all cou n try case), all ben efits go to p rod u cers of th e com m od ity an d th e p rod u cers an d d istribu tors of th e in n ovation . Th e m arket m od el n eed s ad ju stm en t if th e su p p lier of th e tech n o lo gy beh aves as a m o n o p o list . Th is is t h e case fo r bio t ech n o lo gy in n o vation s th at en joy in tellectu al p rop erty p rotection . Here, th e m on op olist is able t o set t h e p rice abo ve m argin al co st s an d as a co n seq u en ce will n o t p ass all su rp lu s t o t h e m arket . Fin ally, wh en ap p lied t o a p art icu lar t ech n o lo gy in a

146 • Chapter 6: What Can We Learn from the Economics of Pesticides?

S0

Price

p1

S1

a

p0

b e

d D

c q0

q1

Quantity FIGURE 6-2. Economic Impact of Biotechnology Innovations

p articu lar sector of th e econ om y, th e m odel sh own in Figu re 6-2 op erates in a p artial eq u ilibriu m m ode, th at is, oth er econ om ywide effects are n ot in clu ded. Th e lim it at io n s o f t h e u se o f t h e m arket m o d el fo r im p act assessm en t o f agricu ltu ral tech n ology h ave been well docu m en ted (Alston et al. 1998). Th ey in clu de th e followin g: • How can we correctly estim ate th e p ercen tage of research -in d u ced red u ction in p rodu ction costs? • How can we estim ate th e size of th e in d u stry affected by th e in n ovation ? • How can we estim ate ch an ges in th e su p p ly of in p u ts in du ced? • Ho w can we est im at e wh en b en efit s fro m ad o p t io n co m m en ce, t h at is, wh at is t h e t im e lag b et ween t h e in t ro d u ct io n o f an in n o vat io n an d it s adop tion ? In addition to th ese m easu rem en t p roblem s, th e m arket m odel can lead to an u n derestim ation or overestim ation of th e ben efits of a tech n ology if a large p rop ortion of th e p rod u ce is n ot m arketed or if p oor in frastru ctu re resu lts in h igh tran saction costs. Overestim ation can occu r if th e tech n ology gen erates n egative extern alities in term s of n atu ral resou rce an d en viron m en tal effects.

Chapter 6: What Can We Learn from the Economics of Pesticides? • 147

Un d erestim ation can occu r if th e tech n ology p rod u ces p ositive en viron m en t al an d n at u ral reso u rce m an agem en t b en efit s n o t in clu d ed in t h e m arket effects. Th e few eco n o m ic st u d ies o f b io t ech n o lo gy in agricu lt u re t o d at e calcu lat ed t h e eco n o m ic su rp lu s. In est im at in g t h e su p p ly sh ift t h at is t h e m o st cru cial variable in su ch stu d ies, th e lesson s learn ed from econ om ic stu d ies of p est icid es were n o t always ap p lied . In st ead , m o d ern b io t ech n o lo gy was treated as a “yield-in creasin g” an d at th e sam e tim e “cost-savin g” tech n ology. Mo st o f t h ese st u d ies were co n d u ct ed o n Bt cro p s in t h e Un it ed St at es. O n e was co n d u ct ed in Ch in a an d an o t h er ex an t e st u d y o n p o t at o es an d sweet p otatoes was con du cted in develop in g cou n tries. In th e stu d y of Falck-Zep ed a an d oth ers (2000) on Bt cotton in th e Un ited States, in form ation from su rveys of farm ers an d on -station exp erim en ts were u sed t o “refin e” eco n o m et ric est im at es o f sh ift s in su p p ly fro m Bt co t t o n . Alth ou gh th e au th ors recogn ized th at th ere was great deal of varian ce in p est pressu re, yields, seedin g rates, an d oth er produ ction ch aracteristics am on g produ cers of Bt corn it is n ot clear h ow th eir m odel takes accou n t of th is variation . Ultim ately, elasticity of su pply taken from literatu re data was treated as a ran dom variable in a stoch astic sim u lation procedu re to m odel econ om ic su rplu s. Fern an d ez-Corn ejo an d McBrid e (2000) su m m arized th e effects of gen etically en gin eered crop s on yields, p esticide u se, an d retu rn s as rep orted in p reviou s stu dies of h erbicide-toleran t soybean s, corn , an d cotton ; Bt cotton ; an d Bt corn . Som e of th ese stu d ies u sed exp erim en tal d ata; oth ers were based on su rveys. Th e au th ors reviewed th e statistical an d p ractical p roblem s en su in g from con trolled exp erim en ts an d th ose resu ltin g from farm su rveys as well as som e solu tion s to overcom e th ese p roblem s. However, it is n ot clear to wh at ext en t t h ese st an d ard s were ap p lied t o t h e eco n o m ic st u d ies o n gen et ically m odified crop s in th e Un ited States. For exam p le, m ost of th e stu dies did n ot d iscu ss th e p roblem of d efin in g a valid referen ce system (Zad oks an d Waibel 2000) becau se n eith er th e con trol p lots in exp erim en ts n or farm ers’ cu rren t p ractices m ay q u alify for th is. Carp en ter an d Gian essi (2001) u p dated th eir p reviou s estim ates of th e ben efit s asso ciat ed wit h t h e ad o p t io n o f gen et ically m o d ified cro p variet ies o f co rn , co t t o n , an d so yb ean s in U.S. agricu lt u re. Th ey d id n o t m en t io n t h e m eth od ological p roced u re of th eir an alysis bu t th ey n everth eless d rew clearcu t con clu sion s. “… Bt corn varieties allowed farm ers to con trol th e Eu rop ean co rn b o rer, an in sect t h at is d ifficu lt t o co n t ro l u sin g co n ven t io n al in sect icides … Prior to th e in trodu ction of Bt corn , few growers were sp rayin g for th e co rn b o rer. In st ead , yield lo sses so m et im es reach ed 300 m illio n b u sh els o f corn p er year. With Bt corn , losses from th e corn borer are elim in ated. Th e p rim ary ben efit o f Bt co rn variet ies h as been in creased yield s” (Carp en t er an d Gian essi 2001,1) Sim ilar con clu sion s were d rawn for h erbicid e-resistan t vari-

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eties an d Bt varieties of oth er crop s. Con versely, th e con clu sion for in sect- an d viru s-resist an t p o t at o es was d ifferen t . “Th e recen t in t ro d u ct io n o f a h igh ly effect ive co n ven t io n al in sect icid e an d t h e refu sal o f p ro cesso rs t o accep t gen et ically m o d ified p o t at o es h ave lim it ed t h e ad o p t io n o f t h ese n ew varieties” (Carp en ter an d Gian essi 2001, 2). In Ch in a, th e stu d y of Pray an d oth ers (2001) exam in ed th e am ou n t an d distribu tion of ben efits am on g differen t grou p s of farm ers an d between farm ers, seed com p an ies, an d research in stitu tes. Th e data were drawn from a sin gle recall su rvey o f 283 co t t o n farm ers in t wo p ro vin ces o f No rt h ern Ch in a an d com p ared adop ters an d n on adop ters of Bt cotton . Am on g both grou p s, a differen tiation was m ade between varieties. Th e au th ors fou n d th at Bt cotton in creased farm ers’ in co m e t h ro u gh in creased yield s an d red u ced p est icid e costs, th e latter gen eratin g ad d ition al h ealth ben efits. Th eir con clu sion s were based on averages, bu t a h igh variation cou ld be observed across location s an d varieties. On ly 14% of th e resp on den ts belon ged to th e grou p of n on adop ters. Th e on ly ex an te stu dy in develop in g cou n tries for viru s resistan ce of p otat o es 4 u n t il n o w was co n d u ct ed b y Q u aim (2000). 5 Th e au t h o r co n clu d ed “h an dsom e” in tern al rates of retu rn of 60% to 77% for biotech n ology in vestm en ts in sweet p otatoes an d of 52% to 56% in p otatoes. A lim itation of th is st u d y is t h at t h e au t h o r ign o red t h e reco m m en d at io n in t h e recen t agricu ltu ral econ om ics literatu re (Davis an d Esp in oza 1998) th at stoch astic sim u lation sh ou ld be u sed in stead of sen sitivity an alysis to ad d ress th e p roblem of u n certain ty. Also, in view of th e sp arse em p irical database u sed by th e au th or, th e validity of h is ex an te an alysis largely dep en ds on th e treatm en t of risk in th e calcu lation s of rates of retu rn . To su m u p ou r coverage of recen t stu dies of GMOs, th e followin g m eth odological lim itation s of p reviou s econ om ic an alyses of crop p rotection related t o bio t ech n o lo gy in n o vat io n s can be o bserved : Th e n at u re o f p est - an d d isease-resistan t varieties as dam age con trol agen ts is ign ored becau se, like in th e earlier an alysis of p esticides, th ey are n ot treated as dam age redu ction factors. Most stu d ies assu m e th at cu rren t p est m an agem en t is in effective in p reven tin g cro p lo ss m ain ly becau se eit h er n o p est icid es are available o r t h ey h ave becom e in effective as a resu lt of p est resistan ce. At th is p oin t, th e q u estion of th e correct referen ce system to be u sed em erges again . To com p are tran sgen ic crop s with “tradition al” crop s first req u ires an op tim ization of th e cu rren t system . In th is regard, all p reviou s stu dies are static. Th ey com p are a “n ew” tech n o lo gy wit h a “d ep reciat ed ” 6 o n e, t h at is, t h ey co m p are d ifferen t p o in t s in th e life cycle of a tech n ology. Fu rt h erm o re, m o st p revio u s st u d ies d o n o t acco u n t fo r risk, alt h o u gh u n cert ain t y wit h t ran sgen ic cro p s is h igh in several resp ect s. Fo r exam p le, p rice risk is h igh b ecau se t h ere can b e d ram at ic co n su m er react io n s in resp on se to h ealth fears, regard less of wh eth er th ese fears are based on scien -

Chapter 6: What Can We Learn from the Economics of Pesticides? • 149

t ific evid en ce o r m erely co n su m er p ercep t io n . Fin ally, n o n e o f t h e st u d ies reviewed at t em p t ed t o acco u n t fo r n egat ive ext ern alit ies fro m GMO s, alt h o u gh so m e o f t h e effect s, su ch as t h e d evelo p m en t o f resist an ce, are exp ected to occu r, wh ile th e exten t of su ch even ts an d th eir tim in g is su bject to con siderable u n certain ty. Th e recen t literature on th e econ om ics of pesticides an d on GMOs h as provid ed som e im p ortan t lesson s. High ligh tin g th e p oten tial overestim ation of ben efits an d esp ecially an u n d erestim ation of th e extern al costs is ju stified wh en followin g a “precaution ary prin ciple” in con ductin g econ om ic studies of n ew tech n ologies. Alth ou gh claim s of p ositive extern alities also h ave been m ade for pesticides (e.g., Avery 1995), an d th e role of GMOs as a public good in figh tin g h un ger an d poverty is often un derlin ed in docum en ts of developm en t organ ization s, available em pirical eviden ce of such addition al ben efits is sparse. Furth erm ore, th ere are serious th eoretical problem s with th e con cept of positive extern alities attributable to ch em ical pesticides (Pearce an d Tin ch 1998).

A Conceptual Framework for Economic Analysis of GM Os We p ro p o se a research -o rien t ed co n cep t fo r t h e eco n o m ic assessm en t o f GMO s. Du rin g t h e in it ial st age o f ad o p t io n , su ch a n o rm at ive ap p ro ach is n ecessary to im p rove th e estim ates of fu tu re ben efits an d costs. Econ om ic assessm en t of p u blic or p rivate in vestm en ts in tran sgen ic crop s req u ires a co m p ariso n o f t h e su m o f t h e exp ect ed d isco u n t ed ben efit s wit h t h at o f kn o wn an d exp ect ed d isco u n t ed co st s. Trad it io n ally, eco n o m ist s u n d ert o o k su ch co st –b en efit an alysis b y ap p lyin g t h e co n cep t o f eco n o m ic su rp lu s, m ostly in a p artial eq u ilibriu m m od e. Th is is ap p rop riate as lon g as forward an d backward lin kages to oth er sectors of th e econ om y are sm all an d n o ext ern alit ies are t o b e exp ect ed fro m t h e t ech n o lo gy. Th e exp erien ce gain ed with syn th etic p esticides (Zadoks an d Waibel 2000) su ggests th at extern al costs exist an d m ay be h igh er th an in itially exp ected. Th e p rop osed in vestm en t in GMOs sh ou ld be assessed again st oth er p oten tial in n ovation s. In th e case of tran sgen ic crop s, wh ich are design ed for better p est m an agem en t, tech n ological op tion s su ch as IPM an d biological con trol m igh t be u sed as referen ce p oin ts. Becau se th e ad op tion of th ose tech n iq u es h as b een im p ed ed b y a lo n g-t erm su b sid y p o licy fo r syn t h et ic p est icid es (Rep etto 1985, Waibel an d Fleisch er 1995), th e n et ben efits of gen etic m odification as a n ew tech n ology can be overestim ated.

Benefit Assessment To assess b en efit s, t h e im p act o n t h e p ro d u ct ivit y o f t h e agricu lt u ral sect o r m u st be m easu red as accu rately as p ossible. Market d istortion s, wh ich occu r

150 • Chapter 6: What Can We Learn from the Economics of Pesticides?

in m ost agricu ltu ral m arkets in in du strial cou n tries, req u ire an op en econ om y fram ewo rk, t h at is, o n e t h at valu es t h e ad d it io n al p ro d u ct io n gain ed o r t h e resou rces saved u sin g sh ad ow p rices. Alth ou gh th e ch oice of th e ap p rop riate m odel to m easu re ben efits is im p ortan t, it is eq u ally im p ortan t th at th e m odel be based on carefu lly collected d ata, wh ich m u st rep resen t th e actu al con d it io n s o f p ract ical farm in g. Th erefo re, d at a co llect ed fro m exp erim en t s co n d u cted in research station s are in ap p rop riate, esp ecially for gen etically m od ified cro p s d esign ed fo r p est co n t ro l. Mo st ly, t h e co n d it io n s o f research station s with con tin u ou s crop p in g of few crop s gen erate h igh er p est p ressu re th an fou n d u n der real-world con dition s. In th e case of con trolled exp erim en ts con du cted in farm er fields, p ossible adju stm en t strategies of farm ers are often ign ored becau se treatm en t strategies are fixed beforeh an d. Th u s ben efits ten d to be overestim ated. Data based on in terviewin g farm ers wh o ad op ted tran sgen ic varieties an d th ose wh o d id n ot often su ffer from a selection bias called self-selection (Fern an dez-Corn ejo an d McBride 2000). In su rveys, farm ers are n ot assign ed ran d om ly to eith er grou p (ad op ters an d n on ad op ters); th ey m ake th e ad op tion d ecision th em selves. Th erefore, ad op ters an d n on ad op ters m ay be system atically d ifferen t , h en ce t h e o b served d ifferen ces in p ro d u ct ivit y m ay n o t b e fu lly attribu table to th e ad op tion d ecision . Alth ou gh th ere are statistical p roced u res t o co n t ro l fo r self-select io n , t h e co rrect io n d ep en d s o n wh et h er all im p o rt an t fact o rs t h at cau se a syst em at ic d ifferen ce are act u ally m easu red . Th is, h owever, often is n ot p ossible in “on e-sh ot” su rveys. In stead of d ata from con trolled exp erim en ts, su rveys, or both , field -based , season -lon g observation s of farm an d p lot-level d ata on th e am ou n t an d th e tim in g of in p u ts are n eed ed to m easu re th e im p act of tran sgen ic crop s at th e farm level. At h arvest tim e, yield s are m ore accu rately m easu red by ap p lyin g crop -cu t sam p lin g. Also, con clu sion s sh ou ld n ot be based on ly on sh ort-term tech n ology adop tion (on e or even two years). In view of th e variation of p est p o p u lat io n s o ver t im e, we su b m it t h at t o m easu re t h e field -level im p act o f tran sgen ic crop s, a p eriod of five years is n eeded. Th is seem s essen tial becau se of th e followin g reason s. First, farm ers are likely to gain exp erien ce an d th u s im p ro ve t h eir p erfo rm an ce via red u ct io n o f p est icid e u se, ch an ges in seed rat es, o r m o d ificat io n s o f t h eir cro p p in g p at t ern s. Seco n d , ext ern alit ies t h at resu lt in ch an ges t o t h e eco syst em will n o t b e n o t iceab le im m ed iat ely, fo r exam p le, ch an ges in t h e n u m b er o f b en eficial in sect s as well as resist an ce bu ild u p in target p ests. Id eally, d ata wou ld h ave to be collected before tran sgen ic crop s were adop ted by th e farm ers. Th is, h owever, is h ardly p ossible as, u n like a t ech n o lo gy t h at is in t ro d u ced b y farm er t rain in g, t h e ad o p t io n o f t ran sgen ic variet ies is n o t kn o wn b efo reh an d . In st ead , early an d recen t ad op ters can be com p ared with a fixed con trol grou p of n on ad op ters. Based on exp erien ce from im p act assessm en t of farm er field sch ools, a m in im u m of

Chapter 6: What Can We Learn from the Economics of Pesticides? • 151

30 t o 50 farm ers p er gro u p is su fficien t (Ken m o re 1996). Th e d at a o n farm eco n o m ic p aram et ers m u st b e co m p lem en t ed b y h ist o rical in fo rm at io n o n th e p est com p lex an d a descrip tion of th e ecological con dition s of th e area. To avoid overestim ation of th e im p act of a tran sgen ic resistan t variety over th e con ven tion al m eth od of p est con trol, first d ata sh ou ld be an alyzed u sin g th e dam age con trol fram ework; secon d data sh ou ld be corrected for econ om ically in efficien t p esticid e u se (wh ich exists as su ggested by th e fact th at IPM can in crease farm p ro fit s). Th e d am age co n t ro l fram ewo rk was ap p lied b y Hu an g an d Qiao (2000) to p esticid e u se in rice in Ch in a an d by Ajayi (2000) to cotton in Côte d’Ivoire.

Costs of Externalities Som e of th e extern alities attribu table to p esticide u se are difficu lt to in tern alize becau se th ey on ly occu r in th e lon g ru n an d becau se th ey affect com m on p ro p ert y reso u rces. Th is is t yp ical fo r p est icid e resist an ce. It h ap p en s o ver tim e, an d it is th e resu lt of th e action s of all farm ers wh o ap p ly p esticides. Th e com bin ed effect of th eir action is th e red u ction of th e resou rce “su scep tibility,” a typ ical com m on -p rop erty resou rce. Sim ilar effects can be exp ected to take p lace with p est resistan ce of a crop variety. W h ile resistan t p lan ts m ay becom e in effective again st p ests, p ests m ay lose th eir su scep tibility toward p esticides. Resistan t varieties p rodu ced by classical breedin g m eth ods even tu ally m ay be attacked by n ew strain s of th e p est again st wh ich th e resistan ce d oes n ot work. Su ch strain s ap p ear n atu rally by m u tation an d recom bin ation of gen es an d m ay be au gm en ted by in d iscrim in at e p est icid e u se. Hu n d red s o f su ch even t s are o n reco rd o ver t h e last 80 years fo r wh eat , p o t at o es, rice, an d sco res o f o t h er cro p s. In eit h er case, a gen etic ch an ge in th e p est p op u lation term in ates th e econ om ic lifetim e of an asset, be it th e p esticide or th e resistan t variety. In eith er case, th e p est p op u lation m ay in crease an d cau se sign ifican t dam age. Th e n atu ral resou rce im p lication s of th e two cases cou ld be differen t. Sim ilarly, tran sgen ic resistan ce m ay becom e in effective. Gen es for Bt toleran ce h ave alread y been fou n d in target p est p op u lation s (Gou ld et al. 1997). As wit h classical b reed in g fo r m o n o gen ic resist an ce (Zad o ks 1993), n ew (tran s)gen es will be kep t in store. Th e loss of h ost p lan t resistan ce th rou gh th e ap p earan ce of n ew p est gen otyp es an d th e ch an ges in p est p op u lation can be con sidered as resou rce dep letion in p est m an agem en t. It is th u s a cost to cu rren t an d fu tu re u sers of p est con trol tech n ology. Measu rin g co st s fo r n ewly in t ro d u ced t ran sgen ic cro p s m ay b e d ifficu lt . Ho wever, ch an ge m igh t b e o b servab le b y co m p arin g recen t ad o p t ers wit h early adop ters as m en tion ed p reviou sly. Also, data from exp erim en ts m ay p rovid e so m e in d icat io n o f t h e t im e sp an u n t il resist an ce o ccu rs. In ad d it io n ,

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exp ert o p in io n can b e u sed t o ju d ge wh en an d h o w rap id ly resist an ce will develop . Con cep tu ally, th e costs of resistan ce d evelop m en t an d th e ben efits of p reven tin g or delayin g it are sh own in Figu re 6-3. Alth ou gh th e gen eral sh ap e of th e cu rve is kn own , th e critical p aram eters th at n eed to be determ in ed are t 1S1 (t 1S2 ) an d t 2S1 (t 2S2 ) in Figu re 6-3. Here, t 1 is t h e t im e wh en resist an ce (breakd own of resistan ce of varieties) starts to take p lace an d t 2 is th e p oin t in tim e wh en th e effective p rice of th e variety h as reach ed th e costs (C s) of a su bstitu te tech n ology. Th e areas (A an d B) u n der th e resistan ce cu rves for two altern ative resistan ce m an agem en t strategies RMS2 an d RMS1 are th e total costs of resist an ce. 7 Th e ben efit o f im p ro ved resist an ce m an agem en t (RMS1 ) is in d icated by area A in Figu re 6-3. To com p are an n u al costs with an n u al ben efits, th ese n eed to be discou n ted an d con verted in to an an n u ity. Th e p aram eters t 1 , t 2 , an d th e slop es of th e resistan ce cu rves of Figu re 6-3 are su b ject t o so m e d egree o f u n cert ain t y, t h at is, t h e exp ert s m ay vary in th eir op in ion s. Hen ce, to calcu late th e costs of resistan ce, th ese assu m p tion s n eed to be su bjected to risk an alysis u sin g stoch astic sim u lation ap p roach es. Here, cu m u lative p robability distribu tion s of an objective variable su ch as n et ben efit are gen erated by ap p lyin g a ran d om gen erator to a set of in p u t variables with defin ed ran ge an d distribu tion typ e. Figu re 6-4 con cep tu alizes th is p rocedu re by h yp oth etically com p arin g two resistan ce m an agem en t strategies

RM S1

Costs and Benefits

RM S2 Cs

A B t 1s2

t 1 s1

t 2 s2

t 2 s1

Time FIGURE 6-3. Costs of Resistance and Benefits of Resistance M anagement

Chapter 6: What Can We Learn from the Economics of Pesticides? • 153

RM S2

RM S1

Cumulative Probability

1

0

Net Benefit FIGURE 6-4. Stochastic Simulation of Net Benefits of Two Resistance M anagement Strategies

RMS1 an d RMS2 . RMS1 in th is con text m ay refer, for exam p le, to m ore restrictive req u irem en ts of refu ge areas with n on tran sgen ic crop s. Alth ou gh th is m eth od will n ot elim in ate th e cau ses of u n certain ty, it will p rovid e a better basis for d ecision m akin g becau se m easu res of econ om ic p erfo rm an ce will be p resen t ed as wh at t h ey really are, p ro babilist ic valu es an d n ot rigid n u m bers. Fu rth erm ore, th e differen ces between m an agem en t strategies can be p resen ted by th eir degree of stoch astic dom in an ce.

Conclusion Carefu l eco n o m ic an alysis o f t h e GMO t ech n o lo gy is n ecessary if so ciet y wan t s t o avo id t h e m ist akes m ad e wit h t h e assessm en t o f syn t h et ic p est icid es. Em p irical an alysis m u st look at th e ben efits as well as at th e risks. Critical ben efit assessm en t is im p ortan t becau se th ere is a ten d en cy am on g scien tists to be overop tim istic at th e begin n in g. Th u s, an ap p rop riate fram ework an d a so lid em p irical b asis are n ecessary. As lo n g as t h e risks o f GMO s are p o o rly u n d erst o o d , an o verest im at io n o f t h eir b en efit s can b e h igh ly m islead in g. From a m eth od ological p oin t of view, GMOs in crop p rotection sh ou ld be t reat ed in a d am age co n t ro l fram ewo rk. Sim p ly lo o kin g at yield can lead t o th e wron g con clu sion s. Also, care n eeds to be taken wh en defin in g th e cou n -

154 • Chapter 6: What Can We Learn from the Economics of Pesticides?

terfactu al. An agroecosystem “d egrad ed ” by m isgu id ed h u m an in terven tion s with in discrim in an t p esticide u se is n ot a su itable referen ce system . Th erefore, t o avo id co m p arin g ext rem e sit u at io n s, co rrect ive ad ju st m en t s m u st b e ap p lied to th e cu rren t farm in g system s. Most of th e d ata collected or m ad e available for th e assessm en t of GMOs are su bject to a con siderable degree of u n certain ty. On th e cost side, h owever, an alysts can arrive at m in im u m valu es rath er th an ign orin g th e risks of tran sgen ic crop s. Based on accep ted ecological p rin cip les, effects like resistan ce are kn own to take p lace, bu t th e tim e wh en th ey will occu r is h igh ly u n certain . Th e costs of resistan ce can be estim ated in itially from th e in terp retation s of act u al field co n d it io n s b y in d ep en d en t exp ert s an d can b e refin ed as m o re tim e-series data becom e available. Sen sitivity an alysis with arbitrary calcu lation s of scen arios will n ot p rovide resu lts con sisten t with econ om ic p rin cip les. In stead , it sh ou ld becom e stan dard p rocedu re of ap p lied econ om ic an alysis to u se stoch astic sim u lation an d to p resen t resu lts as cu m u lative p robability d istribu tion s rath er th an as rigid n u m bers.

Acknowledgements Th e au t h o rs ackn o wled ge t h e assist an ce o f Diem u t h Pem sl an d Im ke Pan sch o w in t h e p rep arat io n o f t h is p ap er. We also t h an k Dr. Pet er Ken m o re (Fo o d an d Agricu lt u re O rgan isat io n o f t h e Un it ed Nat io n s) an d t h e an o n ym ou s reviewers for th eir very h elp fu l com m en ts.

References Ajayi, O. 2000. Pesticide Use Practices, Productivity and Farm ers’ Health: The Case of CottonRice System s in Côte d’Ivoire, W est Africa. Pest icid e Po licy Pro ject , Pu blicat io n Series Sp ecial Issu e No. 3. Han n over, Germ an y: Un iversity of Han n over. Alston , J.M., M.C. Marra, P.G. Pard ey, an d T.J. Wyatt. 1998. Ex Pede Herculem ? A MetaAnalysis of Rates of Return to Agricultural R&D. Davis, CA: Global an d Region al Program on Agricu ltu ral Research , Exten sion , an d Edu cation , In tern ation al Food Policy Research In stitu te (IFPRI) an d Un iversity of Californ ia Agricu ltu ral Issu es Cen ter. An t le, J.M. 1988. Pesticide Policy, Production Risk, and Producer W elfare: An Econom etric Approach to Applied W elfare Econom ics. Wash in gton , DC: Resou rces for th e Fu tu re. Avery, D.T. 1995. Saving the Planet with Pesticide and Plastics. In d ian ap olis, IN: Hu d son In stitu te. Babco ck, B., E. Lich t en berg, an d D. Zilberm an . 1992. Im p act o f Dam age Co n t ro l an d Qu ality of Ou tp u t: Estim atin g Pest Con trol Effectiven ess. Am erican Journal of Agricultural Econom ics 74: 163–72. Blackwell, M., an d A. Pagou latos. 1992. Th e Econ om etrics of Dam age Con trol—Com m en t. Am erican Journal of Agricultural Econom ics 74: 1040–4.

Chapter 6: What Can We Learn from the Economics of Pesticides? • 155 Carlson , G.A. 1977. Lon g-Ru n Prod u ctivity of In secticid es. Am erican Journal of Agricultural Econom ics 59: 543–8. Carp en ter, J.E., an d L.P. Gian essi. 2001. Agricultural Biotechnology: Updated Benefits Estim ates. Wash in gton , DC: Nation al Cen ter for Food an d Agricu ltu ral Policy. Carrasco-Tau ber, C., an d L.J. Moffitt. 1992. Dam age Con trol Econ om etrics—Fu n ction al Sp ecification an d Pesticide Produ ctivity. Am erican Journal of Agricultural Econom ics 74: 158–62. Carson , R. 1962. Silent Spring. Boston : Hou gh ton Mifflin . Ch am bers, R.G., an d E. Lich ten berg. 1994. Sim p le Econ om etrics of Pesticide Produ ctivity. Am erican Journal of Agricultural Econom ics 76(3): 407. Cowan , R., an d P. Gu n by. 1996. Sp rayed to Death : Path Dep en d en ce, Lock-In an d Pest Con trol Strategies. The Econom ic Journal 106: 521–42. Davis, G.C., an d M.C. Esp in o za. 1998. A Un ified Ap p ro ach t o Sen sit ivit y An alysis in Eq u ilib riu m Disp lacem en t Mo d els. Am erican Journal of Agricultural Econom ics 80: 868–79. The Econom ist. 1999. Fran ken stein Foods. Febru ary 20, 1999: 17 Falck-Zep ed a, J.B., G. Traxler, an d R.G. Nelso n . 2000. Su rp lu s Dist rib u t io n fro m t h e In trodu ction of a Biotech n ology In n ovation . Am erican Journal of Agricultural Econom ics 82: 360–9. Feder, G. 1979. Pesticides, In form ation an d Pest Man agem en t u n der Un certain ty. Am erican Journal of Agricultural Econom ics 61: 97–103. Fern an d ez-Corn ejo, J., an d W.D. McBrid e. 2000. Gen etically En gin eered Crop s for Pest Man agem en t . US Agricu lt u re, Farm Level Effect s. AER.786. Wash in gt o n DC: Eco n om ic Research Service/ USDA. Fleisch er, G. 1998. Ökonom ische Ansätze in der Pflanzenschutzpolitik— Das Beispiel der Z ulassungsprüfung. Kiel, Germ an y: Vau k Verlag, Lan d wirt sch aft u n d Um welt , Sch riften zu r Um weltökon om ik, 15. Fleisch er, G. 1998. Ökonom ische Bewertung in der Pflanzenschutzpolitik— Das Beispiel des Z ulassungsverfahrens. Kiel, Germ an y: Sch rift en zu r Um welt ö ko n o m ik, Wissen sch aftsverlag Vau k. Fleisch er, G. 2000. Resou rce Costs of Pesticid e Use in Germ an y—Th e Case of Atrazin e. Agrarwirtschaft (Jo u rn al o f t h e Germ an Asso ciat io n o f Agricu lt u ral Eco n o m ist s) 49 (11): 379–87. Go u ld , F., A. An d erso n , A. Jo n es, D. Su m erfo rd , D.G. Heckel, J. Lo p ez, S. Micin ski, R. Leon ard , an d M. Laster. 1997. In itial Freq u en cy of Alleles for Resistan ce to Bacillus T huringiensis To xin s in Field Po p u lat io n s o f Heliothis virescens. Proceedings of the National Academ y of Sciences of the USA 94: 3519–23. Headley, J.C. 1968. Estim atin g th e Produ ctivity of Agricu ltu ral Pesticides. Am erican Journal of Agricultural Econom ics 50: 13–23. Ho ro wit z, J.K., an d E. Lich t en b erg. 1993. In su ran ce, Mo ral Hazard an d Agricu lt u ral Ch em ical Use. Am erican Journal of Agricultural Econom ics 75: 926–35. Hu an g, J., an d F. Qiao. 2000. Farm Pesticide, Rice Produ ction an d Hu m an Health . Pap er p resen ted at th e In tern ation al Con su ltative Worksh op on Effective an d Su stain able Use o f Bio t ech n o lo gy in In t egrat ed Pest Man agem en t in Develo p in g Co u n t ries. Novem ber 2000, Han gzh ou , P.R. Ch in a. Hu eth , D., an d U. Regev. 1974. Op tim al Agricu ltu ral Pest Man agem en t with In creasin g Pest Resistan ce. Am erican Journal of Agricultural Econom ics 56: 543–53.

156 • Chapter 6: What Can We Learn from the Economics of Pesticides? Hu rd, B. 1994. Yield Resp on se an d Produ ction Risk: An An alysis of In tegrated Pest Man agem en t in Cotton . Journal of Agricultural and Resource Econom ics 19(2): 313–26. Kah n em an , D., an d A. Tversky. 1979. Prosp ect Th eory: An An alysis of Decision Un d er Risk. Econom etrica 47: 263–91. ———. 2000. Choices, Values and Fram es. Cam bridge, U.K.: Cam bridge Un iversity Press. Ken m ore, P. 1996. In tegrated Pest Man agem en t in Rice. In Biotechnology and Integrated Pest Managem ent, edited by G.J. Persley. Wallin gford, U.K.: CABI, 76–97. Lich ten berg, E., an d D. Zilberm an . 1986. Th e Econ om etrics of Dam age Con trol: W h y Sp ecification Matters. Am erican Journal of Agricultural Econom ics 68: 261–73. Oerke, E.-C., H.W. Deh n e, F. Sch ön beck, an d A. Weber. 1994. Crop Production and Crop Protection: Estim ated Crop Losses in Major Food and Cash Crops. Am st erd am : Elsevier. Paarlberg, R.L. 2000. Govern in g th e GM Crop Revolu tion —Policy Ch oices for Develop in g Cou n tries. Food, Agricu ltu re, an d th e En viron m en t. Discu ssion p ap er 33. Wash in gton , DC: In tern ation al Food Policy Research In stitu te. Pan n ell, D.J. 1991. Pest an d Pesticides, Risk an d Risk Aversion . Agricultural Econom ics 5: 361–83. Pearce, R., an d R. Tin ch . 1998. Th e Tru e Price of Pesticides. In Bugs in the System , edited by B. Vorley an d D. Keen ey. Lon don : Earth scan . Pim en tel, D., H. Acq u ay, M. Bilton en , P. Rice, M. Silva, J. Nelson , V. Lip n er, S. Giordan o, A. Horowitz, an d M. D´Am ore. 1993. Assessm en t of En viron m en tal an d Econ om ic Im p act s o f Pest icid e Use. In T he Pesticide Question— Environm ent, Econom ics, and Ethics, edited by D. Pim en tel an d H. Leh m an . New York: Ch ap m an & Hall, 47–84. Pim en tel, D., an d L. Levitan . 1986. Pesticides: Am ou n ts Ap p lied an d Am ou n ts Reach in g Pests. BioScience 36: 86–91. Pray, C.E., D. Ma, J. Hu an g, an d F. Q iao . 2001. Im p act o f Bt Co t t o n in Ch in a. W orld Developm ent 29(5): 813–25. Qu aim , M. 2000. Potential Im pacts of Crop Biotechnology in Developing Countries. Doctoral dissertation . Bon n , Rh ein isch e Friedrich -Wilh elm s-Un iversität. Regev, U., N. Gotsch , an d P. Ried er. 1997. Are Fu n gicid es, Nitrogen an d Plan t Growth Regu lators Risk-Redu cin g? Em p irical Eviden ce from Swiss W h eat Produ ction . Journal of Agricultural Econom ics 48(2): 167–78. Regev, U., A.P. Gu tierrez, an d G. Fed er. 1976. Pest as a Com m on Prop erty Resou rce—A Case Stu d y in Alfalfa Weevil Con trol. Am erican Journal of Agricultural Econom ics 58: 186–97. Reich eld erfer, K.H. 1981. Eco n o m ic Feasibilit y o f Bio lo gical Co n t ro l o f Cro p Pest s. In Biological Control in Crop Production, ed ited by G.C. Pap avizas, B.Y. En d o, D.L. Klin gm an , L.V. Kn u t so n , R.D. Lu m sd en , an d J.L. Vau gh an . Mo n t clair, NJ: Allen h eld Osm u n . Rep et t o , R. 1985. Paying the Price— Pesticide Subsidies in Developing Countries. Research Rep ort No. 2, Wash in gton DC: World Resou rces In stitu te. Rola, A.C., an d P.L. Pin gali. 1993. Pesticides, Rice Productivity and Farm er’s Health: An Econom ic Assessm ent. Los Ban os, Ph ilip p in es: Th e In tern ation al Rice Research In stitu te, an d Wash in gton , DC: World Resou rces In stitu te. Sah a, A., C.R. Sh u m way, an d A. Haven n er. 1997. Th e Econ om ics an d Econ om etrics of Dam age Con trol. Am erican Journal of Agricultural Econom ics 79(3): 773–85. Tisd ell, C.A., B.A. Au ld , an d K.M. Men z. 1984. O n Assessin g t h e Valu e o f Bio lo gical Con trol of Weeds. Protection Ecology 6: 169–79.

Chapter 6: What Can We Learn from the Economics of Pesticides? • 157 Waibel, H., an d G. Fleisch er. 1995. State In terven tion or Free Market Econ om y: Un d erlyin g Con dition s for Dissem in atin g In tegrated Pest Man agem en t. Agricu ltu re + Ru ral Develo p m en t wo rkin g p ap er. Un iversit y o f Han n o ver, Germ an y: Pest icid e Po licy Project. ———. 1998. Kosten und Nutzen des chem ischen Pflanzenschutzes in der Deutschen Landwirtschaft aus Gesam twirtschaftlicher Sicht (So cial Co st s an d Ben efit s o f Ch em ical Plan t Protection in Germ an Agricu ltu re). Kiel, Germ an y: Vau k Verlag. Waibel, H., G. Fleisch er, an d H. Becker. 1999. Th e Eco n o m ic Ben efit s o f Pest icid es : A Case St u d y fro m Germ an y. Agrarwirtschaft (Jo u rn al o f t h e Germ an Asso ciat io n o f Agricu ltu ral Econ om ists), 48(6): 219–30. Waibel, H., an d S. Setboon sarn g. 1993. Resou rce Degrad ation Du e to Ch em ical In p u ts in Vegetable-Based Farm in g System s in Th ailan d. Journal of the Asian Farm ing System s Association 2(1): 107–20. Webster, J.P.G., R.G. Bowles, an d N.T. William s. 1999. Estim atin g th e Econ om ic Ben efits of Altern ative Pesticide Usage Scen arios: W h eat Produ ction in th e Un ited Kin gdom . Crop Protection 18(1991): 83–9. Zadoks, J.C. 1993. Th e Partial Past. Com m en ts on th e History of Th in kin g abou t Resistan ce o f Plan t s again st In sect s, Nem at o d es, Fu n gi, an d O t h er Harm fu l Agen t s. In Durability of disease resistance, ed ited by T. Jacobs an d J.E. Parlevliet. Dord rech t, Th e Neth erlan ds: Klu wer Academ ic Pu blish ers, 11–22. Zad o ks, J.C., an d H. Waibel. 2000. Fro m Ch em ical Pest icid es t o Gen et ically Mo d ified Cro p s—Hist o ry, Eco n o m ics, Po lit ics. N etherlands Journal of Agricultural Science 48: 125–49.

Notes 1. O f cou rse, th e resou rce ren t of su scep tibility an d th e loss-of-con trol op tion s are n ot in tern alized. 2. Su ch exp erim en t s are esp ecially su it ab le t o sh o w t h ese effect s b ecau se o f lo n gterm an d often year-rou n d u se of p esticides. 3. Th e resu lts of Oerke et al. (1994) n eed to be in terp reted with care becau se m ost of th eir data cam e from on -station p esticide trials. 4. Th is stu dy in clu ded tran sgen ic sweet p otatoes in Ken ya an d tran sgen ic p otatoes in Mexico. 5. Qu aim (2000) also in clu d ed ban an a tissu e cu ltu re in Ken ya. However, th is is n ot relevan t in th e con text of ou r top ic. 6. If a p est develop s resistan ce to a p esticide, th at p esticide is com p arable to an asset th at h as reach ed th e term in al p oin t of its service life. Th e sam e will even tu ally h ap p en to th e “n ew” tech n ology, h en ce its p resen t valu e ten d s to be overstated if resistan ce is ign ored. 7. In fact, costs of resistan ce m ay be in fin ite if su scep tibility can n ot be reestablish ed. Hen ce, th e costs of resistan ce m u st be exp ressed as an in fin ite an n u ity.

Commentary

The Role of Ecosystem Complexity in Genetically M odified Organisms Karl Seeley

W

ork in th e 1970s on p esticide resistan ce m ade im p ortan t p rogress, bu t it in clu d ed an im p ortan t sim p lifyin g assu m p tion . Pest in festation s were treated as exogen ou s, as if th e level of in festation facin g a farm er in an y growin g season dep en ded on ly on th e n u m ber of p ests left alive th e p reviou s year p lu s so m e ran d o m fact o rs; all o t h er farm er d ecisio n s were irrelevan t . Th is ap p roach m ade th e an alysis easier becau se it lim ited th e farm er’s decision s to th e ch oice of h ow m u ch p esticide to u se each season . More p esticide th is year m ean t h igh er yield s t h is year an d fewer p est s t o co n t ro l n ext year b u t also m ore resistan ce in th e p est p op u lation . Th e op tim al p ath was d riven by th e relative stren gth of th ese forces. In th is con text, th e ch ap ter by Waibel, Zadoks, an d Fleisch er (Ch ap ter 6) is a valu able con tribu tion to th e literatu re; its key in sigh t is th at p est in festation is in p art en d o gen o u s—it d ep en d s o n m an y farm er d ecisio n s, su ch as cro p rotation s, an d th e p reservation of p redators th at can redu ce p est p op u lation s. Th is p laces th eir work in a m ore recen t tradition th at ackn owledges a broader set of ch oices facin g farm ers in m an agin g p est losses. In p articu lar, th e au th ors com p are p est resistan ce with ecosystem deteriorat io n . Th e h ealt h o f t h e so il (an d t h e resu lt in g h ealt h o f t h e cro p ) an d t h e abu n dan ce of ben eficial p redators p lay cru cial roles in determ in in g th e exten t of losses to p ests. As with resistan ce, d eterioration of th ese attribu tes req u ires in creased p est icid e u se fo r t h e sam e level o f co n t ro l. Bu t eco syst em d eclin e exacts an addition al cost. Pest resistan ce itself h as n o effect on th e efficacy of alt ern at ive st rat egies (e.g., resist an ce t o a given p est icid e gen erally will n o t con fer on a p est an y ad van tage in avoid in g a p red atory in sect), wh ereas th e • 158 •

Commentary: The Role of Ecosystem Complexity • 159

ecosystem itself is th e very fou n dation of th ose altern atives. Th u s if th ere is a lin k bet ween eco syst em d et erio rat io n an d u se o f a p est icid e o r a gen et ically en gin eered crop , th e p robable d evelop m en t of resistan ce is com p ou n d ed by th e in creasin g cost of p u rsu in g altern atives p est-m an agem en t strategies. Ch arles Ben brook (1999) h as n eatly su m m ed u p th e p roblem : Cost-effective u se of p est m an agem en t tech n ology, regardless of its gen esis, dep en ds u p on th e degree to wh ich it h elp s diversify an d com p licate th e ch allen ges faced by p est sp ecies with in farm field s. Man y tech n ologies on ce h erald ed as m ajor in n ovation s h ave failed becau se of agricu ltu re’s ten d en cy to rely on tech n ology to sim p lify an d h om ogen ize system s rath er th an to diversify th em . In o t h er wo rd s, t h e p ro b lem wit h gen et ically en gin eered p lan t s is n o t som eth in g in h eren t bu t rath er th e risk of m isu sin g th em in th e sam e way th at con ven tion al p esticides h ave been m isu sed. Th is raises th e q u estion of h ow to get th e ben efits of p esticid es or gen etically en gin eered p lan ts wh ile d iscou ragin g excessive sim p lification . A d irect ap p roach is Mich ael Gray’s p rop osal for p rescrip tive u se of gen etically m od ified p lan ts in con trollin g corn rootworm (2000). Mu ch as we can n ot p u rch ase m an y m ed icin es wit h o u t a d o ct o r’s p rescrip t io n , farm ers wo u ld h ave t o dem on strate th at th ey h ad scou ted th e p reviou s season an d th at an econ om ic t h resh o ld fo r ad u lt ro o t wo rm s h ad b een exceed ed . W h ile t h is p resu m ab ly wo u ld lim it so cially u n warran t ed u se o f t h e n ew cro p s, it wo u ld also b e exp en sive an d alm o st cert ain ly u n welco m e by farm ers, wh o are n o t u su ally lookin g for addition al regu latory p rocedu res. Bu t it d oes at least start th e d ebate abou t com p lexity in agroecosystem s. I m ake two con jectu res. First, ecosystem com p lexity on farm s is a good becau se it redu ces p esticide u se an d slows th e develop m en t of p est resistan ce. 1 Secon d, b ecau se b o t h p est icid e u se an d p est resist an ce are n egat ive ext ern alit ies, ecosystem com p lexity creates p ositive extern alities. Th e econ om ic ch allen ge th at Waibel, Zadoks, an d Fleisch er p oin t to is to fin d in stru m en ts th at en cou rage u sefu l fo rm s o f co m p lexit y o n farm s. It is h ard t o reward co m p lexit y directly becau se it is h ard to q u an tify th e com p on en ts of it th at are worth fosterin g. We cou ld look, h owever, at m akin g sim p lification m ore costly to farm ers, lead in g th em to avoid it. Th e best tool for th at strategy m ay be a tax on p esticides. Th is is iron ic, becau se gen etically en gin eered p lan ts are seen by m an y as a rep lacem en t fo r p est icid es. If we m ake t h e ch em icals m o re exp en sive, t h at wou ld seem to en cou rage even m ore relian ce on th e n ew crop s an d th u s exacerbate th e m isu se of th e n ew tech n ology th at we were tryin g to p reven t. Bu t fo r t h e fo reseeable fu t u re, t h e sim p lified eco syst em s we wo u ld like t o avo id will con tin u e to dep en d on som e p esticides, even if th e n ew crop s rep lace oth -

160 • Commentary: The Role of Ecosystem Complexity

ers. Th erefo re, a st rat egy t h at m akes sim p lificat io n m o re exp en sive m ay en co u rage wise u se o f b io t ech cro p s. As a m o d el, t h e st at e o f Io wa h as h ad su ccess in redu cin g fertilizer u se with ou t yield loss th rou gh a m odest fertilizer t ax. Th e reven u es o f t h e t ax fu n d ed u cat io n o n carefu l fert ilizer u se. It is worth con siderin g a sim ilar levy on p esticides an d u sin g th e fu n ds to su p p ort p est scou tin g an d oth er m easu res to red u ce farm ers’ costs of m an agin g in tricate ecosystem s on th eir p rop erty.

References Ben brook, C.M. 1999. World Food System Ch allen ges an d Op p ortu n ities: GMOs, Biodiversity, an d Lesson s from Am erica’s Heartlan d . Pap er p resen ted at th e Un iversity of Illin o is Wo rld Fo o d an d Su st ain ab le Agricu lt u re Pro gram . Jan u ary 1999, Urb an aCh am p aign , IL. h ttp :/ / www.biotech -in fo.n et/ IW FS.p df (accessed March 10, 2002). Gray, M.E. 2000. Prescrip tive Use of Tran sgen ic Hybrid s for Corn Rootworm s: An Om in ou s Clou d on th e Horizon ? Pap er p resen ted at th e Un iversity of Illin ois Crop Protection Tech n ology Con feren ce, Jan u ary 2000, Ch am p aign -Urban a, IL. Available at . Zad oks, J.C. W hat Can W e Learn from the Econom ics of Pesticides? Presen ted at RFF Con feren ce on th e Econ om ics of Resistan ce, Ap ril 2001, Warren ton , VA.

Note 1. Jan Zad oks p oin ted ou t th at “com p lexity” sh ou ld n ot be m in d lessly worsh ip ed . He u sed th e exam p le of barberry, wh ich serves as an obligate h ost for wh eat stem ru st. Elim in atin g barberry from wh eat-growin g areas argu ably redu ces th e com p lexity of th e local ecosystem , bu t also redu ces ru st in festation in a su stain able way. Non eth eless, th e sim p lificat io n s p ro m p t ed by o ver-relian ce o n p est icid es (o r p o ssibly gen et ically en gin eered p lan ts) seem u n likely to be of th is ben eficen t kin d.

Chapter 7

Elements of Economic Resistance M anagement Strategies—Empirical Evidence from Case Studies in Germany Gerd Fleischer and Hermann Waibel

Although resistance against pest control agents is perceived as a major threat for crop protection, there is considerable uncertainty about the econom ic justification of resistance m anagem ent strategies. This chapter adopts a resource economic point of view. Pest susceptibility toward control measures is treated as biological capital. The objective is to identify the major factors to consider when evaluating resistance management strategies. The economic theory of nonrenewable resources suggests that three variables need to be taken into account: (a) the uncertainty of decisionmakers about the parameters and the scale of the econom ic im pact of resource depletion, (b) the direction and rate of technological change, and (c) the extent of commonproperty characteristics of pest susceptibility and its effects on different groups of farmers when adaptation to resistance spread is taking place. The im portance of those factors is further explored in tw o case studies using data from Germ an agriculture. The first study underpins the im portance of the sectorwide econom ic consequences of resistance. Such information is considered valuable for designing and implementing effective and efficient resistance management strategies. A log-linear regression model is used to entangle the effect of technological path dependency on pesticide use. With a note of caution, the rising trend in crop protection costs can be attributed to resource degradation, with developm ent of resistance as one important factor. The second case study deals with the costs of weed resistance against atrazine and demonstrates the importance of the discount rate and the distributional consequences of regulatory decisions. Based on a representative set of time-series data, resource costs of atrazine use are assessed

• 161 •

162 • Chapter 7: Elements of Economic Resistance M anagement Strategies by differentiating farm plots according to their share of m aize in the crop rotation. The results show that social costs of resistance development are far higher than private costs. The chapter highlights some of the methodological difficulties in measuring the econom ic im pact of resistance. The analysis nevertheless provides som e evidence that sectorw ide consequences should not be neglected. It also suggests that the sustainability and equity impacts of resistance developm ent should be given m ore weight in regulatory decisionm aking about pesticides.

ren d s in cro p p ro t ect io n are in creasin gly a m at t er o f co n cern , b o t h fo r in du strialized cou n tries with con siderably h igh in ten sity of ch em ical p esticide u se an d for less develop ed cou n tries. Less-develop ed cou n tries still h ave lo wer o verall p est icid e u se levels bu t t h ere is freq u en t o veru se as well, esp ecially in crop s like cotton an d rice. Ch an ges in p est con trol strategies, su ch as t h e ad o p t io n o f in t egrat ed p est m an agem en t , are n ecessary elem en t s o f t h e global agen d a for su stain able agricu ltu ral d evelop m en t (Sch illh orn van Veen et al. 1997). Ap p rop riate p esticid e resistan ce m an agem en t strategies are p art of su ch a strategy. Th e th reats of resistan ce an d th e in d u ced in creased risk of p est ou tb reaks can p u t farm ers o n a p est icid e t read m ill lead in g t h em t o u se everin creasin g am ou n ts an d stron ger p esticid es to kill m u tatin g p ests with severe con seq u en ces (van den Bosch 1978). Resistan ce is in creasin gly p erceived as an im p ortan t con strain t to effective crop p rotection th at lim its th e p rosp ects for m atch in g th e p rojected in crease in global food dem an d, esp ecially in develop in g cou n tries (Yu d elm an et al. 1998). Th erefore, resistan ce m an agem en t is in th e in terest of th e agricu ltu ral com m u n ity (Nevill et al. 1998). Man u factu rers of p lan t p rotection p rodu cts h ave establish ed a n u m ber of in du strywide p u blic–p rivat e co m m it t ees fo r in fo rm at io n exch an ge an d t o creat e awaren ess abou t resistan ce m an agem en t (GCPF 2000). Th ere is still con siderable u n certain ty abou t th e p ayoff of su ch strategies in t erm s o f a n et so cial b en efit b ecau se o f in co m p let e in fo rm at io n ab o u t t h e p oten tial econ om ic con seq u en ces of in action . Un til n ow, few attem p ts h ave been m ade to obtain reliable estim ates on th e costs an d ben efits of resistan ce m an agem en t . Resu lt s were gen erally n o t m ad e available t o d ecisio n m akers, esp ecially t h e en d u sers o f ch em ical p esticid es. Th ere are also con cern s th at availab le est im at es ab o u t t h e so cial co st s o f p est icid e resist an ce co u ld b e flawed becau se farm ers m ay h ave in tern alized th ese costs already in th eir decisio n s abo u t p est icid e u se (Pearce an d Tin ch 1998). Fu rt h erm o re, as d em o n st rat ed b y Pan n ell an d Zilb erm an (2000) fo r weed resist an ce in Au st ralia, farm ers m ay h ave little in cen tive to ad op t resistan ce m an agem en t strategies becau se of existin g socioecon om ic con strain ts.

T

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Th e debate on resistan ce m an agem en t is an alogou s to th e discu ssion abou t p est icid e ext ern alit ies o n h u m an h ealt h an d t h e en viro n m en t . Sim ilarly, m eth od ological p roblem s h ave h am p ered th e in terp retation of th e resu lts of st u d ies o n t h e n egat ive im p act s o f p est icid e u se. O n ly in recen t years h ave eco n o m ic st u d ies b eco m e availab le t h at h ave co n t rib u t ed t o a q u an t it at ive assessm en t of th e extern al costs of cu rren t p esticid e u se levels in agricu ltu re (Pim en t el et al. 1993; St ein er et al. 1995; Waibel an d Fleisch er 1998b). Th is kin d of in form ation allows u s to ju dge th e efficien cy an d cost-effectiven ess of regu latory ap p roach es th at ad d ress th e risks for h u m an h ealth an d th e en viron m en t (Oskam et al. 1997). W h en extern al costs are taken in to accou n t, th e con ven tion ally h eld estim ates abou t th e n et social ben efits of p esticides m u st be adju sted (Pearce an d Tin ch 1998). Sim ilar em p irical evid en ce abou t th e m agn itu d e of th e p rivate an d social costs of resistan ce sh ou ld be p resen ted to m ake th e case for resistan ce m an agem en t strategies. Th is ch ap ter aim s to con tribu te to th e d ebate by p resen tin g m et h o d o lo gies fo r assessm en t , as well as so m e em p irical evid en ce, b y u sin g a resou rce econ om ic fram ework for evalu ation . Th e objectives of th e ch ap ter are as follows: • t o reveal t h e co n d it io n s u n d er wh ich t h e sp read o f resist an ce is likely t o p rodu ce social costs, • t o p resen t m et h o d o lo gies fo r assessin g eco n o m ic co n seq u en ces o f resist an ce, an d • to id en tify factors th at are im p ortan t for d esign in g econ om ically efficien t resistan ce m an agem en t strategies. Th e n ext section exp lain s th e n atu re of th e resistan ce m an agem en t p roblem by u sin g a resou rce econ om ic fram ework. It reveals th e con dition s u n der wh ich con servation of th e su scep tibility resou rce is likely to p ay off. Th e two case stu d ies p resen t q u an titative evid en ce for th e costs of resistan ce d evelop m en t b ased o n case st u d ies in Germ an agricu lt u re. Th e resu lt s o f t h e case stu d ies brin g u s to a con clu sion on d ecisive variables for th e d esign of resistan ce m an agem en t strategies.

Economic Effects of Resistance: When Does Resource Conservation Pay? Th e em ergen ce of resistan ce of p ests, weeds, or diseases again st a p est con trol agen t is a p rocess of th e dep letion of a n atu rally in h eren t resou rce th at is th e su scep t ib ilit y t o ward t h e sp ecific m o d e o f act io n o f t h e p est co n t ro l agen t . Pest su scep tibility th u s can be treated as a biological cap ital (Hu eth an d Regev 1974). Several biological factors determ in e resistan ce develop m en t: th e in itial freq u en cy of resistan t in dividu als in a p est p op u lation , th e target m ode of th e

164 • Chapter 7: Elements of Economic Resistance M anagement Strategies

p est co n t ro l agen t , t h e m o d e o f in h erit an ce, an d t h e relat ive fit n ess o f t h e resist an t in d ivid u als (Zwerger an d Walt er 1994). Am o n g t h e so cio eco n o m ic factors, th e freq u en cy of treatm en t an d th e size of th e treated area are im p ort an t p aram et ers fo r resist an ce m an agem en t st rat egies b ecau se t h o se fact o rs determ in e th e selection p ressu re. From th e p oin t of view of econ om ic efficien cy, farm ers an d oth er p esticide u sers wo u ld m ake p erfect ly rat io n al d ecisio n s ab o u t o p t im al reso u rce u se u n d er two con d ition s: (a) wh en p erfect in form ation on all p aram eters of th e biological p rocess of resistan ce d evelop m en t is available an d (b) wh en extern alit ies are ab sen t , su ch as in t h e case o f t h e sp read o f resist an ce fro m o n e farm t o o t h er eco n o m ic u n it s. Un d er t h e eco n o m ic efficien cy scen ario , n o p u blic in t erven t io n in resist an ce m an agem en t wo u ld be warran t ed becau se th e en d ogen ou s m arket resp on se to resistan ce wou ld d eterm in e an efficien t o u t co m e. In t h is case, all relevan t eco n o m ic im p act s o f resist an ce d evelo p m en t wou ld be in tern alized. At least in so m e cases, t h ese assu m p t io n s d o n o t h o ld . Th en sp read o f resistan ce sh ou ld be con sidered as m arket failu re th at n eeds to be corrected to p ro vid e an efficien t o u t co m e. To d et erm in e so m e crit eria fo r t h e ext en t t o wh ich p u blic p olicy in terven tion m igh t be ju stified, we will take a closer look at t h e ch aract erist ics o f t h e resist an ce p ro blem an d it s im p licat io n s fo r eco n om ic evalu ation . Th is d iscu ssion will u n d erp in th e n eed to d eterm in e sp ecific solu tion s for both th e in form ation an d th e extern ality p roblem s.

Characteristics of the Resistance Problem Relevant to Economic Evaluation

Th e n at u re o f t h e reso u rce su scep t ib ilit y o f an in d ivid u al p est as b io lo gical cap it al n eed s so m e clarificat io n . We can d ist in gu ish b et ween t wo fo rm s o f bio lo gical cap it al: t h e st o ck o f su scep t ibilit y again st a sp ecific p est icid e an d th e stock of su scep tibility again st th e total of available op tion s for p est con trol in a given crop p in g system an d location . Pesticid e treatm en t elim in ates su scep tible in d ivid u als from th e p est p op u lation of a given location . Freq u en t ap p lication cau ses a grad u al sh ift in th e gen et ic co m p o sit io n o f t h e p est p o p u lat io n , wit h a grad u al in crease in t h e sh are o f resist an t in d ivid u als. Even t u ally, t h e st o ck o f su scep t ib le p est s is exh au sted, th u s ren derin g th e p esticide in effective. Dep en din g on th e relative fit n ess o f t h e resist an t in d ivid u als, t h is p ro cess m ay b e reversed o ver t im e wh en th e p esticide is n o lon ger ap p lied. However, in m ost cases of resistan ce, th e su scep tibility resou rce is p ractically d ep leted for th e typ ical tim e h orizon th at is relevan t in agricu ltu ral p rodu ction (Ru bin 1996). Th erefore, in th e follo win g d iscu ssio n , t h e su scep t ib ilit y reso u rce sh all b e assu m ed t o b e q u asiexh au stible becau se th e sh are of su scep tible in dividu als rem ain s below a critical level wh ere th e ecological service p rovid ed by th e su scep tibility resou rce can becom e econ om ically relevan t.

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On ce d ep leted , p est su scep tibility is n o lon ger available in term s of effectiven ess of a con trol m easu re. Th e in tertem p oral su m of th e services p rovided b y a given st o ck o f an exh au st ib le reso u rce is fin it e. If we u se t h e st an d ard resou rce econ om ic m od el, op tim al resou rce u se wou ld be d eterm in ed by th e total in itial stock of th e resou rce, th e ch oke p rice for th e resou rce, th e social d iscou n t rate, an d th e op tim al d ep letion tim e th at is itself a fu n ction of th e oth er p aram eters (Perm an et al. 1996). Th e econ om ic im p acts of resou rce dep letion wou ld be n egligible if altern ative p est con trol tech n ologies are eq u ally cost-effective. Th e ch oke p rice for t h e reso u rce wo u ld n o t d iffer fro m t h e ext ract io n co st s, t h u s ren d erin g t h e valu e of th e resou rce stock zero. Farm ers cou ld dep lete th e resou rce an d th ereafter sim p ly switch to oth er con trol op tion s with ou t su fferin g econ om ic loss. Th e availab le ran ge o f o p t io n s t o co n t ro l a p est also m u st b e seen as a resou rce. On th e on e h an d , th e availability an d th e p rice of su bstitu tes d eterm in e th e valu e of th e resou rce stock th reaten ed by d ep letion th rou gh resistan ce. On th e oth er h an d , th e ran ge of op tion s m igh t be lim ited , alth ou gh in p rin cip le n ew o p t io n s can b eco m e availab le t h ro u gh t h e d isco very o f n ew tech n ologies. Th e ch oke p rice for th e stock of con trol op tion s is d eterm in ed by t h e level o f cro p p ro t ect io n co st s t h at ren d er a cro p p in g syst em u n p ro fitable in a given location . A p est sim p ly becom es u n con trollable u sin g availab le t ech n o lo gies in a co st -effect ive m an n er. Exam p les fo r su ch a scen ario were exp erien ced in m an y p arts of th e world , for exam p le, in cotton p rod u ction in th e Un ited States (NAS 1975), in Latin Am erica (Th ru p p 1996), Cen tral Asia (Yu d elm an et al. 1998), an d Ch in a an d In d ia (Sch illh orn van Veen et al. 1997). Tech n ological progress can postpon e resou rce depletion becau se th e effect is resou rce au gm en tin g. Th e total stock of available option s can be au gm en ted by both h u m an an d p h ysical cap ital. Hu m an cap ital im p roves th e m an agem en t o f t h e reso u rce. Th e availabilit y o f su bst it u t e t ech n o lo gical o p t io n s is d et erm in ed by th e direction an d rate of tech n ological progress an d its related costs. Presen t t ren d s in cro p p ro t ect io n research an d d evelo p m en t su ggest t h at t h e t ech n o lo gical p ro gress is d riven b y t h e st rat egies o f a sm all n u m b er o f large, sp ecialized , m u lt in at io n al firm s. High fixed co st s o f p ro d u ct d evelo p m en t an d registration create en try barriers to th e m arket for sm all firm s (IVA 1999). Man y in n ovation s of n on ch em ical op tion s su ch as im p roved cu ltu ral con trol tech n iq u es can n ot be ap p rop riated by p rivate firm s, wh ich lim its th eir d iffu sion . In som e areas of p est con trol, th e rate of resistan ce d evelop m en t is cu rren tly faster th an th e su p p ly of n ew p est con trol m eth od s. Th is situ ation redu ces th e n u m ber of op tion s available in th e tech n ology basket. Mo reo ver, t ech n o lo gical p ro gress is at risk o f failu re b ecau se t h ere is t h e p oten tial th at u n foreseen n egative extern alities occu r. New tech n ologies with u n kn own risks are trad ed again st available tech n ologies with risks th at, su p p osedly, are fu lly kn own an d regarded as m an ageable.

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Decisionmaking in Resistance M anagement

Th e in d ivid u al farm er as a u ser o f p est icid es is t h e fin al d ecisio n m aker in resist an ce m an agem en t . Assu m in g t h at ext ern alit ies an d p erfect kn o wled ge ab o u t t h e p aram et ers o f resist an ce d evelo p m en t are ab sen t an d t h at farm level d ecision m akers ap p reciate th eir u ser costs, resistan ce cou ld be p erfectly in t ern alized in t o farm -level d ecisio n m akin g. Ho wever, t h ere is co n sid erable u n certain ty in volved becau se of a lack of p rior in form ation on th e p aram eters of th e resistan ce d evelop m en t p rocess. Th is refers both to th e biological factors th at d eterm in e th e selection of resistan t in d ivid u als an d to th e socioecon om ic p aram eters th at d eterm in e th e econ om ic im p ortan ce p erceived by th e farm er, for exam p le th e valu e of su bstitu tive tech n ologies. A fu rth er p roblem stem s from th e fact th at m ost m od els assu m e a sin glep est/ sin gle-p esticide relation sh ip . Som e p ests develop resistan ce again st m ore th an on e p esticid e even wh en th ey h ave n ot yet been u sed (cross-resistan ce), an d som e p esticid es p rovoke resistan ce in m ore th an on e p est sp ecies (Ru bin 1996). Th e st art in g d at e an d t h e p at h o f resist an ce d evelo p m en t can n o t b e p redicted with certain ty, alth ou gh som e research ers con sider resistan ce develo p m en t t o b e in evit ab le (Ru b in 1996). Th erefo re, resist an ce d evelo p m en t m u st be treated in a risk-an alytic fram ework con sid erin g op tion s in d ecision m akin g at th e farm level. In stitu tion s su p p ortin g an d govern in g th e in form ation en viron m en t an d u se con d ition s can d irectly an d in d irectly in flu en ce resistan ce m an agem en t d ecision s. Neglect of resistan ce m ay in d u ce u n d erin vestm en t in th e research an d d evelo p m en t o f alt ern at ive o p t io n s. Th ere is a co n sid erab le t im e lag between th e in cep tion of research an d readin ess for wide adop tion . Th is h olds t ru e fo r o u t p u t fro m cu t t in g-ed ge m o d ern scien ce as well as fo r ad ap t ive research on agroecosystem m an agem en t. In a d yn am ic con text, th e exp ectation s of th e d ecision m akers at both th e farm an d th e research in stitu tion level for th e p aram eters of fu tu re tech n ological p rogress are relevan t. Th is m akes th e discou n t rate of fu tu re costs of adap t at io n t o reso u rce d ep let io n t h e d ecisive variab le fo r d et erm in in g t h e p ro fitability of resistan ce m an agem en t strategies. Th e likelih ood of con certed resistan ce m an agem en t at th e com m u n ity or sector level dep en ds on th e m agn itu de of resistan ce sp read, th at is, th e exten t t o wh ich o p en access t o reso u rce u se is in vo lved . Regev an d o t h ers (1976) argu ed th at th e greater th e m obility of p est p op u lation s is, th e greater th e likelih o o d t h at farm ers wo u ld view p est su scep t ib ilit y as a co m m o n -p ro p ert y resou rce. Pests an d d iseases are m ore likely to be m obile across field m argin s th an are weeds. For p ests, farm ers h ave th e in cen tive to com p letely ign ore th e con seq u en ces of d ecision s th at lead to resistan ce bu ild u p (Carlson an d Wetzst ein 1993). Also , t h e field size is likely t o p lay an im p o rt an t ro le in t h e

Chapter 7: Elements of Economic Resistance M anagement Strategies • 167

bu ildu p of resistan ce. On th e on e h an d, larger p lots ten d to con tain resistan ce wit h in field m argin s. O n t h e o t h er h an d , a st ru ct u re o f sm all p lo t s m ay b e u sefu l to m ain tain sp atial crop or diversity in varieties.

Conclusions on Determining Variables

Ap p lyin g a reso u rce eco n o m ic fram ewo rk sh o ws t h at t o d et erm in e o p t im al resist an ce m an agem en t st rat egies, at least t h ree variab les n eed t o b e t aken in to accou n t: (a) th e u n certain ty of decision m akers abou t th e p aram eters an d scale of th e econ om ic im p act of resou rce dep letion , (b) th e direction an d rate of tech n ological ch an ge, an d (c) th e exten t of com m on -p rop erty ch aracteristics of p est su scep tibility an d its effects on d ifferen t grou p s of farm ers wh en adap tation to resistan ce sp read is req u ired.

Case Study Evidence for Costs of Resistance Th e followin g section p resen ts m eth od ological ap p roach es for m easu rin g th e im p act o f t h e variables m en t io n ed earlier an d em p irical evid en ce fro m case stu d ies in Germ an agricu ltu re. Th e first exam p le u ses aggregated tim e-series d at a fro m t h e Germ an farm acco u n t an cy n et wo rk d at ab ase. Th is an alysis establish es an in tertem p oral lin kage of p esticid e u se p attern s. Growth tren d s in p est icid es can p art ly be exp lain ed by p rio r u sage, wh ich d ep let es n at u ral resou rces. Alth ou gh th e database does n ot allow u s to iden tify a sp ecific resistan ce variable, it can be assu m ed th at on e of th e likely cau ses for risin g sectorwide crop p rotection costs is th e freq u en t ap p earan ce of resistan ce. Th e secon d case stu dy exp lores th e costs of resistan ce on a sp ecific crop . So far, weed resistan ce again st atrazin e h as been th e m ost sign ifican t case in Germ an agricu ltu re. Th e an alysis sh ows th at th e econ om ic valu e of th e su scep tibility resou rce dep en ds on th e discou n t rate. We also discu ss th e distribu tion al con seq u en ces of adap tation to resistan ce sp read.

M easuring Sectorwide Consequences of Short-Term M aximization Strategies in Crop Protection— Pesticide Use in German Agriculture

Th e ap p ro ach u sed in t h is case st u d y co n t rib u t es t o t h e d eb at e ab o u t t h e ap p rop riate m eth od ological ap p roach for p esticid e p rod u ctivity assessm en t. Th e startin g p oin t in th is debate was th e ch allen ge p osed on p rodu ctivity estim at es d erived fro m t h e co n ven t io n al Co b b –Do u glas fu n ct io n ap p ro ach b y Lich t en b erg an d Zilb erm an (1986). Th ey argu ed fo r u sin g a d am age ab at em en t fu n ct io n ap p ro ach . Resu lt s o f p ro d u ct ivit y est im at es d iffer wid ely d ep en d in g o n t h e fu n ct io n al fo rm u sed . So far, t h ere is n o co n clu sive evid en ce o f t h e su p erio rit y o f a sp ecific fu n ct io n al fo rm . O n e reaso n fo r t h is

168 • Chapter 7: Elements of Economic Resistance M anagement Strategies

cou ld be th e lack of in form ation abou t th e role th at th e n atu ral resou rce base p lays in crop p rotection (Waibel et al. 1999). In t h e fo llo win g d iscu ssio n , we exp lo re an in d irect way t o m easu re t h e im p act of resistan ce. Resistan ce h as been sh own to lead to declin in g p esticide p rod u ctivity over tim e (Carlson 1977). Crop loss m u st be p reven ted with an in creasin g am ou n t of resou rces, eith er by in creasin g th e dosage an d freq u en cy o f a ch em ical o r b y swit ch in g t o m o re exp en sive p est co n t ro l m easu res. If resist an ce sp read s sect o rwid e, p est co n t ro l co st s are exp ect ed t o in crease. High er am o u n t s an d m o re exp en sive p est icid es will b e u sed b ecau se t h ese in p u ts d om in ate in p resen t crop p rotection strategies. Th u s, we h yp oth esize an in tertem p oral lin kage between exp en ses for p est con trol in p rior p eriod s an d th ose in followin g crop season s. Th e o verall d evelo p m en t o f cro p p ro t ect io n co st s o ver t im e beco m es t h e m ain in d icator for assessin g th e econ om ic d im en sion of th e resistan ce p roblem . Crop p rotection costs relative to oth er econ om ic factors sh ou ld rem ain con stan t if n o resistan ce or oth er form s of resou rce d egrad ation wou ld occu r, or at least if we can con trol for ch an ges to relative p rices of in p u ts an d tech n ological p rogress. Hen ce, risin g p est con trol costs—relative to th e real costs o f o t h er p ro d u ct io n fact o rs—wo u ld in d icat e eco n o m ic im p act s o f reso u rce degrad ation . In th at case, at least p art of th e observed growth in crop p rotection costs sh ou ld n ot be attribu ted to p rod u ctivity in crease, bu t rath er m u st be in t erp ret ed as seco n d ary co st s o f reso u rce d ep let io n . Act u al co st s o f cro p p rotection Z wou ld deviate from th e p ath of su stain able crop p rotection m an agem en t S (see Figu re 7-1). Th e rat io o f p est icid e co st s t o fert ilizer co st s is an in d icat o r o f p o ssib le resou rce d egrad ation . In Germ an agricu ltu re, th e ratio of exp en ses for p esticid es t o t h o se fo r fert ilizer in t h e sect o r, b o t h exp ressed in co n st an t p rices, in creased co n st an t ly (see Figu re 7-2). So m e o f t h e in crease in p est icid e u se m ay th en be in terp reted as a defen sive exp en se again st risin g crop loss levels, p ossibly cau sed by resou rce degradation th at in clu des resistan ce. Th e gro wt h rat e o f p est icid e u se is d et erm in ed by t ech n o lo gical an d eco n om ic factors as well as ch an ges in th e n atu ral resou rce base.1 Cu rren tly data are t o o sp arse t o d et erm in e t h e st at u s o f t h e n at u ral reso u rce b ase an d it s ch an ges over tim e. Th erefore, th e dam age avoidan ce costs—th at is, addition al p esticid e u se in later p eriod s as a con seq u en ce of p rior in terven tion —is u sed as a p roxy variable for ch an ges in th e n atu ral resou rce base. Resou rce degradation m u st be sep arated from oth er factors th at affect p esticide u se, th at is, th e ratio of relative com m odity an d in p u t p rices, th e level of fertilizer u se, tech n ological p rogress in term s of im p roved cu ltivars, an d so forth . To cap tu re th e effect of resou rce d egrad ation on th e growth rate of p esticid e u se, a lo g-lin ear eco n o m et ric m o d el was u sed . Th e Farm Acco u n t an cy Network of th e Fed eral Agricu ltu ral Min istry in West Germ an y for th e p eriod

Chapter 7: Elements of Economic Resistance M anagement Strategies • 169

Future Crop Protection Costs ( t 1)

Z

S

PS' PS

Current Crop Protection Costs ( t 0) FIGURE 7-1. Resource Costs of Pesticide Use

1981–1982 to 1994–1995 com p rises th e averages of sam p le farm data in differen t farm in g system s from each of th e 42 agroecological zon es. On an average over th e 14 years covered by th e an alysis, d ata from 4,911 farm s were available for each year. Th e m od el th u s p ools tim e-series an d cross-section al d ata on crop yields, in p u t u se, an d p rodu ction costs. A ran d om -effect regression m od el is u sed to d eterm in e th e in flu en ce of all id en t ifiable effect s o n p est icid e u se levels, in clu d in g t h e p ro xy variable fo r resou rce degradation . Data on popu lation s of pest species an d ben eficial organ ism s are n ot available as part of th e farm accou n tan cy database. Th erefore, an in direct approach is ch osen to assess th e im pact of resou rce degradation : ln PSt = β1 + β2 PSt–1 + β3 ln Yw t + β4 Ft + β5 ln M t + β6 Pc/ Pps + β7 Pc/ PF + β8 D m + β9 D S + β10 D I + β11 Τ + υ wh ere w = th e error term b = th e coeffien t on th e in dep en den t variable in th e regression

170 • Chapter 7: Elements of Economic Resistance M anagement Strategies

40 35

Percent

30 25 20 15 10 5 0 66/ 67 62/ 63 70/ 71 74/ 75 78/ 79 82/ 83 86/ 87 90/ 91 94/ 95 64/ 65 68/ 69 72/ 73 76/ 77 80/ 81 84/ 85 92/ 93 88/ 89

Crop Year FIGURE 7-2. Development of the Ratio of Expenses for Pesticides and for M ineral Fertilizers in German Agriculture, from 1962–1963 to 1994 –1995

PSt = am ou n t spen t on pesticides in Germ an Mark (DM) per h ectare in period t Yw t = yield of win ter wh eat in t p er h ectare PSt–1 = am ou n t sp en t on p esticides in th e p rior year D m = du m m y for agroecological zon es in region s of m ediu m altitu de Ft = am ou n t of fertilizer in DM p er h ectare in p eriod t M t = am o u n t o f o rgan ic m an u re p er h ect are in t co n vert ed in t o su bst it u t ive fertilizer valu e Pc/ Pps = ratio of th e in dex of crop p rices to p esticide p rices D S = du m m y for agroecological zon es in sou th ern areas of h igh er average tem p eratu res Pc/ PF = ratio of th e in dex of crop p rices to fertilizer p rices D I = du m m y for in tegrated farm s T = Tren d variable For th e an alysis, on ly fu ll-tim e farm s of two typ es, n am ely cash crop farm s (m ain ly cereal–su gar beet or cereal–rap eseed rotation s) an d in tegrated farm s (com bin ation s of arable farm in g an d livestock) were selected. Th e p rep aration of th e d ata for th e an alysis req u ired som e assu m p tion s to com p u te th e variab les (see Waib el an d Fleisch er 1997, 1998a). Fo r exam p le, t h e am o u n t o f organ ic fertilizer, wh ich p lays an im p ortan t role in th e m ixed farm s, is con verted in to n u trien t eq u ivalen ts of com m ercial fertilizer an d valu ed at rep lace-

Chapter 7: Elements of Economic Resistance M anagement Strategies • 171

m en t co st s. Exp en d it u res o n p est icid es are relat ed t o t h e area o f field cro p s becau se p esticide u se on p astu re is n egligible. Tech n ological ch an ge is cap tu red in th e in crease of th e yield p oten tial of win t er wh eat , wh ich is t h e lead in g cro p in arab le farm in g. Besid es t h is em b o d ied t ech n o lo gical p ro gress, o t h er p ro d u ct ivit y-en h an cin g ch an ge is exp ect ed t o b e in clu d ed in t h e t ren d variab le T . Farm s in m ed iu m -alt it u d e zo n es in t h e cen t ral an d so u t h west ern p art o f t h e co u n t ry gen erally h ave lower levels of in p u t u se becau se of less advan tageou s clim atic an d soil con dit io n s. A co n sid erab le t im e lag in ad o p t in g t ech n o lo gical p ro gress h as b een o b served fo r t h o se areas, as o p p o sed t o lo wlan d s in t h e n o rt h ern p art an d warm er areas in t h e so u t h . Th erefo re, a d u m m y variab le is in clu d ed in t h e regression . Table 7-1 sh o ws t h e resu lt s o f t h e regressio n an alysis fo r t h e fu ll d at aset . Th e lagged variable of p esticid e u se in p rior p eriod s is, as exp ected , p ositive an d h igh ly sign ifican t. Th e sam e is tru e for th e tren d variable. Th ose variables sh ow on ly a sm all correlation , wh ich im p lies th at th e in crease in p esticide u se is in d ep en d en t fro m gen eral t ech n o lo gical ch an ge in t h e sect o r, b u t rat h er disp lays a sp ecific develop m en t in crop p rotection . A step wise m u ltip le regression d em on strated th at th e variable PSt–1 h as th e h igh est exp lan atory p ower. Th e econ om ic variable Pc/ Pps con firm s th e assu m p tion of a p ositive reaction of farm ers t o an in crease in t h e rat io o f cro p p rices t o p est icid e p rices. As exp ected , th e yield level of wh eat an d fertilizer u se h ave a p ositive in flu en ce o n p est icid e u se wit h a m o d erat e elast icit y. Th e d u m m y fo r agro eco lo gical zon es in m ediu m altitu des also sh ows th e exp ected sign . Th ose farm s ten d to be m ore diversified with lower levels of p est p ressu re. Variation s of th e m odel for differen t grou p s of agroecological zon es did n ot ch an ge th e d irection of th e resu lts. Oth er variables, su ch as th e ratio of crop t o fert ilizer p rices an d d u m m y variab les fo r in t egrat ed farm s an d so u t h ern agro eco lo gical zo n es, were n o t sign ifican t in all m o d el ru n s. Becau se t h e Du rbin –Watson coefficien t lies between 1.8 an d 2.2 in all altern ative m od els, it is u n likely th at th ere is au tocorrelation in th e residu als. Th e h yp oth esis of an in tertem p oral relation sh ip in p esticide u se can n ot be reject ed , wh ich su ggest s t h at lo n g-ru n reso u rce d egrad at io n act u ally t o o k p lace. Resou rce d egrad ation h as two elem en ts: th e red u ction of th e p oten tial

TABLE 7-1. Parameter Estimates for German Farm Accountancy Network Data, from 1981–1982 to 1994 –1995 (887 observations) Constant PSt–1 –313**

0.76**

Yw t

Ft

Mt

Pc / Pps

Dm

T

R square

22.5*

0.13**

5.5*

178.41**

–8.6**

4.8**

0.62

Note: *sign ifican t at 5% level, ** sign ifican t at 1% level

172 • Chapter 7: Elements of Economic Resistance M anagement Strategies

o f t h e agro eco syst em fo r self-regu lat io n (e.g., n at u ral en em ies t o p est s) an d th e bu ildu p of resistan ce. Th e first effect is related to th e su bstitu tion of ch em ical p esticides for n atu ral biocon trol, wh ereas th e secon d is th e cost im p act of addition al p esticide u se cau sed by th e redu ction in p est su scep tibility. However, th e an alysis can on ly serve as a first ap p roxim ation becau se th e t wo effect s ap p ear in sep arable in t h e d at abase available. Th e resu lt s su ggest th at m ore research on th e lon g-term develop m en t of th e n atu ral resou rce base m u st be u n dertaken .

Factors in Resistance Cost Assessment— Case Study on Resistance against Atrazine

Evid en ce fo r t h e m agn it u d e o f ad ap t at io n co st s t o resist an ce can be d erived from th e case of th e h erbicid e atrazin e, wh ich is th e best-stu d ied exam p le of resist an ce in Germ an y. At razin e was u sed as a p reem ergen ce an d p o st em ergen ce h erbicide in m aize produ ction for m ore th an th ree decades. Its availability con tribu ted to th e rapid in crease of th e m aize area to m ore th an 1 m illion h ectares in th e early 1990s. Atrazin e was ban n ed in th e sprin g of 1991 with th e im plem en tation of stricter gu idelin es to protect grou n dwater resou rces. Field p lot-level d ata from a rep resen tative p an el su rvey of th e p eriod 1987 to 1993 sh owed an in crease of costs of m aize h erbicide u se from less th an DM 40 m illion in 1987 to DM 111.7 m illion for th e area of form er West Germ an y (Produ kt u n d Markt 1996). Un til its ban , atrazin e h ad been th e dom in an t h erbicid e in m aize gro win g. Resist an ce was d isco vered in field t rials in t h e lat e 1970s an d becam e wid esp read in th e 1980s. For exam p le, in Bavaria, a m ajor m aize gro win g st at e, resist an ce o f several weed sp ecies again st at razin e in creased fro m 5% o f t h e su rveyed area in 1983 t o m o re t h an 60% in 1988 (Kees an d Lu tz 1991). Cro p ro t at io n is regard ed as an im p o rt an t fact o r in resist an ce sp read b ecau se it d et erm in es t h e ap p licat io n freq u en cy o f at razin e (Kees an d Lu t z 1991; Zwerger an d Walter 1994). Th is m ean s th at th e im p act of resistan ce on th e costs of weed con trol can be isolated by categorizin g th e field s accord in g to th eir sh are of m aize in th e crop rotation . Su stain able resou rce u se with ou t th e develop m en t of resistan ce is exp ected to occu r on ly with a sh are of m aize in crop rotation of less th an on e-th ird (Kees an d Lu tz 1991). Th erefore, m aize field p lots are differen tiated in to a grou p with a low m aize crop p in g in ten sity (gro u p 1 = less t h an 30% sh are o f m aize in cro p ro t at io n ), m ed iu m m aize crop p in g in ten sity (grou p 2 = 30 to 60%), an d h igh m aize crop p in g in ten sity (grou p 3 = greater th an 60%). Becau se th e sh are of m aize in th e crop rotation in farm p lots of grou p 1 is low, it is assu m ed th at th e observed h erbicid e costs rep resen t th e costs of followin g th e p ath of con servin g weed su scep tibility to atrazin e. Between 1987

Chapter 7: Elements of Economic Resistance M anagement Strategies • 173

an d 1990, h erbicide treatm en t costs were on average DM 43.88 p er h ectare in gro u p 1. C S in Figu re 7-3 d ep ict s t h e co st s o f su st ain ab le weed co n t ro l t h at rem ain co n st an t if n o resist an ce o ccu rs. C R sh o ws t h e co st s o f weed co n t ro l wh en en t erin g t h e p at h o f resist an ce bu ild u p . Farm ers in crease t h e sh are o f m aize in th e crop rotation to ach ieve sh ort-term p rofit gain s com p ared with altern ative crop s, for exam p le, p erm an en t p astu re an d cereals. C T sh ows th e costs of th e altern ative weed con trol tech n ology. Average h erbicid e treatm en t costs for each grou p are sh own in Table 7-2. Farm ers with a h igh sh are of m aize in th eir crop rotation (grou p s 2 an d 3) h ad h igh er h erb icid e t reat m en t co st s in t h e years 1987 t o 1990 t h an t h o se in grou p 1. Th e cost d ifferen ce between th e grou p s sh ows an acceleratin g p ath . Farm ers u sed at razin e at a h igh er d o sage, m ixed it wit h o t h er h erbicid es, o r m ad e su p p lem en tary treatm en ts of altern ative h erbicid es u n til th e ban cam e in to effect. Becau se ch an ges in crop yield an d p rices were n egligible,2 th e cost in crease in real t erm s ap p ears t o h ave b een cau sed b y farm ers’ react io n t o resistan ce bu ildu p . Farm ers exp erien ced o n ly p art o f t h e co st s o f resist an ce bu ild u p becau se th e ban of atrazin e in 1991 p reven ted fu rth er u se. Th e available data allow u s to m od el th e fu rth er cost in crease th at wou ld h ave h ap p en ed wh ile con tin u in g at razin e u se. Th e p ro cess is exp ect ed t o fo llo w a p o lyn o m ial cu rve (Zwerger an d Walt er 1994), in d u cin g an in crease o f h erb icid e co st s in t h e sam e m an n er. Th e cost of a com p lete su bstitu te to atrazin e as observed after t h e b an o f at razin e can b e t aken as t h e ch o ke p rice K o f co m p let e reso u rce

Cost

f T

C

R

C

b

d

c

e

a

0

T*

TB

Time FIGURE 7-3. Costs of Resistance against Atrazine

S

C

174 • Chapter 7: Elements of Economic Resistance M anagement Strategies TABLE 7-2. Average Herbicide Treatment Costs for Field Plots of Different M aize Cropping Intensity (in DM per hectare)* Group

1987

1 2 3

47.06 48.63 53.36

1 2 3

1.55 1.68 1.77

* Herbicide

1990 Herbicide treatm ent costs (product + application) 42.38 55.62 66.34 Herbicide treatm ent frequency 1.39 1.82 2.03

1991–1993 (average)

91.88 94.01 95.55 1.61 1.68 1.87

p rices at wh olesale level, con stan t p rices of 1985.

Source: Au th or calcu lation s on th e basis of raw data from Produ kt u n d Markt (1996).

dep letion . Th e resu lts dem on strate th at th e tim e sp an of th e resistan ce develop m en t is in flu en ced by th e p attern of crop rotation th at ch aracterizes each gro u p . Th e t o t al d u rat io n o f resist an ce b u ild u p u n t il a fu ll su b st it u t io n o f atrazin e is estim ated as 15 years for farm ers in grou p 3 an d 32 years for grou p 2 farm ers (Fleisch er 2000). Th e p resen t valu e PV o f t h e co st s o f resist an ce b u ild u p d ep en d s o n t h e so cial d isco u n t rat e. Fu ll in fo rm at io n ab o u t t h e so cial d isco u n t rat e wo u ld allo w u s t o d et erm in e t h e u ser co st s an d t h e o p t im al d ep let io n t im e o f t h e resou rce. Society’s tim e p referen ce for th e con servation of biological cap ital is n ot p resen tly kn own . Followin g Clin e (1992), we can h yp oth esize th at a con servat ive ap p ro ach sh o u ld b e t aken wh en n at u ral reso u rce d ep let io n is in vo lved , esp ecially in view o f t h e u n kn o wn p referen ces o f fu t u re gen erat io n s. Th erefo re, a ran ge o f d isco u n t rat es is u sed t o est im at e t h e PV o f t h e co st s o f resist an ce bu ild u p . Th o se co st s are d et erm in ed by t h e d ifferen ce in h erbicid e costs between a p ath of su stain able resou rce u se C S an d th e resistan ce bu ild u p C R (Table 7-3). W h en a low d iscou n t rate of 1% as p rop osed by Clin e (1992) is t aken , t h e so cial co st s o f resist an ce exceed t h e p rivat e co st s com p u ted at a discou n t rate of 8%. Accou n tin g for th e costs of resistan ce bu ild u p also allows u s to assess th e residu al farm -level costs of adju stm en t to th e atrazin e ban . Farm ers in grou p 1 faced h igh er ad ju st m en t co st s co m p ared wit h t h o se in t h e o t h er gro u p s. Farm ers ad o p t in g a cro p ro t at io n wit h a lo w sh are o f m aize, an d t h u s p u rp osely or in volu n tarily delayin g resistan ce develop m en t, were affected disp rop ortion ately by th e ban . Farm ers in grou p 1 m ade u p 37% of th e lan d bu t h ad to bear 69% of th e adju stm en t costs. Early adop ters of a h igh sh are of m aize in crop rotation con tribu ted m ore to widesp read water p ollu tion th at p rom p ted

Chapter 7: Elements of Economic Resistance M anagement Strategies • 175

TABLE 7-3. Present Value of Resistance Buildup Costs of Atrazine Use at Different Discount Rates (DM per hectare) Intensity group Grou p 2 Grou p 3

8% Period Period Period Period

1a 2b 1a 2b

157 54 218 252

Discount rate (i) 4% 358 376 331 888

1% 713 3,949 463 5,511

Notes: a. Presen t valu e of th e costs from th e on set of resistan ce bu ildu p u n til tech n ology switch , PV = ∑ [(C R – C S)t × (1 + i)–t ], eq u ivalen t to ∑(a + b + c) in Figu re 7-3. b. Presen t valu e of th e costs after th e tech n ology switch (p erm an en t loss of op tion ), PV = ∑ [(C T – C S)t × (1 + i)–t ], eq u ivalen t to ∑(d + e) in Figu re 7-3.

th e atrazin e ban th an farm ers in grou p 1. Con versely, farm ers wh o in vested in reso u rce co n servat io n an d gave u p t h e sh o rt -t erm p ro d u ct ivit y gain s t h at th eir fellow farm ers in grou p s 2 an d 3 ach ieved were barred from reap in g th e retu rn s on th eir in vestm en t.

Conclusion Th e th eoretical con sideration s an d th e em p irical stu dies sh ow th e im p ortan ce o f a n u m ber o f variables fo r d et erm in in g resist an ce m an agem en t st rat egies. Th ese are in fo rm at io n ab o u t t h e m agn it u d e an d eco n o m ic im p o rt an ce o f resist an ce even t s, t h e exp ect at io n s ab o u t t h e d ist rib u t io n al effect s t h ro u gh resistan ce sp read, an d th e im p act of adap tation to resistan ce on th e com p etitive p osition of p rodu cers. Th e first case stu dy sh ows th at alth ou gh th ere are clear h in ts toward sectorwide resou rce degradation in m odern crop p rotection p ractices, m ore research is n eeded to effectively ch allen ge th e still widely accep ted p aradigm th at p esticid e u se can be assessed in a static fram ework. Fu tu re research n eed s m ore co llab o rat io n acro ss p aro ch ial in t erest s o f d iscip lin es t o p ro d u ce lo n g-t erm rep resen tative data on ch an ges in agroecosystem p aram eters th at can be an alytically tied to ch an ges in th e farm in g system . Th e secon d case stu dy p oin ts to th e eq u ity im p lication s of resistan ce develop m en t am on g cu rren t an d fu tu re gen eration s of farm ers. Farm ers wh o sacrifice sh ort-term p rofit m axim ization for lon g-term resou rce con servation h ave to bear a h igh er sh are of th e adju stm en t costs cau sed by a regu latory decision su ch as ban n in g a p esticide. Th e atrazin e case sh eds ligh t on th e distribu tion al con seq u en ces of th e cu rren t way th at p esticide u se is regu lated. Alth ou gh th e ban on atrazin e was n ot

176 • Chapter 7: Elements of Economic Resistance M anagement Strategies

lin ked t o resist an ce bu t t o it s effect s o n gro u n d wat er, it is p o ssible t h at t h e eco n o m ic co n seq u en ces o f t h e cu rren t regu lat o ry ap p ro ach p ro vid e t h e wron g sign als to farm ers by m akin g th em d isregard resou rce con servation in relation to crop p rotection . Policies for better resistan ce m an agem en t m ostly con cen trate on providin g m o re in fo rm at io n t o d ecisio n m akers t o creat e awaren ess o f t h e resist an ce p ro blem . Fo r exam p le, p resen t p o licies in Germ an y p ro vid e in fo rm at io n t o farm ers in cooperation with th e private sector u sin g th e m oral su asion strategy to m ake farm ers adopt lon ger-term strategies in pest con trol (BML 1997). However, th is strategy is u n likely to be su ccessfu l. It h as been freq u en tly observed t h at farm ers ad o p t su st ain able p est m an agem en t st rat egies o n ly in case o f a severe crisis in crop protection alth ou gh in form ation abou t lon g-term n egative effects h ad alread y been available earlier. Cowan an d Gu n by (1996) p oin t to t h e ro le o f n et wo rk ext ern alit ies an d self-rein fo rcin g m ech an ism s cau sin g relian ce on ch em ical con trol, path depen den cy, an d h igh adju stm en t costs. Th e d ecisive ro le o f exp ect at io n s ab o u t t h e fu t u re rat e o f t ech n o lo gical p ro gress fo r d et erm in in g t h e eco n o m ic im p o rt an ce o f resist an ce m u st b e stressed. On th e on e h an d, determ in istic m odels m igh t be u n su itable to reveal th e econ om ic im p ortan ce of th e resistan ce th reat as p erceived by th e farm ers. On th e oth er h an d, it is likely th at stakeh olders in th e agricu ltu ral sector sh are h igh exp ect at io n s in t h e fu t u re availab ilit y o f t ech n o lo gical o p t io n s, esp ecially ch em ical p esticides, as in du ced by en dogen ou s m arket sign als. Fou r factors su ggest a m ore con servative ap p roach toward exp ected ben efits from tech n ological p rogress. First, th e on goin g p rocess of con solid ation in t h e agro ch em ical an d life scien ces in d u st ry, wh ich d o m in at e t h e m arket for p est con trol tech n ologies, m ay p rovid e d isin cen tives for coop eration an d reso u rce co n servat io n st rat egies. Firm s wit h p ro d u ct s in t h e early st ages o f t h e p ro d u ct life cycle p u sh fo r co n q u erin g h igh m arket sh ares t o st im u lat e d iffu sion in th e m arket segm en t. Secon d , th e h igh fixed costs of p rod u ct regist rat io n lead t o a n arro win g o f t h e t o t al n u m b er o f p est icid es availab le. Th ird , regu latory in terven tion cau sed by extern alities in oth er field s will trigger fu rth er restriction s on th e availability of p est con trol tech n ologies based o n ch em icals an d gen et ic en gin eerin g. Fo u rt h , t h ere sh o u ld b e a fo cu s o n o verall co st s o f cro p p ro t ect io n fo r b o t h farm ers an d so ciet y as a wh o le. Becau se extern alities from resistan ce are in m an y cases n ot in corp orated in to d ecision m akin g, m arkets m ay p rovid e in cen tives th at are n ot in lin e with th e social op tim u m . In addition to p rovidin g in form ation , govern m en t p olicies sh ou ld view th e reso u rce o f p est su scep t ibilit y as a p u blic go o d . Th is wo u ld warran t a clo ser con sid eration of p u blic in vestm en t in research , d evelop m en t, an d exten sion of a broader ran ge of tech n ology op tion s.

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Acknowledgements Th e au t h o rs t h an k Jan C. Zad o ks an d t h ree an o n ym o u s reviewers fo r t h eir h elp fu l com m en ts.

References BML (Bu n desm in isteriu m fü r Ern äh ru n g, Lan dwirtsch aft u n d Forsten ). 1997. Risikom inderung bei Pflanzenschutzm itteln in Deutschland. Bon n , Germ an y: Federal Min istry for Food, Agricu ltu re an d Forestry. Carlson , G. 1977. Lon g Ru n Produ ctivity of In secticides. Am erican Journal of Agricultural Econom ics 59: 543–8. Carlson , G., an d M. Wet zst ein . 1993. Pest icid es an d Pest Man agem en t . In Agricultural and Environm ental Resource Econom ics, ed it ed b y G. Carlso n , D. Zilb erm an , an d J. Miran owski. New York: Oxford Un iversity Press, 268–318. Clin e, W.R. 1992. The Econom ics of Global W arm ing. Wash in gton , DC: In stitu te of In tern ation al Econ om ics. Co wan , R., an d P. Gu n by. 1996. Sp rayed t o Deat h —Pat h Dep en d en ce, Lo cked -In an d Pest Con trol Strategies. The Econom ic Journal 106: 521–42. Fleisch er, G. 2000. Resou rce Costs of Pesticid e Use in Germ an y. Th e Case of Atrazin e. Agrarwirtschaft 49(11): 379–87. GCPF (Glo b al Cro p Pro t ect io n Fed erat io n ). 2000. Resist an ce Act io n Co m m it t ees. h ttp :/ / www.gcp f.org (accessed Decem ber 12, 2000). Hu eth , D., an d U. Regev. 1974. Op tim al Agricu ltu ral Pest Man agem en t with In creasin g Pest Resistan ce. Am erican Journal of Agricultural Econom ics 56: 543–53. IVA (In du strieverban d Agrar). 1999. Annual Report. Fran kfu rt, Germ an y: IVA. Kees, H., an d A. Lu tz. 1991. Zu r Problem atik d er Triazin resisten z bei Sam en u n kräu tern im Mais u n d in gärtn erisch en Ku ltu ren . Gesunde Pflanzen 43(7): 216–20. Lich ten berg, E., an d D. Zilberm an . 1986. Th e Econ om etrics of Dam age Con trol: W h y Sp ecification Matters. Am erican Journal of Agricultural Econom ics 68: 261–73. NAS (Nat io n al Acad em y o f Scien ces). 1975. Pest Control: An Assessm ent of Present and Alternative Technologies. Wash in gton , DC: NAS. Nevill, D., D. Corn es, an d S. Howard . 1998. Weed Resistan ce. Th e Role of HRAC in th e Man agem en t of Weed Resistan ce. h ttp :/ / p lan tp rotection .org/ HRAC/ weed resis.h tm (accessed Decem ber 12, 2000). O skam , A.J., R.A.N. Vijft igsch ild , an d C. Gravelan d . 1997. Additional EU Policy Instrum ents for Plant Protection Products— A Report within the Second Phase of the Program m e: Possibilities for Future EC Environm ental Policy on Plant Protection Products. Wagen in gen , Th e Neth erlan ds: Wagen in gen Agricu ltu ral Un iversity. Pan n ell, D.J., an d D. Zilberm an . 2000. Econom ic and Sociological Factors Affecting Growers’ Decision Making on Herbicide Resistance. Su stain ability an d Econ om ics in Agricu ltu re (SEA) Workin g Pap er 00/ 07. Nedlan ds, Au stralia: Un iversity of Western Au stralia. Pearce, D., an d R. Tin ch . 1998. Th e Tru e Price of Pesticides. In Bugs in the System , edited by B. Vorley an d D. Keen ey. Lon don : Earth scan . Perm an , R., Y. Ma, an d J. McGilvray. 1996. Natural Resource and Environm ental Econom ics. Lon don an d New York: Lon gm an .

178 • Chapter 7: Elements of Economic Resistance M anagement Strategies Pim en tel, D., H. Acq u ay, M. Bilton en , P. Rice, M. Silva, J. Nelson , V. Lip n er, S. Giordan o, A. Ho ro wit z, an d M. D’Am o re. 1993. Th e Pest icid e Q u est io n —En viro n m en t , Eco n om ics, an d Eth ics. In Assessm ent of Environm ental and Econom ic Im pacts of Pesticide Use, ed ited by D. Pim en tel an d H. Leh m an . New York an d Lon d on : Klu wer, 47–84. Produ kt u n d Markt. 1996. Pan el Data on Pesticide Use in Maize in West Germ an y, 1985 to 1993. Un p u blish ed rep ort. Wallen h orst, Germ an y. Regev, U., A.P. Gu tierrez, an d G. Fed er. 1976. Pests as a Com m on Prop erty Resou rce: A Case Stu d y of Alfalfa Weevil Con trol. Am erican Journal of Agricultural Econom ics 58: 186–97. Ru bin , B. 1996. Herbicide-Resistan t Weeds—Th e In evitable Ph en om en on : Mech an ism s, Distribu tion an d Sign ifican ce. Zeitschrift für Pflanzenkrankheiten und Pflanzenschutz, Son derh eft XV: 17–32. Stein er, R., L. McLau gh lin , P. Faeth , an d R. Jan ke. 1995. In corp oratin g Extern ality Costs in to Prod u ctivity Measu res. A Case Stu d y Usin g U.S. Agricu ltu re. In Agricultural Sustainability: Environm ental and Statistical Considerations, edited by V. Barn ett, R. Payn e, an d R. Stein er. New York: Joh n Wiley, 209–230. Th ru p p , L.A. (ed .). 1996. New Partnerships for Sustainable Agriculture. Wash in gton , DC: World Resou rces In stitu te. van d en Bosch , R. 1978. The Pesticide Conspiracy, Secon d Ed ition . Berkeley, CA: Un iversity of Californ ia Press. van Sch illh orn V., T., D. Forn o, S. Joffe, D. Um ali-Dein in ger, an d S. Cooke. 1997. Integrated Pest Managem ent. Strategies and Policies for Effective Im plem entation. En viro n m en t ally an d Su st ain ab le Develo p m en t St u d ies an d Mo n o grap h s Series No . 13. Wash in gton , DC: Th e World Ban k. Waibel, H., an d G. Fleisch er. 1997. In corp oratin g User Costs in to th e Assessm en t of Pesticid e Prod u ctivity. In Proceedings of the W ageningen W orkshop on Pesticides, EU Concerted Action on Policy Measures for the Control of Environm ental Im pacts, ed ited by A. Oskam an d R. Vijftigsch ild. Wagen in gen , Th e Neth erlan ds: Wagen in gen Agricu ltu ral Un iversity. ———. 1998a. Eco n o m ic Sp ecificat io n fo r Pro d u ct io n Eco lo gy. Co n sid erat io n o f Dyn am ic an d In t ergen erat io n al Asp ect s in Pest Man agem en t Research In Active Methodology. Proceedings of a Sem inar Series 1997/98, edited by A. Stein , M.K. van Ittersu m , an d G.H.J. de Kon in g. Agricu ltu ral Un iversity: Qu an titative Ap p roach es in System s An alysis No. 19. Wagen in gen , Th e Neth erlan ds: Wagen in gen Agricu ltu ral Un iversity, DLO Research In stitu te for Agrobiology an d Soil Fertility, an d th e C.T. de Wit Gradu ate Sch ool of Produ ction Ecology, 41–53. ———. 1998b. Kosten und Nutzen des chem ischen Pflanzenschutzes in der deutschen Landwirtschaft aus gesam twirtschaftlicher Sicht. (Cost-Ben efit An alysis of Pesticid e Use in Germ an Agricu lt u re an d Pest icid es Pro d u ced in Germ an y fo r Majo r Wo rld Cro p s). Kiel, Germ an y: Vau k-Verlag. Waibel, H., G. Fleisch er, an d H. Becker. 1999. Th e Eco n o m ic Ben efit s o f Pest icid es: A Case Stu dy from Germ an y. Agrarwirtschaft 48(6): 219–30. Yu d elm an , M., A. Rat t a, an d D. Nygaard . 1998. Pest Managem ent and Food Production. Looking to the Future. Fo o d , Agricu lt u re an d t h e En viro n m en t Discu ssio n Pap er 25. Wash in gton , DC: In tern ation al Food Policy Research In stitu te. Zwerger, P., an d H. Walt er. 1994. Mo d elle zu m Man agem en t h erb izid resist en t er Un krau tp op u lation en . Zeitschrift für Pflanzenkrankheiten und Pflanzenschutz, Son d erh eft XIV: 409–20.

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Notes 1. Ad d it io n ally, t h ere m ay b e an im p act o f m o re st rin gen t en viro n m en t al regu lat io n s t h at in creases t h e co st s o f p est icid e regist rat io n fo r m an u fact u rers. Ho wever, in corp oratin g a d u m m y variable for th e year 1986 wh en th e p lan t p rotection law was revised an d m ore strin gen t registration criteria cam e in to effect yield ed n o sign ifican t resu lts in th e regression m odel exp lain ed later in th e ch ap ter. 2. Becau se o f p rice st abilizat io n in t h e Co m m o n Agricu lt u ral Po licy Fram ewo rk o f t h e Eu ro p ean Un io n , cro p an d livest o ck p rices rem ain ed st ab le. A large sh are o f t h e m aize crop is u sed as on -farm fod d er resou rce for h og, beef, an d d airy farm in g. Resu lts from research trials sh owed th at oth er h erbicides as well as m ech an ical weed con trol are eq u ally effective as atrazin e.

Commentary

Can We Justify Resistance M anagement Strategies for Conventional Pesticides? Fred Gould

F

leisch er an d Waibel (Ch ap ter 7) exp lain th at th e ju stification for region al p rogram s aim ed at d ecreasin g th e rate at wh ich p ests ad ap t to in secticid es is u n certain . In th eir ch ap ter, th ey m en tion two extrem e, gen eral situ ation s. In th e first, th ere is n o n eed for region al resistan ce m an agem en t p rogram s “(a) wh en p erfect in form ation on all p aram eters of th e biological p rocess of resistan ce develop m en t is available [to farm ers an d oth ers] an d (b) wh en extern alities are absen t, su ch as in th e case of th e sp read of resistan ce from on e farm to oth er econ om ic u n its.” In th e secon d gen eral situ ation , th ese two con d ition s are n ot m et an d resistan ce in a p est resu lts in a crop p in g system th at becom es u n p rofitable. In m ost agricu ltu ral system s, little is kn own abou t th e degree to wh ich th e p rop erties of th e system m atch on e or m ore of th ese extrem e ch aracteristics. With ou t su ch in form ation , th ere will always be d ebate abou t th e u tility of resistan ce m an agem en t. Even if we h ad th is in form ation , m ore sp ecific biological, econ om ic, an d social factors will d eterm in e th e ju stification for a resistan ce m an agem en t p rogram . Fleisch er an d Waibel review p reviou s work on assessin g th e u tility of resistan ce m an agem en t an d th en take a resou rce econ om ics p ersp ective in an alyzin g th e attribu tes of two case stu dies. I will first com m en t on th e case stu dies an d th en m ake m ore gen eral observation s from an agricu ltu ral biologist’s p ersp ective. In th e first case stu dy, th e au th ors exten d th e logic of Carlson (1977), wh o p o in t ed o u t t h at resist an ce can lead t o d ecreased p ro d u ct ivit y o f p est icid es o ver t im e, eit h er becau se o f t h e n eed t o in crease t h e u se o f t h e ch em ical t o

• 180 •

Commentary: Can We Justify Resistance M anagement Strategies? • 181

wh ich resistan ce is develop in g or becau se of th e n eed to adop t a m ore exp en sive p esticide. Fleisch er an d Waibel p rovide a very gen eral an alysis of Germ an agricu ltu re from 1962 th rou gh 1995, in wh ich th ey test th e n u ll h yp oth esis t h at p est icid e exp en ses h ave been m ain t ain ed co n st an t relat ive t o exp en ses for m in eral fertilizers. Assu m in g th at th e p rodu ctivity of fertilizers is n ot bein g eroded, failu re to reject th e n u ll h yp oth esis in dicates th at p esticide p rodu ctivity is relatively con stan t an d h as n ot been affected by evolu tion of p est resistan ce. Th e an alysis d oes reject th e n u ll h yp oth esis an d d em on strates th at th e relative exp en se of p esticides h as in creased dram atically. Fleisch er an d Waibel con clu de th at th is in crease in p esticide exp en se cou ld be cau sed by resistan ce o r d eclin e in n at u ral agen t s t h at co n t ro l p est s an d t h at fu rt h er research is n eeded to determ in e th e con tribu tion of each of th ese factors. I h ave t wo co n cern s ab o u t t h is st u d y. O n e is t ech n ical, an d t h e o t h er is m ore gen eral. First, I am con cern ed abou t th e data on p esticide u se th at were u sed in th is stu d y. If p esticid es in clu d e h erbicid es, th ere was a great in crease in t h e gen eral u se o f h erb icid es b et ween 1962 an d 1995 as a su b st it u t e fo r m ech an ical cu ltivation (Nation al Research Cou n cil 2000). It cou ld be th at th e en tire in crease in p esticid e exp en se fou n d by Fleisch er an d Waibel is cau sed by th e h erbicid e su bstitu tion factor. It wou ld , th erefore, be u sefu l to an alyze p esticides disaggregated in to h erbicides, in secticides, an d fu n gicides. My seco n d co n cern is wit h t h e u n d erlyin g assu m p t io n t h at if p est icid e exp en se in a farm in g system rem ain s con stan t as a p rop ortion of p rod u ction exp en ses, th ere is n o econ om ic im p act of resistan ce. My gen eral sen se is th e cost of in secticid es (p er p ou n d of active in gred ien t) with in a class of in secticid al ch em istry (e.g., organ op h osp h ates) d ecreases as a fu n ction of th e n u m b er o f years sin ce t h e class o f ch em ist ry was in t ro d u ced . Fo r exam p le, t h e cost of p yreth roid s in th e late 1970s was ap p roxim ately $15 p er acre of cott o n sp rayed . Th e average co st o f p yret h ro id s in No rt h Caro lin a b et ween 1995 an d 2000 was $5.25 p er acre sp rayed (Bach eler 2000). In co m p ariso n , Tracer, a p esticid e in a n ew class of ch em istry, cu rren tly costs $15.82 p er acre o f ap p licat io n . Tracer is u sed in co t t o n -gro win g areas wh ere t h e cat erp illar p est, Heliothis virescens, h as d evelop ed resistan ce to p yreth roid s (e.g., Mississip p i, Arkan sas, an d Alabam a, bu t n ot North Carolin a). Exam in in g th e gen eral cost of in secticid e u se in areas th at n ow h ave p yreth roid resistan ce, th e p rice in 2000 is u n likely to be su bstan tially h igh er th an in 1977. However, if t h ere h ad b een n o resist an ce in t h o se areas, t h e p rice in 2000 m igh t h ave been on ly on e-th ird of th e p rice in 1977. In th is case, th e assu m p tion th at a con stan t exp en d itu re d em on strates a lack of a cost from resistan ce is fau lty. Un less a stu d y can d irectly estim ate th e exp en d itu re for an in secticid e with an d with ou t resistan ce, it will be d ifficu lt to d eterm in e th e econ om ic im p act of resistan ce.

182 • Commentary: Can We Justify Resistance M anagement Strategies?

In Fleisch er an d Waib el’s seco n d case st u d y, a m o re sp ecific sit u at io n is assessed : t h e im p act o f at razin e resist an ce o n t h ree gro u p s o f co rn farm ers with low, m od erate, an d h igh u se of atrazin e. Becau se on ly a low fraction of m ost weeds’ seeds m ove from farm to farm , each farm er gen erates m ost of h is or h er own resistan ce p roblem . Farm ers with th e m ost in ten se u se of atrazin e are exp ected to u se u p th e resou rce of su scep tible weed s on th eir lan d faster th an will oth er farm ers. In th is sp ecific case, atrazin e was ban n ed from u se for en viro n m en t al reaso n s at a t im e wh en resist an ce h ad alread y d evalu ed t h e ch em ical for in ten se u sers bu t n ot for th ose with low u se. If atrazin e h ad n ot b een b an n ed , t h e in t en se u sers wo u ld h ave in cu rred a co st fro m h eavy relian ce on atrazin e, bu t in stead , all farm ers h ad to switch to n ew ch em istry at th e sam e tim e becau se of th e ban . Th is resu lted in a n et gain for th e in ten se u sers com p ared with th e low-u se farm ers. Th is cu riou s resu lt em p h asizes th e n eed for an y an alysis to con sid er wh o bears th e cost of p esticide resistan ce. In som e cases, th ose wh o get th e ben efits also bear th e costs; in oth er cases, th e distribu tion of costs does n ot m atch th e distribu tion of ben efits. Sh ou ld society in tercede to m ake th e ben eficiaries p ay a fair sh are of th e cost? Th e cu rren t stu dy on ly exam in es th e effects on farm ers, bu t con su m ers an d th e en viron m en t are also stakeh olders. So wh at are t h e co st s an d ben efit s o f p est icid e resist an ce t o t h e en viro n m en t ? Du rin g t h e b at t le o ver b an n in g DDT, resist an ce t o t h e ch em ical alread y h ad d evelo p ed in m ajo r, t arget ed agricu lt u ral p est s an d d isease vect o rs (Bro wn 1971). It m ay be t h at becau se t h e ben efit s o f DDT were d eclin in g, t h e case n o t t o b an DDT failed m o re q u ickly. If we assu m e t h at t h e rep lacem en t s fo r DDT were less h arm fu l t o t h e en viro n m en t t h an DDT, it can be argu ed t h at DDT resist an ce ben efit ed t h e en viro n m en t . Becau se t h e U.S. En viron m en tal Protection Agen cy h as tigh ten ed en viron m en tal regu lation s for com m ercialization of n ew p esticid es, it cou ld be argu ed th at p esticid e resist an ce gen erally b en efit s t h e en viro n m en t , wit h each rep lacem en t p esticid e bein g m ore ben ign th an th e p esticid e it rep laces. Th e cou n terargu m en t is t h at fo r o ld er classes o f p est icid es, exp erien ce h as u n co vered m an y exp ected an d u n exp ected n egative effects, an d we n ow kn ow h ow to p rotect h u m an s an d th e en viron m en t from th ese effects. In con trast, for n ew p esticid es, we on ly kn ow th at th e exp ected n egative effects are low. We h ave n ot u sed th ese n ew p esticid es lon g en ou gh to kn ow if th ere will be u n an ticip ated effects (Nation al Research Cou n cil 2000).

Commentary: Can We Justify Resistance M anagement Strategies? • 183

References Bach eler, J. 2000. Co t t o n No t es. h t t p :/ / ip m .n csu .ed u / co t t o n / in sect co rn er/ slid esh o w/ sld042.h tm (accessed March 8, 2002). Brown , A.W.A. 1971. Pest Resistan ce to Pesticid es. In Pesticides in the Environm ent, volu m e 1, p art II, edited by R. W h ite-Steven s. New York: Marcel-Dekker, 457–552. Carlson , G.A. 1977. Lon g-Ru n Prod u ctivity of In secticid es. Am erican Journal of Agricultural Econom ics 59(3): 543–48. Nation al Research Cou n cil. 2000. The Future Role of Pesticides in U.S. Agriculture. Wash in gton , DC: Nation al Academ y Press.

Chapter 8

Pesticide Resistance, the Precautionary Principle, and the Regulation of Bt Corn Real Option and Rational Option Approaches to Decisionmaking Benoît M orel, R. Scott Farrow, Felicia Wu, and Elizabeth A. Casman

Few attempts have been made to place the recently advocated precautionary principle in an analytical fram ew ork. If successfully developed, such a framework could prove useful to decisionmakers precisely in situations such as the regulation of Bt corn, including concern for pest resistance, and num erous other decisions involving scientific uncertainty and large or irreversible costs. This chapter (a) sum m arizes how econom ic option theories can be used to structure regulatory decisionm aking under uncertainty and irreversibility, (b) links that structure to the precautionary principle, (c) shows how pest resistance development affects the options analysis, and (d) dem onstrates the im pact of pest resistance developm ent and the option framing for Bt corn. Our empirical application is the decision to allow commercialization of Bt corn. Building from a static m odel of technological change, w e add the dynamic components of pest resistance modeled as a form of depreciation of the investm ent in Bt corn and of other elem ents of value. Using data related to Bt corn, we present preliminary results indicating that a standard cost–benefit analysis supports the regulatory decision to com m ercialize Bt corn, although an options analysis would likely reach the opposite conclusion because the benefits do not sufficienty exceed the costs when taking future uncertainties and irreversible costs into consideration. The impact of pest resistance, when m odeled as occurring with a m ean arrival rate of 12

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Chapter 8: Resistance, the Precautionary Principle, and Regulation • 185 years, has a measurable impact on the economic evaluation, but the largest impact comes from the use of the option framework.

evolu tion ary tech n ological breakth rou gh s can gen erate seriou s ch allen ges to policym akers because un certain ties in volvin g tech n ology, h ealth , m arket beh avior, an d th e en viron m en t are freq u en tly p resen t. Th e ad ven t of gen etically m odified crops is a recen t, particularly acute exam ple. Wh en policym akers approve th e com m ercialization of gen etically m odified organ ism s (GMOs), th ey are m akin g d ecision s with u n certain an d p ossibly irreversible con seq u en ces, both for better an d worse. Recen t even ts in th e use of on e GMO, Bt corn (corn th at h as been gen etically m odified to express an in secticide of bacterial origin ), exem plify som e of th e un certain ties. Th ese in clude th e poten tial for th e develop m en t of p est resistan ce to th e Bt toxin , ch an ges in econ om ic well-bein g, im pacts on n on target species, public perception , an d m ore. Th ere is, h owever, n o accep ted p arad igm for ad visin g d ecision m akers in such a situation . Curren t regulatory practice evaluates wh at risks m ay exist (see, for exam ple, EPA 2001; USDA 1997a, 1997b; FDA 1998). Som e an alysts m ay go furth er an d seek to value th ose risks by gen eratin g in form ation relevan t to th e cost–ben efit paradigm (Hyde et al. 1999; Min or et al. 1999). However, a grou p of advocates su pports th e application of a precau tion ary prin ciple to decision s with large scien tific u n certain ties an d large or irreversible costs, in clu din g th e regulation of GMOs. Alth ough m an y version s of th e prin ciple exist, a succin ct version states th at wh en an activity raises th reats of h arm to h u m an h ealth or th e en viron m en t, precaution ary m easures sh ould be taken even if som e causean d -effect relation sh ip s are n ot establish ed scien tifically (Goklan y 2000). A strin gen t an d con troversial version of th e p rin cip le is d escribed in th e Win gsp read statem en t: “Un certain ty abou t risk req u ires forbid d in g th e p oten tially risky activity u n til th e propon en t of th e activity dem on strates th at it poses no risk” (Wien er forth com in g). In con trast, th e Eu rop ean Un ion h as released a com m un ication th at descriptively places th e precaution ary prin ciple with in th e boun ds of risk an alysis (Com m ission of th e European Un ion 2000). To d at e, t h ere h ave been few, if an y, at t em p t s t o p lace t h e p recau t io n ary p rin cip le with in an an alytically tractable fram ework th at cou ld be u sed in p olicy an d regu latory an alysis. If su ccessfu lly develop ed, su ch a fram ework cou ld p rove u sefu l to d ecision m akers p recisely in situ ation s su ch as th e regu lation o f Bt co rn , o t h er GMO s, an d n u m ero u s o t h er d ecisio n s in vo lvin g scien t ific u n certain ty an d large or irreversible costs. Th is ch ap ter (a) su m m arizes h ow eco n o m ic o p t io n t h eo ries can b e u sed t o st ru ct u re t h e regu lat o ry d ecisio n m akin g issu es su rro u n d in g Bt co rn (t h e exam p le o f Bt co rn is u sed in t h is ch ap ter to brin g sp ecificity to th e issu e of regu latory decision s in th e p resen ce o f u n cert ain t y), (b ) d em o n st rat es h o w t h at st ru ct u re can b e in t erp ret ed as q u an tifyin g th e p recau tion ary p rin cip le, (c) sh ows h ow p est resistan ce d evel-

R

186 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

o p m en t t o Bt co rn affect s t h e o p t io n s an alysis b y ad d in g a t ech n o lo gical d ep reciat io n fact o r an d red u cin g t h e lifet im e o f t h e t ech n o lo gy, an d (d ) d em o n st rat es wit h illu st rat ive d at a relat ed t o Bt co rn h o w t h e o p t io n s ap p roach m igh t yield a differen t regu latory recom m en dation th an a stan dard cost–ben efit an alysis.

Pest Resistance Development in Bt Corn “If th ere is an assu m p tion th at th e Bt toxin s will in evitably lose th eir efficacy th rou gh m assive exp ression in tran sform ed crop s, th is is u n accep table to th e organ ic com m u n ity. Th is objection is based n ot ju st on direct self-in terest bu t also on gen eral grou n ds of sou n d scien ce p olicy” (Lip son 1999). Bt toxin is a n atu rally occu rrin g in secticide produ ced by th e soil bacteriu m Bacillus thuringiensis t h at h as been co m m ercially available p rim arily fo r t h e con trol of lepidopteran (m oth s an d bu tterflies) agricu ltu ral pests for m ore th an 40 years. Very little p est resistan ce d evelop m en t was ever observed over th is t im e m ain ly becau se o f t h e in t erm it t en t ap p licat io n p at t ern s u sed an d t h e toxin ’s rapid degradation in th e en viron m en t, especially wh en exposed to ligh t (NAS 2000). Bt corn is gen etically m odified to con tain a m odified tran sgen e for Bt toxin alon g with regu latory an d prom oter tran sgen es, wh ich allow th e corn to produ ce Bt toxin on a m ore or less con tin u ou s basis. Th e toxin is produ ced in side th e plan t tissu es, an d th e bu lk of it is protected from ph otolysis. With repeated use, all pesticides are expected to lose th eir efficacy as selective pressures favor th e survival an d reproductive success of resistan t in dividuals. By in creasin g th e duration of exposure an d in som e cases by deliverin g in adequate toxin doses to target pest population s, Bt corn is feared to exert greater selective p ressu re on in sect p op u lation s to d evelop resistan ce to Bt com p ared with th e tran sien t, extern al application s favored before th e adven t of Bt corn . If p ests becom e resistan t to Bt corn , th e loss is twofold . First, society will h ave lost th e use of a plan t-in corporated protectan t believed to be m ore ecologically frien dly th an con ven tion al pesticides. Secon d, growers, especially organ ic growers, m igh t n o lon ger be able to use th e m icrobial Bt sprays th at are con sidered som e of th eir few accep table p esticid es if p est resistan ce to Bt sp read to th ose farm s. Microbial Bt spray form ulation s are reported to be th e sin gle m ost im p ortan t off-farm in p u t of organ ic growers for in sect p est m an agem en t. For n in e upper-Midwest states, recen t n ation al survey results in dicated th at 25% of certified organ ic growers in th ese states u se Bt “freq u en tly” or “occasion ally.” For certified organ ic field crop producers in th is region , th e n um ber is 20%; for organ ic fru it crop s it is 52%; an d for vegetable op eration s in th is area, 48% of th e growers use Bt frequen tly or occasion ally (EPA/USDA 1999). Becau se o f t h ese risks, EPA h as en act ed in sect resist an ce m an agem en t req u irem en t s in t en d ed t o d elay resist an ce an d t o p ro lo n g t h e efficacy o f Bt

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 187

co rn . In it s m o st recen t Bio p est icid es Regist rat io n Act io n Do cu m en t fo r Bt corn (EPA 2001), EPA con firm ed a resistan t Bt even t if exp erim en ts on p ests exh ibit all of th e followin g ch aracteristics: (a) th ere is less th an 30% su rvival an d less th an 25% leaf area dam aged in a five-day bioassay u sin g Cry1Ab-p osit ive o r Cry1F-p o sit ive leaf t issu e u n d er co n t ro lled lab o rat o ry co n d it io n s (Cry1Ab an d Cry1F are t wo o f t h e h u n d red s o f Bt t o xin variet ies), (b ) st an dardized laboratory bioassays u sin g diagn ostic doses for Eu rop ean corn borer, So u t h west co rn b o rer, an d co rn earwo rm d em o n st rat e t h at resist an ce h as a gen etic basis an d su rvivorsh ip in excess of 1% (gen e freq u en cy of p op u lation less th an 0.1), an d (c) a leth al con cen tration resu ltin g in 50% m ortality (LC 50 ) in a st an d ard Cry1Ab o r Cry1F d iet b io assay exceed s t h e u p p er lim it o f t h e 95% co n fid en ce in t erval o f t h e st an d ard u n select ed lab o rat o ry p o p u lat io n LC 50 for su scep tible Eu rop ean corn borer, Sou th west corn borer, or corn earworm p op u lation s, as establish ed by th e on goin g baselin e m on itorin g system . Cu rren tly, EPA req u ires a h igh d ose an d refu ge strategy to slow or p reven t resistan ce d evelop m en t. As im p lem en ted , th is strategy req u ires th at growers p lan t on ly cu ltivars exp ressin g h igh con cen tration s of toxin an d th at growers p lan t a “refu ge” of n on -Bt corn occu p yin g an area at least 20% of th e size of t h e Bt co rn p lan t in g. Th e refu ges m ay b e t reat ed wit h in sect icid es. If t h e refu ges are n ot treated with p esticides, th ey on ly n eed to be 5% th e size of th e Bt p lan tin g. Th e refu ge p lan tin g op tion s in clu de sep arate fields, blocks with in fields, or strip s across th e field with in on e-h alf m ile of th e Bt corn (EPA 2001). Th e p u rp o se o f t h e refu ge is t o p ro vid e a so u rce o f Bt-su scep t ible p est s t h at cou ld m ate with p oten tially resistan t p ests em ergin g from n earby Bt corn . Th e go al is t o p ro d u ce an o verwh elm in g n u m ber o f su scep t ible p est s (h et ero zygou s an d h om ozygou s) to every resistan t p est (Alstad an d An d ow 1995; NAS 2000). However, th is strategy is based on th e assu m p tion th at resistan ce to Bt co rn is a recessive t rait . In fact , resist an ce co u ld b e in h erit ed as an in co m p letely dom in an t au tosom al allele, in wh ich case, resistan ce in a p est p op u lation will grow m ore q u ickly th an an ticip ated (Hu an g et al. 1999). However, Hu an g an d oth ers (1999) observed th is gen etic d om in an ce at lower Bt d oses th an are delivered by h igh -dose Bt corn . Th ou gh in freq u en t, resistan ce to Bt toxin s h as been observed in wild lep id o p t eran p o p u lat io n s. Go u ld an d o t h ers (1997) rep o rt ed t h e freq u en cy o f resist an ce alleles in Heliothis virescens p o p u lat io n s at ab o u t 0.0015, an d Tabash n ik an d oth ers (1997) rep orted a freq u en cy of 0.120 in d iam on d back m oth p op u lation s. Pest resistan ce d evelop m en t is on e of m an y factors th at ad d s u n certain ty to th e p roblem of regu latin g Bt corn . Oth er u n certain ties m ay in volve h u m an h ealth effects from con su m p tion of th e Bt corn or from redu ction s in th e u se o f o t h er p est icid es, t h e d egree o f p est p ro t ect io n an d t h e resu lt in g co st savin gs, red u ct io n s in m yco t o xin d am age, h arm t o n o n t arget sp ecies, u n in -

188 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

ten d ed gen e tran sfer, an d th e p rice of corn (con ven tion al or Bt), am on g oth ers. Alt h o u gh n o t m an d at ed in t h e cu rren t ap p ro ach t o regist erin g GMO s, eco n o m ic an alysis p ro vid es a m et h o d t o co m bin e t h ese d isp arat e fact o rs at t h e co st o f in t ro d u cin g yet m o re u n cert ain t y asso ciat ed wit h t h e m o n et ary valu e of th e factors. Recen t ad van ces in d ecisio n m akin g u n d er co n d it io n s o f u n cert ain t y an d irreversible im p acts are th e basis of op tion s an alysis an d often take th e form of wh en to d elay takin g an action com p ared with actin g. Th e resu lt can be a d ifferen t d ecisio n crit erio n t h an t h at o f st an d ard co st –b en efit an alysis an d o n e t h at is co n sist en t wit h so m e o f t h e co n cern s o f p recau t io n ary p rin cip le advocates. In th e Bt corn ap p lication , u n certain ty is clearly p revalen t, bu t th e irreversibility is su bject to debate. Regardin g irreversibility, on ce com m ercial p lan tin gs of Bt corn are allowed, in th e sh ort term it m ay be d ifficu lt to reverse eith er th e im p acts or th e d ecision to rep lace trad ition al agricu ltu re. 1 In th e m ed iu m to lon ger term , th ere m ay b e regu lat o ry irreversib ilit ies, h u m an h ealt h im p act s, o t h er b io lo gical irreversibilit ies t h at in t h e ext rem e co u ld in clu d e ext in ct io n , an d eco n o m ic irreversibilit ies if so m e in p u t s u sed fo r o rgan ic farm in g beco m e in effect ive. Altern ative fram in gs of wh at is irreversible m ay exist, su ch as en viron m en tal im p acts (Farrow an d Morel 2001). Pest resistan ce h as th e p oten tial to affect several of th ese u n certain ties an d irreversib ilit ies, alt h o u gh it s ext en t will d ep en d o n h o w q u ickly resist an ce m ay develop , th e discou n t rate u sed to assess societal valu e of Bt corn over its t ech n o lo gical lifet im e, t h e rat e o f su b st it u t io n o f Bt even t s, t h e sp read o f resistan ce geograp h ically, an d th e reversibility of th e em ergen ce of resistan ce. Th e rem ain in g sect io n s o f t h is ch ap t er will d evelo p t h ese eco n o m ic ap p roach es, lin k th em to sp ecific issu es related to Bt corn , an d p relim in arily ad d ress t h e q u est io n o f wh et h er an o p t io n s an alysis wo u ld be likely t o p ro d u ce a d ifferen t recom m en d ation th an a stan d ard exp ected n et (ben efit less co st ) p resen t valu e an alysis, in wh ich p resen t valu e refers t o co m b in in g a stream of n et ben efits in to th e valu es of a p articu lar year.

Option Theory Op tion th eory was p rim arily d evelop ed in th e con text of fin an cial d ecision s, bu t it is in creasin gly clear th at it h as wid er ap p lication . Th is ch ap ter ap p lies th e op tion th eory p aradigm to th e regu latory decision of wh eth er to allow Bt corn to be com m ercially grown . Op tion th eory is n ot a m on olith ic p aradigm . It h as at least two variation s. Alth ou gh it is very im p ortan t to be aware of th eir d ifferen ces, th ese two version s can n ot be com p letely sep arated . On e of th ose ap p roach es is referred to as “real op tion s” (e.g., Dixit an d Pin d yck 1994). We will refer to th e oth er as

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 189

“rat io n al” o r “fin an cial o p t io n s” (e.g., Hu ll 2000). Real o p t io n t h eo ry is an op tim ization p rocedu re, an d ration al op tion th eory leads to th e Black–Sch oles form u la based on risk n eu trality.

Real Options

Th e real o p t io n t h eo ry ap p lies t yp ically t o irreversib le in vest m en t s u n d er u n cert ain t y. Assu m e o n e is m akin g an in vest m en t t h at will b e p ro d u ct ive (b en efit B) wit h a p ro b ab ilit y p an d u n p ro d u ct ive (lo ss L) wit h p ro b ab ilit y 1 – p: if th e in vestm en t is m ade im m ediately, its exp ected n et p resen t valu e is pB – (1 – p)L. Ho wever, if t h e in vest m en t is n o t m ad e u n t il it is revealed as p ro d u ct ive o r n o t an d t h e u n cert ain t y is co m p let ely reso lved , t h e exp ect ed n et p resen t valu e of th e sam e in vestm en t u n d er th at p olicy is pB (m in u s th e p ossible cost of waitin g). As lon g as th e cost of waitin g or of gath erin g ad d ition al in form ation is less th an th e d ifferen ce between th e n et p resen t valu es of th e two p olicies, delayin g th e decision to in vest is ben eficial. Th e differen ce is th e valu e of th e in form ation . 2 It is also th e valu e of th e op tion of waitin g. Th ere is a real op tion s form u lation of th e sam e in sigh t in con tin u ou s tim e: if I is th e cost of th e in vestm en t, an d V th e valu e of th e in vestm en t, assu m e t h at t h e valu e o f t h e in vest m en t fo llo ws a geo m et ric Bro wn ian m o t io n st o ch astic p rocess, as follows: dV = αV dt + σV dz

(1)

wh ere dt is a sm all in crem en t o f t im e an d dz is t h e in crem en t o f a Wien er p rocess. In words, th is m ean s th at th e valu e of th e in vestm en t in creases with tim e at an average rate α, bu t with a volatility of σ. Th e idea is to m axim ize th e d iscou n ted exp ected valu e of th e retu rn of th e in vestm en t an d , th erefore, is in depen den t of an y degree of risk aversion , th at is, to m axim ize F(V ) = E[e–ρt(V – I)] wh ere E is t h e exp ect at io n s o p erat o r. Th is is a p ro blem o f o p t im izat io n u n der u n certain ty. Th e solu tion is th at th e best policy depen ds on th e relative valu e of th e average rate of growth of V , α, an d th e discou n t rate ρ: 1. If α < 0, th e d ecision is n ow or n ever, as th e valu e of th e in vestm en t on ly decreases with tim e. 2. If α > ρ, t h e best p o licy is t o wait fo rever becau se t h e valu e o f F(V ) n ever stop s growin g. 3. Th e “in terestin g case” occu rs wh en 0 < α < ρ; th en th e best p olicy is to wait fo r t h e t im e wh en t h e valu e V o f t h e in vest m en t b eco m es larger t h an a critical valu e V *, su ch th at V* = Γ I

(2)

190 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

wh ere Γ is th e “p recau tion ary” m u ltip lier. Γ is th e resu lt of th e op tim ization an d is an in creasin g fu n ction of th e volatility σ an d th e oth er p aram eters of th e p roblem . It can be sh own to be greater th an or eq u al to on e, wh ich is its basic lin k to th e p recau tion ary p rin cip le (wh en th e volatility σ = 0, Γ = 1). Con sid er th e p rop erties of Γ an d h ow it relates to con cern s th at m otivate th e p recau tion ary p rin cip le. If th ere is n o u n certain ty (σ = 0), th en Γ eq u als on e, an d th e u su al econ om ic criterion (in vest if th e ben efit exceed s th e cost) ap p lies. As u n cert ain t y in creases, t h e m u lt ip lier in creases, an d a d ecisio n m aker is less likely to take action becau se th e observed valu e V is less likely to exceed V *. Scale is also im p ortan t. Th e larger th e irreversible costs I, th e larger th e ben efits m u st be as th e cost is m u ltip lied by th e p recau tion ary m u ltip lier Γ. Th erefore, we su ggest th at Γ can be u sed as an em p irical m easu re of p recau tion , a m easu re th at is associated with a m issin g ben efit valu e in a stan d ard econ om ic an alysis: th e op tion valu e of waitin g for m ore in form ation .

Rational Options

Th e m o re d o m in an t o p t io n p arad igm fo r assessin g t h e valu e o f an o p t io n d eterm in es a risk-n eu tral p ortfolio. Th e typ ical p roblem is to assess th e valu e of a bu y (call) or sell (p u t) op tion on a sh are of a stock with exercise tim e T som e tim e in th e fu tu re. Th e on e p ayin g for th e op tion of bu yin g or sellin g at t h e exercise t im e (fo r t h e agreed p rice) p ays fo r t h e righ t o f exercisin g t h e op tion wh en th e tim e com es. Th e on e wh o accep ts th e m on ey for th e op tion m u st co m p ly wit h t h e d ecisio n . Th e valu e o f t h e o p t io n is given b y t h e Black–Sch oles form u la: H (V , T ; t ) = V (t )ϕ (d1 ) − e − ρ t Iϕ(d2 )

(3)

In th at form u la, V (t) is th e valu e of th e sh are at tim e t, ρ is th e riskless rate of ret u rn , I is t h e exercise p rice (an alo go u s t o t h e irreversib le co st in t h e real op tion s p aradigm ), T is th e exercise tim e, an d ϕ (d ) =

d1 =

1 π

d

∫e

−x 2

dx

(4)

−∞

⎧⎪ ⎫⎪ ⎡ V (t ) ⎤ ⎛ σ2⎞ T − t )⎬ ( ⎥ + ⎜ρ + ⎨ Log ⎢ ⎟ 2 ⎠ ⎪⎭ ⎢⎣ I ⎥⎦ ⎝ σ (T − t ) ⎪⎩ 1

d2 = d1 − σ (T − t )

(5a)

(5b)

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 191

W h en derivin g th is form u la, V (t) is typ ically assu m ed to follow th e geom etric Bro wn ian m o t io n o f Eq u at io n 1. Th e average rat e o f gro wt h o f t h e sh are a does n ot ap p ear in th e Black–Sch oles form u la (Eq u ation 3). Th is reflects a fu n d am en tal featu re of th e form u la: it assu m es risk n eu trality based on a p ortfolio ap p roach in wh ich it is assu m ed th at th e valu e of th e p ortfolio ch an ges at t h e sam e rat e as t h e riskless b o n d , wh ich h ere is ρ. Th is is an im p o rt an t in sigh t b ecau se it p o in t s t o t h e fu n d am en t al d ifferen ce b et ween t h is ap p ro ach , wh ich is based o n t h e assu m p t io n o f risk n eu t ralit y, an d t h e real op tion s ap p roach , wh ich is an op tim ization . Th e precaution ary prin ciple was in voked to focus in terest on th e precaution ary m u ltip lier Γ in th e real op tion s an alysis. W h at abou t th e relevan ce of th e ration al option s th eory to th e precaution ary prin ciple? Th e in suran ce an alogy is m ean in gful. Wh en an in dividual decides to purch ase an in suran ce policy, h e or sh e m ay be viewed as proceedin g from a precau tion ary prin ciple, an d th e prem iu m of th e in su ran ce policy is com pu ted in a sim ilar way as a pu t option . In th at sen se, ration al option th eory provides a differen t quan titative fram in g of th e precaution ary prin ciple. Ration al option th eory is also particularly appropriate for risk m an agem en t because it is based on iden tifyin g a “risk-n eutral” strategy, th at is, a strategy th at in volves a level of risk com parable with a riskless in vestm en t. In th e case of Bt corn , som e m ay con sider th e riskless approach to be growin g n on Bt corn usin g con ven tion al pesticides (i.e., n ot com m ercializin g Bt corn ).

The Static Economic Core of Analyzing Bt Corn A stan dard cost–ben efit an alysis p roceeds by iden tifyin g variou s static im p acts o f an act io n . Th e n u m ero u s im p act s can b e asso ciat ed wit h cat ego ries o f ch an ge in econ om ic welfare (Zerbe an d Dively 1994). Th e drivin g com m ercial p u rp o se fo r t h e case at h an d is t h at Bt co rn p ro vid es p ro t ect io n again st t h e Eu ro p ean co rn b o rer. Th is p ro t ect io n can b e t h o u gh t o f as a t ech n o lo gical ch an ge th at redu ces th e cost of growin g a given level of th e com m odity. Su ch im p acts are well u n derstood in static cost–ben efit an alysis, wh ich we u se as a startin g p oin t before p roceed in g to th e d yn am ic an alysis associated with real op tion s. Th e areas A th rou gh G in Figu re 8-1 are associated with p arts of con su m er an d p ro d u cer su rp lu s in eit h er t h e befo re o r aft er co m m ercializat io n state of th e world . Table 8-1 id en tifies th e welfare im p acts com p arin g Bt an d t rad it io n al co rn , assu m in g in t h is figu re t h at t h e p rice fo r each co rn will be th e sam e (an assu m p tion relaxed in th e em p irical p ortion ). Static extern ality effects, su ch as th e p oten tial for m ycotoxin red u ction or for h arm to n on target sp ecies, are typ ically estim ated in dep en den tly of Figu re 8-1. Taken togeth er, th ese categories p rovid e th e static em p irical stru ctu re for estim atin g th e total valu e based on a com p arison of th e corn m arket an d its asso ciat ed ext ern alit ies wit h an d wit h o u t a p o licy allo win g t h e co m m ercial

192 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

S0 S1

Price

P0

P1

A B

C

D

E

F

G

Demand

Q0

Q1

Quantity FIGURE 8-1. Welfare Effects of Cost-Saving Technological Change TABLE 8-1. Welfare Impacts of Technological Change W elfare m easure Con su m er su rp lu s Produ cer su rp lu s Total su rp lu s

Traditional corn

Bt corn

Change in welfare

A B+E A+B+E

A+B+C+D E+ F+ G A + B + C + D + E+ F+ G

B+C+D F+ G – B F+ G + C + D

p ro d u ct io n o f Bt co rn . Th e t im e-d ep en d en t asp ect s o f t h e p ro b lem —p est resistan ce an d th e ch an ge in valu e—are discu ssed in th e followin g section s.

Option Theory Applied to the Decision To Permit Commercialization of Bt Corn In th is section , we adapt th e real an d th e ration al option fram ework to a regulatory decision on wh eth er to com m ercialize Bt corn . Th e algorith m s of both real

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 193

option th eory an d ration al option th eory depen d on th e dyn am ics of th e evolution of th e total value of Bt corn , but each algorith m is affected differen tly.

The Real Option Perspective

A fou n dation of th e option valu e, in con trast to stan dard cost–ben efit an alysis, is th e sp ecification of th e stoch astic d yn am ics of th e key variables. Th e first qu estion is wh at gen eral form sh ou ld be given to th e evolu tion of th e valu e of com m ercialized Bt corn . 3 Is it legitim ate to m od el it as a geom etric Brown ian m otion , as was th e case in ou r th eoretical discu ssion of th ese two p aradigm s? Geom etric Brown ian m otion for th e p resen t valu e of Bt com m ercialization gives dB = µBdt + ηBdz B

(6)

wh ere B rep resen t s t h e n et p resen t so cial valu e o f Bt co rn , t h e d rift µ rep resen t s t h e average gro wt h in valu e, an d t h e vo lat ilit y t erm η m easu res t h e u n certain ty. W h at do we kn ow abou t th e two p aram eters µ an d η? Un derlyin g th e drift p aram eter µ is th e evolu tion of th e total (con su m er p lu s p rod u cer) su rp lu s of corn . An alogou s to th e size of total su rp lu s in th e well-kn own d iam on d s an d wat er p arad o x in wh ich t o t al su rp lu s is larger fo r t h e go o d wit h t h e lo wer p rice, in recen t decades, we em p irically observed a con stan t or declin in g p rice of corn , in creasin g p rodu ction , an d an in creasin g total su rp lu s. W h at is good for th e con su m er is n ot n ecessarily good for th e farm er. We assu m e th at th e total su rp lu s in th e corn m arket evolved at th e sam e p ercen tage rate as total p rodu ction , in oth er words, th ere was a u n itary elasticity between p ercen tage ch an ges in p rod u ction an d p ercen tage ch an ges in total su rp lu s. Based on an an alysis of corn an d p rice p rodu ction tren ds,4 as U.S. p rodu ction is estim ated to be in creasin g at a rate of 2.4% p er year, we assu m e th at sam e valu e for th e growth p aram eter of total su rp lu s. Th is is strictly tru e on ly if th e two p rodu ction m eth ods h ave th e sam e fixed costs. In both cases (real an d ration al op tion s), th e volatility η p lays an im p ortan t role. In th e case of th e real op tion form u lation , it is a com p on en t of th e p recau tion ary m u ltip lier d eterm in in g h ow m u ch th e actu al valu e of th e p olicy sh ou ld be above its cost to ju stify takin g action .5 Th e stru ctu re of Eq u ation 6 p rovid es restriction s th at assist in th e estim ation of η. Estim ation of th is term h as been an im p ortan t issu e in th e fin an ce literatu re (Cam p bell et al. 1997), in wh ich th e varian ce of a variable su ch as B h as som etim es been su bstitu ted in correctly for th e in stan tan eou s varian ce of th e diffu sion p rocess. It can be sh own th at dB is log n orm ally distribu ted with a tim e-d ep en d en t varian ce. However, a varian ce-stabilizin g tran sform ation is

194 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

t h at o f d ln B, wh ich fo llo ws sim p le Bro wn ian m o t io n (Cam p b ell, Lo , an d ^ 2 can be based on th e sam MacKin ley 1997, 362) su ch th at th e estim ate of η p le varian ce of d ln B ∧2

η =

1 N

N

∑ ( d ln B − d ln B)2

(7)

n =1

A co st –b en efit m o d el t h at gen erat es a st o ch ast ic t im e series can t h en b e 2 u sed to con stru ct estim ates of d ln B an d to estim ate ^η from Eq u ation 7. 6 In gen eral, we will com p are th e n et p resen t social valu e from p lan tin g Bt corn in com p arison with cu rren t p rod u ction m eth od s (a m ixtu re of p esticid e ap p lication s an d ben ign n eglect). If P rep resen ts th e valu e of th e p resen t way of growin g corn , it too m ay evolve as geom etric Brown ian m otion based on th e growth in total su rp lu s. We th u s assu m e dP = γPdt + σPdz P

(8)

Correlation between th e stoch astic p rocesses for B an d P is also likely becau se m an y o f t h e sam e elem en t s o f weat h er an d d em an d affect t h em b o t h . It wo u ld be an t icip at ed t h at sh o cks in n et valu e cau sed by t h e Eu ro p ean co rn b o rer wo u ld b e red u ced fo r Bt co rn , alt h o u gh o t h er sh o cks su ch as p rice p rocesses an d sh ocks cau sed by extern al effects m ay be larger for Bt corn . Th u s Eq u at io n s 6 an d 8 rep resen t t h e d yn am ic evo lu t io n o f bo t h Bt an d t rad it io n al co rn p ro d u ct io n . In t h e em p irical ap p licat io n t h at fo llo ws, we assu m e th e rate of growth of both to be ap p roxim ately th e sam e, 2.5% (settin g µ eq u al to γ, see footn ote 4). Th e secon d d yn am ic issu e is p est resistan ce d evelop m en t. Th e real op tion fram ewo rk ad d resses t h e q u est io n o f wh en , if ever, t o act wh en co n fro n t ed with an irreversible d ecision u n d er u n certain ty. Th e rate of d evelop m en t an d spread of in sect resistan ce to Bt toxin s m ay be a large sou rce of u n certain ty an d som e of th e irreversibility. As th e su bleth al u se of an an tibiotic can select for bacteria resistan t to th at an tibiotic, on e predictable effect of growin g Bt corn is th e em ergen ce of pests resistan t to Bt toxin , a biological issu e described earlier. Th u s, growin g Bt corn h as th e poten tial to decrease th e am ou n t of tim e du rin g wh ich Bt can be u sed as a p esticid e. In creasin g resistan ce in trod u ces a sp atial an d t em p o ral lim it t o t h e efficacy o f Bt co rn (an d p o t en t ially t o t h e u se o f o t h er Bt fo rm u lat io n s). Bu t t h e t im e lim it it self is n o t kn o wn an d co u ld d ep en d on th e regu latory p olicy ad op ted . However, in ou r sim p lified m od el, we represen t th e developm en t of resistan ce to Bt as in stan tan eou s, u biqu itou s, an d irreversible, an ap p ro ach t h at wo u ld p ro vid e an u p p er bo u n d o n it s im p ortan ce in th e d ecision p rocess. For in stan ce, resistan ce is m ore likely to develop locally an d radiate th rou gh parts of th e corn growin g areas, ach ievin g a p atch y d istribu tion (Park et al. 2001). Fu rth erm ore, if resistan ce is d etected before it h as becom e widespread (for in stan ce by u sin g in sect resistan ce m on i-

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 195

torin g tech n iqu es), rem edial action s are available to slow or h alt th e spread of resistan t in sects (e.g., ch an ge in p esticid e regim en an d crop rotation ). Th u s, resistan ce wou ld n ot tru ly be u biqu itou s or n ecessarily persist irreversibly. Ou r ap p roach is to m odel th e in flu en ce of p est resistan ce on th e lifetim e of Bt corn as a form of “dep reciation ” (Dixit an d Pin dyck 1994, 200). Th at is, we assu m e th at th e stop p in g tim e wh en resistan ce is com p lete is ran dom an d follows a Poisson p rocess. If th e resistan ce h as n ot em erged at tim e T, we assu m e th at th ere is a p robability λdT th at th is will h ap p en du rin g th e n ext in terval of tim e dT. Th e p robability den sity fu n ction of su ch an even t, th erefore, is λe–λT with th e estim ated m ean rate of arrival7 of resistan ce (λ) eq u al to 1/ T. Th is is effectively a steady state m odelin g ap p roach th at ign ores th e tran sition states o f p art ial an d in creasin g resist an ce. It is as if t h e resist an ce ju m p s fro m n o resist an ce t o co m p let e resist an ce. Ho wever, t h is fo rm o f d ep reciat io n h as a m ath em atically eq u ivalen t effect on exp ected p resen t valu e, as wou ld geom etrically declin in g p rodu ctivity cau sed by gradu ally in creasin g resistan ce. We will n o w ch aract erize t h e real o p t io n s so lu t io n t o t h e d ecisio n o f wh et h er t o co m m ercialize Bt co rn , in clu d in g t h e ch aract erizat io n o f p est resistan ce develop m en t. In th e real op tion ap p roach , th e exp ression to m axim ize is t h e p ayo ff b et ween t h e so cial valu e o f gro win g Bt co rn (B) an d o f growin g con ven tion al corn (P):

[

]

F( B, P ) = E e −ρ t ( B − P)

(9)

Th e so lu t io n t o t h is m axim izat io n p ro blem is o u t lin ed in Ap p en d ix A. Th e resu lt is t h at t h e o p t im al t im e t o allo w fo r co m m ercializat io n o f Bt co rn o ccu rs wh en t h e so cial valu e o f Bt co rn an d t h e valu e o f t h e co n ven t io n al crop exceed th e th resh old relation sh ip β ⎛ B⎞* =Γ ⎜ ⎟ = ⎝ P⎠ β −1

(10)

Th is is a m odified cost–ben efit criteria, with β defin ed in Eq u ation 11 ⎛

β+ =

−⎜ µ − γ − ⎝

{η

2

η2 − 2 ξ ησ + σ 2 ⎞ ⎟ 2 ⎠

− 2 ξ ησ + σ 2

}

2

+

⎛ η2 − 2 ξ ησ + σ 2 ⎞ 2 2 ⎜µ − γ − ⎟ + 2 (ρ − γ ) η − 2 ξ ησ + σ 2 ⎝ ⎠

{η

2

− 2 ξ ησ + σ 2

{

}

}

(11)

196 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

Note th at th e d en om in ator is th e varian ce of th e d ifferen ce of two correlated ran d om variables with ξ d en otin g th e correlation . If dB an d dP are p erfectly co rrelat ed , an d t h eir vo lat ilit y is o f t h e sam e size, t h en it is as if t h e u n certain ty d isap p ears in th e ch oice between Bt an d n on -Bt corn an d th e p recau t io n ary m u lt ip lier ap p ro ach es 1. As n o t ed in Ap p en d ix A, β > 1 (an d h en ce th e p recau tion ary m u ltip lier Γ > 1) h olds as lon g as ρ > µ. W h ere does resistan ce ap p ear? If π is th e in stan tan eou s social valu e with Bt corn , th e exp ected p resen t valu e p rofit (Π) ign orin g resistan ce is

[

T

] ∫

E Π(T ) = e

− ρt

π(t )dt = π0

0

T

∫

[1 − e( ) ] µ −ρ T

µ −ρ t e( ) dt = π0

0

(ρ − µ )

(12)

Becau se we m o d eled t h e d ep reciat io n b y a Po isso n p ro cess, t h e p ro b ab ilit y den sity th at T will be th e du ration of th e p roject is λe–λT . Th e “valu e” B of th e p roject of growin g Bt corn takin g in to accou n t th e p oten tial for resistan ce is th en (u sin g Eq u ation 12) ∞

∫ [

]

B = E Π(T ) λe − λT dT = 0

π0

(ρ − µ ) + λ

(13)

W h en co m bin ed wit h t h e d ecisio n t h resh o ld fo r act io n o f Eq u at io n 10, t h e level of p recau tion (Γ) h as n ot ch an ged , alth ou gh th e m easu red cost–ben efit rat io (B/ P) is sm aller becau se o f in co rp o rat in g resist an ce. Th e p ro babilit y o f p assin g t h e t h resh o ld h as t h u s b een red u ced as in ferred fro m Eq u at io n 14 wh ere com m ercialization is allowed if ⎞ ⎛ B⎞* ⎛ π0 β =Γ ⎟⎟ > ⎜ ⎟ = ⎜⎜ ⎠ ⎝ β P −1 ⎝ (ρ − µ ) + λ P ⎠

{

}

(14)

The Rational Option Perspective

In th e altern ative ration al op tion ap p roach , th e decision to allow com m ercial p rodu ction of Bt corn can be viewed as p art of a “corn p rodu ction p ortfolio.” An oth er key com p on en t of th at p ortfolio is th e am ou n t of resou rces in vested in t h e cu rren t m et h o d o f p ro d u cin g co rn . In t h is ap p ro ach , t h e id ea is t o d eterm in e th e m ost p ru d en t way to m an age th e u n certain ty associated with th e exp loitation of Bt corn as an altern ative to n on -Bt corn . We assu m e “risk n eu trality” su ch th at th e total am ou n t of lan d in vestm en t in corn cu ltivation is con stan t. Con seq u en tly, we assu m e th at som e of wh at was in vested in n on -

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 197

Bt co rn is t ran sferred in t o Bt co rn an d “research .” Research is t h e p art su b tracted from th e origin al in vestm en t in corn th at is u sed to p rovid e in form ation on Bt corn su ch as th e develop m en t of p est resistan ce. By defin ition , th e am ou n t tran sferred in to Bt corn (W 1 ) an d research (W 3 ) balan ce th e red u ced am ou n t of n on -Bt corn (W 2 ). We u se t h e assu m p t io n o f “risk n eu t ralit y” t o gen erat e a m easu re o f t h e valu e o f t h e in vest m en t in research . Th is is m easu red b y t h e valu e o f t h e op tion of p lan tin g Bt corn . Th e resu ltin g lan d in vestm en t p ortfolio is assu m ed to in clu de th ree p rop ortion s: • W 1 of resou rces is in vested in growin g Bt corn , with m argin al valu e B(t) • W 2 is in vested in n on -Bt corn , with m argin al valu e P(t), an d • W 3 is in vested in research reflectin g th e sh ift from each of th e oth er categories. By defin ition , W 1 + W 2 + W 3 = 0. We write th e total corn p ortfolio as Π = W 1 B(t ) + W 2 P(t ) + W 3 H (t )

(15)

H(t) m easu res t h e m argin al valu e o f t h e o p t io n o f u sin g Bt co rn (recall Eq u ation 3). W h en H(t) is p ositive, it is ben eficial to com m ercialize Bt corn . Th e relative valu e of com m ercializin g Bt corn is eq u ivalen t to th e valu e of an op tion or con tin gen t claim . It dep en ds on th e valu e of B(t), P(t), an d T with T as th e “tim e h orizon ” or p lan n in g tim e. Risk n eu trality (th e key con strain t for a ration al op tion ) occu rs wh en th e corn p ortfolio is th e sam e with Bt corn as with ou t. It corresp on ds to dΠ = 0. Th e p lan n in g tim e T d ep en d s in large p art on h ow q u ickly p ests d evelop resistan ce to Bt corn . As will be seen in th e eq u ation s below, as T ap p roach es in fin ity, th e n et ben efits of Bt corn in crease relative to th e n et ben efits of con ven tion al (n on -Bt) corn . Th at is to say, th e lon ger we can delay p est resistan ce d evelo p m en t , t h e great er t h e n et p resen t valu e o f Bt co rn is in co m p ariso n with con ven tion al corn . Th e solu tion , wh ose derivation can be fou n d in Ap p en dix B, is H ( B, P, T ; t ) = B(t )ϕ(d2 ) − P(t )ϕ(d1 ) W h ere ϕ is defin ed as before, an d d1 =

⎧⎪ ⎡ B(t ) ⎤ T ⎥+ ⎨ Log ⎢ 2 T ⎩⎪ ⎢⎣ P(t ) ⎥⎦ 2

⎫⎪ ⎬ ⎭⎪

d2 =

⎧⎪ ⎡ B(t ) ⎤ T ⎥− ⎨ Log ⎢ 2 T ⎪⎩ ⎢⎣ P(t ) ⎥⎦ 2

⎫⎪ ⎬ ⎪⎭

1

1

(16)

198 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

wh ere T is t h e cu m u lat ive u n cert ain t y o ver t im e (see also Ap p en d ix B). Nam ely τ

T =

∫ [σ

2

] [

]

− 2 ξση + η2 ds = σ 2 − 2 ξση + η2 τ = ψ 2 τ

0

A few rem arks are in order: • If t h ere were n o u n cert ain t y (ψ2 = 0), t h e eq u at io n wo u ld read :8 H(B, P, T ; t) = B(t) – P(t). Th e valu e o f d eregu lat in g Bt co rn wo u ld be d irect ly t h e d ifferen ce b et w een t h e valu e o f Bt co rn an d t h e valu e o f t h e co n ven t io n al co rn . • d2 an d d 1 are in verted with resp ect to th e Black–Sch oles form u la. Th e m ath em atical origin of th e differen ce is exp lain ed in Ap p en dix B. • Th e m ain reason wh y H(B, P, T; t) ≠ B(t) – P(t) is becau se of th e u n certain ties or risks associated with Bt corn . Th e valu e of Bt corn h as to be sign ifican tly larger th an th e valu e of con ven tion al corn to ju stify its registration for com m ercial u se. • To ju stify a regu latory action to com m ercialize Bt corn , th e valu e of Bt corn m u st be above a certain critical valu e B*, wh ich corresp on ds to H = 0. B(t) ≥ B* = P(t)[ϕ(d2 )]/ [ϕ(d 1 )]

(17)

• B* dep en ds on th e stop p in g tim e T. Th e sm aller th e T or th e larger th e B*, th e m ore difficu lt it is to ju stify allowin g com m ercialization of Bt corn . If T → ∞, th e con dition becom es B(t) ≥ B* = P(t). However, in th e h igh stoch ast icit y regim e d escribed as fo llo ws, if T gro ws, t h e valu e o f Bt co rn always b eco m es n egat ive. Th is m ean s t h at wh en t h e u n cert ain t ies o f t h e risks associated with Bt corn are large in a very sp ecific, q u an titative sen se, a regu latory decision to com m ercialize it is n ot a good ch oice. To elab o rat e o n t h is p o in t : t h e valu e o f H is st ro n gly d ep en d en t o n t h e valu e of T. W h en th e p lan n in g h orizon can be m ad e large (i.e., in th e lim it wh ere resist an ce can be co n t ro lled ) t wo scen ario s h ave t o be d ist in gu ish ed , d ep en d in g on th e sign of γ – (ψ2 / 2). If γ – (ψ2 / 2) > 0, in th e lim it T → ∞, d 1 = d 2 → ∞ an d H(B, P, T; t) = B(t) – P(t). Bu t if γ – (ψ2 / 2) < 0, in th e lim it T → ∞, d 1 → +∞ an d d 2 → –∞, m ean in g th at even tu ally H(B, P, T; t) ≤ 0 an d th at it is n ot d esirable to com m ercialize Bt corn . Th e in terp retation of th at resu lt p oin ts to an im p ortan t m ean in g of op tion th eory. Th e case γ – (ψ2 / 2) < 0, corresp on d s to th e case with large u n certain ty. We assu m e th at we “kn ow” h ow th e valu e o f B(t) an d P(t) will evo lve wit h u n cert ain t y. Wit h in t h o se assu m p t io n s, we com p u te u n d er wh ich con d ition s H(B, P, T; t) > 0. As lon g as th is con d ition is

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 199

filled , th ere is an exp ected ben efit (u n d er th e assu m p tion of risk n eu trality) th at d eregu latin g Bt corn is ad van tageou s. Bu t becau se of th e large size of th e u n certain ty, th e tim e h orizon is sh orten ed . It is on ly to th e exten t th at on e is com fortable u sin g a p lan n in g h orizon sh ort en ou gh to m ake H(B, P, T; t) > 0 th at allowin g Bt corn is a p ru d en t p olicy in th e case of large stoch asticity. Th is d ich o t o m y is illu st rat ed in Figu re 8-2, wh ich sh o ws a grap h o f t h e valu e of th e op tion H(T) as a fu n ction of T, for d ifferen t levels of th e stoch asticity. Th e d ifferen t cu rves corresp on d to d ifferen t valu es of th e p aram eter ψ2 . A sm all valu e of ψ2 corresp on d s to th e low stoch asticity regim e in wh ich H is p ositive an d grows slowly with T. In th e h igh stoch asticity regim e, H ten d s to be n egative. In fact, from an econ om ic p oin t of view, th e valu e of th e op tion of Bt corn seem s t o b e m o re sen sit ive t o t h e size o f t h e risk t h an t o t h e len gt h o f t h e stop p in g tim e. Th is p oin ts to th e n atu re of th e ration al op tion : it is a tool for risk m an agem en t so it sh ou ld n ot be a su rp rise if th e resu lt is m ore sen sitive to th e risk th an to th e stop p in g tim e.

Empirical Application: Whether To Commercialize Bt Corn Does th e th eory of th e precedin g section m atter in em pirical application ? In th is section , we in vestigate som e of th e m ajor u n certain com p on en ts of th e social value of Bt corn . From th is partial an alysis, we seek to in fer wh eth er it is em pirically fruitful to pursue th e application of option s an alysis in a policy settin g.

0.4

H

0.05

Low Stochasticity Regime

0.2

T 10 –0.2

15

20

25

30 High Stochasticity Regime

–0.4

FIGURE 8-2. Values of the Rational Option H as a Function of the Stopping Time T

200 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

Th e p o licy q u est io n we in vest igat e t o o k p lace in t h e m id -1990s: Fro m a social p ersp ective, sh ou ld govern m en t p olicym akers allow Bt corn to be com m ercially p lan ted at all (refu ge p rop ortion of 1) or with a refu ge area of 20%? Th e latter p olicy was ad op ted . We u se in form ation as of 2001 in th is illu strat ive an alysis so t h e resu lt is n o t a t est o f t h e co rrect d ecisio n in t h e 1990s, wh ich h ad a differen t in form ation base. Nor do we q u an tify all im p acts h ere. We d efin e th e “with ap p roval” case to be th e fu ll d iffu sion of Bt corn to th e lim it p rescribed by regu lation , 80% of p lan ted area. As a con seq u en ce of th ese lim it at io n s, t h e resu lt s are m erely illu st rat ive o f t h e p o t en t ial q u an t it at ive valu e in ap p lyin g an op tion s ap p roach to p olicy q u estion s. Th e an alysis p ro ceed s u sin g t h e real o p t io n s ap p ro ach t o o b t ain an est im ate of Γ, th e p recau tion ary m u ltip lier, to determ in e if th e econ om ically “recom m en ded” decision differs from th at of stan dard cost–ben efit an alysis. First, key elem en ts of th e social valu e of Bt corn an d tradition al corn are estim ated based on a literatu re su rvey an d sim u lation m eth ods to in corp orate statistical d ist rib u t io n s o f u n kn o wn variab les. Th e gro wt h p aram et ers, vo lat ilit y, an d correlation p aram eters are th en in corp orated or estim ated an d u sed in Eq u ation s 11 an d 10 to estim ate Γ. Th e ben efit an d cost categories, th eir th eoretical m easu re, an d a su m m ary of th eir em p irical m easu rem en t are p resen ted in Table 8-2 (ad d ed d etail is in Ap p en dix C). Th e resu lts of sim u latin g th e illu strative n et social valu e from Bt an d cu rren t corn growin g p ractices (n on -Bt) are su m m arized in Table 8-3. Colu m n 1 iden tifies th e growin g m eth od (wh ich im p licitly is th e size of th e refu ge), colu m n 2 rep o rt s t h e m ean o f t h e p resen t valu e o f each m et h o d (B an d P). A stan dard cost–ben efit an alysis, n otin g th e p relim in ary an d in com p lete n atu re of th e resu lts, wou ld com p are th e exp ected valu e of th e ben efits from u sin g Bt corn with a refu ge req u irem en t of 20% to th e exp ected ben efits from growin g n on -Bt corn . Th e social exp ected n et p resen t valu e of Bt corn , wh eth er with or with ou t m o d elin g resist an ce (ro ws t wo an d t h ree) is larger t h an t h e so cial exp ect ed valu e of trad ition al corn . In corp oratin g resistan ce h as relatively little im p act becau se th e base level of p rodu cer su rp lu s is u n ch an ged as farm ers can revert to cu rren t p ractice (n otin g th at th e effect on organ ic agricu ltu re is n ot in corp orated). Based on th ese illu strative data an d u sin g stan dard exp ected valu e criteria, th e com m ercialization of Bt corn sh ou ld h ave been allowed, a con clu sion th at is som ewh at stron ger if th e an alyst ign ores resistan ce. In con trast, th e p recau tion ary m u ltip lier Γ is rep orted in colu m n 3 with a valu e of 1.83. A d ecision ru le th at in corp orates u n certain ty based on real op tion s wou ld reject a regu latory decision to allow com m ercial p lan tin g of Bt corn becau se th e ben efits do n o t exceed 1.83 t im es t h o se o f n o n -Bt co rn . Co n seq u en t ly, t h e d ecisio n fo r

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 201

TABLE 8-2. Summary of Benefit and Cost Categories, M easurement, and Parameters Category

Bt or Non-Bt (N)

Theoretical m easure

Em pirical m easure*

Benefit Produ cer su rp lu s

N

Ch an ge in Bt con su m er an d p rodu cer (total) su rp lu s In itial con su m er N, Bt su rp lu s Oth er: p esticide Bt exp osu re avoided, m ycotoxin dam age redu ced

B + E of Figu re 8-1 F+G +C +D of Figu re 8-1

A of Figu re 8-1 Hu m an h ealth an d an im al risk avoided

Op eratin g p rofit (reven u es less cash exp en ses) Cost savin gs becau se of Bt corn , som e cap tu red by Bt corn p rodu cer Assu m ed p rop ortion al to social valu e so can cels in Eq u ation 10 Not in clu ded

Cost Pest resistan ce

Bt

Extern ality Extern ality Extern ality

Poisson arrival rate 1/ T wh ere T dep en ds on refu ge size Ben efit tran sfer from En glish valu e for n on u se valu e Not estim ated Allergen icity for Bt Not estim ated

Bt

Refu ge p rop ortion

0.2 as im p lem en ted

Bt, N

Op p ortu n ity cost

7% real from th e Office of Man agem en t an d Bu dget

Growth p aram eters Volatility

Bt (µ), N (γ) Bt (η), N (σ)

Percen tage growth Eq u ation 12

Correlation

Bt, N

2.5% from p rodu ction data Estim ated as sam p le varian ce of d ln X . Estim ated as correlation of dBt, dN.

Im p act on Bt, N n on target sp ecies Mycotoxin dam age N Hu m an h ealth Bt, N Oth er: h orizon tal Bt gen e tran sfer from m arker or oth er gen e; su bstitu tion ; cost to organ ic agricu ltu re if Bt n o lon ger effective; system disru p tion

Dep reciation Extern ality

Other param eters Regu latory altern ative Discou n t rate r

E(dz Bdz P)/ dt

*See Ap p en dix C for detail, m ost m easu red with u n certain ty u sin g statistical distribu tion s.

202 • Chapter 8: Resistance, the Precautionary Principle, and Regulation Table 8-3. Real Option Precautionary M ultiplier and Partial Net Present Social Value Growing m ethod, resistance Bt, λ = 0.083 Bt, λ = 0 (n o resistan ce) P (n on -Bt)

Mean

Precautionary m ultiplier Γ

$132 billion $136 billion $127 billion

1.83

Note: Th ese n u m bers are for illu stration an d are n ot su fficien tly develop ed for p olicy decision s.

action wou ld be reversed, an d th e recom m en dation wou ld be n ot to com m ercialize Bt co rn . Alt h o u gh n o t rep o rt ed in d et ail h ere becau se o f t h e p relim in ary n at u re o f t h e resu lt s, t h e relat ively sm all p recau t io n ary m u lt ip lier is cau sed by a h igh co rrelat io n bet ween o u t co m es fo r Bt an d n o n -Bt co rn an d becau se th e estim ated size of th e volatilities are sim ilar. Had an op tion s an alysis been carried ou t th at ign ored th e u n certain ty in growin g n on -Bt corn , th e m u ltip lier wou ld h ave been su bstan tially h igh er bu t on ly as a resu lt of om ittin g th e u n certain ty with wh ich farm ers already con ten d. Th ese illu st rat ive resu lt s are m ean t m erely t o co n vey t h e p o ssib ilit y o f a regu lat o ry reversal. Kn o wn effect s are o m it t ed fro m t h e calcu lat io n s, an d t h o se t h at are in clu d ed wo u ld b en efit fro m refin em en t b efo re an y act u al ap p lication to p olicy. W h at we believe h as been d em on strated is th e u sefu ln ess o f ap p lyin g an o p t io n ap p ro ach t o regu lat o ry d ecisio n m akin g an d t h e p o t en t ial, in t h is p ro b lem , fo r a d ifferen t reco m m en d at io n b ased o n eco n o m ic crit eria. A q u an t it at ive m easu re o f p recau t io n can be co m p u t ed , an d d ecisio n s m ay ch an ge d ep en d in g o n it s valu e. In t h is illu st rat io n , based o n actu al bu t in com p lete d ata an d an alysis, it ap p ears worth wh ile to in vestigate fu rth er th e em p irical an alysis of p recau tion .

Conclusion Bt co rn is an exam p le o f h o w a n ew t ech n o lo gy can creat e a co m p lex an d u n certain situ ation for p olicym akers in volvin g a variety of costs an d ben efits. Po licym akers sh o u ld n o t au t o m at ically reject t h e o p p o rt u n it ies o ffered b y su ch n ew p rodu cts n or sh ou ld th ey ign ore p ossible costs. Am on g th e m an y qu estion s raised by th e issu e of com m ercializin g Bt corn , two were ad d ressed th rou gh th e fram ework of op tion th eory as an exten sion of cost–ben efit an alysis. Both qu estion s stem from th e sam e origin : plan tin g Bt corn am ou n ts to releasin g a n ew biological agen t. It is alm ost certain to trigger som e n on trivial reaction from th e en viron m en t. On e qu estion is th e likely creation of pest resistan ce to th e toxin s produ ced by Bt corn . Th is even tu ally will

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 203

sign al t h e en d o f t h e u sefu ln ess o f p art icu lar variet ies o f Bt co rn . Th e seco n d qu estion is a set of u n certain im pacts su ch as th ose on n on target species. Seen from a n orm ative p oin t of view, th e p roblem raised by resistan ce an d ext ern alit ies is a case o f o p t im izin g t h e t im e t o co m m ercialize t h e p ro d u ct u n d er u n certain ty an d irreversibility. Th is stron gly p oin ts to th e relevan ce of t h e real o p t io n t h eo ry. We h ave sh o wn t h at (a) real o p t io n t h eo ry can b e ap p lied em p irically to regu latory p roblem s, an d (b) th e resu lts m ay differ from th ose of a stan dard cost–ben efit an alysis. A related con cern for p olicym akers d ealin g with th e u se of a n ew an d revolu tion ary tech n ology is balan cin g th e ben efit of th e n ew tech n ology with its risks. Alth ou gh related to th e real op tion op tim ization fram ework, th is is a differen t p roblem . In th is form u lation , th e econ om ic p roblem is on e of risk m an agem en t. Th e ration al op tion th eory req u ires th at th e larger th e u n certain ty of th e ou tcom e is, th e m ore Bt corn m u st p rove su p erior to con ven tion al corn to ju stify its u se. Both real an d ration al op tion fram in g can be u sed com p lem en tarily as th ey em p h asize differen t facets of th e p roblem . Both p aradigm s can be in t erp ret ed as co n t ain in g elem en t s o f t h e p recau t io n ary p rin cip le, as t h ey an swer th e q u estion , “With u n certain ty an d p oten tially large irreversible risks, h o w lo n g a d elay, if an y, in co m m ercializin g Bt co rn is ju st ified b ased o n it s exp ected valu e to th e econ om y?” Man y issu es rem ain for fu rth er research : (a) im p roved sp atial an d tem p oral ch aract erizat io n o f t h e d evelo p m en t o f resist an ce, (b ) t h e in co rp o rat io n o f en d o gen o u s in fo rm at io n an d d ecisio n p h ases in t o t h e o p t io n ap p licat io n , (c) refin em en t of th e em p irical evalu ation of im p acts, (d) con sideration of altern ative fram in g of wh at is irreversible, an d (e) em p irical im p lem en tation of th e ration al op tion ap p roach . In con clu sion , we believe th at th e op tion s fram ework yields both a th eoretical an d an em p irical ap p roach to th e p recau tion ary p rin cip le, p roblem s related t o p est resist an ce, an d t h e regu lat o ry d ecisio n s su rro u n d in g t h e ad o p t io n o f n ew an d u n certain tech n ologies.

Acknowledgements For in sigh tfu l com m en ts, we th an k Ch ris Gilligan , Klaas van t Velt, an d sem in ar p art icip an t s at t h e Reso u rces fo r t h e Fu t u re Co n feren ce o n t h e Eco n o m ics o f An tibiotic an d Pest Resistan ce; th e Association of En viron m en tal an d Resou rce Econ om ists 2001 Su m m er worksh op ; an d th e North Carolin a Ben efits Tran sfer worksh op . Su p p ort was p rovid ed by th e EPA Star Fellowsh ip Program . Gen eral fu n d in g was p ro vid ed t o t h e Cen t ers fo r t h e Hu m an Dim en sio n s o f Glo b al Ch an ge an d t h e St u d y an d Im p ro vem en t o f Regu lat io n at Carn egie Mello n Un iversity.

204 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

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Chapter 8: Resistance, the Precautionary Principle, and Regulation • 205 Min or, H.C., C.G. Morris, H.L. Mason , D.R. Kn err, R.W. Hasty, G.K. Stafford , an d T.G. Fritts. 1999. Corn: 1999 Missouri Crop Perform ance. Un iversity of Missou ri-Colu m bia Sp ecial Rep ort 521. Colu m bia, MO: Un iversity of Missou ri-Colu m bia. Mou rato, S., E. Ozdem iroglu , an d V. Soster. 2000. Evalu atin g Health an d En viron m en tal Im p acts of Pesticide Use. Environm ental Science and Technology 34(8): 1456–61. NAS (Nation al Academ y of Scien ces). 2000. Genetically Modified Pest-Protected Plants: Science and Regulation. Wash in gton , DC: Nation al Academ y Press. Ostlie, K., W. Hu tch ison , an d R. Hellm ich . 1997. Bt Corn and European Corn Borer, NCR p u blication 602. St. Pau l, MN: Un iversity of Min n esota. Park, A.W., S. Gu bbin s, an d C.A. Gilligan . 2001. In vasion an d Persisten ce of Plan t Parasites in a Sp atially Stru ctu red Host Pop u lation . Oikos 94: 1–13. Pim en t el, D., an d P. Raven . 2000. Bt Co rn Po llen Im p act s o n No n t arget Lep id o p t era: Assessm en t of Effects in Natu re. Proceedings of the National Academ y of Sciences of the USA 97(15): 8198–9. Rogers, M.D. Forth com in g. Gen etically Mod ified Plan ts an d th e Precau tion ary Prin cip le. Journal of Risk, Decision, and Policy. Slade, M. 2001. Valu in g Man agerial Flexibility: An Ap p lication of Real Op tion Th eory to Min in g In vest m en t . Journal of Environm ental Econom ics and Managem ent 41(2): 193–233. Tabash n ik, B., Y.B. Liu , N. Fin son , L. Masson , an d D.G. Heckel. 1997. On e gen e in Diam on d back Moth Con fers Resistan ce to Fou r Bacillus thuringiensis Toxin s. Proceedings of the National Academ y of Sciences of the USA 94: 1640–4. Tolley, G., D. Ken kel, an d R. Fabian . 1994. Valuing Health for Public Policy. Ch icago: Un iversity of Ch icago Press. USDA (U.S. Dep artm en t of Agricu ltu re). 1997a. 96-079-2 Dekalb Gen etics Corp .; Availab ilit y o f Det erm in at io n o f No n regu lat ed St at u s fo r Gen et ically En gin eered Co rn h ttp :/ / www.ap h is.u sd a.gov/ p p d / rad / Old Ru les/ 96-079-2.f (accessed Febru ary 2001). ———. 1997b. 96-095-2 Mon san to Co.; Availability of Determ in ation of Non regu lated St at u s fo r Gen et ically En gin eered Co rn . h t t p :/ / www.ap h is.u sd a.go v/ p p d / rad / OldRu les/ 96-095-2.f (accessed Febru ary 2001). U.S. EPA (U.S. En viro n m en t al Pro t ect io n Agen cy). 2001. Bio p est icid es Regist rat io n Act io n Do cu m en t : Bacillus thuringiensis Plan t -In co rp o rat ed Pro t ect an t s, 2001. h ttp :/ / www.ep a.gov/ p esticides/ biop esticides/ reds/ brad_bt_p ip 2.h tm (accessed March 13, 2002). U.S. EPA/ USDA (U.S. Dep art m en t o f Agricu lt u re). 1999. Wo rksh o p o n Bt Cro p Resist an ce Man agem en t , h eld Ju n e 18, 1999. h t t p :/ / www.ep a.go v/ p est icid es/ biop esticides/ oth erdocs/ btcorn p roceedin gs.h tm (accessed March 13, 2002). ———. 2001. EPA Bio p est icid es Regist rat io n Act io n Do cu m en t : Bacillu s t h u rin gien sis Plan t -In co rp o rat ed Pro t ect an t s. h t t p :/ / www.ep a.go v/ p est icid es/ bio p est icid es/ red s/ brad_bt_p ip 2.h tm (accessed Novem ber 3, 2002). Wien er, J.B. Forth com in g. Precau tion in a Mu lti-Risk World . In The Risk Assessm ent of Environm ental and Hum an Health Hazards, Secon d Edition , edited by Den n is Pau sten bach . New York: Joh n Wiley & Son s. Zerbe, R., Jr., an d D. Dively. 1994. Benefit-Cost Analysis in Theory and Practice. New York: Harp er Collin s College Pu blish ers.

206 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

Appendix A: Real Option Approach with Two Uncertain Variables* dB = µBdt + ηBdz B dP = γPdt + σPdz P Let x = B/ P. Use Ito’s Lem m a an d d efin e ξ as th e correlation between th e two stoch asticities, E[dz p dz B] = ξ dt. We are in terested in F(B, P) = E[e–ρt (B – P)]. Let B⎞ ⎛B ⎞ ⎛ Ph ⎜ x = ⎟ = F( B, P) = PE[ e − ρt ⎜ − 1⎟ ] ⎝P ⎠ ⎝ P⎠ Altern atively, B ⎞ F( B, P) ⎛ h ⎜x = ⎟ = = E[ e − ρt ( x − 1)] ⎝ P⎠ P ∂x ⎧ ∂F ⎪ ∂B = Ph' ( x ) ∂B = h ' ( x ) F( B, P) = Ph ( x ) ⇒ ⎨ ∂F ∂x ⎪ = Ph' ( x ) = h ( x ) − xh' ( x ) ∂P ⎩ ∂P Th e Bellm an eq u at io n fo r t h is p ro b lem , aft er d efin in g dF u sin g It o ’s Lem m a, is dF = 0, ⎧η2 x 2 h '' ( x ) − 2 ξ ησx 2 h '' ( x )⎫⎪ ⎬=0 2 2 ⎪⎩+ σ x h '' ( x ) ⎪⎭

(γ − ρ)h ( x ) + (µ − γ ) xh ' (x ) + 21 ⎪⎨

(A1)

Th is is a p artial differen tial eq u ation for h, with bou n dary con dition s h ( x *) = x * −1

(A2)

h ' ( x *) = 1

A n atu ral form as a solu tion of Eq u ation A1 is h(x) = Ax β Su bstitu tin g in Eq u ation A1 leads to th e q u adratic eq u ation for β: γ − ρ + β(µ − γ ) + β(β − 1)

{

}

1 2 η − 2 ξησ + σ 2 = 0 2

* See also Dixit an d Pin dyck 1994, 207–11.

(A3)

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 207

wh ere t h e last t erm o n t h e righ t is id en t ifiable as t h e varian ce o f t h e d ifferen ce of two ran dom variables with correlation ξ. Th e solu tion s are as follows:

β± =

⎛ η2 − 2 ξ ησ + σ 2 ⎞ −⎜ µ − γ − ⎟ 2 ⎝ ⎠

{η

2

− 2 ξ ησ + σ 2

}

2

⎛ η2 − 2 ξ ησ + σ 2 ⎞ 2 2 µ γ − − ⎜ ⎟ + 2 (ρ − γ ) η − 2 ξ ησ + σ 2 ⎝ ⎠

±

{η

2

− 2 ξ ησ + σ 2

{

}

}

Th e p rodu ct of th e two roots is n egative wh en ρ > γ. Th erefore, u n der th at co n d it io n , o n e is p o sit ive, an d o n e is n egat ive. It can b e sh o wn t h at β+ > 1 req u ires ρ > µ. Th is con dition is iden tical to th e case in wh ich th ere is on ly on e stoch astic variable. Usin g Eq u ation A-3, th e bou n dary con dition s becom e A( x *) = x * −1 β

βA( x *)

β −1

= 1 ⇒ A( x *)

β

⎫ x* β ⎪ = x * −1 ⇒ x * = x*⎬ ⇒ β β −1 = β ⎪⎭

Appendix B: Rational Option Approach As in Ap p en dix A, dB = µBdt + ηBdz B dP = γPdt + σPdz P ξ is th e correlation between th e two stoch asticities, th at is, E[dz p dz B] = ξ dt. H(t), t h e valu e o f t h e o p t io n t o in vest in t h e p ro gram , is a d erivat ive o f t h e valu e of B(t) an d P(t). Th at is, u sin g th e eq u ation s above an d Ito’s Lem m a

dH =

⎧⎪ 1 ∂H ∂H dP + ⎨ dB + ∂P ∂B ⎪⎩ 2

⎤ ∂H ⎫⎪ ⎡ ∂2 H 2 2 ∂2 H 2 2 ∂2 H σ P + 2ξ ησBP ⎥ + ⎢ 2 η B + ⎬dt 2 ∂B∂P ∂P ⎥⎦ ∂t ⎪⎭ ⎢⎣ ∂B

(B1)

Eq u ation B1 can be written dH = βdt + δdz B + εdz P H

(B2)

208 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

Im p lyin g βH =

1 2

⎡ ∂2 H 2 2 ∂H ∂H ∂2 H 2 2 ⎤ ∂H ∂2 H + γP + µB ησBP + σ P ⎥+ ⎢ 2 η B + 2ξ 2 ∂P ∂ ∂ ∂ ∂ B t B P ∂ ∂ P B ⎥⎦ ⎢⎣

(B3a)

∂H ηB ∂B ∂H εH = σP ∂P

δH =

(B3b)

By defin ition of W 1 , W 2 , an d W 3 , W 1 + W 2 + W 3 = 0.

(B4)

Th e valu e of th is “p rogram p ortfolio” Π is affected by th e relative ch an ges in th e valu es of th e exp ected reven u e B(t) an d in vestm en t P(t). d Π = W1

dB dP dH +W2 +W3 B P H

(B5)

Risk n eu trality occu rs wh en dΠ = 0.

(B6)

Eq u ation s B2, B4, an d B5 lead to

[

]

[

0 = dt (µ − γ )W 1 + (β − γ )W 3 + dz B ( ηW 1 + δW 3 ) + dz P (ε − σ )W 3 − σW 1

]

wh ich in fact tran slates to th ree eq u alities

[(µ − γ )W + (β − γ )W ] = 0 1

3

(ηW 1 + δW 3 ) = 0 (ε − σ)W 3 = σW 1

(B7)

Th e eq u ation s in B7, in tu rn , lead to th e relation s ε W 1 (β − γ ) δ = = =1− σ W 3 (µ − γ ) η

(B8a)

∂H δ ε ∂H =1− ⇔ B +P =H ∂B ∂P η σ

(B8b)

− Eq u ation B8a im p lies

If we assu m e th at

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 209

H ( B, P) P

B⎞ ⎛ = h ⎜x = ⎟ ⎝ P⎠

(B9)

Th is im p lies ∂H ∂h ∂x ∂h =P = ∂B ∂x ∂B ∂x ∂2 H ∂ ∂h ∂ 2 h ∂ x 1 ∂ 2 h = = = 2 ∂B ∂x ∂ x 2 ∂ B P ∂ x 2 ∂B ∂H ∂ = [ Ph ] = h + P ∂∂Ph = h + P ∂∂hx ∂∂Px = h − x ∂∂hx ∂P ∂P ∂2 H x ∂2 h =− ∂B∂P P ∂x 2 2 ∂ H ∂ ⎡ ∂h ⎤ ∂h ∂x ∂h ∂2 h ∂x x 2 ∂2 h = −x 2 − = h−x = ⎥ ⎢ 2 ∂P ⎣ ∂x ⎦ ∂P ∂P ∂x P ∂x 2 ∂P ∂x ∂P Eq u ation B8b is au tom atically satisfied. If x = B/ P, u sin g Ito’s Lem m a 2 ⎤ ∂x ∂x ∂2 x ∂2 x 1⎡ 2 2 ∂ x dP + dB + ⎢ η2 B2 BP P ξ ησ σ + + 2 ⎥dt ∂P ∂B ∂B∂P 2 ⎢⎣ ∂B 2 ∂P2 ⎥⎦ ⎡ ∂x σ 2 P2 ∂2 x ⎤ ∂x η2 B2 ∂2 x ∂2 x dx = ⎢ γP + µB + + ξησBP + ⎥dt 2 ∂B ∂B∂P 2 ∂B 2 ∂P2 ⎥⎦ ⎢⎣ ∂P ∂x ∂x + σP dz P + ηB dz B ∂P ∂B dx = − γ + µ − ξησ + σ 2 dt − σdz p + ηdz B x

dx =

[

(B10)

]

Eq u ation B3a becom es ⎡ ∂2 H 2 2 ∂H ∂H ∂2 H 2 2 ⎤ ∂H ∂2 H + γP + µB ησBP + σ P ⎥+ ⎢ 2 η B + 2ξ 2 ∂P ∂ ∂ ∂ ∂ B t B P ∂ ∂ P B ⎥⎦ ⎢⎣ ⎤ ∂h ⎤ ∂h 1⎡ ∂h ∂2 h ∂2 h ∂2 h ⎡ + γP ⎢h − + µB βPh = ⎢η2 xB 2 − 2 ξ 2 ησBx + 2 σ 2 x 2 P ⎥ + P ∂x ⎥⎦ ∂x 2 ⎢⎣ ∂t ∂x ∂x ∂x ⎣ ⎥⎦

βH =

1 2

⎡

2

2

2

⎤

⎢⎣

∂x

∂x

∂x

⎥⎦

(B11)

(β − γ )h = 21 ⎢η2 x 2 ∂ h2 − 2 ξ ∂ h2 ησx 2 + ∂ h2 σ 2 x 2 ⎥ + ∂∂ht + (µ − γ )x ∂∂hx Th e relat io n [(β – γ)/ (µ – γ)] = δ/ η im p lies (µ – γ)B(∂H/ ∂B) + γH = βH. Th is, in tu rn , im p lies

210 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

(β − γ )Ph = (µ − γ )B ∂∂hx ⇒ (β − γ )h = (µ − γ )x ∂∂hx

(B12)

Eq u ation B12 su bstitu ted in to Eq u ation B11 leads to 0=

[

]

∂2 h ∂h x 2 2 ∂2 h ∂h x2 2 + η − 2 ξησ + σ 2 ψ = + 2 2 ∂x 2 ∂t ∂x 2 ∂t

(B13)

wh ere

[

ψ 2 = η2 − 2 ξησ + σ 2

]

To in tegrate Eq u ation B13, we defin e t

(

T = ψ 2 ( s)ds ⇒ dT = ψ 2 (t )dt

∫

)

0

So th at Eq u ation B13 becom es th e well-kn own eq u ation ∂h x 2 ∂2 h =− ∂T 2 ∂x 2 wh ose solu tion is h ( x ) = x ϕ(d2 ) − ϕ(d1 )

d1 =

⎧⎪ ⎡ B(t ) ⎤ T ⎥+ ⎨ Log ⎢ 2 T ⎩⎪ ⎢⎣ P(t ) ⎥⎦ 2

⎫⎪ ⎬ ⎭⎪

d2 =

⎧⎪ ⎡ B(t ) ⎤ T ⎥− ⎨ Log ⎢ 2 T ⎪⎩ ⎢⎣ P(t ) ⎥⎦ 2

⎫⎪ ⎬ ⎪⎭

1

1

or eq u ivalen tly (u sin g th e assu m p tion in Eq u ation B9) H ( B, P, T ;t ) P(t )

=

B(t ) P(t )

ϕ(d2 ) − ϕ(d1 )

Eq u ation B14 is eq u ivalen t to Eq u ation 16 in th e text.

(B14)

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 211

Appendix C: Variable Explanations Som e of th e item s in Table 8-2 are described in m ore detail below. A com m ercially available sim u lation tool (Crystal Ball) was u sed to sim u late th e distribu tion of th e n et social valu e of Bt corn . Th at valu e was com pu ted as th e su m of th e p resen t valu e of th e in itial p rod u cer su rp lu s, th e ch an ge in total su rp lu s, an d th e extern al effects th at were approxim ately qu an tified for th e illu stration .

Producer Surplus

Th e m ean an d varian ce are based on U.S. Dep artm en t of Agricu ltu re rep orts on th e “gross valu e of p rod u ction less cash exp en ses p er acre” for corn from 1985 to 1995, adju sted to 1998 dollars u sin g th e con su m er p rice in dex: m ean , $80/ acre; stan dard error, $36. A trian gu lar distribu tion with a lower bou n d at zero (based on exitin g th e in du stry if less th an zero p rodu cer su rp lu s) an d an u p p er bou n d of two stan dard errors from th e m ean were u sed.

Change in Total Surplus

A regressio n was co n st ru ct ed fro m d at a in O st lie (1997) t o p red ict t h e farm ben efits per acre from Bt corn as a fu n ction of price, yield, an d severity of in festation (th e vertical distan ce between S0 an d S1 , th e origin al an d th e n ew su pply cu rves ). Th e resu ltin g regression (available from th e au th ors) was u sed as a prediction equ ation for ben efits. Th e distribu tion of price u sed as a ran dom in pu t in to th e prediction equ ation u sed a lower bou n d of $1.20 per bu sh el to captu re som e u n certain ty abou t th e acceptability of Bt corn . $1.80 per bu sh el was u sed as th e m ean . Th e freq u en cy of severe corn borer ou tbreaks was set at 3/ 8 followin g Ostlie. Th e per-acre figu re was m u ltiplied by 60 m illion acres based on fu ll diffu sion of Bt corn to 80% of th e approxim ately 75 m illion acres plan ted to corn . Th is valu e likely overstates th e ben efits becau se th e com p arison is to ben ign n eglect of th e corn borer an d n ot a m ixtu re of treatm en t with p esticides an d becau se fu ll diffu sion m ay in volve fewer acres. Fu rth er, a sign ifican t p art o f t h e co st savin gs are cap t u red by t h e p ro d u cers o f t h e Bt co rn seed . Alth ou gh th is is a tran sfer an d so still a ben efit (assu m in g zero m argin al cost of produ ction of Bt corn com pared with tradition al corn ), th e effect wou ld be to redu ce th e ch an ge in con su m er su rplu s if th e su pply cu rve sh ifts less, as m igh t also h appen becau se of th e refu gia requ irem en t.

Base Consumer Surplus (A)

Base Con su m er Su rp lu s was assu m ed to be eq u ip rop ortion al to both th e tradition al an d Bt corn social valu es so th at th is m u ltip licative factor can cels ou t in

212 • Chapter 8: Resistance, the Precautionary Principle, and Regulation

th e d ecision ru le. In an y even t, it is d ou btfu l th at th is n u m ber can be m ean in gfu lly estim ated . For estim ation p roblem s of su ch m easu res of total valu e, see Bockstael an d oth ers (2000).

Pest Resistance

We in vestigate p est resistan ce p aram etrically by settin g th e exp ected term in al date of com p lete resistan ce at 12 years wh en a 20% refu ge exists based loosely on Hu an g an d oth ers (1999) an d Alstad an d An d ow (1995). If th e size of th e refu gia is in vest igat ed as a p ro b ab ilit y d ist rib u t io n , t h is wo u ld in crease t h e varian ce in th e real op tion ap p lication an d be exp ected to in crease th e degree of p recau tion .

Impact on Nontarget Species

Th e im p act on n on target sp ecies of both stan d ard p esticid es an d gen etically m odified crop s is a lively su bject of debate (Pim en tel an d Raven 2000). In th e illu st rat io n in t h e t ext , we ap p ly t h e sam e valu e t o b o t h t rad it io n al an d Bt corn . Th at valu e is based on a ben efits tran sfer of n on u se valu es from a con tin gen t valu ation stu d y in En glan d (Mou rato et al. 2000). Th at stu d y in vestigat ed t h e ad d it io n al p rice t h at co n su m ers were willin g t o p ay t o red u ce t h e d eclin e o f o n e o f n in e sp ecies o f field b ird s t h at are b elieved in d eclin e becau se of th e u se of agricu ltu ral ch em icals. Usin g average yields, we tran slate a p rice p er a o n e-p o u n d lo af o f bread in t o a valu e p er acre an d assu m e t h at th e p er-acre basis is in dep en den t of th e crop grown on it, as between wh eat or corn . For illu stration p u rp oses, we u se an u n certain fraction (m ean of 0.05) of th e valu e stated for th e ben efit of redu cin g th e declin e in bird p op u lation s. As a sen se of scale, th e m ean valu e of effect is larger th an th e average p rod u cer su rp lu s at th e cu rren t level of p rodu ction . Th ere is also eviden ce th at farm ers th em selves are willin g to p ay to redu ce p esticide u se, alth ou gh th at figu re was n ot in clu ded in ou r estim ate (Loh r et al. 1996).

Human Allergenicity

In form ation su bm itted in su p p ort of Bt corn ap p lication s (NAS 2000) su p p orts n o allergen icit y fo r several Bt st rain s wh ereas raisin g a q u est io n ab o u t t h e Cry9C strain (StarLin k, wh ich was with d rawn in 2001). Th is is a top ic of scien t ific u n cert ain t y, alt h o u gh recen t wo rk red u ces t h e p ro b ab ilit y o f su ch a lin k (CDC 2001). We assu m e a d ist rib u t io n o f allergy cases wit h a lo wer bou n d of zero based on th e p oten tial for allergic reaction in th e 35 com p lain ts after discovery of StarLin k traces in Kraft taco sh ells. Th e U.S. Food an d Dru g Ad m in ist rat io n in it ially d eclared t h at o n ly 10 m igh t h ave allergen ic b ases,

Chapter 8: Resistance, the Precautionary Principle, and Regulation • 213

su b ject t o fu rt h er in vest igat io n . In 2001, CDC fo u n d n o n e o f t h e cases t o h ave been related to StarLin k based on a p articu lar test. We assu m e a rep ortin g p ercen tage of actu al cases an d a rate of exp osu re to gen erate an estim ate of th e n u m ber of cases. We valu e th ese even ts u sin g a valu e of severe food p oison in g p er d ay of $130 from Tolley an d oth ers (1994). Th e m ean n u m ber of rep o rt ed cases in o u r illu st rat io n is 5 wit h a m ean rep o rt in g p ercen t age o f 0.25. Th e valu e of th is im p act is relatively sm all.

Notes 1. Seq u en t ial d ecisio n m akin g can b e fram ed as an o p t io n ap p ro ach (Dixit an d Pin dyck 1994; Farrow 2000). Here we treat th e regu latory decision as if it is a on ce-an dfor-all decision , an assu m p tion to be relaxed in later work. 2. Fish er (2000) an alyzes th e p arallel between th e con d ition al valu e of in form ation in q u asi-op tion valu e an d th e real op tion fram ework. 3. Slade (2001) h as in vestigated th e sen sitivity of decision s u sin g real op tion s to th e sp ecification of th e stoch astic p rocess. 4. A logarith m ic regression of tim e on th e U.S. p rodu ction of corn yields from 1985 to 1995 resu lted in an average p ercen tage in crease of corn p rodu ction p er year of 2.4% (t statistic = 10), wh ich is rou n ded to 2.5% for em p irical p u rp oses. 5. In t h e case o f rat io n al o p t io n s, η en t ers t h e co m p u t at io n o f t h e valu e o f t h e op tion . 6. Cop elan d an d An tikarov (2001) also su ggest an altern ative estim ator based on two adjacen t tim e p eriods. 7. See Green e on th e top ic of h azard fu n ction s (1997, 738). 8. W h en ψ2 = 0, d 1 = d 2 = ∞, an d ψ(∞) = 1.

Chapter 9

Resistance Economics of Transgenic Crops under Uncertainty A Real Option Approach Justus Wesseler

The development of pest resistance is one of the many concerns about the long-term success of transgenic crops. This chapter discusses resistances as additional irreversible costs related to the release of transgenic crops. These irreversible costs, their uncertainty, and the uncertainty about future direct benefits result in a real option value favoring a delay in the release of transgenic crops. This is a result well known in real option theory but ignored in most of the cost–benefit studies on transgenic crops. In addition to irreversible costs, how ever, a release of transgenic crops also may provide irreversible benefits. For example, a reduction in pesticide use reduces pest resistance to pesticides and has positive impacts on human health, groundwater quality, and biodiversity. These irreversible benefits provide an incentive for an im m ediate release of transgenic crops in the environment. The optimal decision to release transgenic crops depends not only on the direct costs and benefits, which we call additional net benefits, but also on the trade-off between irreversible environmental costs and benefits. Assuming uncertain additional net benefits, constant irreversible costs and benefits and applying the real options approach allows us to define the maximal tolerable irreversible costs as an important benchmark value. The real option approach was applied by using contingent claim analysis, which allows deriving solutions that are independent of risk and time preference. Those concerned about the environm ental risks of transgenic crops and those who just want to maximize their income would come to the same conclusion about the timing of release.

• 214 •

Chapter 9: Resistance Economics of Transgenic Crops • 215 The effects of policies on the timing of releasing transgenic crops are analyzed by identifying the impact of marginal parameter changes on the maxim um tolerable irreversible costs. The m ost counterintuitive result w as the increase in the likelihood of an earlier release with a decrease in additional net benefits. This result was explained by the opposite impact that simultaneous changes in the growth rate and the variance rate have on the maximum tolerable irreversible costs. M andatory refuge areas for pest resistance m anagem ent and a tax on transgenic crops to com pensate for possible environmental risks have this kind of effect on the timing of release.

gro b io t ech n o lo gy ch allen ges t h e p o lit ical eco n o m y o f agricu lt u re in m an y cou n tries. Never before h as a n ew tech n ology in th e field of agricu ltu re been so em otion ally d ebated am on g d ifferen t stakeh old ers. Develop in g cou n tries’ scien tists are relu ctan t to be byp assed by th e n ew tech n ology (Wam b u gu 1999). At t h e sam e t im e, gro u p s o f co n su m ers, p o lit ician s, an d n o n go vern m en t al o rgan izat io n s, b o t h in d evelo p ed an d d evelo p in g co u n tries, op p ose th e in trodu ction of tran sgen ic crop s, wh ich th ey see as p osin g a th reat to biod iversity, h u m an h ealth , an d th e econ om y of ru ral com m u n ities an d u lt im at ely en d an gerin g su st ain ab le d evelo p m en t . Rad ical gro u p s h ave gon e as far as destroyin g research p lots an d laboratory eq u ip m en t. Con su m ers are fu rth er discon certed by th e disagreem en t am on g scien tists abou t th e en viro n m en t al an d h u m an h ealt h im p act o f t ran sgen ic cro p s. Alt h o u gh so m e h igh ligh t th e p oten tial risks, oth ers argu e th at th ey are n egligible. W h atever p eop le believe p erson ally, th e p u blic d ebate in d icates th at both b en efit s an d co st s are exp ect ed fro m t h e release o f t ran sgen ic cro p s in t h e en viro n m en t . Th ese b en efit s an d co st s are h igh ly u n cert ain . No b o d y can exact ly p red ict t h e im p act t ran sgen ic cro p s will h ave o n t h e eco syst em an d h o w su ccessfu lly t h ey can co m p et e in t h e m arket p lace wit h n o n t ran sgen ic crop s. Neverth eless, decision s regardin g th e release of tran sgen ic crop s h ave to be m ade an d are bein g m ade. An y su ch decision s in clu de, im p licitly or exp licitly, a com p arison of costs an d ben efits. Even a decision based on th e assu m p t io n t h at t h e risk can n o t be est im at ed an d , t h erefo re, t h at t ran sgen ic cro p s sh o u ld n o t be released , im p licit ly assu m es t h at t h e exp ect ed co st s fro m t h e risks are h igh er th an th e exp ected ben efits.

A

Irreversible Costs and Benefits of Transgenic Crops Th e costs of agricu ltu ral biotech n ology are u n certain , an d som e of th e costs are also irreversible. From th e resistan ce econ om ic p oin t of view, th ree areas are of sp ecial con cern . First, gen e flow in p lan ts can en able dom esticated p lan ts to becom e p ern iciou s weeds or en h an ce th e fitn ess of wild p lan ts, wh ich m igh t tu rn ou t to be

216 • Chapter 9: Resistance Economics of Transgenic Crops

seriou s weeds, th u s sh iftin g th e ecological balan ce in a n atu ral p lan t com m u n ity. Herbivore-resistan t traits h ave a com p arative advan tage again st n on resistan t traits, an d if th e tran sgen ic crop h ybrid izes with oth er p lan ts, for exam p le wild relat ives, t h e t ran sfer o f gen es will b e virt u ally in evit ab le u n d er p lan tin g at a com m ercial scale (Marvier 2001). Gen e flows from dom esticated t o wild relat ives o f t h e wo rld ’s 13 m o st im p o rt an t fo o d cro p s are co m m o n (Ellst ran d et al. 1999). Th ese gen e flo ws h ave resu lt ed in m o re aggressive weed s an d t h e ext in ct io n o f wild relat ives, an d t h e sam e is p o ssib le fo r t h e tran sfer of gen es from tran sgen ic crop s to wild relatives. Ken d all an d oth ers (1997, 19) co n clu d ed “… it is clear t h at an y gen e t h at exist s in a cu lt ivat ed cro p o r p lan t , irresp ect ive o f h o w it go t t h ere, can b e t ran sferred fo llo win g h ybridization to its wild or sem idom esticated relatives.” Secon d , p lan tin g p est-resistan t crop s in creases th e selection of p ests resistan t to th e p lan t-p rod u ced p esticid e. For exam p le, Bt corn , corn th at can p rod u ce toxin s of Bacillus thuringiensis, h as been d evelop ed to con trol th e Eu rop ean corn borer (Ostrinia nubilalis). Larvae th at feed on Bt corn are exp ected to be killed ; h owever, a wid esp read ad op tion of Bt corn is exp ected to in crease th e ch an ces th at p est resistan ce will evolve (Tabash n ik et al. 2000). Farm ers in th e Un ited States are req u ired to p rovid e refu ge areas wh ere n on -Bt crop s are grown to con trol th e ch an ces of p est resistan ce (EPA 2000a). Th ird , th e u se of m arker gen es in tran sgen ic crop s can in crease th e resistan ce of bacteria to an tibiotics (Krim sky an d Wru bel 1996). Marker gen es with in form ation abou t an tibiotic resistan ce are u sed to id en tify tran sform ed cells an d are in tegrated in th e gen om es of tran sgen ic crop s. If th e tran sgen ic crop s are con su m ed, th e p ossibility exists th at th e gen es carryin g in form ation abou t an tibiotic resistan ce are tran sferred to h u m an p ath ogen s. Th e p ath ogen s m ay b eco m e resist an t again st t h e sp ecific an t ib io t ic, an d t h e effect iven ess o f an t ib io t ics fo r m ed ical t reat m en t s d ecreases. Ho wever, t h is m ay b e very u n likely becau se “… m o st o f t h e an t ibio t ic resist an ce m arker gen es u sed in t ran sgen ic cro p s are o f n o clin ical im p o rt an ce an d are wid ely sp read in m icroflora” (Malik an d Saroh a 1999, 3). Oth er issu es raised abou t p ossible irreversible effects of tran sgen ic crop s are t h at n ew viru ses co u ld d evelo p fro m viru s-co n t ain in g t ran sgen ic cro p s (Ken dall et al. 1997) an d th at th ey m ay h ave u n kn own effects on soil com m u n ities (Saxen a et al. 1999). In su m m ary, th e evid en ce p rovid ed in th e literatu re cited clearly in d icates th at th e p roblem s of resistan ce to tran sgen ic crop s are in evitable if th e crop s are released in th e en viron m en t. Becau se th e p ossibility to con trol p ests an d d iseases can be seen as a n o n ren ewable reso u rce (Hu et h an d Regev 1974), a loss of th is resou rce is irreversible. In t h e Un it ed St at es, t ran sgen ic cro p s h ave b een ad o p t ed rap id ly (Jam es 2000). Stu d ies con firm th at on average th e gross m argin p er area from tran s-

Chapter 9: Resistance Economics of Transgenic Crops • 217

gen ic cro p s is ab o u t as h igh an d so m et im es h igh er t h an t h e gro ss m argin from n on tran sgen ic crop s. However, th ere is a region al differen ce in th e distribu tion of ben efits, wh ich can be exp lain ed by region al factors su ch as in festation level an d clim atic con dition s. Th e em p irical stu dies also in dicate th at th e am ou n t of p esticid es u sed m ay d ecrease for tran sgen ic crop s bu t on ly in sp ecific region s an d sp ecific years, d ep en d in g on th e sam e factors as m en tion ed earlier. In so m e regio n s, p est icid e u se h as act u ally in creased (Carp en t er an d Gian essi 1999; Fern an dez-Corn ejo et al. 1999; Fu lton an d Keyowski 1999). 1 Th e rap id ad op tion of tran sgen ic crop s am on g farm ers in North ern Am erica h as been exp lain ed by th e greater ben efits th at farm ers gain from p lan tin g t ran sgen ic cro p s. Variab le p ro d u ct io n co st s are red u ced b ecau se o f red u ced p est m an agem en t an d labor costs. Gross reven u es are in creased becau se of an in crease in yield from im p roved p lan t sp acin g. Ad d ition al ben efits arise from im p ro ved risk m an agem en t an d in su ran ce again st p est s an d a red u ct io n in eq u ip m en t costs in zero-tillage p rod u ction system s (Kalaitzan d on akes 1999). Bt co t t o n 2 also h as b een in t ro d u ced su ccessfu lly in Ch in a. O n e o f t h e m ajor reason s for ad op tion h as been th e savin gs on p esticid es. Pray an d oth ers (2001) rep orted a d ecrease in p esticid e costs of abou t 80% after ad op tion of Bt cotton in Ch in a. Th e decrease in p esticide u se n ot on ly redu ces th e exp en ses of farm ers bu t also redu ces th e p ressu re on th e bu ildu p of p est resistan ce to p esticides. Addition ally, th e red u ced ap p lication of p esticid es h as several p ositive im p acts on t h e en viro n m en t an d h u m an h ealt h (An t le an d Pin gali 1994; Waib el an d Fleisch er 1998; Fleisch er 1998). Th e red u ced p ressu re on th e bu ild u p of p est resist an ce an d so m e o f t h e o t h er ext ern al co st s o f p est icid e ap p licat io n are irreversible. If th e in trod u ced tran sgen ic crop s resu lt in less p esticid e ap p licat io n , t h e in t ro d u ct io n p ro vid es ad d it io n al b en efit s. Hen ce, t h e release o f tran sgen ic crop s p rodu ces n ot on ly irreversible costs bu t also irreversible ben efit s, 3 a t erm in t ro d u ced by Pin d yck (2000) in t h e co n t ext o f green h o u se gas abatem en t. Th at is, th ere is a trad e-off from th e resistan ce econ om ic p oin t of view from releasin g tran sgen ic crop s between th e in crease in p est su scep tibility becau se of a decrease in p esticide u se an d th e in crease in resistan ce to p esticides an d an tibiotics becau se of th e p lan tin g of tran sgen ic crop s. Th e irreversib ilit y effect s o f t ran sgen ic cro p s an d t h e u n cert ain t y ab o u t th eir fu tu re costs an d ben efits will h ave an im p act on th e op tim al tim in g of releasin g t h em . Irreversible co st s, u n cert ain t y, an d t h eir im p act o n o p t im al in vest m en t h ave b een wid ely an alyzed (e.g., McDo n ald an d Siegel 1986; Pin dyck 1991; Dixit an d Pin dyck 1994). In th e literatu re on real op tion valu ation s, th e op p ortu n ity to in vest is valu ed in an alogy to a call op tion in fin an cial m arkets. In vestors h ave th e righ t bu t n ot th e obligation to exercise th eir in vestm en ts. Th is righ t, th e op tion to in vest (real op tion ) h as a valu e, wh ich is a resu lt of th e op tion own er’s flexibility an d is sim ilar to th e q u asi-op tion

218 • Chapter 9: Resistance Economics of Transgenic Crops

valu e d evelop ed earlier by Arrow an d Fish er (1974) an d Hen ry (1974) (Fish er 2000). Ch avas (1994) p ro vid ed sim ilar resu lt s in h is ap p licat io n t o in vest m en ts in agricu ltu re. Dixit an d Pin d yck (1994) also su ggested an ap p lication n o t o n ly t o in vest m en t p ro b lem s b u t also t o all kin d s o f d ecisio n m akin g u n d er t em p o ral u n cert ain t y an d irreversibilit y. 4 Recen t ly, t h e ap p ro ach h as been ap p lied t o , am o n g o t h ers, t h e ad o p t io n o f so il co n servat io n m easu res (Win ter-Nelson an d Am egbeto 1998; Sh ively 2000), m arketin g (Rich ard s an d Green 2000), wild ern ess p reservation (Con rad 2000), agricu ltu re labor m igration (Rich ard s an d Patterson 1998), an d th e an alysis of govern m en t reform s (Leit zel an d Weism an 1999). Leit zel an d Weism an (1999) argu ed t h at n ew go vern m en t p o licies req u ire in vest m en t s in t h e fo rm o f t rain in g o f go vern m en t officials, h irin g of addition al workers, an d bu yin g of eq u ip m en t. Part of th ese costs is irreversible, bu t th e su ccess of th e im p lem en ted p olicy is u n certain , wh ich resu lts in a p ositive valu e of th e op tion to delay th e im p lem en tation of th e p olicy. In th e case of tran sgen ic crop s, th ere wou ld be ad d ition al irreversible govern m en t p olicy costs, for exam p le, from th e im p lem en tation of biosafety regu lation s an d ch an ges in p aten t laws. Th is ch ap ter em p h asizes th e econ om ic im p act of tran sgen ic crop s on p est resistan ce, wh ich are eith er irreversible costs or irreversible ben efits. Th e irreversible costs of regu latory p olicies, wh ich m ay well be greater th an th e en viron m en tal on es, as an an on ym ou s reviewer of th is ch ap ter in dicated, also can b e in clu d ed in t h e an alysis b u t wo u ld ch an ge t h e fo cu s o f an alysis an d are th erefore left ou t for fu tu re research . Recen t ex an te stu dies on th e costs an d ben efits of tran sgen ic crop s (Qaim an d von Brau n 1998; Sian esi an d Ulp h 1998; O’Sh ea an d Ulp h 2000) h ave n ot con sidered th e irreversible costs an d ben efits of tran sgen ic crop s. Th u s, on e of th e objectives of th is ch ap ter is to con tribu te to th e existin g literatu re on ex an t e assessm en t o f t ran sgen ic cro p s in gen eral. Fu rt h erm o re, as t h e real op tion ap p roach u sed in th is ch ap ter allows u s to d erive solu tion s in d ep en d en t of in d ivid u al p referen ces, th is con tribu tion m ay h elp to ration alize th e d ebate on tran sgen ic crop s. Also, p olicy op tion s for p est resistan ce m an agem en t, like m an datory refu ge areas an d th eir im p act on th e decision to release tran sgen ic crop s, will be discu ssed. Th e ch ap ter en ds with con clu sion s for p est resistan ce p olicies an d su ggests areas for fu tu re research .

M ethodological Approach To Assess the Benefits and Costs of Agrobiotechnology Con sid er a d ecision m aker or a d ecision m akin g bod y sim ilar to th e U.S. En viro n m en t al Pro t ect io n Agen cy (U.S. EPA) t h at h as t h e au t h o rit y t o d ecid e wh eth er a p articu lar tran sgen ic crop , for exam p le, a toxin -p rodu cin g crop like Bt corn , 5 sh ou ld be released for com m ercial p lan tin g. Th e agen cy can ap p rove

Chapter 9: Resistance Economics of Transgenic Crops • 219

an ap p lication for release or can p ostp on e th e d ecision . Th e objective of th e agen cy is to m axim ize th e welfare of con su m ers livin g in th e econ om y, an d it ign ores p ositive an d n egative tran sbou n d ary effects. Th e su p p ly for all tran sgen ic cro p s is p erfect ly elast ic, an d d em an d is p erfect ly in elast ic p er u n it o f t im e. 6 Ex an t e effect s o f t h e d ecisio n t o release t ran sgen ic cro p s o n t h e u p stream sector of th e econ om y are ign ored by th e agen cy. With in th is settin g, th e welfare effect of releasin g a sp ecific tran sgen ic crop can be described as th e n et p resen t valu e V T from th e p oin t of release T u n til in fin ity of th e ad d ition al an n u al n et ben efits at th e farm level Bt , wh ich will be fu rth er defin ed below, m in u s th e differen ce between irreversible costs I an d irreversible ben efits R. R an d I are assu m ed to be kn own an d con stan t, wh ich is a u sefu l sim p lification for two reason s. First, n ot m u ch is kn own abou t th e m agn itu de of irreversible costs I. As will be sh own later, th e m od el can be solved for th e irreversible costs an d p rovid e in form ation abou t an accep table level, wh ich can th en be com p ared with available in form ation . Secon d, in form ation abou t th e irreversible d am ages from p esticid e u se on a p er-h ectare level, wh ich are th e irreversible ben efits R of p lan tin g tran sgen ic crop s, is available an d can easily be in clu ded in th e m odel. In an alo gy t o fin an cial o p t io n s –(I – R) < 0 is eq u ivalen t t o t h e exercise p rice of a call op tion on a stock, h ere with th e righ t bu t n ot th e obligation to release t ran sgen ic cro p s in t h e en viro n m en t . If t h e o p t io n t o release t ran sgen ic cro p s F(V ) is exercised , t h e d ecisio n m aker acq u ires t h e ad d it io n al n et b en efit s V T fro m t ran sgen ic cro p s eq u ivalen t t o t h e d ivid en d st ream o f a stock. Th e d ifferen ce V T – (I – R) is th e intrinsic value of th e op tion to release t ran sgen ic cro p s. Becau se it is n o t o p t im al t o exercise a fin an cial o p t io n im m ed iately if th e in trin sic valu e becom es p ositive (e.g., Hu ll 2000), it is n ot op tim al to exercise th e op tion to release tran sgen ic crop s eith er. Th e op tion h as a valu e o f wait in g, t h e so -called tim e value. Th e o p t io n sh o u ld b e exercised if t h e tim e value o f t h e o p t io n falls t o zero . Th e o b ject ive o f t h e d ecision m aker can be d escribed as m axim izin g th e valu e of th e op tion to release tran sgen ic crop s:

{[

]

m ax F(V ) = m ax E V T − ( I − R) e −λT

}

(1)

wh ere E is t h e exp ect at io n o p erat o r, T is t h e u n kn o wn fu t u re p o in t in t im e wh en th e tran sgen ic crop is released in to th e en viron m en t, an d λ is th e d iscou n t rate. Becau se th e release of a tran sgen ic crop h as alm ost n o effect on th e fixed costs, th e n et ben efits from a tran sgen ic crop at farm level for a sp ecific region are t h e t o t al su m o f gro ss m argin s o ver all farm s. Th e welfare effect at farm

220 • Chapter 9: Resistance Economics of Transgenic Crops

level in year t, h en ce, is t h e d ifferen ce b et ween t h e su m s o f gro ss m argin s from tran sgen ic crop s (BGM t – CGM t ), m in u s th e total su m of gross m argin s from th e altern ative n on tran sgen ic crop (BCCt – CCC t) (or con ven tion al crop ). Fro m n o w o n , t h is d ifferen ce will b e called t h e ad d it io n al n et b en efit fro m tran sgen ic crop s Bt . Oth er ad d ition al ben efits arisin g from th e ap p lication of th e n ew tech n ology, su ch as th rou gh “p eace of m in d “ (Mon san to 1999), are assu m ed t o b e b alan ced b y co n cern s ab o u t t h e n ew t ech n o lo gy o n average an d are th erefore ign ored. 7 Th u s Bt = ( BGM t − CGM t ) − ( BCCt − CCCt )

(2)

Th e b en efit s an d co st s o f Eq u at io n 2 are t h o se t h at are n o t irreversib le. Growers of tran sgen ic crop s can stop p lan tin g th em if Bt tu rn s ou t to be n egative; th ey can p lan t con ven tion al crop s in stead an d m ove back to tran sgen ic cro p s if it t u rn s o u t t o b e p o sit ive again wit h o u t b earin g ad d it io n al co st s. W h en fu t u re ad d it io n al n et b en efit s Bt are d isco u n t ed at λ = µ—t h e riskadju sted rate of retu rn derived from th e cap ital asset p ricin g m odel (CAPM)— an d grow an n u ally at a rate α, startin g from th e p oin t of release T, th en th e p resen t valu e of addition al n et ben efits at th e p oin t of release T is:8 V ( BT ) =

BT µ ( − α)

(3)

Th e d ifferen ce between µ an d α is th e con ven ien ce yield δ. If sp ecu lative b u b b les will b e ru led o u t an d as V (0) = 0, Eq u at io n 3 also will d escrib e t h e valu e o f releasin g t ran sgen ic cro p s in t h e en viro n m en t . In clu d in g co n st an t irreversib le co st s I an d irreversib le b en efit s R, t ran sgen ic cro p s sh o u ld b e released in th e en viron m en t if V (BT ) > (I – R). Th is is sim ilar to th e n eoclassical or Marsh allian op tim ality con d ition u n d er certain ty, wh ich states th at tran sgen ic crop s sh ou ld be released if th e ad d ition al n et ben efits are greater th an th e irreversible costs m in u s th e irreversible ben efits. Becau se V is a con stan t m u ltip le of B, th e valu e of th e op tion to release tran sgen ic crop s d ep en d s on B; th erefore, writin g F(B) is p referred over writin g F(V ).9 Fo llo win g Dixit an d Pin d yck (1994), t h e m axim al valu e o f F(B) u n d er u n cert ain t y will be d erived by ch o o sin g a st o ch ast ic p ro cess t h at ad d it io n al n et b en efit s Bt fo llo w, so lvin g t h e m o d el u sin g co n t in gen t claim an alysis, wh ich resu lts in a stoch astic differen tial eq u ation . Ch oosin g ap p rop riate fu n ct io n s an d so lvin g fo r t h e u n kn o wn p aram et ers acco rd in g t o t h e b o u n d ary con d ition s can allow u s to fin d a solu tion to th e stoch astic d ifferen tial eq u ation . Th is will p rovide th e n ew op tim ality con dition s, in clu din g th e op tion to delay th e release of tran sgen ic crop s in th e en viron m en t.

Chapter 9: Resistance Economics of Transgenic Crops • 221

To start with , a p rocess rep licatin g th e stoch astic p ath of th e addition al n et b en efit s Bt o ver t im e is ch o sen . Th e geo m et ric Bro wn ian m o t io n h as b een u sed freq u en tly to m od el retu rn s from agricu ltu ral crop s (Sh ively 2000; Price an d Wetzstein 1999) an d farm in vestm en ts (Kh an n a et al. 2000; Win ter-Nelson an d Am egbeto 1998; Pu rvis et al. 1995). Th e geom etric Brown ian m otion is a n on station ary, con tin u ou s-tim e stoch astic p rocess in wh ich α is th e con stan t d rift rate, σ is th e con stan t varian ce rate, an d dz is th e Wien er p rocess, with E(dz) = 0 an d E(dz)2 = dt dB = αBdt + σBdz

(4)

Th e geo m et ric Bro wn ian m o t io n is t h e lim it o f a ran d o m walk (Co x an d Miller 1965), h en ce it is con sisten t with th e assu m ption of log n orm ality of th e stoch astic variable with zero drift an d is often ch osen by econ om ists becau se of its an alytical tractability. Th e expected valu e of th is process grows at th e rate α. A positive growth rate assu m es th at ben efits grow con tin u ou sly over tim e. An exam ple of a geom etric Brown ian m otion is sh own in Figu re 9-1. Rich ard s an d Green (2000) su ggest ed d eco m p o sin g ret u rn s fro m agricu lt u ral cro p s. Th ey m o d eled cro p p rices as a geo m et ric Bro wn ian m o t io n an d crop yields as a geom etric Brown ian m otion com bin ed with a Poisson p rocess, wh ere t h e geo m et ric Bro wn ian m o t io n rep resen t s “n o rm al” years an d t h e Poisson p rocess years with extrem e yields. If addition al n et ben efits Bt are ch osen as stoch astic variable, it can be assu m ed th at extrem e yields are sm ooth ed, an d , h en ce, a d eco m p o sit io n o f p rices an d yield s wo u ld n o t b e n ecessary.

Value

Sample Path

Trend

Time FIGURE 9-1. Sample Paths of a Geometric Brownian M otion

222 • Chapter 9: Resistance Economics of Transgenic Crops

Addition al n et ben efits Bt cou ld also be m odeled by a m ean -revertin g p rocess, in wh ich it is assu m ed th at addition al n et ben efits Bt are decreasin g over tim e. Th e d ecrease cou ld be exp lain ed by th e observation th at p ests are becom in g resist an t t o p lan t -p ro d u ced p est icid es an d weed s are b eco m in g resist an t t o broadban d h erbicides. Wesseler (forth com in g) com p ared th e resu lts of m odelin g ad d it io n al n et ben efit s wit h a geo m et ric Bro wn ian m o t io n an d a m ean revertin g p rocess an d sh owed th at th e d ifferen t p rocesses cou ld resu lt in d ifferen t decision s. Th is leads to th e p roblem of iden tifyin g th e relevan t p rocess. Th e iden tification of th e relevan t p rocess based on tim e-series data is difficu lt, becau se t h e resu lt s are am bigu o u s (Pin d yck an d Ru bin feld 1991). Dixit an d Pin d yck (1994) th erefore recom m en d id en tifyin g th e p rocess based on th eoretical argu m en ts. In t h is ch ap t er, t h e geo m et ric Bro wn ian m o t io n is u sed t o m o d el ad d ition al n et ben efits, an d h en ce it is assu m ed th at research in to tran sgen ic crop s resu lts in n ew tran sgen ic crop s th at can rep lace older on es con tin u ou sly. Th e ap p en d ix sh ows th e solu tion for th e op tim al level of ad d ition al n et ben efits B* u sin g co n t in gen t claim an alysis fo llo win g t h e ap p ro ach o f Dixit an d Pin dyck (1994, 147–52) with th e followin g resu lts: B* =

β1 δ( I − R) β1 − 1

(A6)

2

with β1 =

1 r−δ 2r ⎡r − δ 1 ⎤ − 2 + ⎢ 2 − ⎥ + 2 >1 2 2⎦ σ σ ⎣ σ

(A8)

an d I > R wh ere r is th e risk-free rate of retu rn an d β1 is th e p ositive root of th e solu tion to th e secon d-order differen tial Eq u ation A2 in th e ap p en dix. Th e resu lt o f Eq u at io n A6 p ro vid es as a ru le t h at it is o p t im al t o release t ran sgen ic cro p s if t h e ben efit s are eq u al t o t h e d ifferen ce bet ween t h e irreversible costs an d ben efits an n u alized by th e con ven ien ce yield δ an d m u ltip lied by th e factor β/ (β – 1). Th e factor β/ (β – 1) also is called th e h u rd le rate (Dixit 1989); accordin gly [β/ (β – 1)]δ is called h ere th e an n u alized h u rdle rate. In com parison with th e Marsh allian optim ality con dition s, th e addition al n et ben efits h ave to be h igh er by th e factor β/ (β – 1). As Equ ation A4 in dicates, th e fu ll valu e of releasin g tran sgen ic crops in th e en viron m en t V (B*) h as to in clu de n ot on ly th e irreversible costs an d ben efits bu t also th e real option valu e F(B*) of th e release (Dixit an d Pin d yck 1994, 141). Th is is illu strated in Figu re 9-2. Th e h o rizo n t al axis in d icat es t h e ad d it io n al n et ben efit s B fro m t ran sgen ic crop s. Th e straigh t lin e sh ows th e p resen t valu e of releasin g tran sgen ic crop s im m ediately. Th e slope of th e straigh t lin e is 1/ (µ – α) an d tu rn s positive at B = I – R an d is called h ereafter accord in gly th e Marsh allian lin e. Th e n on lin ear

Chapter 9: Resistance Economics of Transgenic Crops • 223

lin e sh o ws t h e o p t io n valu e o f releasin g t ran sgen ic cro p s, in t h e fo llo win g called th e op tion lin e. Th e op tion valu e starts at zero an d sm ooth ly m atch es th e Marsh allian lin e at B*. From B* on ward , th e op tion valu e con tin u es lin early with th e Marsh allian lin e. To th e left of B*, th e option valu e is above th e valu e from releasin g tran sgen ic crop s im m ed iately, an d th ere th e gain s from d elayin g t h e release o f t ran sgen ic cro p s are h igh er t h an t h e gain s fro m an im m ediate release. Th e valu e of th e option to release is equ al to th e valu e of an im m ediate release to th e righ t of B*. If th e addition al n et ben efits Bt are as h igh as B* or h igh er, th e option to release tran sgen ic crops sh ou ld be exercised. Eq u ation A6 also in dicates th at th e irreversible ben efits of tran sgen ic crop s offset th e irreversible costs an d th erefore red u ce th e op p ortu n ity costs of th e p roject. In clu din g th e irreversible ben efits redu ces th e req u ired p ercen tage by wh ich th e ad d ition al n et ben efits h ave to be above th e irreversible costs. Th e h igh er t h e irreversib le b en efit s o f t ran sgen ic cro p s are, t h e lo wer t h e ad d it io n al b en efit s B* m u st b e t o ju st ify t h e release. Th is is sim ilar t o a p arallel u p ward m o ve o f t h e Marsh allian lin e as illu st rat ed in Figu re 9-3. Th e n ew op tim al level of addition al n et ben efits B*’ m oves to th e left of th e in itial op tim ality level B* with an in crease in R. On th e con trary, with an in crease in th e irreversible costs, th e n ew op tim ality level m oves to th e righ t. Th e irreversible ben efits of releasin g tran sgen ic crops m ay even be h igh er th an th e irreversible costs of releasin g th em . In th is case, a release of tran sgen ic crops in to th e en viron m en t m ay be justified if th e addition al n et ben efits are n egative. Un der th is scen ario th ere is n o tim e value, an d th e value of th e option to release

V( B) – ( I – R), F( B)

F ( B*), V( B*) – ( I – R)

–( I – R)

Option Line M arshallian Line

B*

Additional Annualized Net Benefits B of Transgenic Crops

FIGURE 9-2. Value of the Option To Release Transgenic Crops as a Function of Net Benefits B

224 • Chapter 9: Resistance Economics of Transgenic Crops

V( B) – ( I – R) , F( B)

F( B* )

F( B*' )

B*'

B*

–( I – R' ) –( I – R)

Additional Annualized Net Benefits B of Transgenic Crops FIGURE 9-3. Effects of a Decrease in Net Irreversible Costs –( I – R) on the Optimal M inimum Level of Additional Net Benefits B*

V( B) – ( I – R), F( B)

tran sgen ic crops is equ ivalen t to th e valu e of im m ediately releasin g tran sgen ic crops. Th e Marsh allian criteria can be applied, an d h en ce tran sgen ic crops sh ould be released im m ediately if V (B) – I + R > 0. If th ere are n o irreversible costs of releasin g tran sgen ic crops, th ey sh ould be released if V(B) + R > 0. Th e situation in wh ich irreversible ben efits are greater th an th e irreversible costs is illustrated in Figure 9-4. Th e optim al level of B* is to th e left of th e origin .

–( I – R)

B*

Additional Annualized Net Benefits B of Transgenic Crops

FIGURE 9-4. Optimal M inimum Level of Additional Net Benefits B* with Irreversible Benefits Greater Than Irreversible Costs, R > I

Chapter 9: Resistance Economics of Transgenic Crops • 225

Defining M aximal Tolerable Irreversible Costs Th e sim p le m o d el p resen t ed h ere p ro vid es in sigh t s in t o t h e o p t im al t im in g fo r releasin g t ran sgen ic cro p s in t h e en viro n m en t . In t h e m o d el it was assu m ed th at th e irreversible costs were certain . Th is is a h eroic assu m p tion becau se m ost of th e en viron m en tal effects of tran sgen ic crop s are n ot kn own an d t h o se t h at are kn o wn are n o t cert ain . So lvin g Eq u at io n A6 fo r t h e irreversible costs can redu ce th e relevan ce of u n certain ty abou t irreversible costs. Th is p rovides I* = R +

BT / 2 B B /δ = R+ T − T β / β −1 δ β

(5a)

or I * = R + γBT , with γ =

β −1 βδ

(5b)

wh ere γ is th e slop e p aram eter. In stead of id en tifyin g th e ad d ition al n et ben efits req u ired to release tran sgen ic crop s in to th e en viron m en t, th e m axim u m tolerable irreversible costs u n d er given ad d ition al n et ben efits BT an d irreversible ben efits R are id en tified. If th ey are kn own , a sp ace can be design ed th at sh ows areas of rejection an d ap p roval of releasin g tran sgen ic crop s. Th e tolerable costs of an in crease in resist an ce cap t u red in I* will b e h igh er t h e h igh er t h e b en efit s fro m a red u ced p ressu re on resistan ce bu ild u p are, cap tu red in R, an d th e h igh er th e cu rren t ben efits from tran sgen ic crop s are, cap tu red in B. Eq u ation 5a can be form u lated as a ru le th e agen cy sh ou ld follow wh en it h as to decide wh eth er a tran sgen ic crop sh ou ld be released: Postpone the release of a transgenic crop into the environm ent if the irreversible costs are higher than the irreversible benefits plus the present value of an infinite stream of instantaneous additional net benefits, using the convenience yield as the relevant discount rate, divided by the hurdle rate. Th is ru le h as t wo im p o rt an t p ro p ert ies, wh ich resu lt fro m t h e u se o f t h e con tin gen t claim an alysis (see ap p en dix). First, fu tu re costs an d ben efits h ave been d iscou n ted u sin g rates p rovid ed by th e m arket. No in d ivid u al d iscou n t rat es h ave been u sed . Seco n d , u n cert ain t y abo u t t h e ad d it io n al n et ben efit s h as been in clu ded by u sin g a riskless h edge p ortfolio, an d, h en ce, th e evalu ation of th e ben efits is in dep en den t of attitu des toward risk, wh ich redu ces th e im p act of risk p referen ces on decision m akin g.

226 • Chapter 9: Resistance Economics of Transgenic Crops

Th e secon d expression of th e m axim u m tolerable irreversible costs in Equ ation 5a illu strates th e effect of waitin g becau se of u n certain ty an d irreversibilit y. Th e first t wo t erm s, R an d B/δ, illu st rat e t h e resu lt s o f t h e o rt h o d o x ap p roach . With ou t exp licitly recogn izin g irreversibility an d u n certain ty, th e ben efits are th e su m of th e irreversible ben efits p lu s th e p resen t valu e of in fin ite addition al n et ben efits. By in clu din g irreversibility an d u n certain ty, a prop ortion of th e p resen t valu e of in fin ite ad d ition al n et ben efits, (BT / δ)/ β, m u st be d ed u ct ed . Th is p ro p o rt io n in t h is co n t ext can be in t erp ret ed as t h e eco n om ic valu e of u n certain ty an d th e irreversibility of releasin g tran sgen ic crops.

Impact of Different Policies Th e op tim al level of B* or I* is n ot fixed. Th eir valu es will ch an ge dep en din g on p rices, in terest rates, u n certain ty, an d oth er variables. Th is op en s th e win d ow for p olicy im p acts on th e op tim al level an d h en ce on wh eth er it is op tim al to release tran sgen ic crop s im m ediately. Th e an alysis of p olicy im p acts starts by stu d yin g th e effect of ch an ges in d ifferen t m o d el p aram et ers o n B *. If n o t st at ed o t h erwise, t h e figu res p resen ted in th is ch ap ter are based on th e followin g p aram eter valu es: α = 0.04, σ = 0.4, r = 0.04, an d µ = 0.08. Th e im portan t param eters of th e m odel are th e drift rate α an d th e varian ce rate σ. An in crease in th e drift rate α decreases β an d th erefore th e ratio β/ (β – 1) in creases. Th is is offset by a decrease of th e con ven ien ce yield δ, resu ltin g in a n et decrease of B* for reason able param eter valu es as sh own in Table 9-1 an d illu strated in Figu re 9-5. Th is can be explain ed by two effects. First, an in crease in th e drift rate α m akes th e fu tu re m ore valu able an d th erefore in creases th e valu e of th e option to release tran sgen ic crops. Th e option lin e m oves u pward. Secon d, an in crease in th e drift rate redu ces th e con ven ien ce yield δ (see Equ ation 3), an d th e valu e of im m ediate release V (B) in creases as well, as in dicated by th e differen t slop es of th e Marsh allian lin e in Figu re 9-5. Th e overall effect is a h igh er valu e of tran sgen ic crop s, lower valu es of B*, an d h en ce an earlier release. Th e im pact on th e optim al level of I* is an in crease in th e slope param eter γ, wh ich resu lts in h igh er tolerable irreversible costs, as ⎛ β − 1⎞ ⎛ β⎞ ⎛ B⎞ ∂⎜ ∂⎜ ⎟ ⎟ ∂⎜ ⎟ ⎝ δ⎠ β ⎝ δ⎠ β B ⎝ β ⎠ B ∂I ∂β = = + + β −2 >0 ∂α ∂α ∂α β − 1 ∂ ∂α β − 1 δ ∂α *

(6)

On th e con trary, an in crease in th e u n certain ty of th e addition al n et ben efits resu lts in a h igh er valu e of B*. An in crease in u n certain ty p laces a h igh er valu e on th e fu tu re an d in creases th e option valu e of releasin g tran sgen ic crops bu t h as n o effect on th e valu e of an im m ediate release if th e con ven ien ce yield

Chapter 9: Resistance Economics of Transgenic Crops • 227

TABLE 9-1. Annualized Hurdle Rates for Different Parameter Settings.a Drift rate α (%)

0.10

1.0 2.0 4.0 6.0

0.080 0.071 0.057 0.049

0.20

standard deviation σb 0.40

0.80

1.20

0.103 0.095 0.080 0.068

0.174 0.166 0.149 0.134

0.423 0.414 0.396 0.378

0.827 0.817 0.798 0.779

a. Th e an n u alized h u rd le rate as d efin ed in Eq u ation A6. Th e recip rocal valu es are th e slop e for th e m axim al tolerable irreversible costs fu n ction .

V( B) – ( I – R), F( B)

b. Th e rate of retu rn µ is set to 8%, th e risk-free rate of retu rn r is set to 4%, an d th e in d ep en d en ce between con ven ien ce yield δ an d stan dard deviation σ is assu m ed.

a = 0.06 a = 0.04 a = 0.02 a = 0.01

I–R

Additional Annualized Net Benefits B of Transgenic Crops FIGURE 9-5. Optimal M inimum Level of Additional N et Benefits B* from Transgenic Crops for Different Drift Rates a When the Risk-Adjusted Rate of Return µ Depends on the Drift Rate a

δ is in depen den t of th e varian ce rate σ. Th e slope an d th e in tersect of th e Marsh allian lin e rem ain th e sam e. Th is is illu strated in Figu re 9-6 an d Table 9-1. Figu re 9-6 an d Table 9-1 also d em on strate th e sen sitivity of B* to ch an ges in th e u n certain ty of fu tu re addition al n et ben efits. If tran sgen ic crops redu ce th e u n certain ty abou t n et ben efits from crops in gen eral, th e u n certain ty abou t th e addition al n et ben efits also will be redu ced, an d h en ce th e valu e of B* will be lower an d th e m axim al tolerable irreversible costs will be h igh er, as

V( B) – ( I – R), F( B)

228 • Chapter 9: Resistance Economics of Transgenic Crops

r = 0.02

r = 0.04

–( I – R)

Additional Annualized Net Benefits B of Transgenic Crops FIGURE 9-6. Optimal M inimum Level of Additional N et Benefits B* from Transgenic Crops for Different Risk-Free Rates of Return r W hen the RiskAdjusted Rate of Return µ Depends on the Risk-Free Rate of Return r

⎛ β − 1⎞ ∂⎜ ⎟ * ∂I B ⎝ β ⎠ B −2 ∂β = β 1 2 2 σ σ ⎦ ⎣ σ

(A8)

Chapter 9: Resistance Economics of Transgenic Crops • 237

Notes 1. Ervin an d oth ers (2000) p rovid e a d etailed su rvey of th e m ost recen t em p irical stu dies on th e en viron m en tal effects of tran sgen ic crop s. 2. Bt co t t o n is gen et ically m o d ified co t t o n t h at p ro d u ces t o xin s o f t h e so il b acteriu m Bacillus thuringiensis to con trol Lep idop teran p ests. 3. I am th an kfu l to Vittorio San tan iello for stressin g th is p oin t. 4. Nobel lau reate Robert C. Merton (1998) p rovided an in terestin g overview of th e ap p lication of op tion p ricin g th eory ou tsid e fin an cial econ om ics. Th e book by Am ram an d Ku latilaka (1999) in clu des several case stu dies of real op tion p ricin g. 5. Mo d ified co rn t h at p ro d u ces t h e δ-en d o t o xin s o f t h e so il b act eriu m Bacillus thuringiensis to con trol th e Eu rop ean corn borer. 6. Th is assu m p tion is often u sed for th is kin d of an alysis (e.g., Alston et al. 1998; Maredia et al. 2000). 7. Mon san to (1999) cited th e p ositive m en tal effect on u sers becau se of th e p ositive im p act of tran sgen ic crop s on th e en viron m en t as on e p ositive ben efit from tran sgen ic crop s. Th e com p an y called th is kin d of ben efit “p eace of m in d.” 8. Th e m otivation for ch oosin g th e risk-adju sted rate of retu rn is th at th e risk of th e ad d ition al ben efits cou ld be tracked with a d yn am ic p ortfolio of m arket assets. µ = r + φσρbm , wh ere r is th e risk-free in terest rate, φ is th e m arket p rice of risk, σ is th e varian ce p aram et er, an d ρbm is t h e co efficien t o f co rrelat io n b et ween t h e asset o r p o rt fo lio o f asset s t h at t rack B an d t h e wh o le m arket p o rt fo lio . See Dixit an d Pin d yck (1994, 147–50) for an elaboration of th is assu m p tion . 9. Th is fo llo ws fro m Eq u at io n 3, V T = BT / (µ – α), wh ere µ an d α are co n st an t s. Hen ce, dV = d[B/ (µ – α)] = [1/ (µ – α)]dB = αV dt + σV dz. 10. Th e effect of an in crease in u n certain ty on th e op tion valu e ch an ges if th e con ven ien ce yield δ is n ot in dep en den t of th e varian ce rate σ an ym ore. Modeled th is way, an in crease in th e varian ce rate σ in creases th e con ven ien ce yield δ. Th e overall effect is a lower op tion valu e, bu t becau se of ch an ges in th e valu e of an im m ediate release V (B), th e overall effect on B* is p ositive. Un d er both m od elin g ap p roach es, th e total effect is an in crease in B*. 11. O f co u rse, t h e lim it s t o t axat io n o r refu ge area are reach ed b y a 100% t ax o r 100% refu ge area, wh ich is sim ilar to n ot releasin g th e tran sgen ic crop . 12. A rem oval, for exam p le, of th e Eu rop ean Un ion m in im u m p rice p olicy, wh ich exists for m an y p rodu cts, m ay in th e sh ort ru n resu lt in an in crease in p rice u n certain ty. In th e lon g ru n , m arkets to h edge th e risk m ay evolve an d redu ce th e p rice u n certain ty.

Commentary

Economics of Transgenic Crops and Pest Resistance: An Epidemiological Perspective Christopher A. Gilligan

P

ercep tion s differ: biologists an d econ om ists view th e dep loym en t of tran sgen ic cro p s fo r p est resist an ce t h ro u gh d ifferen t len ses. By fo cu sin g o n u n certain ty an d irreversibility, th e p ap ers by Morel an d oth ers (Ch ap ter 8, th is vo lu m e) an d Wesseler (Ch ap t er 9, t h is vo lu m e) p ro vid e an ap p ealin g fo cu s from wh ich to bridge th e discip lin es, to ch allen ge assu m p tion s, an d to bu ild a co h eren t fram ewo rk fo r t h e d ep lo ym en t o f t ran sgen ic cro p s. Th e st rat egic d ecisio n abo u t t h e d ep lo ym en t o f t ran sgen ic cro p s co m m o n t o eco n o m ist s an d b io lo gist s, is “sh o u ld we release n o w, sh o u ld we release lat er, o r n o t at all?” Cau tion com es from u n certain ty in th e ben efits an d costs of releasin g a crop carryin g gen es th at h ave n ever before been p resen t in th e gen etic backgrou n d of a widely cu ltivated sp ecies. Th e com m on grou n d between biology an d econ om ics lies in u n certain ty, alth ou gh p ercep tion s of u n certain ty d iffer between th e d iscip lin es, an d to a cert ain ext en t , wit h in t h e t reat m en t s in t h is bo o k by Mo rel an d o t h ers an d Wesseler. Eco n o m ist s fo cu s o n variabilit y in t h e ben efit s an d co st s o f t ran sgen ic cro p s an d o f co n ven t io n al cro p s t o get h er wit h irreversib le co st s an d ben efit s asso ciat ed wit h t ran sgen ic cro p s t h at also m ay be su bject t o u n cert ain t y. Breakd o wn o f resist an ce is assu m ed t o b e in evit ab le an d t h e co st s estim able, alth ou gh th e tim e of breakdown is u n kn own . Th e vagaries of yield, of p est an d p ath ogen d am age, an d of th e growth an d d eclin e of viru len t an d aviru len t p est s are in t egrat ed in t o aggregate variables for econ om ic ben efits th at are su bject to lon g-term tren ds with year-to-year variation s. Th is form of “t o p -d o wn ” an alysis sit s co m fo rt ab ly wit h b o t h b io lo gist s an d eco n o m ist s, alth ou gh we sh all see later th at th e d etails m ay d iffer. More im p ortan t, h ow• 238 •

Commentary: Economics of Transgenic Crops and Pest Resistance • 239

ever, is t h e p ercep t io n o f risk o f resist an ce breakd o wn . Mo lecu lar bio lo gist s m ay con ten d th at breakdown will n ot occu r becau se th e dem an ds th at n ovel form s of resistan ce, su ch as ch itin ase or m ajor gen eric h yp ersen sitive resp on se (St u iver an d Cu st ers 2001), im p o se o n t h e p est o r p at h o gen p o p u lat io n are t o o great fo r t h em t o su rvive. Po p u lat io n bio lo gist s, m o re fam iliar wit h t h e “boom -an d-bu st cycle” of con ven tion ally bred crop s, are likely to be less con fid en t b u t st ill u n willin g t o assert t h at t h e b reakd o wn o f resist an ce is in evitable. An ep idem iologist th erefore asks • Will a viru len t form arise in th e p est or p ath ogen p op u lation th at can overcom e tran sgen ic resistan ce? • Will it in vade? Will it p ersist? • Will it coexist with th e aviru len t form ? • How lon g will it take before th e resistan t form reach es a critical den sity? • Ho w d o es t h e sp at ial p at t ern o f t ran sgen ic cro p s in t h e lan d scap e affect in vasion an d p ersisten ce? • If Bt corn fails in on e state, m u st it be with drawn from all states? Variabilit y o ver t im e an d sp ace is t h erefo re im p o rt an t in bo t h eco n o m ic an d ep id em iological an alyses. Som e season s are m ore con d u cive th an oth ers. Man y n em at o d e an d in sect p est s an d p at h o gen ic m icro o rgan ism s (m ain ly fu n gi an d viru ses as well as som e bacteria) are cap able of rap id m u ltip lication o r d eat h . Th e d yn am ics are h igh ly n o n lin ear. A sm all ch an ge at a crit ical p h ase in p o p u lat io n gro wt h can h ave a p ro fo u n d effect o n su b seq u en t d yn am ics; con versely a larger p ertu rbation m ay h ave little effect as th e p est rap id ly reco vers. Perio d s o f gro wt h are fo llo wed b y su rvival b et ween cro p s wh en t h e viru len t fo rm m ay be at a d isad van t age relat ive t o t h e p revio u sly en d em ic aviru len t form . An d sp read occu rs at th e farm , region al, an d con tin en t al scale in so -called sp at ially ext en d ed syst em s acro ss a h et ero gen eo u s m osaic of fields th at can th em selves lim it th e sp read of disease. So h ow d o we op en u p th e d ialogu e between th e p ion eerin g an d ch allen gin g work of Morel an d oth ers (Ch ap ter 8, th is volu m e) an d Wesseler (Ch ap ter 9, th is volu m e) wh o an alyzed d ep loym en t in th e p resen ce of u n certain ty an d irreversible costs an d ben efits with th e ep id em iological ap p roach es th at focu s o n st o ch ast icit y an d n o n lin earit y in p erio d ically d ist u rb ed an d sp at ially exten d ed system s? In th is com m en tary, I p rop ose to su m m arize an ep id em iologist’s p ersp ective of th e p rin cip al “take-h om e m essages” from Morel an d o t h ers an d Wesseler in t h is b o o k an d t o review t h e p rin cip al assu m p t io n s an d im p licat io n s o f t ran sgen ic cro p s fo r p est resist an ce. Th en , u sin g exam p les d rawn fro m recen t wo rk in ep id em io lo gy, I p ro p o se very b riefly t o review t h e irreversib ilit y o f resist an ce b reakd o wn an d t o id en t ify sp at ial strategies for m in im izin g th e risks of in vasion . Fin ally, I sh all revert to con sid eration of stoch asticity an d scale in brid gin g th e in terface. Th e treatm en t

240 • Commentary: Economics of Transgenic Crops and Pest Resistance

is n o t exh au st ive. It is select ive an d d esign ed t o ad van ce t h e d ialo gu e between econ om ists an d biologists on th e release of tran sgen ic crop s for p est an d d isease con trol.

Principal Results Con ven tion al wisdom in th e dep loym en t of n ew varieties of crop s focu ses on cost–ben efit an alysis. A n ew variety is released im m ediately if th e n et ben efits (calcu lated as th e d ifferen ce between variable ben efits an d variable costs) are greater th an for th e con ven tion al crop . In th e case of tran sgen ic crop s, variable p esticid e costs are red u ced , an d gross reven u es m ay in crease becau se of en h an ced yield from a n ew agron om ically im p roved an d p est-resistan t variety. Morel an d oth ers an d Wesseler con vin cin gly argu ed th at th is relian ce on cost–ben efit an alysis is n aïve. First, th ey state th at it fails to take in to accou n t m ajo r irreversib le co st s an d b en efit s t h at m ay acco m p an y t h e release o f a tran sgen ic variety. Secon d, it fails to take in to accou n t u n certain ty in year-toyear variation in yield , p est d am age, an d oth er in p u t variables. Decision m akin g u n d er u n cert ain t y—sh o u ld we release t h e t ran sgen ic cro p n o w, lat er, o r n ever?—leads to form u lation of th e p roblem via op tion th eory. Pu t sim p ly, t h is m ean s (t o a n o n sp ecialist ) t h at a go vern m en t o r o t h er organ ization obtain s th e righ t to dep loy a tran sgen ic crop with in a given tim e fram e. Th e tim e at wh ich to release th e crop is obtain ed by op tim izin g a fu n ct io n t h at in co rp o rat es ben efit s an d co st s u n d er u n cert ain t y wit h a d isco u n t rate on th e in vestm en t. Th is yields a critical valu e (variou sly rep resen ted as V * or B*) for n et ben efits of th e tran sgen ic crop n ecessary for release of th e crop . Release is t h erefo re d elayed u n t il n et b en efit s m at ch o r su rp ass t h e crit ical valu e. Th e delay reflects th e op tion of waitin g for m ore in form ation to assess wh eth er th e ben efits are greater th an th e costs. A sim p lified sch em e to illu st rat e t h e ap p ro ach es o f Mo rel an d o t h ers an d Wesseler is given in Tab le 1. So m e o f t h e p rin cip al variab les an d p aram et ers are su m m arized in Tab les 2 an d 3, bu t n ote th at p aram eters with th e sam e m ean in g h ave d ifferen t sym bols in th e two p ap ers. Th ree im p ortan t resu lts em erge. First, th e critical valu e th at m u st accru e for release o f a t ran sgen ic cro p is am p lified in t h e p resen ce o f u n cert ain t y [see Eq u ation 2 in Morel an d oth ers (Ch ap ter 8), Eq u ation A6 in Wesseler (Ch ap ter 9), an d Tab le 1 in t h is co m m en t ary]. Seco n d , so m e co u n t erin t u it ive resu lt s em erge for an alysis of Bt corn wh ereby m an datory refu ge areas an d tax in cen tives th at m igh t be exp ected to d elay release actu ally p rom ote earlier release (Wesseler). Th ird, in illu stratin g th e ap p lication of real op tion s an alysis to th e release o f Bt co rn , Mo rel an d o t h ers sh o w t h at wh ile a sim p le co st –b en efit an alysis wou ld favor release, p relim in ary allowan ce for u n certain ty d oes n ot.

Commentary: Economics of Transgenic Crops and Pest Resistance • 241

TABLE 1. Simplified Scheme To Summarize Approaches of M orel and Others (Chapter 8) and Wesseler (Chapter 9) Real option Morel and

Rational option

othersa

Generic m odel a Model

dV = αV dt + σV dz

Meth od

F(V ) = m ax E[(V − I )e −ρt

In feren ce/ decision

Criterion

Bt corn

αρ Wait forever

0 0

Γ = f ( α, ρ, σ )

H (V , T ; t ) = V (t )φ( d1 ) − e − ρt Iφ( d2 ) di = f (T ,V , ρ, σ )

dB = µBdt + ηBdz dP = γPdt + σPdz

dB = µBdt + ηBdz dP = γPdt + σPdz

V > V * = ΓI

m odela

Model

Meth od

F( B, P) = m ax E[( B − P)e −ρ

H ( B, P, T ; t ) = B(t )φ( d1 ) − e − ρt P(t )φ(

Criterion

β ⎛ B⎞* =Γ ⎜ ⎟ = ⎝ P⎠ β −1

B(t ) ≥ B* =

Γ = f ( µ, γ , η, σ, ξ, ρ)

di = f ( B, P, T ), T = g( σ, ξ, η

φ( d2 ) P(t ) φ( d1 )

W esseler a Model

dB = αBdt + σBdz

Meth od

F(V ) = m ax E[(V − ( I − R))e −λT ]

Criterion

B* =

β1 = δ( I − R) β1 − 1

B(T ) ⎛ β1 − 1 ⎞ ⎟ ⎜ δ ⎝ β1 ⎠ β1 = f (r, δ, σ ) I* = R +

a. Prin cip al variables an d p aram eters are su m m arized in Tables 2 an d 3.

Th e detailed ap p roach es differ between th e two ch ap ters. Morel an d oth ers distin gu ish ed in p articu lar between real op tion s (Dixit an d Pin dyck 1994) an d rat io n al o p t io n ap p ro ach es (Hu ll 2000) (Table 1), wh ereas Wesseler co n cen t rat ed o n real o p t io n s. Each ap p ro ach lead s t o a t h resh o ld crit erio n fo r n et

242 • Commentary: Economics of Transgenic Crops and Pest Resistance

ben efit of tran sgen ic crop s. Morel an d oth ers derived th e criterion V > V * = ΓΙ, wh ere Γ is an em p irical m easu re of p recau tion th at reflects th e u n certain ty in th e ben efits, V is th e valu e of th e n et ben efits of growin g a tran sgen ic crop , an d I is th e cost of in vestm en t. Th e p recau tion ary m u ltip lier (Γ) d eterm in es h o w m u ch t h e act u al valu e o f t h e p o licy sh o u ld be abo ve it s co st t o ju st ify releasin g a n o vel cro p [see also t h e an n u alized h u rd le rat e u sed by Wesseler (Table 9-2)]. Becau se Γ is greater th an or eq u al to on e (with Γ = 1 wh en th ere is n o u n certain ty), Morel an d oth ers argu ed th at it can be u sed as a q u an titative in terp retation of th e p recau tion ary p rin cip le for u se in regu latin g p olicy. Th e p rin cip le req u ires th at p recau tion ary m easu res be taken wh en th ere is a p erceived th reat for u n certain decision s with irreversible costs. Th is is an in terestin g an d ch allen gin g ap p roach th at id en tifies a way forward . It d em an d s fu rth er work, h owever, on several im p ortan t issu es. Th ese will n ot be d iscu ssed fu rth er h ere bu t in clu de: • d efin it io n , q u an t ificat io n , an d est im at io n o f irreversib le co st s fo r t ran sgen ic crop s; • recon ciliation of su bjective an d freq u en tist p robabilities (Barn ett 1999) for costs an d ben efits with in th e th eoretical fram ework; an d • com p arison of th e op tion s ap p roach with form al decision th eoretic fram eworks th at in corp orate u tilities an d Bayesian an alysis to u p date p rior in form ation (Ch ern off an d Moses 1959; Sm ith 1988). W h atever th e form of an alysis, th e irreversible costs of tran sgen ic crop s on t h e righ t -h an d sid e o f t h e t h resh o ld crit erio n will seld o m be kn o wn . Mo rel an d oth ers th erefore su bsu m ed it in to th eir later an alysis as a com p on en t of variab le co st s an d b en efit s asso ciat ed p rin cip ally wit h co n ven t io n al cro p s. Th e argu m en ts for th is strategy are su btle, bu t it does allow th em to in corp orate u n certain ty for th ese costs in to th e m od el. Wesseler skillfu lly tu rn ed th e p roblem arou n d to ackn owled ge th at th e irreversible costs I are n ot kn own , b u t it is p o ssib le t o so lve fo r I* t o d efin e t h e m axim u m t o lerab le co st s fo r given n et ben efits (B) an d irreversible ben efits (R) (see Table 2). He th erefore com p u ted th e m axim al tolerable irreversible costs I* = R +

B(t ) B(t ) − δ δβ

in wh ich t h e seco n d t erm acco u n t s fo r irreversib ilit y an d u n cert ain t y an d accordin gly deflates th e critical valu e for I for wh ich release of th e tran sgen ic crop is d elayed . Th is still leaves th e irreversible ben efits to be estim ated , bu t th e two ap p roach es offer scop e for fu rth er an alysis. Both ch ap ters sh ow th e effects of selected p olicy im p acts on th e decision to release tran sgen ic crop s. Th ese can be u n d erstood by an alyzin g th e effects of

Commentary: Economics of Transgenic Crops and Pest Resistance • 243

ch an ges in t h e gro wt h rat e (α) an d t h e varian ce (σ) o f B o n eit h er V * o r I*. Som e of th ese are su ccin ctly su m m arized in Table 9-2 in Wesseler. W h ereas th e real op tion s ap p roach em p loys op tim ization , Morel an d oth ers sh o wed t h at t h e rat io n al o p t io n b ased o n t h e Black–Sch o les fo rm u la focu ses on risk n eu trality. Hen ce, th e ration al op tion seeks to fin d a “risk-n eu t ral” st rat egy t h at in vo lves a level o f risk co m p arab le wit h a riskless in vest m en t su ch as a govern m en t bon d . In th e case of Bt corn , th e riskless strategy m ay argu ab ly b e seen as gro win g co n ven t io n al co rn . Th e crit ical valu e fo r action n ow dep en ds on th e stop p in g tim e wh en resistan ce is con sidered to be co m p let e an d t h e t ran sgen ic cro p m u st b e wit h d rawn (see Tab les 2 an d 3). Th e an alysis allo wed Mo rel an d o t h ers t o d ist in gu ish b et ween t wo regim es (on e in volvin g low stoch asticity an d th e oth er h igh stoch asticity) an d th eir relation sh ip s with stop p in g tim e.

Variables and Parameters It is co n ven ien t t o assess t h e eco n o m ic m o d els in t erm s o f t h e variab les, p aram eters, assu m p tion s, an d in feren ces th at em erge to assist th e bridge with biology in order to lin k econ om ic an d ep idem iological th eory.

Variables

Several can didate variables ap p ear. Each m ay be su bject to u n certain ty with a m ean valu e t h at ch an ges o ver t im e. In p ract ice, so m e irreversib le co st s are co n sid ered kn o wn o r fixed , wh ile sim p lificat io n o f t h e an alysis su p p o rt s aggregat io n o f variables. Here im p o rt an t d ist in ct io n s em erge bet ween Wesseler, wh o m o d eled t h e n et b en efit s o f t ran sgen ic relat ive t o co n ven t io n al crop s by a sin gle stoch astic d ifferen tial eq u ation , an d Morel an d oth ers, wh o in trodu ced sep arate stoch astic eq u ation s for n et ben efits in tran sgen ic an d in con ven tion al crop s, wh ile d rop p in g irreversible costs an d ben efits wh en th ey an alyzed th e release of Bt corn (see Table 1). Sep aration allows m ore con trol over th e tren d in n et ben efits for th e two crop s as well as in th e year-to-year variability. It also allows for correlation in th e varian ces wh en con ven tion al an d tran sgen ic crop s are su bject to sim ilar p attern s of extern al forcin g su ch as weath er or p rices. Th ere is scop e for m ore carefu l con sideration of th e relative im p ortan ce of biologically, en viron m en tally, an d econ om ically d riven in flu en ces in th e m agn itu d e of tren d s, varian ces, an d covarian ces in th e u n d erlyin g variables. We m ay fin d th at for certain crop s, p reoccu p ation s with biologically an d en viron m en tally d riven varian ces m ay be im p ortan t in in flu en cin g q u alit at ive beh avio r—fo r exam p le wh et h er o r n o t a viru len t fo rm em erges. Th ey m ay be less im p ortan t for th e q u an titative effect of th e year-to-year variation in n et ben efit, bu t we do n ot yet kn ow.

244 • Commentary: Economics of Transgenic Crops and Pest Resistance

Th e t em p o ral d yn am ics o f t h e aggregat ed variab les are m o d eled b y st o ch ast ic d ifferen t ial eq u at io n s fo r geo m et ric Bro wn ian m o t io n fro m wh ich two im p ortan t in flu en ces em erge: variability is m od eled by a Wien er p rocess t h at is elegan t an d sim p le (see Figu re 9-1 in Wesseler) an d fo r wh ich Mo rel an d oth ers id en tified a robu st m eth od for estim atin g th e associated varian ce p aram et er. Rat h er m o re su rp risin g fo r t h e b io lo gist is t h e assu m p t io n o f a sim p le exp o n en t ial t ren d fo r t h e co n t in u ed gro wt h in n et b en efit . Lim it at io n s t o gro wt h are m o re fam iliar t o bio lo gist s, fo r wh ich o t h er m o d els are availab le [see, fo r exam p le, Dixit an d Pin d yck (1994) fo r eco n o m ics, Gard in er (1985) fo r p h ysical scien ces, an d Nisb et an d Gu rn ey (1982) fo r b io logy]. Th e exp on en tial tren d is ju stified by Morel an d oth ers an d Wesseler by referen ce t o em p irical d at a fo r co rn . It seem s likely, h o wever, t h at fu t u re wo rk will exam in e alt ern at ive m o d els t h at im p o se so m e asym p t o t ic lim it . Wesseler (2001) h as alread y exp lo red t h e u se o f a m ean -revert in g p ro cess (Dixit an d Pin d yck 1994) t o acco u n t fo r d ecreasin g n et b en efit fro m t ran sgen ic crop s as p ests becom e resistan t to p lan t-p rod u ced toxin s. Not su rp risin gly, th is can m arked ly ch an ge th e in feren ces. Th e selection of an u n d erlyin g m od el for n et ben efits n eed s to be con sid ered alon g with th e tim e cou rse over wh ich sim u lation s are ru n an d th e ran ge over wh ich th e stop p in g tim e fo r gro wt h o f t h e cro p relat ive t o resist an ce is en visaged . Param et ers an d o t h er co n st rain t s m ay ch an ge o ver lo n g p erio d s, n ecessit at in g a st ep p ed o r grad u al ch an ge in p aram eters an d p erh ap s too a ch an ge in m od el stru ctu re. I co n clu d e t h at aggregat io n o f n et b asic variab les is u sefu l. Mo re wo rk n eeds to be don e in exp lorin g altern ative m odels for th e ch an ge in n et ben efit s o ver t im e an d fo r t h e in t erp lay bet ween en viro n m en t al, bio lo gical, an d econ om ic drivers in th ese variables.

Parameters

Th ree fu n d am en t al classes o f p aram et ers can b e reco gn ized in t h e m o d els (see Tab le 3). Th ese are (a) m ean gro wt h rat es fo r n et b en efit s (t o wh ich wo u ld b e ad d ed o t h er lim it in g p aram et ers fo r asym p t o t ically lim it ed m o d els), (b ) d isco u n t rat es fo r t h e ret u rn o n in vest m en t (in clu d in g risk-free in t erest rat es fro m go vern m en t b o n d s fo r co m p ariso n wit h in vest m en t in t ran sgen ic cro p s), an d (c) varian ces (also kn o wn as vo lat ilit ies) an d co varian ces for n et ben efits. A fou rth class con sists of d erived p aram eters th at are u sed as p recau t io n ary m u lt ip liers t o allo w fo r u n cert ain t y in d ecisio n s t o release tran sgen ic crop s. Th ese are strategically th e m ost im p ortan t p aram eters becau se th ey lin k u n certain ty an d h en ce en viron m en tal, biological, an d econ om ically d riven variability with criteria for d ecision s abou t wh eth er it is econ om ically ju stified to release tran sgen ic crop s. In th e followin g section , I will d iscu ss th e relation sh ip between econ om ic an d biological varian ces.

Commentary: Economics of Transgenic Crops and Pest Resistance • 245

TABLE 2. Summary of the Principal Variables Used in Economic Analyses Description Variable ben efits of tran sgen ic crop

Variable costs of tran sgen ic crop s

Variable ben efits of con ven tion al crop Variable costs of con ven tion al crop Irreversible ben efits of tran sgen ic crop Irreversible costs of tran sgen ic crop

Com ponents

Ma

W

a

Yield, p est, an d p ath ogen dam age driven by en viron m en tal an d dem ograp h ic stoch asticity Com m odity p rices Fertilizer, p esticide in p u t for n on target p ests, h arvestin g In p u t p rices Im p osition of q u otas or en viron m en tal taxes Man agem en t con strain ts (e.g., refu gia) Resp on ses to m an age em ergen ce of viru len t p ests Sam e as for tran sgen ic crop Sam e as for tran sgen ic crop with addition al p esticide in p u ts Lower p esticide u se leadin g to Redu ced residu es in soil, water, an d crop s Redu ced risk of resistan ce to th ese p esticides Pest or p ath ogen overcom es resistan ce in tran sgen ic crop b Gen e tran sfer to oth er sp ecies esp ecially weeds Harm to n on target sp ecies su ch as oth er in vertebrates Sq u an derin g of resistan ce or toxin gen es by p rom otin g p rem atu re bu ildu p of cou n ter m easu res in p est p op u lation Loss of Bt toxin as a p esticide

R

I

Aggregated variables Net ben efit of tran sgen ic crop Net ben efits of con ven tion al crop Net ben efits of tran sgen ic over con ven tion al crop s

= ben efits – costs

B

= ben efits – costs

P

= (ben efits – costs) tran sgen ic – (ben efits – costs) con ven tion al

B

Critical tim es Tim e of release of tran sgen ic crop Stop p in g tim e for rem oval of tran sgen ic crop

T

T

a. M,W sym bols u sed by Morel an d oth ers (Ch ap ter 8) an d Wesseler (Ch ap ter 9). b. Pest resistan ce is com m on ly regarded as irreversible bu t m ay be a variable cost if it is m an ageable.

246 • Commentary: Economics of Transgenic Crops and Pest Resistance TABLE 3. Principal Parameters Used in the Economic Analyses Morel and others Generic Bt corn m odel m odel

Param eter Mean growth rates Drift rates for n et ben efits/ valu e Discount rates Discou n t rate on in vestm en t Risk-free in terest rate Variances Varian ce/ volatility in n et ben efits/ valu e Covarian ce between u n certain ty in tran sgen ic an d con ven tion al crop s Derived param eters Precau tion ary m u ltip lier Hu rdle rate Con ven ien ce yield

α

GM a

CC b

µ

γ

ρ

σ

W esseler

α

ρ ρ

η

λ, µ r

σ

σ

ξ Γ = β/ (β – 1) β/ (β – 1) δ=µ–α

a. Gen etically m odified, tran sgen ic crop . b. Con ven tion al crop

Assumptions and Biological Implications Assumptions

Th e an alyses are based on th ree im p ortan t assu m p tion s abou t th e growth of t ran sgen ic cro p s co n cern in g sp ace an d t h e way t h at resist an ce arises. Mo st im p ortan t, from an ep id em iological p ersp ective, is th e assu m p tion of m ean field resp on ses, wh ereby th e growth of a tran sgen ic crop in a state or even a cou n try is treated as th ou gh it occu rs in a sp atially u n iform en viron m en t. Th e seco n d assu m p t io n is t h at resist an ce is in evit ab le. Th e t h ird assu m p t io n is t h at resist an ce is in st an t an eo u s (albeit at so m e u n kn o wn t im e), u biq u it o u s, an d irreversible. Th ese assu m p tion s can be ch allen ged, bu t th ey are still a n ecessary an d valu able startin g p oin t. Th e assu m p tion of sp atial h om ogen eity in p articu lar is d iscu ssed below. Irreversibility of resistan ce is im p licitly relaxed in th e way th at Morel an d oth ers an alyzed th e d yn am ics of Bt corn by op tim izin g wit h resp ect t o n et b en efit s fo r t ran sgen ic an d co n ven t io n al cro p s each su bject to u n certain ty (see Table 1) bu t with ou t allowan ce for irreversible costs. Th is im p lies th at th e irreversible costs are su bsu m ed in to th e n et ben e-

Commentary: Economics of Transgenic Crops and Pest Resistance • 247

fits for th e con ven tion al crop , th ereby allowin g for som e u n certain ty in th e irreversible costs (Farrow 2001). Th e distin ction , q u an tification , an d in terp retation of irreversible costs an d th eir relation sh ip to p est resistan ce deserve fu rth er detailed stu dy.

Biological Implications

Pu t sim p ly, t h e p rin cip al b io lo gical im p licat io n o f t h e an alyses is t h at t h e great er t h e u n cert ain t y in n et b en efit s an d irreversib le co st s o f t ran sgen ic crop s, th e m ore cau tiou s we sh ou ld be in releasin g th ese n ovel crop s. Morel an d oth ers sh owed th is elegan tly in th eir illu strative an alyses of Bt corn given in th eir Table 8-3 in wh ich th ey com p ared stan dard cost–ben efit an alysis th at fails t o t ake u n cert ain t y in t o acco u n t wit h t h e real o p t io n ap p ro ach . Th ey con clu ded th at wh ereas a stan dard an alysis leads to a con clu sion to release Bt co rn , t h e p recau t io n ary m u lt ip lier fo r t h e real o p t io n ap p ro ach is su ch t h at allo wan ce fo r u n cert ain t y m ilit at es again st im m ed iat e release. Mo reo ver, an alysis with an d with ou t a breakd own of resistan ce su rp risin gly ap p ears to m ake little differen ce, im p lyin g th at variability in year-to-year yield of crop s is dom in an t over th e risk of Bt resistan ce. Th is req u ires fu rth er sen sitivity an alysis o f t h e m o d el t o t h e p aram et ers as well as t o t h e assu m p t io n s an d fu n ction al form s. Morel an d oth ers stressed th at th eir an alysis is p relim in ary an d n ot p rescrip tive. O n e o f t h e d ecisio n s is t o d elay release o f a t ran sgen ic variet y. Th is is exp lo red in Wesseler’s ch ap t er an d clearly illu st rat ed in h is Figu res 9-3 th rou gh 9-7. W h eth er later release is recom m en ded dep en ds on • co n t in u ed gro wt h in n et b en efit s su ch t h at t h e n et b en efit s even t u ally exceed th e critical valu e, • red u ct io n in u n cert ain t y as m o re in fo rm at io n b eco m es availab le so t h at th e p recau tion ary m u ltip lier is redu ced, an d • reliable estim ates for irreversible costs associated with en viron m en tal risk d am age associated with th e tran sfer of Bt or oth er toxin s to weed sp ecies. Th e assu m p tion of con tin u ed growth in yield is reason able on ly so lon g as agricu lt u re rem ain s free o f m ajo r ch an ges, su ch as t h e im p o sit io n o f severe p en alties for th e u se of p esticid es an d a m ove toward lower in p u t, lower ou tp u t crop s. Notwith stan d in g d evelop m en ts in p est forecastin g an d im p roved efficien cy in fertilizer u se, sign ifican t red u ction s in th e u n certain ties associated with crop growth are u n likely to occu r, bu t it m ay well be p rofitable to an alyze th e com p on en ts of variability an d th e degrees of correlation . Fu rt h er wo rk o n sen sit ivit y an alysis in it iat ed by Wesseler an d Mo rel an d o t h ers is im p erat ive t o get h er wit h co n t in u ed d ialo gu e wit h b io lo gist s t o exp lore th e sen sitivity an d dyn am ics of th e system s.

248 • Commentary: Economics of Transgenic Crops and Pest Resistance

Reversible and Irreversible Costs and the Invasion and Persistence of Pest Resistance W h eth er th e occu rren ce of a resistan t p est or p ath ogen is a reversible or irreversib le co st d ep en d s fro m a b io lo gical p ersp ect ive o n t h e p o p u lat io n d yn am ics of in vasion , p ersisten ce, scale, an d h eterogen eity. Th eoretical an d exp erim en tal work in th is area is sp read th rou gh a d iverse bu t related ran ge o f d iscip lin es. A co h eren t t h eo ret ical fram ewo rk, h o wever, is slo wly em ergin g th at lin ks th e in vasion of weed s, p ests, an d p ath ogen ic m icroorgan ism s, in clu d in g p esticid e an d fu n gicid e resistan ce an d th e sp read of an tibiotic an d an tiviral d ru g resistan ce in bacterial an d viral p op u lation s. Th e fu n d am en tal q u est io n s su p p o rt in g t h e fram ewo rk are essen t ially t h e sam e. Will a resist an t, aggressive, or viru len t strain in vad e th e p arasite p op u lation or will it be elim in at ed ? Will it p ersist ? If it d o es in vad e, will it co m p let ely rep lace t h e su scep tible or aviru len t strain , or can th e two strain s coexist? How lon g will it take before th e resistan t form reach es a critical d en sity? Coexisten ce m att ers. It reflect s a balan ce o f select io n fo rces an d fit n ess co st s an d affect s t h e st abilit y o f eq u ilibria o bt ain ed by gen et ic st rat egies fo r t h e co n t ro l o f p est s an d d isease. Here I wan t to m ake th e followin g p oin ts. • Th eoretical p rogress can be m ade in p redictin g th e risk of in vasion an d p ersisten ce of resistan t p ests an d p arasites. • Determ in istic m odels are u sefu l in iden tifyin g cru de criteria for in vasion . • Stoch astic m odels are essen tial for u n derstan din g th e risks of in vasion an d for iden tifyin g criteria for p ersisten ce. • In vasion is n ot in evitable, even wh en a resistan t form arises. • Th e sp atial stru ctu re of th e tran sgen ic an d con ven tion al crop s in th e lan dscap e are critical in determ in in g th e ch an ces of in vasion an d p ersisten ce. • Failu re to allow for sp atial stru ctu re m ay seriou sly bias estim ates of in vasion an d assessm en ts of th e risk of breakdown of resistan ce. Two im p o rt an t m et h o d o lo gical an d d yn am ic feat u res em erge fro m wo rk on in vasion an d p ersisten ce. Th ese are h eterogen eity in sp ace an d tim e. Tem p o ral h et ero gen eit y o ccu rs as p erio d ic an d st o ch ast ically d riven ch an ges in d rivin g variables su ch as tem p eratu re. It also arises as d iscon tin u ities between crop an d in tercrop p eriod s. Th is, in tu rn , affects th e ability of th e viru len t or co u n t erresist an t st rain s t o co m p et e wit h wild -t yp e st rain s. Sp at ial h et ero gen eit y reflect s t h e d ist ribu t io n o f cro p p lan t s. Large t ract s o f a sin gle cro p , su ch as corn , with a u n iform m od e of resistan ce to a p est or d isease are n otorio u sly su scep t ible t o in vasio n by a viru len t o r co u n t erresist an t st rain . Th is was d evast at in gly sh o wn b y t h e h u ge lo sses cau sed b y So u t h ern co rn leaf

Commentary: Economics of Transgenic Crops and Pest Resistance • 249

b ligh t in t h e Un it ed St at es in 1970. Lo sses am o u n t in g t o 15% o f t h e t o t al U.S. cro p (2.5 × 10 7 h ect ares) o ccu rred wh en race T o f t h e fu n gu s Bipolaris m aydis sp read rap id ly t h ro u gh t h e p revio u sly resist an t cro p (Zad o ks an d Sch ein 1979). Alt h o u gh co rn variet ies at t h e t im e carried several d ifferen t gen es for resistan ce to B. m aydis, 85% of th e U.S. acreage was p lan ted to a relatively sm all n u m ber of varieties of h ybrid m aize th at carried th e sam e cytop lasm ic m ale st erilit y gen e. Th is ren d ered 85% o f t h e cro p gen et ically u n ifo rm an d su scep t ib le t o race T o f t h e p at h o gen , wit h d evast at in g co n seq u en ces t h at led t o co m p let e lo ss in m an y p laces b ecau se o f t h e efficien t an d rap id aerial d isp ersal o f t h e fu n gu s. Th e wo rk o f Peck an d o t h ers (1999; 2000) an d Tabash n ik (1994) h as focu sed on Bt cotton an d corn , wh ere con sid erable atten tion is given to h igh -d ose strategies togeth er with th e role o f refu gia, in wh ich p o p u lat io n s o f su scep t ib le p est s are su st ain ed t o d elay t h e b u ild u p o f resist an ce t o t h e t o xin in p est p o p u lat io n s. Man y cro p s in Eu rop e are grown in h eterogen eou s m osaics with in th e lan d scap e. An exam p le is given in Figu re 1 for growth of su gar beet in East An glia an d th e Un ited Kin gd om . 1 Th e figu re sh ows stoch astic realization s of th e sp read of an in trod u ced d isease, Rh izo m an ia, in East An glia (Figu re 1a an d b). Th is viru s d isease is carried b y a fu n gal vect o r an d is sp read b y m o vem en t o f so il o n m ach in ery bet ween farm s. Th e sp read is lo calized aro u n d a few in it ial fo ci. Figu re 1d , e, an d f sh ows th e resu lt of two sim u lation s for th e sp read of d isease in to oth er su gar-beet growin g areas in th e Un ited Kin gd om . From Figu re 1 it m ay be seen th at m arked ly d ifferen t scen arios m ay be obtain ed for id en t ical p aram et ers fo r in t en sificat io n , cro p su scep t ib ilit y, an d t ran sm issio n wh en allowan ce is m ad e for stoch astic variability. In vasio n an d p ersist en ce o f resist an t an d su scep t ib le st rain s p lay an im p o rt an t p art in assessin g u n cert ain t y an d in t h e sp at ial an d t em p o ral d ep lo ym en t o f t ran sgen ic cro p s. Each o f t h ese p ro cesses im p in ge o n t h e reversible an d irreversible costs an d ben efits listed in Table 2 as well as on th e crit ical t im es fo r release an d rem o val o f t ran sgen ic cro p s in ways t h at h ave yet t o b e rigo ro u sly exp lo red . Th e t h reat s t o t ran sgen ic cro p s are clear if a resist an t p est arises. Bu t p ersist en ce an d co exist en ce o f co m p et in g st rain s t h at can gro w o n co n ven t io n al cro p s affect t h e m ean p erfo rm an ce an d u n certain ty of th ese in q u ite su btle bu t, argu ably, p red ictable ways. Con sid erable p ro gress m ay be m ad e by est im at in g t h e m agn it u d e o f t h ese effect s o n t h e u n cert ain t ies relat ive t o eco n o m ically d riven ext ern alit ies. O n ly if t h e bio lo gically an d en viro n m en t ally d riven co m p o n en t s are sm all can t h ey be safely ign o red . In t h e fo llo win g sect io n , I sh o w b riefly h o w t h resh o ld s fo r in vasion can be d erived from sim p le ep id em iological assu m p tion s an d h ow th ese can be elaborated to allow for stoch asticity an d sp atially exten d ed p op u lation s of field s of tran sgen ic crop s.

250 • Commentary: Economics of Transgenic Crops and Pest Resistance

King's Lynn Norwich Peterborough

Bury St. Edmunds Cambridge Ipswich

A

King's Lynn Norwich Peterborough

Cambridge

Bury St. Edmunds

Ipswich

B FIGURE 1. Spatial Heterogeneity of Disease Spread through a Heterogeneous M osaic within the Landscape ( Figure continues on the following page.) Note: Please see n ote 1 at th e en d of th e ch ap ter.

Commentary: Economics of Transgenic Crops and Pest Resistance • 251

King's Lynn

Norwich

Peterborough

Bury St. Edmunds Cambridge Ipswich

C

King's Lynn Cambridge Bedford

Ipswich London

D FIGURE 1. Spatial Heterogeneity of Disease Spread through a Heterogeneous M osaic within the Landscape ( continued) ( Figure continues on the following page.)

252 • Commentary: Economics of Transgenic Crops and Pest Resistance

King's Lynn Cambridge Bedford Ipswich London

E FIGURE 1. Spatial Heterogeneity of Disease Spread through a Heterogeneous M osaic within the Landscape ( continued)

Invasion and Persistence In vasion in volves th e m u tation of an en dem ic strain or th e im m igration of a resist an t st rain fo llo wed b y sp read wit h in t h e su scep t ib le p o p u lat io n . Th e stu dy of in vasion n atu rally gives rise to th e con cep t of th resh olds. Th is m ean s th at invasion is not inevitable. Certain criteria m u st be satisfied for in vasion to occu r. Hen ce th e resistan t strain m ay be elim in ated ; it m ay in crease rap id ly, exh au st th e su p p ly of su scep tible h osts, an d be elim in ated; or it m ay switch to a n ew eq u ilib riu m st at e an d co exist wit h t h e h o st an d p revio u sly en d em ic (su scep tible) strain s of th e p arasite. In vasion th resh olds often are related to th e basic reprodu ctive n u m ber of a parasite R0 , u su ally defin ed as th e average n u m ber of n ew in fection s produ ced wh en a sin gle in fective in dividu al is in trodu ced in to a wh olly su sceptible h ost p op u lation (Heesterbeek an d Roberts 1995). Th is con cep t is cen tral to th e an alysis of th e popu lation dyn am ics of h ost–parasite in teraction s an d, clearly, for a parasite to in vade requ ires R0 > 1. In vasion criteria also can be defin ed in term s of a th resh old h ost den sity above wh ich in vasion can occur. Th e relation sh ips between th ese two criteria are an alyzed in Gubbin s an d oth ers (2000).

Commentary: Economics of Transgenic Crops and Pest Resistance • 253

In vasion criteria reflect th e p aram eters of th e u n d erlyin g m od el. Th u s for a sim p le ep id em io lo gical m o d el d efin in g t h e flo ws o f su scep t ib les (S) t o in fected s (I) dS = (b0 −b1 N )S − (d0 + d1 N )S − βIS dt

dI = βIS − (µ + d0 + d1 N ) I dt

wh ere N = S + I is t h e t o t al h o st d en sit y. Th e cro p p o p u lat io n h as d en sit ydep en den t birth (b 0 – b 1 N) an d death (d0 + d 1 N) rates, wh ich im p ly th at, in th e ab sen ce o f in fect io n , t h e h o st p o p u lat io n in each p at ch gro ws lo gist ically with n et rate r = (b0 – d0 ) to carryin g cap acity κ = (b 0 – d 0 )/(b 1 + d 1 ). Th e p aram eter µ is th e d isease-in d u ced d eath rate of in fected h osts. Th e corresp on d in g valu e for R0 is given by R0 =

βκ µ + d0 + d1 κ

If R0 < 1, th e in fection is elim in ated, an d th e su scep tible p op u lation grows to its carryin g cap acity κ. Con versely, if R0 > 1, th e in fection can establish itself, an d t h e su scep t ible an d in fect ed h o st s co exist at st able levels. Th e in vasio n crit erio n can b e rewrit t en in t erm s o f a crit ical p at ch size t h at m u st b e exceeded for an in vasion to occu r (Gu bbin s et al. 2000). In th is case, th e p arasite can on ly in vade th e h ost p op u lation p rovided th at κ>

µ + d0 β − d1

wh ere κ is n ow th e critical p atch size. If th e p atch size is below th e th resh old level, th e p arasite can n ot p rodu ce su fficien t n ew in fection s to establish itself. Alth ou gh m ost m odels like th ese were design ed with plan ts as th e u n its an d fields defin in g popu lation size, th e m odels can be scaled u p to con sider popu lation s of field s in wh ich wh ole field s are classified as su scep tible or in fected an d th e critical p atch size n ow d efin es aggregation s of field s. Exp loration of th e p aram eter sp ace th en allows som e cru d e in sigh t in to h ow ch an ges in th e param eters associated with tran sm ission rates an d croppin g frequ en cies can be u sed t o in h ibit in vasio n . Th e m o d els can be ext en d ed t o co n sid er field s as occu piable poin ts, an d th e spread of resistan t form s is m odeled as a probabilistic cellu lar au tom aton (Keelin g an d Gilligan 2000) or as a p ercolation p rocess o n a lat t ice (see fo r exam p le, Bailey et al. 2000) fro m wh ich it is p o ssible t o com pu te th e probability of th e spread of a resistan t form . More u su ally, sp ace is exp licitly in clu d ed by th e u se of d isp ersal kern els or as m etap op u lation (Park et al. 2001) in wh ich fields or region s are regarded as

254 • Commentary: Economics of Transgenic Crops and Pest Resistance

aggregation s of loosely cou p led su bp op u lation s on a lattice or ran dom grap h . Carefu l an alysis o f t h e resu lt in g m et ap o p u lat io n m o d el id en t ifies t h ree key p aram et ers t h at can b e u sed t o ch aract erize in vasio n d yn am ics (Park et al. 2001). Th ese are t h e wit h in -field b asic rep ro d u ct ive n u m b er [n o w m o re strictly den oted by Rp to distin gu ish th e local or p atch from th e global rep rodu ctive n u m ber (Park et al. 2001)], th e stren gth of cou p lin g between fields (ε), an d th e size of th e n eigh borh ood of in teraction (ρ), wh ich determ in es th e distan ce over wh ich in ocu lu m is disp ersed (see Figu re 2). 2

Deterministic versus Stochastic M odels Alth ou gh d eterm in istic m od els are u sefu l in id en tifyin g in vasion th resh old s an d th e key p aram eters th at con trol in vasion , th ey ign ore cru cial asp ects of th e p op u lation d yn am ics an d , in p articu lar, often fail to cap tu re th e p attern s of p ersisten ce. Th ree th resh olds are iden tified for a stoch astic m etap op u lation in Figu re 2, taken from Park an d oth ers (2001). Above th e th resh old, th e p arasite is always able to in vad e th e h ost p op u lation in th e d eterm in istic m od el. Ho wever, in t h e st o ch ast ic m o d el, t h ere is a fin it e p ro b ab ilit y o f in vasio n above th e th resh old th at in creases from zero to on e. Moreover, com p arison of th e d eterm in istic an d stoch astic th resh old s sh ows th at th e stoch astic th resh old is effectively h igh er th an th e determ in istic an alogu e. Parasit e p ersist en ce d ep en d s crit ically o n t h e d yn am ics o f in fect io n in p ostep id em ic trou gh s th at u su ally d evelop between crop s wh en th e p op u lat io n s d ro p t o very lo w levels (Diekm an n et al. 1995). In a d et erm in ist ic m o d el, n u m erical sim u lat io n s im p ly t h at if t h e p arasit e can in vad e, it also can m ain tain itself in a h ost p op u lation in th e lon g term . Con seq u en tly, th e in vasio n t h resh o ld (see Figu re 2a) is also t h e p ersist en ce t h resh o ld . Th is is n ot correct, h owever, becau se it fails to take in to accou n t elim in ation wh en p op u lation levels are low. In m arked con trast, th ere are d istin ct in vasion an d p ersisten ce th resh old s in th e stoch astic m od el (see Figu re 2c). So in stoch ast ic, sp at ially exp licit p o p u lat io n s t yp ical o f agricu lt u ral cro p s (Park et al. 2001), th ree scen arios m ay be id en tified (see Figu re 3): (a) th e resistan t p arasit e fails t o in vad e, (b ) t h e p arasit e in vad es an d p ersist s, o r (c) t h e p arasit e in vad es bu t can n ot p ersist. 3 It is a relatively sim p le m atter to exten d an alyses t o d erive est im at es fo r t im es t o ach ieve crit ical d en sit ies o r t h e co ro llary o f tim es to extin ction for d ifferen t sp atial d ep loym en ts of su scep tible crop s. An exam p le for an an im al d isease is given in Swin ton an d oth ers (1998). Th ese an alyses can b e u sed t o in fo rm d ecisio n s ab o u t t h e risk o f resist an ce, an d m u ch h as alread y b een d o n e wit h in sect s an d Bt resist an ce an d t h e n at u re an d st ru ct u re o f refu gia (Rau sh er 2001). So m e an alyt ical wo rk is p o ssible in com p u tin g th e so-called critical com m u n ity size for th e p ersisten ce of p ests an d d isease, bu t m ore is n eed ed .

Commentary: Economics of Transgenic Crops and Pest Resistance • 255 (a)

2.0

Within Patch Basic Reproductive Number ( Rp )

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Within Patch Basic Reproductive Number ( Rp )

(b )

Within Patch Basic Reproductive Number ( Rp )

0.2

0.3 0.4 0.5 0.6 0.7 0.8 Strength of coupling ( ε)

0.9

1.0

2.0

1.0

1.8

0.9

1.6

0.8

1.4

0.7

1.2

0.6

1.0

0.5

0.8

0.4

0.6

0.3

0.4

0.2

0.2

0.1

0.0

( c)

0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Strength of coupling (ε)

20

1.0

18

0.9

16

0.8

14

0.7

12

0.6

10

0.5

8

0.4

6

0.3

4

0.2

2

0.1

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Strength of coupling (ε)

FIGURE 2. Invasion Thresholds for M etapopulations Note: Please see n ote 2 at th e en d of th e ch ap ter.

t = 0.3

1

2

3

4

5

0

6

7

8

9

5

10

1

10

2

3

0

5

6

7

8

9

1

2

3

4

5

1 6

6

7

8

9

1

10

2

3

0

4

5

6

200

t = 0.0

7

8

9

400

10

2

3

4

5

6 5

7

9

6

7

8

9

10

1 0

2

3

4 200

5

6

1

4

2

0

2

3

50

4

5

6

7

100

8

9

3

4

1

2

3

0

7

8

9

10

6

7

1

4

5

5

t = 1.1

400

5

0.5

8

10

1 2

6

7

8

10

9

2

3 60

4

5 80

6 100

7

3

120

9

10 140

5

6

7

8

9

0.5

1

2

0

3

4

50

t = 1.5

8

4

10

1 1

10

2

3

4 20

5

6

3

7

8

9 40

5

6

7

8

9

10

0.5

5

6

100

7

8

9

150

10

1

200

2

0

3

4

50

t = 2.6

30

4

1

t = 10.0

5

6

100

7

8

150

9

10

200

t = 4.3

10 9 8 7 6 5 4 3 2 1 1

2

0

10 9 8 7 6 5 4 3 2 1

10

15

10 9 8 7 6 5 4 3 2 1 1

2

0

t = 5.0

FIGURE 3. Examples of Infection Dynamics in the Stochastic M odel for Invasion Note: Please see n ote 3 at th e en d of th e ch ap ter.

9

1.5

10 9 8 7 6 5 4 3 2 1

10

150

t = 2.4 10 9 8 7 6 5 4 3 2 1

t = 2.4

10 9 8 7 6 5 4 3 2 1

10 10

5

10 9 8 7 6 5 4 3 2 1

t = 0.3

8

4 2

1

600

t = 2.2 10 9 8 7 6 5 4 3 2 1

t = 1.4

10 9 8 7 6 5 4 3 2 1 1

3

10 9 8 7 6 5 4 3 2 1

10

10 9 8 7 6 5 4 3 2 1

0

2

0

t = 0.6

5

t = 1.9 10 9 8 7 6 5 4 3 2 1

10

4

10 9 8 7 6 5 4 3 2 1

10 9 8 7 6 5 4 3 2 1

0

( c)

4 2

t = 0.0

(b )

t = 0.6 10 9 8 7 6 5 4 3 2 1

10 9 8 7 6 5 4 3 2 1

10 9 8 7 6 5 4 3 2 1

10 9 8 7 6 5 4 3 2 1

10

1 0

2

3

4

5 2

6

7

8

9 4

10

1 0

2

3

4

5 0.5

6

7

8

9

10 1

256 • Commentary: Economics of Transgenic Crops and Pest Resistance

t = 0.0

(a)

Commentary: Economics of Transgenic Crops and Pest Resistance • 257

Conclusion: Linking Epidemiological with Economic Theory Mu ch still rem ain s to be d on e in lin kin g ep id em iological th eory an d p op u lation d yn am ics of p est an d d isease with econ om ic th eory p rop osed by Morel an d o t h ers an d Wesseler, bu t so m e ap p ro ach es are evid en t . Th ese are list ed below: • rean alyze an d redefin e variables for ben efits an d costs, esp ecially reversible an d irreversible costs an d th e relation sh ip s with p est an d disease dyn am ics; • realize t h at breakd o wn o f resist an ce in t ran sgen ic cro p s is n o t in evit able even if th e cou n terresistan t strain arises in th e p op u lation ; • com p are th e relative m agn itu des of econ om ically driven with en viron m en tally an d biologically driven sou rces of variability; • an alyze in vasion an d p ersisten ce in stoch astic, sp atially exten d ed settin gs to sim u late th e risk of breakdown of resistan ce in th e lan dscap e; • d efin e th e sp atial scale for an alyses of risk of resistan ce breakd own for d ifferen t crop s, p ests, an d p ath ogen s; • p ro vid e a sim ilar d efin it io n o f t em p o ral scales wit h in wh ich p aram et ers can be reason ably assu m ed to be con stan t; an d • an alyze strategies to allow sp atially an d tem p orally bu ffered in trod u ction s o f t ran sgen ic cro p s rat h er t h an b lan ket co verage an d rap id sat u rat io n o f th e lan dscap e. More d etailed tech n ical con sid eration s con cern ed with n on lin earities an d st o ch ast icit ies sh o u ld fo llo w, fo r exam p le, id en t ifyin g t h e feed b acks in t h e system an d h ow th ese affect th e p robability of in vasion an d p ersisten ce. More im p ortan t is th e ch allen ge of stoch asticity an d h ow it can be estim ated, m odeled, an d u sed to sh ed ligh t rath er th an darkn ess.

Acknowledgements I am grat efu l t o Ju st u s Wesseler at Wagen in gen Un iversit y an d Research Cen t re an d t o Sco t t Farro w an d h is co lleagu es at Carn egie Mello n Un iversit y fo r gen ero u s d iscu ssio n o f t h eir wo rk wit h a n o n eco n o m ist . Un cert ain t ies in eco n o m ic t h eo ry in t h is co m m en t ary are, o f co u rse, o f m y o wn m akin g. So m e o f t h e w o rk referred t o fro m t h e Ep id em io lo gy an d M o d ellin g G ro u p at C am b rid ge w as fu n d ed b y t h e Bio lo gical an d Bio t ech n o lo gical Research C o u n cil, t h e N at u ral En viro n m en t Research C o u n cil, t h e Ro yal So ciet y an d Leverh u lm e Tru st in t h e Un it ed Kin gd o m , w h ich I grat efu lly ackn o wled ge.

258 • Commentary: Economics of Transgenic Crops and Pest Resistance

References Bailey, D.J., W.O . O t t en , an d C.A. Gilligan . 2000. Perco lat io n , Het ero gen eit y an d t h e Sap rotrop h ic In vasion of Soil by th e Fu n gal Plan t Path ogen Rhizoctonia solani. New Phytologist 146: 535–44. Barn ett, V. 1999. Com parative Statistical Inference. New York: Joh n Wiley. Ch ern off, H., an d L.E. Moses. 1959. Elem entary Decision Theory. New York: Dover Pu blication s, In c. Diekm an n , O ., J.A.P. Heest erb eek, an d J.A.J. Met z. 1995. Th e Legacy o f Kerm ack an d McKen d rick. In Epidem ic Models: T heir Structure and Relation to Data, ed it ed b y D. Mollison . Cam bridge, U.K.: Cam bridge Un iversity Press, 95–115. Dixit, A.K., an d R.S. Pin d yck. 1994. Investm ent under Uncertainty. Prin ceton , NJ: Prin ceton Un iversity Press. Farrow, Scott. 2001. Com m u n ication with th e au th or, Decem ber 17, 2001. Gard in er, C.W. 1985. Handbook of Stochastic Methods for Physics, Chem istry and the Natural Sciences. Berlin , Germ an y: Sp rin ger–Verlag. Gu bbin s, S., C.A. Gilligan , an d A. Kleczkowski. 2000. Pop u lation Dyn am ics of Plan t-Parasite In teraction s: Th resh olds for In vasion . Theoretical Population Biology 57: 219–33. Heesterbeek, J.A.P., an d M.G. Roberts. 1995. Math em atical Models for Microp arasites of Wildlife. In Ecology of Infectious Diseases in Natural Populations, edited by B.T. Gren fell an d A.P. Dobson . Cam bridge, U.K.: Cam bridge Un iversity Press, 90–122. Hu ll, J. 2000. Options, Futures, and Other Derivatives. Up p er Sad d le River, NJ: Pren t ice Hall. Keelin g, M.J., an d C.A. Gilligan . 2000. Bu bon ic Plagu e: A Metap op u lation Mod el of a Zo o n o sis. Proceedings of the Royal Society of London Series B-Biological Sciences 267: 2219–30. Nisbet , R.M., an d W.S.C. Gu rn ey. 1982. Modelling Fluctuating Populations. Ch ich est er, U.K.: Wiley. Park, A.W., S. Gu bbin s, an d C.A. Gilligan . 2001. In vasion an d Persisten ce of Disease in a Sp atially Stru ctu red Metap op u lation . Oikos 94: 162–74. Peck, S.L., S.P. Elln er, an d F. Go u ld . 1999. Sp read o f Resist an ce in Sp at ially Ext en d ed Regio n s o f Tran sgen ic Co t t o n : Im p licat io n s fo r Man agem en t o f Heliothis virescens (Lep idop tera: Noctu idae). Journal of Econom ic Entom ology 92: 1–16. ———. 2000. Varyin g Migration an d Dem e Size an d th e Feasibility of th e Sh iftin g Balan ce. Evolution 54: 324–7. Rau sh er, M.D. 2001. Co-Evolu tion an d Plan t Resistan ce to Natu ral En em ies. Nature 411: 857–64. Sm ith , J.Q. 1988. Decision Analysis: A Bayesian Approach. Lon don : Ch ap m an an d Hall. St u iver, M.H., an d J.H.H.V. Cu st ers. 2001. En gin eerin g Disease Resist an ce in Plan t s. Nature 411: 865–8. Swin ton , J., J. Harwood , B.T. Gren fell, an d C.A. Gilligan . 1998. Persisten ce Th resh old s fo r Ph o cin e Dist em p er Viru s In fect io n in Harbo u r Seal Phoca vitulina Met ap o p u lation s. Journal of Anim al Ecology 67: 54–68. Tabash n ik, B.E. 1994. Delayin g In sect Ad ap tation to Tran sgen ic Plan ts: Seed Mixtu res an d Refu gia Recon sidered. Proceedings of the Royal Society of London Series B-Biological Sciences 255: 7–12. Wesseler, J. 2001. Assessin g th e Risk of Tran sgen ic Crop s—Th e Role of Scien tific Belief System s. In Integrative System s Approaches to Natural and Social Sciences— System s Sci-

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Notes 1. Figu re 1a, b, an d c sh ows th e sp read at su ccessive tim es of an in trod u ced d isease Rh izo m an ia (large d ark d o t s) o f su gar b eet t h ro u gh farm s (sm all ligh t d o t s) in East An glia. Large p ale dots rep resen t in fested bu t n ot yet sym p tom atic farm s. Th e ou tbreaks are p red icted by a stoch astic sp atial m od el. Th e sp read is localized arou n d th ree in itial foci. Figu re 1d an d e sh ows th e resu lt of two sim u lation s for th e sp read of d isease in to oth er su gar-beet growin g areas in th e Un ited Kin gdom (ligh t dots rep resen t su scep tible farm s, an d dark dots rep resen t in fested farm s). Th e disease dyn am ics are h igh ly n on lin ear an d stoch astic. Markedly differen t scen arios m ay be obtain ed from iden tical p aram eters for in ten sification , crop su scep tibility, an d tran sm ission wh en allowan ce is m ad e for stoch astic variability. (Rep rodu ced with p erm ission from Dr. A. Stacey, Ep idem iology an d Modellin g Grou p , Cam bridge, U.K.) 2. (a) In vasio n t h resh o ld s fo r a d et erm in ist ic m o d el o f d isease in t ro d u ced in t o a m etap op u lation (i.e., a p op u lation com p risin g 100 su bp op u lation s with loose cou p lin g b et ween co n t igu o u s su b p o p u lat io n s). Th e figu re sh o ws h o w t h e in vasio n t h resh o ld varies with th e stren gth of cou p lin g between su bp op u lation s an d th e ability to m u ltip ly with in su bp op u lation s (h ere d en oted as Rp; eq u ivalen t to R0 for a sin gle su bp op u lation u sed in t h e t ext ). Th e d et erm in ist ic m o d el im p lies t h at t h e p arasit e can n o t in vad e in th e black region an d always in vades in th e wh ite region . In vasion th resh olds also corresp on d to p ersisten ce th resh olds: On ce it in vades, a determ in istic m odel p redicts th at it will p ersist. (b) In vasion th resh old s for th e stoch astic version of th e m od el. In vasion is n ow sh own as a stoch astic p rocess den oted by th e gray scale for th e p robability of in vasion , ran gin g from zero p robability (black) to a p robability of on e (wh ite). (c) Com p arison of in vasion an d p ersisten ce th resh old s for th e stoch astic m od el. In creasin g on e of t h e p aram et ers (Rp) reveals t h ree regim es in t h e b eh avio r o f a p arasit e: n o in vasio n (lo wer black regio n ), in vasio n and p ersist en ce (m id regio n ), an d in vasio n fo llo wed by elim in at io n (u p p er black regio n ). Th e m o d el is a sp at ially ext en d ed gen eralizat io n o f th e sim p le SI m odel in th e text with th e in trodu ction of a sm all am ou n t of p arasite n ear th e cen ter of a 10 × 10 array of su bp op u lation s an d allowan ce for d isp ersal with in an d between su bp op u lation s. Details are given in Park et al. (2001). 3. (a) Parasit e can n o t in vad e (Rp = 0.5); (b) p arasit e in vad es an d p ersist s (Rp = 8.0); an d (c) p arasite in vades bu t can n ot p ersist (Rp = 16.0). Th e p lots sh ow th e in fection level in each su bp op u lation at variou s tim es. Th e rad iu s of th e n eigh borh ood of in teraction is ρ = 1, th e stren gth of cou p lin g is ε = 0.1, an d th e rem ain in g d efau lt p aram eters an d in itial p op u lation s are given in Park et al. (2001). Sim ilar resu lts can be derived for system s with m ore distan t disp ersal across su bp op u lation s.

PART III

The Behavior of Firms

Chapter 10

An Economic M odel of a Genetic Resistance Commons: Effects of M arket Structure Applied to Biotechnology in Agriculture Douglas Noonan

Genetic resistance resources represent an em erging class of environm ental resources. These resources are the subject of increasing public interest, especially for resistance in agriculture and antibiotic use. This chapter m odels genetic resistance resources as com m on-pool resources. The static m odel applies directly to the case of Bt corn, whose seeds are bioengineered to contain a pesticide. Firm s produce an agricultural output (corn) using tw o inputs: Bt corn seeds and refuge areas. Production also depends on the common stock of environmental resistance. Seed use contributes to greater resistance, whereas refuge areas abate resistance. This costly form of abatement represents another (positive) externality, which allows for the optim al seed use to be greater than the com petitive level. The use of seeds and refuge areas by other firms can be shown to be substitutes and complements in production, respectively, for each firm. This simple model of externalities is complicated by introducing another important feature common to genetic resistance resources: m onopoly supply in the biotechnology factor m arket. M onopoly provision of seeds, with imperfect price discrimination, leads the monopoly to act as a gatekeeper of the commons, which tries to maximize its ow n rents rather than the rents from the resource. This divergence in interests leads to a deadw eight loss because seed use is curtailed through higher monopoly prices. This equilibrium is compared with the competitive and the optimal cases. The way in which the resistance externality operates— through dam aging others’ output or through affecting their m arginal productivities—suggests whether the monopoly improves the efficiency of the seed market. Further consideration is given to the possibility that the monop-

• 263 •

264 • Chapter 10: An Economic M odel of a Genetic Resistance Commons oly determ ines the firm s’ level of abatem ent. Assum ing som e enforcem ent mechanism, the monopoly chooses higher abatement levels to increase factor demand for seeds and increase its rents. Under some plausible conditions, a monopoly supplier of the input that accesses the genetic resistance commons can be shown to actually improve welfare by mandating a higher level of care that also maximizes its profits. The distributional consequences of the different m arket structures are shown, noting how gains for the m onopoly com e at the expense of firm s. In 2000, EPA and M onsanto required purchasers of Bt corn to plant specific refuge areas to forestall resistance. This approach is readily extended to other cases, such as pesticides more generally or antibiotic use in the production of health services by households.

A

t th e n exu s of several bu rgeon in g field s of research an d p u blic in terest is gen etic resistan ce. Th e rap id growth an d ap p lication of biological scien ce in th e p ast cen tu ry h as u sh ered in dram atic advan ces in h ealth care an d h igh yield agricu ltu re. Health care an d agricu ltu re sh are im p ortan t ch aracteristics besides th eir biological roots an d p olitical p rom in en ce. Th ey often evoke very p assion ate resp on ses from en viron m en talists an d in tern ation al d evelop m en t p olicy an alysts. Both fields h ave com e u n der in creasin g scru tin y in areas con cern in g m icro b io lo gical in t eract io n s b et ween h u m an s, fo o d , b act eria, an d oth er organ ism s. Ten sion s are m ou n tin g as an tibiotics an d p esticides fail, viral ou tbreaks an d crop in festation s occu r, an d a th reat to th e food su p p ly loom s. Perh ap s t h eir m o st im p o rt an t , an d m o st o verlo o ked , co m m o n lin k is t h eir p ervasive relian ce o n en viro n m en t al gen et ic su scep t ib ilit y in p ro d u ct io n . W h eth er it is a p atien t u sin g an tibiotics or a farm er sp rayin g p esticid es, both fields rely on th e biological organ ism ’s in ability to resist th e treatm en t. Given th at th ese stocks of gen etic resistan ce are typ ically com m on -p ool resou rces, it is lit t le wo n d er t h at m an y p eo p le call fo r n o n m arket resp o n ses t o recen t develop m en ts.

Background Hist o ries o f h u m an civilizat io n wo u ld n o t b e co m p let e wit h o u t p ro m in en t discu ssion of lin kages between gen etic resistan ce, agricu ltu re, an d h ealth care. Jared Diam on d’s Pu litzer Prize-win n in g Guns, Germ s, and Steel (1999) gives th e u ltim ate in flu en ce of germ s an d agricu ltu re its du e. Th rou gh ou t th e cou rse of h u m an h ist o ry, t h e relat io n sh ip b et ween gen e p o o ls an d p ro d u ct io n h as affect ed t h e way in wh ich eco n o m ies d evelo p an d u lt im at ely wh ich gro u p s p rosp er. Alth ou gh su ch a van tage is p erh ap s too broad for con ven tion al econ om ic an alysis, h u m an h istory is rep lete with exam p les of gen etic resistan ce affect in g welfare. Eco n o m ies an d gen e p o o ls are m u t u ally ad ap t in g t o each oth er an d h ave been doin g so for m an y m illen n ia. In m odern tim es, th is rela-

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 265

t io n sh ip b eco m es even m o re p ro n o u n ced wit h scien t ific an d eco n o m ic p rogress. Ju st as an im al dom estication led to en h an ced Eu rasian resistan ce to d isease (an d th e lack of su ch resistan ce in th e Am ericas), th e u se of biotech n o lo gy en h an ces resist an ce at a m u ch fast er p ace. Th e co n seq u en ces o f t h e lack of certain resistan ce in th e Am ericas after th e rap id in trod u ction of n ew organ ism s du rin g colon ization was catastrop h ic. At th e root of th is story, an d cou n tless sm aller-scale exam p les, are fu n dam en tal issu es of gen etic resistan ce an d sp illovers with in an d between com m u n ities. St o ries o f gen et ic resist an ce fill t h e p o p u lar p ress, recan t in g t h e fam iliar story: a farm er u ses a n ew weap on again st crop -dam agin g p ests, an d soon er or later th e p ests ad ap t a resistan ce to th e weap on . Th e “su p erp ests” th en con t in u e t o p lagu e farm s. Man y t im es t h is p ro cess is liken ed t o an “arm s race” again st n atu re in wh ich scien ce’s best tech n ology is u ltim ately cou n tered by n atu ral adap tive forces, leavin g society back wh ere it started or worse. In agricu ltu re, th is race again st n atu re’s adap tation is bein g ru n on n u m erou s fron ts an d h as been ru n fo r ages. Perh ap s t o d ay t h e o n ly d ifferen ce is t h at we can ru n faster. Nu m erou s farm in g tech n iq u es, from breed in g selectively to sp rayin g in secticid es to bioen gin eerin g crop s, cap italize on n atu re’s vu ln erabilities to in crease p rod u ction . Th e effectiven ess of th ese in n ovation s, wh eth er th ey are stron ger p lan ts or m ore leth al p esticid es, is often observed to d eclin e rap id ly, becom in g u seless with in a few years. Th e req u ired d osages for p esticid es in crease over tim e as p ests tu rn in to su p erp ests, an d even in sect-resistan t crop strain s lose effectiven ess. O t h er t ech n o lo gies, esp ecially in h ealt h care, also m u st grap p le wit h gen et ic resist an ce. In creased an t ib io t ic u se h as led t o gro win g resist an ce am on g bacteria. Resistan ce to an tibiotics h as been observed both at large in co m m u n it ies an d wit h in p art icu lar h o sp it als. Resist an ce h as been o bserved fo r an t ibio t ics like azit h ro m ycin , cip ro flo xacin , m et h icillin , m et ro n id azo le, p en icillin , strep tom ycin , an d van com ycin . Th is resistan ce ch allen ges effective treatm en ts for in fection s cau sed by Escherichia coli, Streptococcus pneum oniae, Salm onella typhim urium , Mycobacterium tuberculosis, an d Neisseria gonorrhoeae bacteria. Resistan ce h as been fou n d in diseases ran gin g from m alaria to p n eu m o n ia. Th e u se o f an t ib io t ics o n livest o ck h as p ro d u ced sim ilar resist an ce effects. Th e u se of an tisep tics an d disin fectan ts also m ay cau se resistan ce. Th e costs of resistan ce clim b with its in cid en ce becau se secon d ary treatm en ts are freq u en tly m ore costly or less effective (GAO 1999). Costs from an tim icrobial resistan ce in U.S. h osp itals alon e ap p roach $10 billion each year (W HO 2000). With h eigh ten ed con cern h as com e a wid esp read p ercep tion , esp ecially in th e h ealth care field, th at “overu se” or “m isu se” of th e biological tools (an tibiotics, in secticid es, biotech crop s, an d so forth ) is largely resp on sible for th eir d eclin e in effect iven ess. O n e-t h ird o f all an t ib io t ic p rescrip t io n s m ay b e u n n eed ed , an d m o st d o ct o rs h ave ap p aren t ly p rescribed t h em again st t h eir

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better ju dgm en t (Levy 1998). Sim ilar refrain s sou n d ou t in agricu ltu re: “wastefu l” or “excessive” u se of certain tools h as accelerated n atu ral ad ap tation . In th e race to keep u p , research ers h ave sp en t con siderable tim e in vestigatin g th e relation sh ip between th e u se of th ese tech n ologies an d th e even tu al on set of su p erbu gs an d su p erp ests. Practition ers are exp erim en tin g with tech n iq u es to slo w t h e o n set o f resist an ce in t h e en viro n m en t . Th ese in clu d e ro t at in g an tibiotic u se, develop in g h ybrid in sect-resistan t crop s, u sin g m u ltip le-an tibiotic d ru gs (“cocktails”), establish in g refu ge areas, an d ap p lyin g m ore con cen trated treatm en ts of an tibiotics an d p esticides. Early resu lts su ggest th at som e tech n iq u es h old p rom ise, wh ile oth ers do n ot.

An Economic Approach W h at is t h e efficien t level o f an t ib io t ic u se? Un d er wh at co n d it io n s will biotech n ology crop s im p rove welfare? An econ om ic ap p roach to th ese gen etic resistan ce p roblem s p rovides a p owerfu l an alytical tool. Ultim ately, th is ch ap ter attem p ts to in dicate where th e “p roblem ” lies an d to su ggest how efficien cy m igh t be im p roved wh en op tim al solu tion s are u n available. At issu e is a co m m o n -p o o l o f reso u rces (n am ely, t h e su scep t ib ilit y o f “b u gs” t o cert ain t ech n o lo gies) t h at is d ep let ab le as m o re u sers t ap in t o it . Like a co m m o n p ast u re o r fish ery, p ro d u cers will o verexp lo it t h e p o o l’s reso u rces becau se t h ey d o n o t bear t h e fu ll so cial co st fo r t h eir act io n s. Th e co st s o f t h eir ap p ro p riat io n o f t h e p o o l’s reso u rces are b o rn e in p art b y all u sers o f t h e reso u rce. Wit h o t h ers fo o t in g t h e b ill fo r t h eir u se o f t h e co m m on -p ool, u sers can be exp ected to ration ally overexp loit th e resou rce. Th e gen etic resistan ce in th e en viron m en t is a com m on -p ool resou rce. Th e level of resistan ce, alth ou gh a “bad ,” fits th e two p rim ary criteria for a com m on -p ool resou rce: dep letability an d op en access. First, as m ore p rodu cers u se th e resou rce, it becom es less valu able to everyon e. Secon d, th ere is n o (direct) p rice for access to th is resou rce—n obod y own s it (Bad en an d Noon an 1998). Gen etic com m on s p ose p articu larly in tractable p roblem s. Usu al solu tion s to co m m o n s p ro b lem s in clu d e p rivat izat io n , m ergers, an d t axat io n o r regu lat io n . Each co n ven t io n al p o licy so lu t io n seem s in feasib le in t h e fo reseeab le fu tu re becau se of on e or m ore of th e followin g: m oral an d eth ical p roblem s, large grou p coordin ation an d tran saction costs, an d in form ation costs. Private own ersh ip of gen e p ools ap p ears as p olitically p alatable as “m ergin g” all corn farm ers or as tech n ically p ossible as p ickin g th e p erfect tax. Th e lack of availab ilit y o f first -b est so lu t io n s warran t s t h is in q u iry in t o u n co n ven t io n al ap p roach es to m an agin g th e gen etic com m on s. Th e level of gen etic resistan ce can be th ou gh t of as a stock of n atu ral cap ital G. Th e u se of som e in p u ts by p rod u cers can cau se an in crease in G. Tech n o lo gies t h at rely o n gen et ic su scep t ib ilit ies in t h e en viro n m en t (su ch as

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 267

in secticid es or som e biotech crop s) will becom e less effective as G in creases. Alth ou gh th e in p u ts th em selves m ay h ave a p rice (e.g., th e p rice of bioen gin eered seeds), th e extern ality cau sed by th eir u se is n ot p riced by th e m arket. Becau se a p rodu cer’s u se of th e in p u t can redu ce th e effectiven ess of all oth er p ro d u cers’ t ech n o lo gies, p ro d u cers will gen erally o veru se t h e in p u t , an d a socially su bop tim al level of G (too m u ch resistan ce) p revails in eq u ilibriu m . Th e m odel th at follows form alizes th is story after discu ssin g som e earlier literat u re o n t h e su b ject . It is t h en ext en d ed t o in clu d e m it igat in g b eh avio r b y p rodu cers an d a m on op oly su p p lier of th e tech n ology.

Brief Literature Review Form al in quiries in to th e th eoretical n ature of en viron m en tal extern alities an d com m on pools are n um erous. Begin n in g with H. Scott Gordon (1954) th rough m ost in term ediate m icroecon om ic textbooks today, com m on -property resources or im pure public goods h ave received con siderable atten tion . A len gth y discussion of variou s extern ality m odels like th is can be fou n d in Bau m ol an d Oates (1988). Th e bu lk of th e en viron m en tal econ om ics literatu re ad d resses th is fu n d am en tal issu e of extern alities in on e of two ways. Pigovian taxes an d Coasian p rop erty righ ts occu p y a cen tral p lace in en viron m en tal econ om ics an d p olicy. Alth ou gh both ap p roach es to solvin g th e extern ality p roblem face con siderable p ractical p roblem s—owin g p redom in an tly to in form ation an d tran sact io n co st s, resp ect ively—research ers h ave an alyzed t h e im p licat io n s o f n u m ero u s d ifferen t assu m p t io n s. O n e p ro m in en t st rain in t h e lit erat u re exam in es th e effect of m arket stru ctu re on extern alities an d op tim al taxation p olicy. Bu ch an an (1969) op en ed th e door for extern alities in n on com p etitive m arket stru ctu res. Th e m on op oly’s d esire to set MR = MC (wh ere MR is m argin al reven u es an d MC is m argin al co st s) creat es t h e p o ssibilit y t h at a Pigo vian tax actu ally redu ces welfare wh en th e fin al p rodu cts m arket rem ain s distorted . Barn ett (1980) sh owed h ow taxin g a m on op oly eq u al to its m argin al dam ages (a Pigovian ap p roach ) m igh t exacerbate th e deadweigh t loss becau se of th e m on op oly’s restricted ou tp u t. Ideally, a two-p art tax wou ld correct both th e u n d ersu p p ly of th e ou tp u t by th e m on op olist an d th e oversu p p ly of th e extern ality sep arately an d sim u ltan eou sly. In addition to th eir role in gen eratin g extern alities, m on op olies can p lay a ro le in m an agin g ext ern alit ies. A co m m o n in t u it io n , exp ressed b y Kn igh t (1924) wit h regard t o ro ad co n gest io n , h o ld s t h at gran t in g o wn ersh ip o f a co m m o n -p o o l reso u rce is akin t o in t ern alizin g an ext ern alit y. Th e o wn er cou ld th eoretically ch arge firm s th eir fu ll m argin al costs (in clu din g sp illovers) an d th ereby op tim ize p rod u ction . In p ractice, h owever, th e own er p ossesses m on op oly p ower. A m on op oly wou ld ch oose to lim it access to th e com m on s,

268 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

above an d beyon d correctin g an y extern ality, to eq u ate m argin al reven u e an d m argin al co st fo r t h e fin al o u t p u t . A p rice-d iscrim in at in g m o n o p o ly wo u ld p ro fit m o st b y ch argin g u sers eq u al t o t h eir m argin al ext ern al d am ages (t o eq u ate th e valu e of th eir m argin al p rodu cts to th eir social costs). Th ey wou ld th en extract a fran ch ise fee eq u al to u sers’ ren ts. A m on op oly own er of a com m o n s co u ld ach ieve t h e so cially o p t im al o u t co m e in t h is way. A m o n o p o ly cap able of on ly a sin gle p rice wou ld p artially accou n t for th e sp illover am on g its cu stom ers with resp ect to th eir in terd ep en d en t d em an d s for th e m on op o ly’s reso u rce. No n et h eless, it wo u ld st ill rest rict o u t p u t b ased o n m argin al reven u e rath er th an p rice at social m argin al cost. Mills (1981) d em on strated th is for con gestion -p ron e facilities.

The Formal M odel Competitive Allocation of g

Begin with a sim p le m od el in wh ich com p etitive firm s p rod u ce q. Th ey u se g as an in p u t in p rodu ction , with factor p rice w. Firm s also u se a com m on , en viron m en tal resou rce G as an in p u t, wh ere th e level of G is join tly d eterm in ed by th e firm ’s own u se of g an d oth er firm s’ u se of g, den oted by g~. Th u s, th eir p rodu ction fu n ction is q = f [g, G(g, g~)]. Each firm takes g~ as exogen ou s. G is a “bad ” in p u t (e.g., gen et ic resist an ce) t h at im p airs p ro d u ct io n . Th e m argin al p rodu ct of G is n egative (∂f/ ∂G < 0) an d decreasin g (∂2 f/ ∂G2 < 0). Assu m e th at th e m argin al p rod u ct of g is n on in creasin g in G (∂2 f/ ∂g∂G ≤ 0). Th e u se of g con tribu tes to G at a rate in creasin g in g (i.e., ∂G/ ∂g > 0, ∂G/ ∂g~ > 0, ∂2 G/ ∂g2 > 0, ∂2 G/ ∂g~2 > 0, ∂2 G/ ∂g∂g~ > 0). Firm s sell q for a fixed p rice p. A typ ical firm ’s p rofit fu n ction is as follows:

[

]

Π = pf g , G( g , g˜ ) − wg Th e firm m axim izes its profits Π by ch oosin g g. Assu m e th rou gh ou t th is ch apter th at p rofit fu n ction s are n egative sem id efin ite at th e op tim u m ch oice to satisfy th e secon d-order con dition s. Th e first-order con dition for th e represen tative firm u sin g g > 0 is

p

⎡ ∂f ( g , G ) ∂f ( g , G ) ∂G ( g , g˜ ) ⎤ df + = p⎢ ⎥=w ∂G ∂g ⎥⎦ dg ⎣⎢ ∂g

(1)

Th e m argin al reven u e p ro d u ct h as a p o sit ive co m p on en t from g’s d irect u se an d a n egat ive co m p o n en t in d irect ly fro m g’s co n t ribu t io n t o G. Th e firm ’s ch oice dep en ds join tly on all u sers of g’s ch oices. An asid e o n t h e exist en ce o f well-beh aved fact o r d em an d fu n ct io n s is in o rd er. Eq u at io n 1 im p licit ly d efin es a fact o r d em an d fu n ct io n g*(p, w, ~ g ).

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 269

Co rn es an d San d ler (1986) d iscu ssed t h e n at u re o f Nash eq u ilib ria am o n g ~ firm s, selectin g th eir g given th eir exp ectation of oth er firm s’ ch oices (g ). Th is ch ap ter assu m es (for th is an d every oth er exten sion wh erein a factor dem an d fu n ction is u sed for an extern ality-cau sin g in p u t) th at eq u ilibria exist to su p ~ p ort a con tin u ou s in verse factor dem an d fu n ction w *(p, g, g). Ch an ges in p or ~ in g will cau se th e w *(g) cu rve to sh ift. Th e effect on g* of in creasin g ou tp u t ~ p rice is p ositive. Th e effect of g on g* can be seen from th e im p licit fu n ction th eorem ∂2 Π ∂ 2 f ∂G ∂ 2 f ∂G ∂G ∂f ∂ 2 G + + * ˜ ∂g ∂g∂g ∂g∂G ∂g˜ ∂G 2 ∂g˜ ∂g ∂G ∂g∂g˜ 0. Th e first p art o f Eq u at io n 3 is t h e u su al m argin al reven u e p ro d u ct (MRP) t erm , an d it is fo llo wed b y t h e m argin al so cial d am age (MD) o f gi. Nat u rally, MD is n egat ive. In t h e MD t erm , t h e

270 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

ch oice of gi affects th e m argin al reven u e p rodu ct of G for all oth er firm s (j ≠ i) th rou gh its con tribu tion to G. Th e obviou s d ifferen ce between th e op tim u m n ecessary con dition in Eq u ation 3 an d th e com p etitive con dition in Eq u ation 1 is t h at t h e co m p et it ive firm s d o n o t in clu d e t h e m argin al so cial d am age t erm MD in t h eir calcu lu s. A Pigo vian t ax eq u al t o MD wo u ld co rrect t h is, align in g p rivate an d social m argin al costs. En try still occu rs u n til p = AC for th e m argin al firm , bu t firm s op tim ally p ay for th e added costs th ey in flict on o t h ers. W h en g is su p p lied at it s m argin al co st , MC(g), t h e o p t im al eq u ilib riu m is ch aracterized by MC = w = MRP + MD

(4)

Allowin g com p etitive firm s to u se g u p to th e p oin t wh ere MC = MRP leads to overu se of g. In th is sim p le m odel, G is also too large (G* > Go an d g* > go).

M onopoly

An in terestin g exten sion of th e m odel in volves m on op oly p rovision of g. Th e m on op oly p rovides g for a p rice w; “th e firm ” or “firm s” always refer to actors wh o u se g t o p ro d u ce q. Th e d o wn st ream m arket fo r q rem ain s co m p et it ive wh ile th e u p stream m arket for g h as a sin gle seller an d an extern ality am on g u sers of g. Th e cu rren t in vestigation begin s with two differen t ways to fram e m on op oly con trol of g th at yield d ifferen t resu lts. First, th e m on op oly m igh t m erge with th e firm s, op eratin g th em by givin g th em g an d sellin g th eir ou tp u t. Th e “m erger” m on op oly h as reven u es of p∑q an d costs of C(∑g). Maxim izin g th e differen ce by ch oosin g each gi, th e ith first-order con dition is ⎛ ∂f ∂f ∂G ⎞ p⎜ i + i ⎟+ ⎝ ∂gi ∂G ∂gi ⎠

∂f ∂G

∑ p ∂Gj ∂gi = MC ( g ) j ≠i

(5)

for all gi* > 0. Com p arin g Eq u ation 5 to Eq u ation 4 reveals th at th e “m erger” m on op oly ach ieves th e efficien t allocation of resou rces (assu m in g th rou gh ou t th at p is fixed). A secon d approach h as a “gatekeeper” m on opoly sellin g access righ ts to g to each firm at a price w i for th e ith firm . Th is problem is fu n dam en tally differen t for th e m on op oly own er of g an d yield s q u ite d ifferen t resu lts. As sh own earlier, th e m on opoly cou ld ach ieve th e optim al equ ilibriu m an d m axim ize total ren t s by ch argin g w = MC – MD. Th is p rice, h o wever, leaves p ro fit s fo r t h e firm s. Th e m on op oly cap tu res th ese ren ts in th e m erger ap p roach earlier bu t can n ot d o so as a gatekeep er. In stead , th e m on op oly h as th e in cen tive to set

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 271

MR = MC an d to claim som e of th ose profits for its own . Con sider th e m on opoly’s profit fu n ction , ∏M = ∑w i*gi – C(∑g) (wh ere M den otes th e m on opolist). If th e m on op oly m axim izes th is p rofit by ch oosin g giM , with w i*, an in verse factor dem an d fu n ction , th e ith first-order con dition is as follows: w i + gi

∂w i + ∂gi

∂w

∑ g j ∂gij = MC ( g )

(6)

j ≠i

Th e left -h an d sid e o f t h is eq u at io n rep resen t s t h e m argin al reven u e o f gi, wh ich is th e fam iliar MR term s p lu s th e (n egative) m argin al reven u e effect of gi on oth er firm s’ dem an d for g. Th e m on op oly eq u ates th e MR of gi to its m argin al co st p lu s t h e m argin al reven u e lo st fro m t h e sp illo ver. Th is co n d it io n differs sign ifican tly from Eq u ation 5 in h ow th e sp illover is treated. Eq u ation 5 exp licit ly acco u n t s fo r t h e m argin al d am age o f g an d raises t h e effect ive p rice acco rd in gly. Eq u at io n 6 t akes it in t o acco u n t p art ially b y raisin g t h e p rice accordin g to h ow m u ch addition al g redu ces its valu e to oth er firm s. Th e op tim al solu tion com p en sates for d am ages regard less of h ow resp on sive oth ers’ dem an ds are.1 Firm s’ p rofits n eed n ot be zero with a gatekeep er, u n like in th e “m erger” m od el in wh ich th e m on op oly cap tu res all p rofits. Th e d own ward slop in g dem an d cu rves of firm s, wh ile n ot in con sisten t with th e efficien t equ ilibriu m , will distract th e lim ited m on opoly away from th e optim um . Even a gatekeeper m on opoly capable of ch argin g a differen t price to each firm would deviate from th e efficien t outcom e. Maxim izin g its own ren ts is n ot th e sam e as m axim izin g th e total ren ts from th e resource wh en th e m on opoly can n ot capture th em all. A m on opoly able to supplem en t its ch oice of w by ch argin g a fixed fran ch ise fee to th e firm s cou ld ach ieve th e efficien t ou tcom e wh ere w = MC – MD an d th e fran ch ise fee captures firm profits. In practice, m ore lim ited m on opolies sh ould n ot be expected to m an age th e resource optim ally. M onopoly Contracting over α

As an oth er exten sion , con sider th e m odel in wh ich th e produ ction fu n ction is ~ q = f [g, α, G(g, g)]. Let α be som e oth er in pu t in to th e produ ction of q. To m ake th is ch an ge in terestin g, con sid er th e p ossibility th at th e m on op oly is able to costlessly req u ire a p articu lar level of α u se by firm s. Th e m on op oly will u se th is as a tool to extract m ore ren t from firm s by ch oosin g α an d g for each firm . Raisin g α i above wh at is optim al for th e firm lowers its profits.2 Th e h igh er αi, den oted α ic, also en tails a h igh er gi (or else wh y wou ld th e m on opoly regu late α?). Firm s’ factor dem an ds for g will depen d on w i, p, oth er firm s’ u se of g, an d ~ th e level of α ic set for th em . Hen ce, in verse factor d em an d will be w i* (p, g, g, α ic), an d at so m e level o f α ic, t h e firm will sh u t d o wn . W h et h er ∂w i*/ ∂α ic > 0

272 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

d ep en d s o n t h e co m p lem en t arit y in p ro d u ct io n o f in p u t s g an d α. Fo r a m on op oly-set level of α i, den oted αic, firm s’ p rofits will declin e.3 Firm s’ factor dem an ds for g will depen d on w i, p, oth er firm s’ u se of g, an d th e level of α ci set ~ for th em . Hen ce, in verse factor d em an d will be w i* (p, g, g , α ic), an d at som e level o f αic, t h e firm will sh u t d o wn . W h et h er ∂w i*/ ∂α ic > 0 d ep en d s o n t h e com plem en tarity in produ ction of in pu ts g an d α. Th e m on opoly ideally sets each firm s’ g an d α to m axim ize its profit fun ction : ∏M = ∑w i*gi – C(∑g). Th e first-order con dition s for its ch oice of g ic an d α ic are w i* +

∑ gj j

∑ gj j

∂w *j ∂α i

∂w *j ∂gi = gi

≤ MC ( g ) ∂w *i ≤0 ∂α i

with eq u ality wh en gic > 0 an d α ic > 0. Th e first con d ition is u n ch an ged from th e on e-in p u t case. Th e secon d con dition , h owever, su ggests th at th e m on op oly will raise α u n til th e m argin al reven u e from doin g so h as been exh au sted. Becau se th e factor dem an d for g does n ot dep en d on oth er firm s’ u se of α, th e secon d con d ition req u ires ∂w i*/ ∂αi = 0 or gi = 0. If g an d α are com p lem en ts, th e m on op oly will raise α ic > α i* u n til th e in p u ts cease to be com p lem en ts or th e firm becom es u n p rofitable an d stop s u sin g g altogeth er, p erh ap s becau se α is costly to th e firm . If g an d α are su bstitu tes, th e m on op oly lowers α ic < α i* u n til th e in p u ts cease to be su bstitu tes or gic = 0. Th e m on op oly’s ch oice of αc effectively sh ifts th e factor d em an d cu rves for g ou tward (relative to allowin g α t o b e ch o sen co m p et it ively), lead in g t o h igh er w i, gi, an d ∏M . W h en t h e in p u ts are su bstitu tes, G is larger th an in th e com p etitive case. Th e effect on G is am bigu ou s for com p lem en tary in p u ts. A com p arison of th ese d ifferen t scen arios is p resen ted in Figu re 10-1. Th e m arket for g is sh own with th ree d ifferen t factor d em an d cu rves. Th e m id d le on e, w *(g), rep resen ts th e com p etitive d em an d for g, wh ere w = MRP. Im p osin g a Pigo vian t ax o n firm s sh ift s t h e fact o r d em an d cu rve b y MD t o w o(g). Th e t h ird d em an d cu rve, w c(g), rep resen t s fact o r d em an d wh en α c ≠ α*, wh ere α* is t h e co m p et it ively ch o sen level o f α. Th e m argin al reven u e cu rves fo r w * an d w c are sh o wn as MR* an d MRc resp ect ively. Th e effect o f m on op oly p rovision of g can be seen in red u cin g th e q u an tity of g an d raisin g w. W h et h er g* is m o re o r less t h an go, h o wever, d ep en d s o n t h e m agn itu d e of th e m argin al d am age an d th e elasticity of d em an d . Figu re 10-1 (arbitrarily) sh ows g* < go. Th e effect of con tractin g over α is to sh ift d em an d an d m argin al reven u e ou tward . Th is n ecessarily lead s to gM > g*. Th is m igh t be a m ovem en t toward th e op tim al allocation of go, alth ou gh th is is n ot a n ecessary resu lt.

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 273 w

MC

–M D wc M R* gM

go

gc

w* M Rc

wo

g*

g

FIGURE 10-1. Comparison of M arket Structures for g in the Basic M odel

The Extended M odel Th is section exten ds th e basic m odel by in clu din g abatem en t an d ap p lies it to bio en gin eered seed s in agricu lt u re. Th ese m o d els in co rp o rat e abat em en t by allo win g fo r an o t h er fact o r t o affect G. Sp ecifically, t h e in p u t α ab at es t h e ~ h arm fu l effects of G. Let α den ote oth er firm s’ u se of α. Assu m e th e followin g ~ ~ tech n ological relation s h old for G(g, α, g, α), for an y firm s’ u se of g or α:

∂G >0 ∂g

∂2G >0 ∂g 2

∂G 0 ∂α 2

∂2G 0 ∂g ∂g

∂ 2 f ( g , α, G ) ∂2 f = 2 0 = ∂α ∂α

∂2 f ( g , α, G ) ∂2 f = 0 an d α* ≥ 0 satisfy th e first-order con dition s ⎡ ∂f ∂Π ∂f ∂G ⎤ = p⎢ + ⎥−w =0 ∂g ⎣ ∂g ∂G ∂g ⎦

(7)

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 275

∂Π ∂f ∂G ⎤ ⎡ ∂f = p⎢ + ⎥−r ≤ 0 ∂α ⎣ ∂α ∂G ∂α ⎦

(8)

Eq u at io n 8 h o ld s wit h eq u alit y fo r α* > 0. Farm ers wh o select α* = 0 im p ly th at th e total m argin al reven u e p rodu ct for α is less th an r. Com petitive firm s equate their m arginal revenue product to factor price for each input. Producer Optimization ( α Exogenous)

No w co n sid er firm s t h at face a flo o r fo r α. Alt h o u gh t h ey co u ld o p t fo r a h igh er α*, th ey con tin u e to assu m e th at at least locally th e m argin al p rofit of α is n o n p o sit ive. Th e firm ’s ch o ice essen t ially b eco m es o ver g wit h α as a p aram eter. Th e p rofit fu n ction can be rewritten as Π = pf ( g , G; α ) − wg − rα Th e first-order con dition in ch oosin g gc wh ere α = α c is ⎡ ∂f ∂Π ∂f ∂G ⎤ = p⎢ + ⎥−w ≤0 ∂ ∂g ∂ g G ∂g ⎦ ⎣

(9)

with eq u ality for gc > 0. Th e firm con tin u es to ch oose gc su ch th at its m argin al reven u e p rodu ct eq u als its p rice, given th at αc is u n p rofitably h igh . 6 W hen one input is fixed, firm s still producing equate m arginal revenue product to factor price for the other input.

Comparative Statics for the Firm

Before p roceedin g, recall th e fu n ction al assu m p tion s m ade to th is p oin t. Prod u ction is con cave in in p u ts g an d α. Th e in p u t G is d etrim en tal to p rod u ction , an d G is a fu n ction of g an d α. G rises in creasin gly in g an d falls decreasin gly in α. Th e seco n d -o rd er co n d it io n s fo r m axim izin g a p ro fit fu n ct io n wh ere α is en dogen ou sly determ in ed are ∂2 Π ∂2 Π = < 0, 0 ∂g 2 ∂α 2 ⎜⎝ ∂g∂α ⎟⎠

276 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

wh ere ⎡ ∂2 f ∂2 f ∂G ∂2 f ∂G ∂G ∂f ∂2 G ⎤ ∂2 f ∂G ∂2 Π + + + + = p⎢ ⎥ 2 ∂g∂α ⎣⎢ ∂g∂α ∂g∂G ∂α ∂α∂G ∂g ∂G ∂α ∂g ∂G ∂g∂α ⎥⎦

(10)

Th e first t erm in Eq u at io n 10 co u ld b e p o sit ive o r n egat ive. Th e rem ain in g t erm s are all p o sit ive. It seem s likely t h at ∂2 Π/ ∂g∂α > 0, an d it is n ecessarily tru e wh en ∂2 f/ ∂g∂α ≥ 0. ~ ~ ~ ~ Let g* = g*(w, p, r, g, α ) an d α* = α*(r, p, w, g, α ) be factor dem an d fu n ction s fu lfillin g th e first-ord er con d ition s in Eq u ation s 7 an d 8. Th e effects of p rice ch an ges are ∂2 Π ∂2 Π ∂2 Π ∂2 Π ∂2 Π − 2 * ∂g ∂g∂α ∂α∂w ∂α ∂g∂w ∂α 2 = = 0, th e cross-p rice effects are n egative. Th e effect s o f p rice ch an ges fo r t h e case in wh ich α is exo gen o u s can b e fo u n d m o re easily. Th e co n cavit y o f t h e p ro fit fu n ct io n in g d et erm in es t h e resp on siven ess of th e firm to ch an ges in w. Th e effect of α on th e ch oice of g* can be fou n d as ∂2 Π * ∂g ∂g∂α =− 2 ∂α ∂ Π ∂g 2

(13)

Th e sign of ∂g*/ ∂α dep en ds on th e com p lem en tarity of in p u ts. W h en α n egatively affects th e total m argin al p rodu ct of g, th e firm will decrease its u se of g ~ ~ wh en α is raised. Factor dem an d for g also dep en ds on p aram eters g an d α . In ~ a fash ion sim ilar to Eq u ation 13, th e sign of ∂g*/ ∂α is determ in ed by

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 277

⎡ ∂2 f ∂G ∂2 f ∂G ∂G ∂f ∂2 G ⎤ ∂2 Π = p⎢ + + ⎥>0 ˜ ˜ ∂G 2 ∂α ˜ ∂g ∂G ∂g∂α ˜ ⎦⎥ ∂g∂α ⎢⎣ ∂g∂G ∂α

(14)

~

As exp ect ed , Eq u at io n 14 sh o ws g an d α are co m p lem en t s, regard less o f wh eth er g an d α are com p lem en ts. An ap p roach sim ilar to Eq u ation 2 sh ows ~ th at g an d g are su bstitu tes. W hen g and α are com plem entary inputs, raising the floor on α leads to higher seed use. Others’ use of care com plem ents seed use, and their use of seeds is a substitute.

Externality

Th e m odel p resen ts extern alities in th e u se of both g an d α. With su p erscrip ts id en t ifyin g t h e so u rce o f t h e ext ern alit y, t h e m argin al d am ages cau sed by a rep resen tative firm are as follows: ∂f ∂G

MD g = p

∑ ∂G ∂g

MD α = p

∑ ∂G ∂α > 0

0, given factor p rice w *, th e first-order con dition is w * = MC(g). Th e m arket p rice is d et erm in ed by t h e in t ersect io n o f t h e su p p lier’s MC an d t h e in verse aggregate factor dem an d w *. Su p p o se in st ead t h at a m o n o p o ly su p p lies t h e seed m arket . It p ro vid es a q u an tity gi to each firm for p rice w i to m axim ize ΠM = ∑wg – C(∑g). In th e case wh ere gi > 0, th e ith first-order con dition s is ˜)+ w i* ( g , g˜ , α

∑ j

gj

˜) ∂w *j ( g , g˜ , α ∂gi

= MC( g )

Th is con dition for m on op oly p ricin g p arallels th at of Eq u ation 6. Th e m on op oly p rices g to extract th e m ost ren t p ossible from th e resou rce. From Eq u ation 2, th e effect of g on th e m argin al reven u e from sales to all firm s is n egative, so th e m on op oly raises w over its m argin al cost. Eq u ation s 11 an d 12 sh ow th e effect s o f in creasin g w o n g* an d α*. Mo n o p o ly m arku p o f w cau ses g* t o d ecrease. For com p lem en tary in p u ts, th e m on op oly eq u ilibriu m exh ibits less α th an th e com p etitive eq u ilibriu m . For su bstitu tes, α will in crease an d G will u n am bigu ou sly decrease. How th is com p ares with th e op tim al ou tcom e, h owever, dep en ds on com p arin g Eq u ation s 15 an d 16 wh ere w = MC(g) with Eq u ation s 7 an d 8 wh ere w in clu d es t h e m o n o p o ly m arku p . W h et h er t h e m o n o p o ly m arku p in flat es α an d th e effective p rice of g m ore th an th e Pigovian taxes will d eterm in e h ow g* an d α* com p are with go to α o. As n oted earlier, th is dep en ds on wh eth er th e m argin s g cau ses m o re d am age t o firm s t h an it elicit s in su b st it u t io n away

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 279

from g. Th e cru x of th e differen ce between th e m on op oly an d com p etition , to p u t it an oth er way, is th e differen ce between th e extern ality’s effect on oth ers’ ou tp u t an d its effect on oth ers’ m argin al p rod u ctivity. If th e form er effect is larger, th e m argin al d am age will be larger. If resistan ce p red om in an tly m akes seeds less p rodu ctive, th en th e m on op oly m arku p will be larger. A m onopoly raises w based on each firm ’s im pact on others’ m arginal productivity, not their dam age to others’ output. M onopoly Contracting over α

Th e m on op oly m igh t be able to extract m ore ren t by req u irin g each firm to u se α at a certain level, α ic. For a fixed α ic, th e firm ’s factor d em an d fu n ction ~ ~ for g is gic (p, w, r, α ic, g, α ) im p licitly defin ed by Eq u ation 9. Usin g th e in verse factor d em an d fu n ction for gic, w ic (gi, αic, ⋅), th e m on op oly m axim izes p rofits ∏M = ∑(w cg) – C(∑g) by ch oosin g g an d α c for each firm . Th e first-order con dition s arise for th e ith firm in th e g m arket:

(

( ) ∑ ∂g ∂w ( g , α , ⋅) ≤0

w ic gi , αic , ⋅ +

gj

j

∑ gj j

c j

i

) = MC( g )

∂w cj gi , αic , ⋅ i

c i

∂αi

with eq u ality wh en α c > 0. Th e first con dition rep resen ts th e MR = MC con dition for th e m on op oly, wh ere each firm ’s w is in flated over MC by th e am ou n t o f gi’s effect o n t h e m argin al reven u e fro m all firm s. Th e seco n d co n d it io n , MR = MC for α, sh ows h ow th e m on op oly will raise α u n til doin g so n o lon ger in creases its (n et) reven u es from sales of g to all firm s. Raisin g α ic alters th at firm ’s d em an d for g acco rd in g to Eq u at io n 13. Raisin g α ic in creases d em an d ~ fo r g b y o t h er firm s b ecau se g an d α are always co m p lem en t s. As α ic clim b s h igh er, firm s will ap p ro ach t h eir sh u t d o wn p o in t an d so m e m ay exit , u n t il th e n ecessary con dition th at th e n et MR of raisin g α ic be zero is satisfied. More g an d m o re α lead t o am b igu o u s effect s o n G. Resist an ce u n d er m o n o p o ly cou ld be above or below th e op tim u m . Fin ally, briefly con sid er th e case in wh ich th e m on op oly is u n able to d is~ crim in ate between its con su m ers. Assu m e w * (Σg, p, r, α ) is th e in verse aggregate factor dem an d. If it can on ly ch arge a sin gle w = w * for all u sers, th en its first-order con dition s becom e th e followin g: W h ere α is com p etitively determ in ed an d ∏M = w * ∑g – C(∑g), we h ave w*

(∑ g ) +

∂w *

(∑ g )

∂g

∑ g = MC( g )

280 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

W h ere th e m on op oly sets on e α = α c for all firm s an d ∏M = w *(α c, ⋅ )∑g – C(∑g), we h ave

(∑ ) ∂w (∑ g , α , ⋅)

g, αc , ⋅ +

wc

c

c

∂α

∂w c

(∑ g, α , ⋅) c

∂g

∑ g = MC( g )

∑g =0

Contracting over care allows the m onopoly to shift out the dem and for seeds, extract m ore rents from firm s, and increase seed use and care.

Efficiency

Con sid er th e effects on efficien cy in th e factor m arket of rem ovin g Pigovian taxes, p rovid in g g via a m on op oly, an d th en h avin g th at m on op oly con tract over α. Let su p erscrip ts {o, *, M, c} rep resen t th e op tim al, com p etitive, sim p le m o n o p o ly, an d m o n o p o ly-co n t ract in g-o ver-α cases, resp ect ively. Rem o vin g th e Pigovian taxes wh ere ∂2 Π/ ∂g∂α > 0 leads to in creased g an d decreased α by all firm s: g* > go an d α* ≤ α o. Th erefore, G* > Go. W h ere ∂2 Π/ ∂g∂α < 0, h owever, th e total ch an ges in g an d α d ep en d on th eir su bstitu tability an d th e m agn itu des of MD g an d MD α. Th e case of ∂2 Π/∂g∂α > 0 h as im portan t efficien cy im plication s for m on opoly factor supply. Th e m on opoly exerts its power, an d seed use an d care will declin e (w M > w *, gM < g*, αM < α*). Th e effect of m on opoly on G is am bigu ou s. If α* = αM = 0, th en GM < G*. Th ou gh th e extern ality en cou rages overu se of g an d m on opoly pricin g reduces th is, it is possible th at th e m on opoly overcorrects for th e extern ality. Also, th e m on opoly captu res m ore of th e resou rce ren ts at th e expen se of th e firm s. If possible, th e m on opoly m igh t requ ire in creased abatem en t to boost sales of g. Th is leads to α c > αM, gc > gM, an d w c > w M. Figu re 10-2 illu st rat es o n e p o ssib le series o f t h ese ch an ges fo r t h e fact o r m arket. Followin g th e sam e ap p roach as Figu re 10-1, let w o, w *, an d w c be th e in verse factor dem an ds for g u n der Pigovian taxes, u n der n o taxes, an d u n der a α c > αM set by th e m on op oly. Margin al reven u e cu rves are given for th e two m on op oly cases (MRM an d MRc). If th e effect of th e Pigovian taxes is to m ove th e d em an d for g d own to w o, th e m arket will clear at go < g*. In stead , if th e m on op oly con trols g, th e u se of g will declin e, p ossibly to a p oin t below go as sh own in Figu re 10-2. Th e m on op oly gain s con siderable ren ts, wh ile th e firm s lose su rp lu s. Moreover, a m on op oly th at ach ieves go will still n ot be op tim al if ~ α rem ain s su bo p t im al. W h en d em an d fo r g an d α are p o sit ively relat ed , t h e m on op oly th at raises α c sh ifts th e dem an d for g ou tward an d in creases ou tp u t (an d w an d p rofits). Th e in crease in g m igh t m ove th e eq u ilibriu m closer to go,

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 281 w

MC

M onopoly M arkup

–M D wc w* M R* g

M

g

o

g

c

g*

M Rc

wo g

FIGURE 10-2. Comparison of M arket Structures for g in the Extended M odel

alth ou gh th is ou tcom e is n ot n ecessary. Th e p ossibility of raisin g α leaves th e m on op oly with still m ore p rofits, p ossibly at th e exp en se of firm s. Th is m o d el p ro vid es a fram ewo rk t h an can b e ap p lied easily t o gen et ic resistan ce resou rces. W h en a gen etically en gin eered crop becom es available, farm ers often im p lem en t it with α = 0. If th e extern alities were corrected, th e eq u ilibriu m wou ld sh ift to α > 0. Un der m on op oly p rovision of g, exp ect w to rise an d g an d G t o fall. Th e am o u n t o f care rem ain s b o u n d ed at zero . W h et h er resist an ce p red o m in an t ly affect s seed s’ m argin al p ro d u ct ivit y o r yield s sh o u ld serve as a q u alit at ive in d icat o r o f wh et h er t h e m o n o p o ly m arku p exceed s th e m argin al d am ages. Allowin g th e m on op oly to req u ire a h igh er α sh o u ld brin g win d fall gain s t o t h e m o n o p o ly, h igh er w an d g, an d p o ssib ly so m e exit fro m t h e in d u st ry. In so m e cases (esp ecially t h o se wit h large m on op oly m arku p s an d large “dam ages” from u n deru sin g α), efficien cy gain s can be m ade. Th is story sh ou ld be su bjected to em p irical tests. Th e d o wn st ream m arket fo r q also m ay figu re p ro m in en t ly in welfare an alysis, esp ecially wh en th e fin al p rod u ct (e.g., cotton , corn ) p rovid es su bst an t ial co n su m er su rp lu s. Th e effect s o f u p st ream m arket st ru ct u re o n t h e

282 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

m argin al costs for q are n ot in vestigated form ally in th is ch ap ter. Non eth eless, Figu re 10-3 can illu st rat e t h e d o wn st ream im p licat io n s o f m arket st ru ct u re. Su p p ose th at correctin g th e extern alities lowers th e m argin al costs of q from th e com p etitive case MC * > MC o. Su p p ose th at m on op oly p ricin g of w raises th e m argin al costs of q, d esp ite an y cost savin gs of lower G. Fin ally, su p p ose t h at m an d at in g a h igh er α lead s t o lo wer m argin al co st s as t h e in p u t m ix ap p roach es th e op tim u m .7 Figu re 10-3 d ep icts MC M > MC * > MC o an d MC M > MC c. An arro w is in clu d ed fo r MC c becau se alt h o u gh it is t o t h e righ t o f t h e MC M cu rve, th is case m igh t n ot h ave lower m argin al costs th an th e com p etit ive o n e. If it d o es, t h en t h e welfare gain s in t h e d o wn st ream m arket fro m h avin g a m on op oly con tract over α are eviden t. As a p olicy m atter, a m on op o ly co n t ract in g o ver α m igh t b e p referred t o req u irin g t h e fact o r m arket t o p rice at m argin al co st . It is also wo rt h n o t in g t h at t h e d o wn ward slo p in g d em an d cu rve in Figu re 10-3 h as n o t been in co rp o rat ed in t o t h e p reced in g an alyses th at fixed p. Su ch a dem an d cu rve wou ld en tice th e m on op oly to fu rth er restrict g an d raise th e p rice of q.

p M CM

M C* M CC

M Co

D

q

FIGURE 10-3. Downstream M arket for q

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 283

Household Production A sim ilar m od el, bu ild in g off of Grossm an ’s (1972) m od el of h ou seh old p rodu ction of h ealth services, can be ap p lied to th e h ealth care side of th e gen etic p o o l co m m o n s. Th e ap p eal o f t h e p reced in g an alysis is it s ap p licabilit y t o a broad fam ily of gen etic resistan ce p roblem s in wh ich p rod u ction in volves an im p u re p u blic good an d costly abatem en t op tion s are available. W h ereas in Grossm an ’s m odel, th e h ou seh old p rodu ces h ealth y days u sin g in p u ts su ch as m edical services an d h ealth y tim e, addition al in p u ts are sp ecified: g an d G. As earlier, g rep resen ts th e u se of an tibiotics an d G is a m easu re of an tim icrobial resistan ce. Op tim ization of th e h ou seh old p rodu ction wou ld follow in a sim ilar way as th e firm s op tim ized th eir ou tp u t of q. Market stru ctu re m ay sim ilarly p lay an im p ortan t role to th e exten t th at a m on op oly con trols th e su p p ly of an tibiotics to th e h ou seh old . Th is cou ld be th e case wh en a d om in an t p h arm aceu t ical firm su p p lies t h e m ed icin e p ro t ect ed b y p at en t s. Alt ern at ively, a large-scale h ealt h m ain t en an ce o rgan izat io n m ay p o ssess su fficien t m arket p o wer t o affect abat em en t beh avio r by d ict at in g p rescrip t io n gu id elin es t o it s p h ysician s o r req u irin g m o re d iagn o st ic t est s. A h ealt h m ain t en an ce o rgan izat io n m ay in t ern alize t h e effect s o f t h e resist an ce sp illo ver m u ch like h osp itals m ay be exp ected to do likewise. Fu rth er work is n eeded to fu lly elaborate th is m odel.

Conclusion Man y asp ect s o f a sim p le m o d el o f p ro d u ct io n ext ern alit ies h ave b een exp lored . Th e basic extern alities m od el is ap p lied to a stock of gen etic resistan ce t h at is co n t rib u t ed t o b y u sers o f a p art icu lar in p u t , su ch as b io t ech seed s. Th e m od el also in vestigates th e im p lication of an oth er costly in p u t, a form of abatem en t affectin g th e stock of resistan ce. Abatem en t beh avior rep resen t s an im p o rt an t , an d o ft en o verlo o ked , asp ect o f resist an ce m an agem en t . 8 O t h er firm s’ ab at em en t levels are co m p lem en t s in p ro d u ct io n t o a firm ’s u se o f seed s, ju st as o t h ers’ u se o f seed s m akes each firm ’s o wn u se o f seed s less valu able. Th is relat io n sh ip acro ss firm s can m ake h igh er levels o f ab at em en t co n sist en t wit h great er fact o r d em an d fo r seed s, irresp ect ive o f abat em en t an d t h e fact t h at seed s are su bst it u t es wit h in a firm . Wit h p rices n ot reflectin g th e social cost of seed u se (or th e social ben efit of abatem en t), too m u ch resistan ce can be exp ected in eq u ilibriu m . Th is ch ap t er ext en d s t h is m o d el t o d iscu ss m o n o p o ly o wn ersh ip o f t h e crit ical in p u t (e.g., seed s). Desp it e essen t ially co n t ro llin g access t o t h e co m m on -p ool resistan ce resou rce, a m on op oly lackin g p erfect p rice d iscrim in atin g abilit y will in efficien t ly st eward t h e reso u rce. A m o n o p o ly in cap able o f cap tu rin g all of th e resou rce ren ts raises th e seed p rice above its m argin al cost

284 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

of p rodu ction . In doin g so, seed u se declin es relative to th e com p etitive eq u ilib riu m . If t h e o p t im al u se o f seed s is less t h an t h e co m p et it ive level, t h en m on op oly p ricin g m ay sh ift th e eq u ilibriu m closer to th e op tim al q u an tity of seed s. Fo r a fixed level o f ab at em en t , t h e co m p ariso n b et ween t h e o p t im al an d th e m on op oly p rices of seed s is straigh tforward . Com p arin g th e m on op oly m arku p to th e Pigovian tax in volves com p arin g

∑ gj j

˜) ∂w *j ( g , g˜ , α ∂g i

an d p

∂f ∂G

∑ ∂Gj ∂gi j ≠i

Th e m on op oly m arku p d ep en d s on th e p rice elasticity of factor d em an d for all firm s wit h resp ect t o a firm ’s u se o f seed s, wh ereas t h e Pigo vian t ax dep en ds on th e firm ’s m argin al dam age to oth er firm ’s ou tp u t. Th is resu lt su ggests th at th e efficien cy gain s to m on op oly p ricin g dep en d in p art on h ow th e resist an ce sp illo ver affect s o t h er firm s’ m argin al p ro d u ct ivit y an d t h eir o u t p u t . Th e m o n o p o ly d eviat es fro m o p t im al p ricin g b ecau se t h e resist an ce ext ern alit y o p erat es p red o m in an t ly t h ro u gh t h e m argin al p ro d u ct ivit y o f seeds an d n ot th rou gh ou tp u t or vice versa. In co rp o rat in g abat em en t co m p licat es m at t ers bu t also reflect s an im p o rt an t feat u re o f resist an ce ext ern alit ies. Users o f t h e resist an ce reso u rce can u n dertake costly abatem en t, wh ereas th e m on op oly su p p lier typ ically can n ot. Given t h e o p p o rt u n it y (in clu d in g so m e en fo rcem en t m ech an ism ), t h e m on op oly will ch oose to req u ire a level of abatem en t above th e com p etitive level t o sp u r d em an d fo r it s reven u e-gen erat in g p ro d u ct , t h e seed s. Th is h igh er level of abatem en t, h owever, dep en ds on ly on th e cost of en forcem en t an d th e com p lem en tarity of abatem en t an d seed u se. It d oes n ot n ecessarily relate to op tim al resou rce u se. Th e d ead weigh t loss from th e m on op oly p ricin g o f seed s m ay, in fact , b e exacerb at ed wh en t h e firm can req u ire in efficien tly costly levels of abatem en t. If th e m on op oly m arku p exceed s th e m argin al d am age cau sed b y seed u se, h o wever, t h e p o ssib ilit y rem ain s t h at allowin g th e m on op oly to con tract over th e level abatem en t can lead to welfare gain s in th e seed m arket. Th e d ifferen t m arket stru ctu res exam in ed h ere also h ave an effect on th e d own stream m arket (for corn or m ed ical services), wh ere con siderable con su m er su rp lu s m ay be at stake. Th is an alysis ap p lies read ily to th e beh avior of a d om in an t biotech n ology su p p lier to farm s. Mon op oly su p p liers m ay con serve resistan ce resou rces better th an a com p etitive m arket, esp ecially wh en th e m argin al resistan ce extern alit y is large. In ad d it io n , ab at em en t is an im p o rt an t asp ect o f resist an ce m an agem en t . If t h e m argin al resist an ce d am age is sm all relat ive t o t h e m on op oly’s m arku p , req u irin g m ore abatem en t m ay red u ce th e d ead weigh t losses. Moreover, th e m on op oly h as an in terest, albeit lim ited , in su p p ortin g

Chapter 10: An Economic M odel of a Genetic Resistance Commons • 285

su ch a req u irem en t . Mo n san t o , In c., fo r exam p le, regu larly co n t ract s o ver “refu ge areas” in farm s u sin g th eir seeds, so as to m itigate th e develop m en t of gen et ic resist an ce. In 2000, EPA an d Mo n san t o req u ired all u sers o f Bt co rn seeds to p lan t 20% of th eir acreage with n on -Bt corn in an attem p t to p rovide refu ges for n on resistan t in sects to dilu te an y gen etic advan tage th at resistan ce m ay con fer. Th is m od el su ggests h ow su ch a p olicy (α c = 0.25g) m igh t be in th e in terests of Mon san to an d also rep resen t efficien cy gain s. Several im p ortan t elem en ts h ave been n eglected in th e p resen t treatm en t, m ost esp ecially th e dyn am ic n atu re of th e p roblem . Fu tu re research m ay in tegrate th e tem p oral n atu re of decision m akin g. Prelim in ary in dication s su ggest t h at t h is st at ic m o d el su fficien t ly cap t u res t h e im p o rt an t elem en t s o f t h e act o rs’ ch o ice o f t h e u se o f seed s an d ab at em en t . Yet m an agin g gen et ic reso u rces req u ires m o re t h an m erely o p t im ally u sin g t h e cu rren t st o ck. Ch an gin g tech n ologies an d im p rovin g th e stock are cru cial tasks. Historically, gen etic resistan ce often h as been m ore effectively addressed by in ven tin g n ew in p u ts to keep on e step ah ead of advan cin g adap tation th an by u sin g existin g in p u t s m o re efficien t ly. Research an d d evelo p m en t in t o n ew t ech n o lo gies su ch as biotech crop s an d an tibiotics yield welfare gain s n ot con sidered h ere. On e obviou s con n ection between d evelop in g n ew tech n ologies an d m an agin g th em on ce th ey are im p lem en ted is m on op olies. Mon op oly con trol over n ew tech n ologies m ay d o m ore th an allow for som e regu lation of extern alities—it p ro vid es t h e ren t s th at en co u rage research an d d evelop m en t in vestm en t in th e first p lace (Aledort et al. 2000). Th e m o d el is rip e fo r ext en sio n s in t o o t h er areas wit h gen et ic co m m o n p o o l reso u rces. Th is basic fram ewo rk p o in t s t o p o licies likely t o rem ed y t h e overu se of certain resou rces. Ch an gin g in cen tives via p rop erty righ ts an d regu lation of abatem en t beh avior h old som e p rom ise. Research in an tibiotic u se su ggests th at “better ed u cated ” p rod u cers an d con su m ers are u n likely to p rovide m u ch h elp (Gon zales et al. 1999). Given th e en orm ity an d com p lexity of resist an ce ext ern alit ies, first -b est p o licy so lu t io n s d o n o t ap p ear feasib le. Ch an ges in in stitu tion al d esign (e.g., m on op olizin g certain in p u ts, en cou ragin g p ro d u cer-regu lat ed ab at em en t ) m ay o ffer t h e b est aven u e fo r reso u rce con servation . Th e n ext step is to fin d an d assess em p irical eviden ce in ligh t of th is fram ework. Th is ch ap ter attem p ts to lay th e grou n dwork for a rigorou s econ om ic treatm en t o f o n e asp ect o f p ro d u ct io n in agricu lt u re t h at is gro win g in salien ce. Th is ap p ears d u e in p art t o gen et ic co m m o n s’ im m u n it y t o t ech n ical so lu t io n s an d co n ven t io n al eco n o m ic so lu t io n s (p rivat izat io n , m erger, o r st at e con trol). Form al an alysis of d ifferen t m an agem en t p ossibilities m erits atten tion . Th is ch ap ter begin s th at p rocess.

286 • Chapter 10: An Economic M odel of a Genetic Resistance Commons

References Aled ort, J., R. Laxm in arayan , D. Howard , an d E. Seigu er. 2000. Final Conference Report. International W orkshop on Antibiotic Resistance: Global Policies and Options. Cam bridge, MA: Cen t er fo r In t ern at io n al Develo p m en t at Harvard Un iversit y, h ttp :/ / www.cid .h arvard .ed u / cid abx/ fin al_con f_rep ort.h tm (accessed Ju n e 19, 2001). Baden , J., an d D. Noon an . 1998. Managing the Com m ons. Bloom in gton , IN: In dian a Un iversity Press. Barn ett, A.H. 1980. Th e Pigou vian Tax Ru le u n der Mon op oly. Am erican Econom ic Review 70 (5): 1037–41. Bau m o l, W.J., an d W.E. O at es. 1988. T he T heory of Environm ental Policy. Cam b rid ge, U.K.: Cam bridge Un iversity Press. Bu ch an an , J.M. 1969. Extern al Disecon om ies, Corrective Taxes, an d Market Stru ctu re. Am erican Econom ic Review 59(1): 174–7. Corn es, R., an d T. San dler. 1986. The Theory of Externalities, Public Goods, and Club Goods. Cam bridge, U.K.: Cam bridge Un iversity Press. Diam on d , Jared . 1999. Guns, Germ s, and Steel: The Fates of Hum an Societies. New York: W. W. Norton & Co. GAO (U.S. Gen eral Acco u n t in g O ffice). 1999. Antim icrobial Resistance: Data To Assess Public Health T hreat from Resistant Bacteria Lim ited. Rep o rt t o Co n gressio n al Req u esters. GAO/ HEHS/ NSIAD/ RCED-99-132. Wash in gton , DC: GAO. Gon zales, R., J.F. Stein er, A. Lu m , an d P.H. Barrett, Jr. 1999. Decreasin g An tibiotic Use in Am bu latory Practice: Im p act of a Mu ltid im en sion al In terven tion on th e Treatm en t of Un com p licated Acu te Bron ch itis in Adu lts. Journal of the Am erican Medical Association 281(16): 1512–9. Gord on , H.S. 1954. Th e Econ om ic Th eory of a Com m on -Prop erty Resou rce: Th e Fish ery. Journal of Political Econom y 62(2): 124–42. Gro ssm an , M. 1972. O n t h e Co n cep t o f Healt h Cap it al an d t h e Dem an d fo r Healt h . Journal of Political Econom y 80 (2): 223–55. Kn igh t, F.H. 1924. Som e Fallacies in th e In terp retation of Social Cost. Quarterly Journal of Econom ics 38: 582–606. Levy, S.B. 1998. Th e Ch allen ge o f An t ib io t ic Resist an ce. Scientific Am erican 278(3): 46–53. Mills, D.E. 1981. Own ersh ip Arran gem en ts an d Con gestion -Pron e Facilities. Am erican Econom ic Review 71(3): 493–502. W HO (Wo rld Healt h O rgan izat io n ). 2000. Overcom ing Antim icrobial Resistance: W orld Health Organization Report on Infectious Diseases 2000. Gen eva, Switzerlan d: W HO.

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Notes 1. Con sider a sim p le system in wh ich p rodu ction is con cave in g an d decreasin g lin ~ early in G (e.g., q = g0.1 – G). Also, su p p ose G = ∑g. Th en ∂g*/ ∂g = 0, an d th e gatekeep er m o n o p o ly ign o res t h e ext ern alit y an d act s as a t rad it io n al m o n o p o ly wit h MR = MC. Th e m erger m on op oly sets w = MC + Np , for N firm s. 2. Wh en th e m on opoly is con strain ed to dictate a sin gle α for th e en tire in dustry, som e m argin al firm s m ay exit as th e m on opoly equates th e MR of α (across all firm s) to zero. 3. O n ly t h e n egat ive effect o f g o r t h e n egat ive in t eract io n b et ween g an d α are n eeded in th is m odel if th e oth er is zero or sm all. Th e form er con dition is on e in wh ich a actu ally redu ces resistan ce, wh ich m ay n ot be con sisten t with som e biological dyn am ics. Th e latter su ggests th at α m itigates g’s con tribu tion to G. 4. Th ese in clu de th e n et p resen t valu e of a firm ’s own im p act on G. 5. Th is assu m p tion can be m otivated from an ecological viewp oin t. Su p p ose a certain n u m ber of p ests in vade a farm with biotech -seeded lan d an d refu ges. As m ore p ests becom e resistan t, th e p rod u ctivity of an ad d ition al biotech seed d ecreases becau se th e p ests th at lan d on it are m ore likely to resist its biological defen ses. Th e p rodu ctivity of an ad d it io n al refu ge area, h o wever, is u n likely t o d ecrease wit h resist an ce, b ecau se resistan t p ests h ave n o advan tage in th e refu ge. If an yth in g, m ore p ests m igh t sp ill over from th e refu ges wh en resistan ce in creases becau se th e resistan t p ests d o n ot com p ete with th e vu ln erable p ests on th e rest of th e farm . 6. A com p arable an alysis cou ld be m ade for α bein g set below th e com p etitive valu e. α c > α* is u sed h ere to h igh ligh t th e differen ce from th e com p etitive eq u ilibriu m wh ere often α* = 0. 7. Fu tu re research will in vestigate th ese con jectu res. Th e m on op oly seekin g to m axim ize dem an d for g h as in cen tives to exp an d th e down stream m arket for q by th eir selection of α c. Ch oosin g α c closer to th e op tim al m igh t accom p lish th is by lowerin g MC. 8. In differen t con texts, th is abatem en t beh avior can take m an y differen t form s like refu ge areas, carefu l p esticid e ap p lication , d iagn ostic screen in g for bacterial in fection s, “fin ish in g off” a p rescrip tion , an d th e like.

Commentary

Does the M onopolist Care about Resistance? Carolyn Fischer

I

n p u ts to agricu ltu re often h ave effects extern al to th e p articu lar farm er u sin g th em . Som e, like fertilizer ru n off or h abitat creation or d estru ction , d o n ot affect agricu lt u ral p ro d u ct ivit y. O t h ers, like resist an ce t o p est icid es o r t o gen et ically en gin eered cro p s, d o affect t h at p ro d u ctivity, creatin g situ ation s akin t o co m m o n -p o o l reso u rces. In t h ese t yp es o f p ro b lem s, wit h u n clear p ro p ert y righ t s o r d iffu se o wn ersh ip , in d ivid u al u sers d o n o t t ake in t o accou n t th e effect th eir im p act on th e resou rce stock h as on all oth er u sers. Two classic exam p les are o verfish in g, wit h m o re reso u rces sp en t t o cat ch fewer fish o verall, o r t raffic co n gest io n , wit h m o re d rivers an d lo n ger co m m u te tim es th an op tim al. In th e case of Noon an ’s ch ap ter (Ch ap ter 10), th e im p lication is in creased p est resistan ce, with overu se of th e biotech p rod u ct an d redu ced effectiven ess. For biotech p rodu cts, h owever, own ersh ip of th e resou rce (effectiven ess) is often con cen trated in th e h an ds of th e sin gle p rodu cer with th e p aten t. A sin gle own er does recogn ize th e im p act of th e extern ality becau se u sin g m ore of t h e p ro d u ct red u ces t h e valu e o f t h e u n it s alread y in u se. In t h e classic resou rce m odels, sin gle own ersh ip can lead to th e socially efficien t ou tcom e— if th e own er derives th e fu ll valu e of th e u se of th e resou rce. For a m on op olist to “own ” all th e ren ts from its biotech corn , it wou ld h ave to be able to ch arge each farm er a fixed licen sin g fee eq u al to th e farm er’s su rp lu s from u sin g th e co rn . Th en t h e m o n o p o list wo u ld ch o o se t h e p rice o f t h e co rn t h at m axim izes t h e co llect ive su rp lu s, wh ich is t h e so cially efficien t allo cat io n o f t h e fact o r in p u t , b u t all t h e ren t s wo u ld b e t ran sferred fro m t h e farm ers t o t h e m on op olist. • 288 •

Commentary: Does the M onopolist Care about Resistance? • 289

However, th e m on op olist m ay n ot be able to ch arge a fixed fee; rath er, it m ay offer th e farm er a p er-u n it p rice for th e corn . Th e m on op olist still recogn izes th e effect of th e extern ality bu t th rou gh its effects on th e p rodu cer’s reven u es rath er th an on th e farm ers’ ren ts. Th is co m m en t ary co m bin es t wo t rad it io n s o f eco n o m ic an alysis, t h at o f im p erfect m arket stru ctu re an d th at of com m on -p rop erty resou rces, to in vestigate th e im p act of m on op olistic p rovision of th e biotech in p u t on th e level an d efficien cy of its u se. An im p ortan t in n ovation —an d com p lication —is th e effect of an oth er in p u t, ch aracterized as “care,” th at is costly to p rovid e bu t th at gen erates a p ositive extern ality by m itigatin g resistan ce. As with th e n egative extern ality, in dividu al farm ers on th eir own wou ld n ot reap th e ben efits of th eir care on oth er farm ers, an d th ey wou ld u se too little, su ch as p lan tin g too few refu ge areas. A sin gle own er reap in g all th e ren ts from th e u se of th e biotech corn wou ld su bsid ize or req u ire th e u se of th e efficien t levels of care. However, a reven u e-m axim izin g m on op olist wou ld req u ire care to th e exten t it in creases th e valu e of its sales. Th e distin ction is im p ortan t n ot on ly for th e p rofits of th e biotech p rod u cer bu t also for its strategy of settin g th e p rice of its p rodu ct. Alth ou gh th e an alysis is of a factor m arket, th e in tu ition is iden tical to th at of a tradition al m arket of con su m ers an d su p p liers. In th is case, th e con su m er is th e farm er, wh ose willin gn ess to p ay for th e m on op olist’s biotech p rodu ct is d erived from th e valu e of th e corresp on d in g p rod u ction . Th e p rod u ctivity of an ad d it io n al u n it o f seed co rn t o o n e farm er is a fu n ct io n n o t o n ly o f t h e exten t of h is own u se an d th e exten t of h is own care bu t also of th e u se an d care o f all t h e o t h er farm ers. Th e valu e o f t h at ad d it io n al p ro d u ct io n also d ep en d s o n t h e p rice received by farm ers fo r t h eir co rn h arvest . Th ese variables togeth er determ in e each farm er’s dem an d cu rve. Th e p rodu cer’s willin gn ess t o su p p ly t o a farm er t h en reflect s t h e m argin al co st s o f p ro d u cin g t h e biotech corn , as well as th e im p act of th e extern ality on its ren ts. Becau se th e ext ern alit y is resist an ce, wh ich cau ses a p ro d u ct ivit y ch an ge, t h e co st s are tran sm itted th rou gh sh ifts in th e dem an d cu rves of all th e farm ers. A social p lan n er wou ld m axim ize total su rp lu s, th at is, th e areas u n der th e dem an d cu rves less th e p rodu ction costs of biotech corn an d care. At th e op tim u m for u se of th e factor, th e p rice eq u als m argin al costs p lu s a tax reflectin g t h e ext ern al co st o f m argin al d am ages. A m o n o p o list , h o wever, m axim izes total reven u e less costs. For tradition al p ollu tion p roblem s wh ere th e dam ages are extern al to th e firm s, th e m on op olist sets m argin al reven u e eq u al to m argin al p rodu ction costs, an d th e m on op olist can p rice above or below th e op tim u m , dep en din g on wh eth er th e m arku p overcom p en sates or u n dercom p en sat es fo r t h e ext ern alit y. Ho wever, wh en t h e m o n o p o list in t ern alizes t h e ext ern alit y, as wit h an y p ro d u ct io n co st , t h e m o n o p o list eq u at es m argin al reven u e with total m argin al costs, in clu din g m argin al dam ages. Th e resu ltin g

290 • Commentary: Does the M onopolist Care about Resistance?

m on op oly p rice is greater th an th e socially efficien t p rice, as in th e tradition al case of im p erfect com p etition with ou t extern alities. Th e d ecision for care p resen ts a m ore com p lex in n ovation in th e m on op o ly p ro blem . Alt h o u gh o n e m ay o ft en t h in k o f care in p rop ortion s, like th e sh are of lan d p lan ted for refu ge areas, th e m odel in Noon an ’s ch ap ter u ses levels of care. A p oin t n ot elaborated is th at th is d istin ction allows on e to con sid er t h e farm er’s d em an d fo r t h e m o n o p o list ’s p ro d u ct sep arat e fro m t h e level of care, u p to a p oin t. Given an y m an dated level of care, th e cost of care is fixed for th e farm er, an d, as lon g as it is less th an th e farm er’s su rp lu s, sm all ch an ges in t h e co st o f care d o n o t affect t h e farm er’s d em an d . Ho wever, alth ou gh tradition al m odels h ave u sed fixed fees as a form of ren t extraction , t h is m o d el h as t wo im p o rt an t d ifferen ces: t h e m o n o p o list d o es n o t it self ch arge for an d p rofit from care; rath er, care in du ces a p ositive extern ality th at en ables it to cap tu re m ore ren t from its p rodu ct sales. As a resu lt, th e m on op olist’s decision with resp ect to m an datin g care is differen t from a social p lan n er’s. W h ile a p lan n er wou ld seek to m axim ize total p rod u ctivity of th e biotech in p u t, less th e costs of care, th e m on op olist seeks t o m axim ize m arginal p ro d u ct ivit y. Fu rt h erm o re, t h e m o n o p o list d o es n o t in corp orate th e cost of care in to its decision s as lon g as th e farm er’s p rofits are p ositive. Th is latter p oin t rep resen ts an im p ortan t caveat recogn ized bu t n ot exp licit ly m o d eled in No o n an ’s ch ap t er. Th e m o n o p o list is co n st rain ed in ch oosin g levels of sales an d care by th e p rofits of th e farm er: th e factor costs it im p o ses o n t h e farm er can n o t exceed t h e su rp lu s, o r else t h e farm er wo u ld n ot u se th e p rodu ct. Given an y level of biotech corn u se, th e m on op olist sh ou ld dem an d m ore care th an th e p lan n er, as lon g as care is costly. Becau se a farm er wou ld h ave p ositive su rp lu s at th e social op tim u m ,1 th e m on op olist wou ld n ot p erceive a cost to itself from raisin g th e level of care, an d it wou ld d o so u n til m argin al p ro d u ct ivit y is m axim ized o r u n t il t h e farm er’s p ro fit s are zero . 2 Th e p ro fit con strain ts are th erefore im p ortan t: th ey d eterm in e h ow m u ch th e m on op olist can ch arge for its biotech p rod u ct an d h ow m u ch care it can req u ire d istin ct from wh at it wou ld want to d o if con cern ed with p rod u ctivity ch an ges alon e. Revisitin g th e sales d ecision , th e con strain ed m on op olist wou ld n ot on ly set m argin al reven u e eq u al to m argin al costs p lu s m argin al d am ages bu t also take in to accou n t h ow on e p rice ch an ge affects every farm er’s p rofits becau se th e extern ality m ay ch an ge wh at p rice an d care it can ask of th e oth ers. 3 Th e m ain effect o f t h e co n st rain t wo u ld b e t o t em p er t h e reven u e effect s o f in creasin g p rice o r care levels becau se bo t h red u ce in d ivid u al p ro fit s. Ho wever, t h ey also lo wer t h e ext ern alit y, wh ich t en d s t o raise t h e p ro fit s (an d loosen th e con strain ts) of th e oth er farm ers.

Commentary: Does the M onopolist Care about Resistance? • 291

Given th e level of biotech sales offered by th e m on op olist, th e level of care is gen erally h igh er th an wou ld be d esired by a social p lan n er. As a resu lt, th e m on op olist is able to sell m ore of th e in p u t at a h igh er p rice th an it wou ld at th e socially efficien t level of care. Th is effect m itigates th e m on op olist’s con t ract io n o f b io t ech sales relat ive t o t h e efficien t level, alt h o u gh t h e p rice rem ain s u n am bigu ou sly h igh er. Still, in eq u ilibriu m , th e overall level of care req u ired by th e m on op olist m igh t be m ore or less care th an th at req u ired by th e p lan n er. Alth ou gh th e m on op olist m igh t on ly p erceive a sh are of th e m argin al cost of extra care th rou gh th e farm er’s p rofits con strain t, if it sells less of th e biotech p rodu ct, th e m argin al im p act of extra care is also sm aller. In su m m ary, Noon an ’s work con sid ers a com m on -p ool resou rce, sold by a m on op olist th at can n ot cap tu re all th e corresp on din g ren ts, bu t it can ch arge each bu yer a p er-u n it p rice for th e p rod u ct an d also req u ire a certain level of care. Th e resu ltin g eq u ilibriu m is gen erally ch aracterized by • a h igh er p rice of th e resou rce com p ared with th e op tim u m , wh ich is itself h igh er th an th e com p etitive (n o-p olicy) p rice; • a m o n o p o ly m arku p co n st rain ed by t h e p ro fit s rem ain in g t o t h e farm ers after th e care req u irem en t; • greater care th an wou ld be efficien t, given sales, bu t fewer sales th an wou ld be efficien t, given care; an d • greater sales an d a h igh er p rice th an if th e m on op olist cou ld n ot con tract over care. Th e act u al eq u ilibriu m levels o f care an d bio t ech sales wo u ld d ep en d o n th e com p lex in teraction s between th e farm ers’ p rodu ction fu n ction s, in dividu al an d overall u se, an d care. For exam p le, if resistan ce of a certain p est is a local p roblem , th e farm er m ay in tern alize a large p art of th e resistan ce costs of ad d ition al u se. If it is wid esp read , th e m on op olist m u st in corp orate m ore of th e extern al effects. Th e typ e of care also m ay differ widely. Larger refu ge areas m ay red u ce t h e p ro d u ct ivit y o f an in d ivid u al farm er’s st o ck o f bio t ech co rn becau se less lan d rem ain s to p lan t it in , alth ou gh th e areas m ay en h an ce p rod u ct ivit y o verall b y red u cin g resist an ce b u ild u p . Carefu l t ech n iq u es in t h e ap p lication of p esticid es, h owever, m igh t h ave ben eficial resu lts for crop s as well as resistan ce p reven tion . Un d erstan d in g th ese in teraction s is im p ortan t b ecau se h o w exact ly t h e ext ern alit ies sh ift fact o r p ro d u ct ivit y is crit ical t o d eterm in in g th e d ifferen ce between m argin al su rp lu s an d m argin al reven u e. Regard less, th e th ird resu lt is p rovocative in its im p lication s for p olicy. In d iscu ssio n s o ver refu ge gu id elin es, t h e assu m p t io n is t h at t o o lit t le care is affo rd ed . Th is assu m p t io n wo u ld b e co rrect fo r a co m p et it ively p ro vid ed in p u t or for a case in wh ich th e m on op olist cou ld n ot req u ire care itself. In th is latter case, on e n eeds to con sider th e secon d-best p olicy altern ative: wh at

292 • Commentary: Does the M onopolist Care about Resistance?

wou ld be th e ap p rop riate refu ge p olicy, given a m on op olist’s p ricin g strategy? If t h e m o n o p o list can req u ire care, co u ld welfare b e m u ch im p ro ved b y a refu ge p olicy, an d wou ld th at take th e form of a m an d atory ceilin g, a system of su bsidies, or both ? Noon an ’s work rep resen ts a first step toward u n derstan din g th e im p ortan t in teraction s between m arket stru ctu re an d th e p rovision of a com m on -p ool reso u rce wit h a seco n d ary co m m o n p o o l o f m it igat io n act ivit ies. It h as t h e p oten tial for several oth er in terestin g exten sion s, in clu din g th e case in wh ich th e m on op olist also sells th e in p u t with th e secon d extern ality. Related ap p lication s wou ld be a m on op olist sellin g com p lem en tary good s with an extern ality. Su ch d ou ble-extern ality an d d ou ble-m on op oly m od els, th ou gh ch allen gin g, will b ear fru it in u n d erst an d in g m an y reso u rce an d resist an ce p roblem s, th e m an agem en t of n ot on ly p est-resistan t p lan ts bu t also “Rou n du p ready” corn or an tibiotic “cocktails” th at in volve two or m ore dru gs.

Notes 1. Noon an ’s ch ap ter m akes th is assu m p tion im p licitly to h ave an in terior solu tion . 2. If p ro d u ct ivit y always in creases wit h care, ab sen t t h e p ro fit co n st rain t , t h e m on op olist wou ld always d em an d m ore care u n til every farm er’s p rofits are zero. Th is co n d it io n is t h at o f Eq u at io n 10 in No o n an ’s ch ap t er. If m argin al p ro fit s are st rict ly in creasin g in care, th en th e con strain ts m u st always bin d : th e m on op olist will req u ire as m u ch care as p ossible, given th e total p rofit con strain t, an d th e sh adow valu e of th at co n st rain t will m at t er bo t h fo r t h e level o f care an d sales o f t h e in p u t . To ign o re t h e p rofit con strain t, on e m u st assu m e eith er th at care is costless or th at it u ltim ately h as a n egative im p act on p rodu ctivity. 3. Note th at if th e p rofit con strain t bin d s for an y farm er, all th e oth er eq u ilibriu m p rices are affected. Ch an gin g th e u se of in p u ts or care by on e farm er gen erates an extern alit y fo r t h e o t h ers, in clu d in g t h e o n e facin g t h e bin d in g co n st rain t . Th e ch an ge in reven u es t h at can b e ap p ro p riat ed fro m t h e co n st rain ed farm er fo llo ws n o t o n ly t h e ch an ge in m argin al p rodu ctivity bu t also th e ch an ge in th e con strain t.

Chapter 11

The Interaction of Dynamic Problems and Dynamic Policies Some Economics of Biotechnology Timo Goeschl and Timothy Swanson

In this chapter, we describe biotechnology as the sector that addresses recurring problems of resistance such as those that occur in the pharmaceutical and agricultural industries. The sector may be conceived of as the research and development layer of a three-tiered industry that makes the fundamental determination regarding the allocation of biological resources between stabilization and production objectives. We examine the capacity for decentralized, patent-based incentive mechanisms to result in socially optimal outcomes in the biotechnology industry. We demonstrate a fundamental incompatibility between the dynamics of the patent system and the dynamics of the resistance problem. The patent-based incentive mechanisms are incapable of sustaining society against a background of increasing resistance problems. In addition, the externalities within a patent-based system indicate that decentralized mechanisms will result in systematic underinvestment in the stabilization objective.

u m an in t erven t io n s wit h in t h e b io lo gical wo rld p ro d u ce n at u ral resp o n ses t h at au t o m at ically ero d e t h e effect iven ess o f t h e in it ial in t erven tion . Th is effect is seen in th e p h en om en on of an tibiotic resistan ce in th e h ealth con text an d in th e p h en om en on of p est resistan ce in th e agricu ltu ral con text. Th ese resp on ses from n atu re are p red ictable an d au tom atic becau se wh en we ch oose to m ake a biological resou rce m ore p revalen t th an it wou ld o t h erwise b e we are sim u lt an eo u sly select in g h igh er rat es o f p revalen ce fo r t h e p est s an d p at h o gen s t h at p rey o n t h at reso u rce. Th ese p est s an d p ath ogen s will p rosp er from ou r ch oices an d erode an y gain s from th e in itial in terven tion u n less we can in terven e again to restore th e origin al gain . Th u s,

H

• 293 •

294 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

by in terven in g with in th e biological world , we are com m ittin g ou rselves to a co n t in u in g race o f in n o vat io n again st n at u re. Su st ain in g p ro d u ct io n in t h e face of th ese con tests of biological in n ovation is th e essen ce of th e task th at society assign s to th e biotech n ological in du stries. Weitzm an (2000) recen tly an alyzed th e p oten tially u n su stain able im p acts of h u m an in terven tion with in biological system s. He p rop osed th at a su stain ab ilit y co n st rain t o n h u m an in t erven t io n in t h e b io lo gical wo rld co u ld b e eq u at ed wit h t h e o p t im al allo cat io n o f b io lo gical reso u rces b et ween an “u n st able” p ro d u ct io n o bject ive an d t h e m o re in h eren t ly st able “d iversit y” objective. Con cern abou t su stain ability with in biological system s will lead to th e im p osition of con strain ts on th e exten t of h u m an in terven tion with in th e b io sp h ere. We exp an d o n t h is in t u it io n b y d evelo p in g t h e evo lu t io n ary d yn am ics th at cau se th e p rod u ction sector to ten d toward in stability an d by in corp oratin g th e d yn am ics th at cau se th e reserve or d iversity sector to p rom o t e st ab ilit y. Th is fo cu s en ab les u s t o d efin e m o re clearly t h e ro le o f a biotech n ology sector in m an agin g th e race of biological in n ovation an d allocatin g biological resou rces between p rod u ction an d su stain ability objectives. We depart from Weitzm an ’s fram ework by focusin g on th e in dustrial dim en sion s to th is p roblem . Ou r em p h asis is on th e u se of p aten t-based in cen tive m ech an ism s for m otivatin g th e biotech n ology in du stry. Th e an alytical fram ework th at we use is th e m odel of “creative destruction ” devised by Agh ion an d Howitt (1992). Th eir m odel con siders th e dyn am ics occurrin g with in an in dustry m otivated by th e p u rsu it of p aten t-based ren ts from in n ovation . Th is is a secon d , p arallel race of in n ovation between in d u strial com p etitors, in wh ich success is m easured by th e displacem en t of a rival’s in n ovation with on e’s own . Th u s ou r ch ap ter exam in es th e in tersection between two d istin ct races of in n ovation —on e biological an d on e in d u strial. We exam in e th e in teraction b et ween t h e d yn am ics o f t h e p ro b lem s o f b io lo gical resist an ce an d t h e d yn am ics o f t h e p o licies b ased o n p at en t -b ased in cen t ive m ech an ism s. We h ave th ree fu n dam en tal en q u iries con cern in g biotech n ology. Ou r in itial en q u iry con cern s th e n atu re of th e social valu e of th e biotech n o lo gy sect o r. Ho w sh o u ld a sect o r t h at p ro vid es o n ly su st ain abilit y be balan ced again st t h o se t h at p ro vid e p ro d u ct io n wit h in t h e eco n o m y? W h at sh are (or weigh tin g) of in vestm en t sh ou ld be allocated to each objective? Ou r first t ask is t o set o u t wh at so ciet y’s o bject ives sh o u ld be wh en m an agin g a biotech n ology sector (see gen erally Goesch l an d Swan son 2002). Th e secon d en q u iry con cern s th e u se of decen tralized in cen tive system s to m otivate th e p u rsu it of th ese objectives. Th e Agh ion an d Howitt fram ework en ables u s to in vestigate th e im p act of p aten t-based in cen tive system s on th e biotech n ology in du stry. Un der p aten t-based research an d develop m en t (R&D) system s, firm s com p ete for p aten ts th at p rovide reven u e stream s u n til an oth er in n ovation ren ders th at p aten t obsolete. In th e biotech n ology in du stry, th ese

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 295

p at en t s will b e d isp laced b y a co m p et it ive firm ’s creat io n o r a co m p et it ive p at h o gen ’s ad ap t at io n . Ho w will firm s o p erat in g u n d er a p at en t syst em resp o n d t o t h e ch allen ge im p lied b y t h ese b io lo gical co n t est s? Are p at en t s adeq u ate to ach ieve th e gain s sou gh t by society? Th e distin ction between th e social objectives regard in g biotech n ology an d th e p aten t-based in cen tives to p u rsu e th em is th e secon d focu s of th is en q u iry. Fin ally, a cru cial determ in ation to be m ade by th e biotech n ology in du stries is th e allocation of biological resou rces between th e R&D an d p rodu ction sect o rs. Th is q u est io n h as b een in t im at ed in t h e earlier wo rk b y Weit zm an (2000). Ju st as society m u st give a relative weigh tin g to p rod u ction an d su stain ability, th e biological world also m u st be allocated between th e two objectives. Th u s th e biological world u ltim ately m u st be allocated between two sectors—on e u sed for sp ecialized p rod u ction (su ch as agricu ltu re) an d th e oth er u sed t o m ain t ain t h e st ab ilit y o f t h e first . Th ese are t h e p ro d u ct io n an d reserve sectors, resp ectively.1 Th e biological resou rces with in th e reserve sector act as in p u ts in to th e biotech n ology in d u stry to gen erate solu tion s to p roblem s d evelop in g with in th e p rod u ction sector. Will th e biotech n ology in d u stry cap tu re su fficien t valu e u n der a decen tralized system ? Will th e biotech n olo gy in d u st ry ch an n el t h is valu e t o ward t h e m ain t en an ce o f reserves? Th e cap acit y o f t h e in d u st ry t o affect t h e so cially o p t im al allo cat io n o f n at u ral resou rces to th is stability fu n ction is th e th ird en q u iry of th is ch ap ter.

Resistance Problems and R&D Policies: The Intersection of Dynamic Systems We will u se biotech n ology to refer to th e u se of biological resou rces as in p u ts in to th e research an d d evelop m en t for th e d evelop m en t of solu tion s to biolo gical p ro b lem s wit h in t h e co n t ext o f evo lu t io n ary p ro cesses. Bio lo gical p roblem s are p erceived by evolu tion ary biologists as zero-su m gam es between com p etin g p red ators. Th u s an in festation or in fection sim p ly rep resen ts th e ap p rop riation of a larger sh are of th e available su rp lu s by a com p etin g organ ism . Th e evolu tion ary p rocess is th e com bin ed resu lt of th e p rocesses of selection , adap tation , an d rep rodu ction . Th u s th e ap p lication of a p articu lar p esticid e or p h arm aceu tical to a p est p op u lation sim p ly selects d isp rop ortion ately th ose in th e p op u lation th at are resistan t to it, wh ich resu lts in disp rop ortion ate rep rod u ction by resistan t p ests an d th e observed ad ap tation of resistan ce over tim e. Table 11-1 p resen ts em p irical exam p les of th ese kin ds of p rocesses. Th e biotech n ology in d u stries en gage in an on goin g con test to solve th ese biological p roblem s again st th e backgrou n d of th ese evolu tion ary p rocesses. Fo r exam p le, t h e p h arm aceu t ical in d u st ry d eals wit h su ch p ro blem s in it s research in to an tibiotics; it attem pts to h alt th e progress of path ogen s su ccessfu lly reprodu cin g th em selves with in th e h u m an popu lation . After application

296 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

of an an tibiotic, th e in d u stry m u st th en d eal with th e con seq u en ces of select io n an d ad ap t at io n wh en t h e p at h o gen p o p u lat io n begin s t o d em o n st rat e resistan ce to th e an tibiotic (Laxm in arayan an d Brown 2001). Th e agricu ltu ral in du stry deals with su ch problem s in its research in to n ew plan t varieties wh en it attem pts to produ ce n ew varieties to replace th ose with declin in g yields. Th e com m ercially obsolete p lan t variety, as h ost to an in creasin gly su ccessfu l p est p op u lation , d em on strates th e sam e p roblem p reyin g on th e h u m an p op u lation in th e p h arm aceu tical con text. Again , th e in trodu ction of th e n ew p lan t variety in d u ces th e resp on ses of th e p est p op u lation by selection an d ad ap tation , an d th e n ew variety begin s its declin e (Evan s 1993; Sch effer 1997). On e u n u su al ch aracteristic of th ese sorts of p roblem s is th eir refu sal to go away (Mu n ro 1997). W h en a solu tion h as been fou n d an d ap p lied with in th e biological world , th e n atu re of th e biological world is su ch th at it will com m en ce im m ed iately to erod e th e u sefu ln ess of th at ap p lication (Goesch l an d Swan son 2000). Ad ap tation of biota (p ests an d p ath ogen s) to wid ely u sed p h arm aceu ticals an d p lan t s is a fact o f life, an d it su ggest s t h at t h e wid esp read u se o f an y biotech n ology m u st n ecessarily im p ly its own even tu al dem ise (An derson an d May 1991). Even m ore p erversely, th e p ace at wh ich tech n ological in n ovation p roceeds will sim p ly in crease th e n u m ber of resp on ses by th e p ath ogen p op u lat io n b ecau se in n o vat io n im p lies select io n . Wid esp read an d rap id rat es o f in n ovation by biotech n ologists, th erefore, lead to wid esp read an d rap id rates o f in n o vat io n b y t h e p at h o gen s as well. Bio lo gist s refer t o t h ese as “Red Qu een ” con tests, in wh ich it is n ecessary to in n ovate m ore an d m ore rap id ly m erely to m ain tain p arity with in th e con test (Mayn ard Sm ith 1976).2 Wit h in t h is co n t ext , t h e m ean in g o f t ech n o lo gical p ro gress is m u ch less straigh tforward. If th e widesp read u se of a tech n ological advan ce m u st n ecessarily im p ly th e in creasin g rate of th e arrival of p roblem s, th en wh at is to be th e m easu re of su ccess? Th in k of th e biotech n ology sector as en gaged in a race by th e in n ovator ru n n in g u p th e “d own ” escalator. Th en su ccess in th e race m u st be m easu red relat ive t o act u al p ro gress u p t h e escalat o r, n o t ju st st ep s taken by th e in n ovator. Im agin e as well th at th e escalator belt ru n s freely, so th at qu icker or larger steps by th e in n ovator sim ply resu lt in brin gin g th e stairs down m ore q u ickly. Given th at in d ivid u al attem p ts at p rogress resu lt in both discrete m oves forward an d an in creasin g pace of th e backgrou n d con test, th e fu ll im p act of an in n ovation m u st be discern ed by its aggregate im p act across tim e. Sm all in itial advan ces m igh t u ltim ately aggregate in to large n et losses. In terestin gly, th e presen ce of a biological con test of in n ovation im plies a dual fun ction for th e set of biological resources set aside for “reserve use” (or n on produ ction ). Weitzm an n oted on e fu n ction of th e reserve sector is th at of an ep id em iological bu ffer th at h elp s lim it th e p ressu re on p ath ogen s to evolve in a specific direction an d provides a form of static in suran ce again st a sudden suc-

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 297

TABLE 11-1. Characteristic Time for the Appearance of Resistance in Some Specific Biological Systems Species Avian coccidia Eim eria tenella

Gu t n em atodes in sh eep Haem onchus contortus Ticks on sh eep Boophilus m icroplus

Black flies (Jap an ) Sim ulium aokii Sim ulium dam nosum An op h elin e m osq u itoes (differen t localities) Anopheles sacharovi An. m aculipennis An. stephansi An. culicifacies An. annuaris An. sundaicus An. quadrim aculatus An. pseudopunctipennis

Control agent

Tim e to resistance Generationsa Years

Bu q u in olate Glycarbylam ide Nitrofu razon e Clop idol Roben iclin e Am p roliu m Zoalen e Nicarbazin

6 ( 0 is an in n ovation p rodu ction fu n ction . Th e im p act of an in n ovation con sists of a discrete sh ift in th e level of p rodu ctivity in th e fin al sector, wh ich we den oted in Eq u ation 1 by At. Th is sh ift is of m agn itu de γ > 1 su ch th at AI+1 = AI × γ.8 Th e in dex I den otes th e cu rren t level of tech n ology in u se in fin al goods p rodu ction . In n o vat io n s also h ave a d est ru ct ive facet t o t h eir ch aract ers wit h in t h e in du strial con text. Th e occu rren ce of a “tech n ological in n ovation ” is an even t th at ren ders th e cu rren tly p revailin g tech n ology with in th e in du stry obsolete, th at is, in n ovation s in th is m odel are “drastic.” 9 Hen ce each act of creation is an act of destru ction with regard to th e u sefu ln ess of all p reviou s in n ovation s. Un d er a p at en t syst em , t h is is eq u ivalen t t o st at in g t h at an “in n o vat io n ” is defin ed to be on ly th at am ou n t of tech n ological ch an ge su fficien t to warran t p aten t p rotection . We will stan d ard ize in n ovation at th is m agn itu d e to p rovid e a stan d ard m easu re of in n ovation with wh ich to com p are tech n ological p rogress across variou s system s of organ ization . Hen ce we will m easu re aggregat e t ech n o lo gical ch an ge as t h e su m o f t h e n u m b er o f d iscret e “st ep s” o f in n ovation of th e m in im u m len gth req u ired to acq u ire a p aten t. Innovation and Adaptive Destruction Th e biotech n ology sector h as th e u n u su al ch aracteristic th at th e ap p lication of its in n ovation s with in th e p rodu ction sector resu lts in an in du ced resp on se in th e form of “biological in n ovation s” by p ath ogen s. Th is h ap p en s becau se of th e widesp read u se of th e in n ovation in th e p rodu ction sector an d th e con seq u en t adap tation of th e p ests an d p ath ogen s to th e p articu lar ch aracteristics of th at in n ovation . Th eir ad ap tation th en ren d ers th e in n ovation obsolete, a p rocess we term ed “ad ap tive d estru ction .” Biological in n ovation red u ces th e econ om ic p rodu ctivity of th e fin al goods sector by elim in atin g th e gain s gen erated by th e adop tion of th e cu rren t tech n ology. An alyt ically, we m o d el t h is d yn am ic p ro cess o f b io lo gical in n o vat io n s forced by selection p ressu re as a Poisson p rocess rep resen ted by λ. 10 Th e freq u en cy o f in n o vat io n in creases wit h t h e u se o f t h e in t erm ed iat e in p u t t h at em bo d ies t h e cu rren t t ech n o lo gy in acco rd an ce wit h an in d u ced evo lu t io n fu n ction a(x), a(0) = 0, a′ > 0.11 Hen ce, p ath ogen s adap t to an d overcom e cu rren t tech n ologies at a rate of λ a(x).12 As in d icated earlier, th e rate an d exten t of ad ap tation d ep en d s on th e rate an d exten t of u n iform adop tion of th e in n ovation . Becau se we h ave assu m ed

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 305

th at in n ovation s are “d rastic,” a tech n ological in n ovation d isp laces all oth er com p etitors from u se th rou gh ou t th e fin al goods sector. 13 Th en th e exten t of u se of th e in n ovation will dep en d on ly on th e relative size of th e p rodu ction sector (relative to th e reserve sector). Th u s, th e on ly lim itation on th e u se of th e in term ediate good x will be th e exten t of th e reserve sector v, an d we can eq u ivalen tly exp ress th e fu n ction d eterm in in g th e rate of biological in n ovation as a fu n ction of th e size of th e reserve sector. Th u s th e in du ced evolu tion fu n ction will h en ceforth be exp ressed in th e form a(v). A b io lo gical in n o vat io n is n o rm alized so t h at a sin gle in n o vat io n elim in ates th e relative advan tage of th e cu rren t tech n ology.14 Th is resu lts in a sh ift of γ–1 in p rodu ctivity. 15 Th u s, with D den otin g th e stage of biological in n ovat io n s (i.e., d ep reciat io n ), A D+1 = A D × γ–1 . Th is im p lies t h at aft er a bio lo gical in n ovation h as occu rred, th e econ om y reverts to a tech n ology of th e p reviou s p rodu ctivity level. 16 The Net State of Technology Th ese two p rocesses of in n ovation an d ad ap tation join tly d eterm in e th e cu rren t state of p rodu ctivity (A) with in th e fin al goods sector. Each tech n ological in n o vat io n t h at o ccu rs rep resen t s a p o sit ive sh ift in sect o r p ro d u ct ivit y, wh ereas each biological in n ovation rep resen ts a n egative sh ift. With s d en otin g th e cu rren t tech n ological stage given a h istory of in n ovation s an d adap tation s, th e p rodu ctivity at stage s is th en 17

As = A0 γ S = A0 γ I − D

(3)

Eq u at io n 3 t h erefo re d escribes t h e cu rren t st at e o f t ech n o lo gy in u se in t h e fin al go o d s sect o r as a sin gle p aram et er exp ressin g t h e h ist o ry o r aggregat e im p act o f t h e co n t est s o f creat ive an d ad ap t ive d est ru ct io n . Pro gress in t h e p ro d u ct io n sect o r in t h e sen se o f ab so lu t e im p ro vem en t s in p ro d u ct ivit y o ccu rs o n ly t o t h e ext en t t h at t h e n u m b er o f t ech n o lo gical in n o vat io n s exceeds th e n u m ber of biological on es.

The Social Objective for Biotechnology We assu m e so ciet y co n sist s o f a co n t in u u m o f in d ivid u als o f m ass 1, each with an in tertem p oral u tility fu n ction u(y) lin ear in th e con su m p tion of fin al good y, of th e typ e u(y ) =

∞

∫

e −r τ ydτ

τ=0

wh ere r is th e social rate of tim e p referen ce an d τ is tim e.

(4)

306 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

In th is rep resen tation of th e p roblem , th e in dividu als con cern ed are givin g n o d irect co n sid erat io n t o t h e co st s o f in st ab ilit y, u n cert ain t y, o r risk. Th e in dividu als in th is society valu e on ly th e flow of con su m p tion goods from th e fin al p rod u ction sector, givin g n o in h eren t valu e to th e p rod u cts of th e R&D sector. Th is social objective creates a role for an in term ed iate good s sector in wh ich R&D ou tp u ts are em bodied, an d it m akes clear th at an y in crease in p rodu ction will be con sidered eq u ally valu able.18 Hen ce th e decision p roblem we are con cern ed with is th e op tim al allocation of n atu ral resou rces (lan d) in th e p u rsu it of th e objective of m axim u m p rod u ction . Th e im p ortan ce of su stain ability with in th is objective will be in ferred from th e n eed to m ain tain p rodu ction again st th e backgrou n d of p ath ogen adap tation . Notin g th at th e total am ou n t of lan d will be allocated between th e variou s sectors of th is in du stry, th is im p lies th e existen ce of th e con strain t (for L = 1) 1=v +d + g

(5)

We n ow n eed to in corp orate th e con cep ts of creative an d adap tive destru ction with in th e m od el. We u se th e p robability d istribu tion s Π(I,t) (th e p robability of I tech n ological in n ovation s by th e tim e t) an d Π(D,t) (th e p robability of D biological in n ovation s by th e tim e t) defin ed as Π( I , t ) =

I − φi ( v )]t 1 φi (v )t e [ I!

[

]

(6)

an d Π( D , t ) =

[

1 λa (v )t D!

]

[

]

D − λa ( v ) t

e

(7)

We are n ow in a p osition to set ou t th e social objective for a biotech n ology sector. As sh own in th e ap p en d ix, we can com bin e Exp ression s 1 th rou gh 7 an d aggregate over all in d ivid u al u tilities u to restate th e social objective for th e biotech n ology sector of m axim u m social u tility U as follows: ∞

∞

∞

∑ ∑[

]

e −rt Π( I , t ) × Π( D , t ) As F( x )dt Max U = v I =0 D =0 t =0

∫

(8)

Th e social objective is to m axim ize Eq u ation 8 by ch oosin g th e p rop ortion v of th e essen tial in p u t L to be allocated to R&D, su bject to Eq u ation 5. Th is o bject ive co n t ain s t h e race o f in n o vat io n . A S rep resen t s t h e cu rren t st at e o f tech n ology, wh ich is gen erated by th e h istory of p ast in n ovation s. Th e p robability distribu tion s in dicate th e cu rren t p eriod’s con test, th at is, th e n u m ber of in n ovation s an d ad ap tation s occu rrin g with in th at p eriod . Prod u ction is th e

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 307

o u t co m e o f b o t h t h e n et st at e o f t ech n o lo gy gen erat ed b y t h e race (rep resen t ed b y A S) an d t h e am o u n t o f lan d d ed icat ed t o p ro d u ct io n . Th u s t h e rest at ed o b ject ive in t im at es t h e t rad e-o ff b et ween in vest in g b io lo gical resou rces in to p rodu ction or in to in n ovation . We are able to see th e exp licit n atu re of th e trade-offs in volved by in tegratin g Eq u at io n 8 o ver real t im e an d m akin g u se o f Eq u at io n 4. Th e ap p en d ix sh ows h ow to arrive at th e followin g exp ression for th e p resen t valu e of social welfare from th e allocation of th is in p u t between th ese sectors. Th e Role of th e Biotech n ology Sector: U=

[

A0 F(•)

]

r − φi(v ) − λa (v )γ −1 ( γ − 1)

(9)

wh ere F(• ) is F[β–1(1 – v – g)] an d a’(v) < 0 from Eq u ation 5. Eq u at io n 9 cap t u res t h e d ifferen t iat ed ro les o f t h e p ro d u ct io n an d R&D sectors in gen eratin g social welfare over tim e. Th e im p act on ou tp u t from th e allo cat io n o f lan d s t o t h e p ro d u ct io n sect o r is d en o t ed in t h e n u m erat o r, wh ereas t h e im p act fro m allo cat io n o f lan d s t o ward t h e R&D sect o r is cap tu red in th e den om in ator. In sim p lest term s, th e ch oice of th e size of th e p rod u ction sector d eterm in es th e in itial level of p rod u ction , wh ereas allocation of resou rces to th e R&D sector determ in es th e growth p ath of p rodu ction . Th e role of th e biotech n ology sector is th en th e determ in ation of th e trajectory of welfare gen erated with in th e p rodu ction sector by su stain in g th e sector in th e biological con test. Th e n u m erator exh ibits a straigh tforward im p act of in creased lan d in p rodu ction becau se redu cin g v ben efits th e ou tpu t in th e fin al sector. Th e den om in ator gives a sort of “own d iscou n t rate of biod iversity” th at m u st be ap p lied to determ in e th e valu e of th e perpetu ity th at is th e flow of fin al sector ou tpu t over th e in fin ite tim e h orizon . It is a com posite of th e social rate of tim e preferen ce r redu ced 19 by th e rate of tech n ological in n ovation φi(v) an d in creased 20 by th e rate of biological in n ovation λa(v). Th is o wn d isco u n t rat e cap t u res t h e exp ect ed im p act o f t h e co n t est o f in n ovation between th e biotech n ology sector an d th e biological world. Th ere are really t h ree cases. If t h e sect o r is su ccessfu l in m ain t ain in g in n o vat io n rates sign ifican tly in excess of ad ap tation s, th en th e own d iscou n t rate m ay ap p roach zero, im p lyin g a su bstan tial m u ltip lier on in itial p rod u ction levels. In th is case, th e growth trajectory is very steep . Con versely, if th e biotech n ology sector is very u n su ccessfu l, th e n u m ber of ad ap tation s will sign ifican tly exceed th e n u m ber of in n ovation s, an d th e growth trajectory will be d own ward. Th en th e p rodu ction system is u n su stain able, th e tim e h orizon is sh ort, an d th e m u ltip lier is very low. Th is is essen tially th e case of p oten tial collap se

308 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

in vest igat ed b y Weit zm an (2000). Th en t h ere is t h e sit u at io n in wh ich t h e b io t ech n o lo gy sect o r is in a clo sely co n t est ed Red Q u een race in wh ich it at t em p t s t o m ake ad van ces again st t h e b ackgro u n d o f a syst em always resp on din g to dep reciate th ose gain s. We believe th at, in th e lon g ru n , th is is t h e co rrect way t o view t h e ro le o f t h e bio t ech n o lo gy sect o r. It is t h e sect o r resp o n sible fo r at t ain in g an d m ain t ain in g sm all am o u n t s o f relat ive ad van tage with in a con test of biological adap tation .

The Optimal Allocation of Resources to the Biotechnology Sector Solvin g Eq u ation 9 an d m akin g u se of Eq u ation 2 for th e op tim al level of v, we get th e followin g exp ression for th e socially op tim al level of in vestm en t in th e biotech n ology sector. Socially Op tim al Allocation of Resou rces to Biotech n ology Sector:

[

]

φi ′(v ) − λa ′(v )γ −1 F(•) F′(•) = β+z r − φi(v ) − λa(v )γ −1

[

]

(10)

at th e op tim u m with F(• ) = F[β–1 (1 – v – g)]. 21 Th e left-h an d sid e of Eq u ation 10 is th e m argin al cost of in creased allocation s to R&D (i.e., in term s of lost p rod u ction ). Th e righ t-h an d sid e of Eq u ation 10 is th e m argin al ben efit from in creasin g su ch allocation s. Th is is eq u al to th e n et p resen t valu e of th e n et in crease in p rodu ctivity (in th e fin al goods sector F) from th e m argin al in crease in th e rate of arrival of in n ovation s an d t h e m argin al red u ct io n in t h e rat e o f bio lo gical in n o vat io n . 22 Th e o wn d iscou n t rate ap p lied is, as d iscu ssed later, th e com p osite rate u sed by th e social p lan n er, wh ich t akes in t o acco u n t t h e rat es o f t ech n o lo gical an d bio lo gical in n ovation . 23 In sh ort, th e trad e-off is between an in itially in creased level of p rodu ction an d a p erp etu al in crease in th e rate of growth . To d em on strate, con sid er Eq u ation 9. Th is exp ression d efin es an exp ected exp an sio n p at h fo r fin al o u t p u t in t h e eco n o m y alo n g t h e p at h [φi(v *) – λa(v *)γ–1 ] ln γ. Th is p ath is u n am bigu ou sly in creasin g in R&D in vestm en ts v. An y sm all ad van t age acq u ired in t h e cu rren t p erio d ’s co n t est o f in n o vat io n m ay be warran ted by th e ch an ge in p ath th at it im p lies. Eq u ation 10 m ay be seen as an oth er ren d ition of Weitzm an ’s Eq u ation 12 (Weitzm an 2000), wh ich exp licitly d eterm in es th e relative weigh ts th at society will give to th e goals of p rodu ction versu s stabilization with in th e biological sect o r. In o u r ch ap t er, t h ese weigh t s are d et erm in ed im p licit ly b y t h e bio t ech n o lo gy in d u st ry d et erm in in g t h e relat ive allo cat io n s o f reso u rces t o th e “p rod u ction ” an d “d iversity” sectors req u ired to im p lem en t th ose goals. As in Weitzm an ’s m od el, th e th reat of u n su stain ability m ay be viewed as th e

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 309

ch o ice o f an y p at h t h at m igh t lead u lt im at ely t o ward zero p ro d u ct io n , b u t m ore gen erally th e p roblem of op tim al biotech n ology in vestm en t m ay be an y decision th at p laces th e sector on a p ath with in adeq u ate rates of in n ovation .

Firm Decisionmaking and Investments in R&D for Resistance Problems A d ecen t ralized R&D in d u st ry req u ires su bst an t ial p o licy in t erven t io n t o be op erable. Th e ben efits gen erated from in vestm en ts in R&D are u su ally in ap p rop riable or very in exactly ap p rop riable, an d th is situ ation lead s to su bop tim al levels o f in vest m en t in R&D (Arro w 1962). O n e p o licy resp o n se t o t h is p roblem is th e creation of m on op oly righ ts in th e m arketin g of in term ed iate good s th at em bod y som e of th is in form ation , for exam p le, p aten t righ ts. We will in itially exp lore h ow an in dividu al firm in p u rsu it of a p aten t in th e in term ed iat e go o d s sect o r will ap p ro ach t h e sam e d ecisio n faced b y t h e so cial p lan n er, t h at is, t h e allo cat io n o f an essen t ial in p u t b et ween t h e R&D an d p rodu ction sectors.

Patent-Based Profits in the Intermediate Good M arket

Th e in it ial q u est io n co n cern s t h e m agn it u d e o f t h e reward s t o b e o b t ain ed t h ro u gh in n o vat io n . Firm s in p o ssessio n o f a p at en t h ave t h e cap acit y t o ch oose th e op tim al level of ou tp u t for th e in term ed iate good em bod yin g th e p at en t ed t ech n o lo gy. Becau se we are assu m in g a p erfect ly co m p et it ive fin al go o d s sect o r, t h e o p t im al am o u n t o f go o d x p ro d u ced is t h e level o f o u t p u t th at m axim izes reven u es m in u s th e cost of p rod u cin g th e in term ed iate good on lan d g(x), wh ere lan d com m an ds th e p rice p p er u n it.

[

x s* = arg m ax As × F′( x )x − p ( x ) gx

]

(11)

In th e con text of an in du stry with an effective m on op son y over th e u se of th e essen tial in p u t, th e p rice of th at factor m ay be en d ogen ized . 24 Th en th e m on op olist wou ld con sid er th e effect of its in term ed iate ou tp u t d ecision on t h e d em an d fo r lan d gen erat ed by t h e fin al an d in t erm ed iat e go o d s sect o rs an d th u s on th e p rice of lan d. With th e p rice of lan d p a fu n ction of x, th en x* = −

F′ ( x )

F′′( x )

(12)

Th is m ean s th at m on opolistic profits ps in th e tech n ological state s would be

( ) ( )

2

⎡ F′ x * ⎤ s ⎥ ⎢ ⎦ × ⎛1 − z ⎞ π s = − As × ⎣ ⎜ ⎟ * β⎠ ⎝ F′′ x s

(13)

310 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

Private Firm’s Investment in R& D

Assu m e th ere are n firm s in th is sector of th e econ om y, on e of wh ich will h old a p aten t for th e cu rren t tech n ology. Th e balan cin g con d ition for in vestm en t is t h at at t h e m argin t h e exp ect ed p ro fit s gen erat ed b y in vest m en t in R&D m u st eq u al t h e o p p o rt u n it y co st o f cap it al (Kam ien an d Sch wart z 1982). Hen ce, takin g in to accou n t th e exp ected obsolescen ce of tech n ological in n ovation s (becau se of th e p rocesses of both creative an d ad ap tive d estru ction ), each firm t h at is n o t cu rren t ly p ro d u cin g t h e in t erm ed iat e go o d faces t h e R&D balan cin g con dition th at rV I +1 = π I +1 − (n − 1)φi(v I +1 )V I +1 − λα( x I +1 )V I +1

(14)

Th is con dition states th at th e expected return on th e n ext in n ovation (th e righ th an d side) m ust equal th e opportun ity cost of capital on th e left-h an d side. Th e expected return con sists of th e m on opolistic profits from sellin g th e in term ediate good em bodyin g th e in n ovation to th e fin al goods sector in th e future tech n ological stage m in us th e expected im pact from obsolescen ce of th e tech n ology becau se of tech n ological in n ovation s m ad e by on e of th e (n – 1) com p etitors m in us th e expected im pact from obsolescen ce of th e tech n ology because of biological in n ovation . Note we assum e th at tech n ologies of th e previous tech n ological stage are supplied com petitively, im plyin g a zero-profit con dition on tech n ologies of earlier vin tage. 25 Rearran gin g Eq u ation 14 an d m akin g u se of Equation 3, we get th e n et presen t value of a sin gle tech n ological in n ovation : V I +1 =

π I +1 r + (n − 1)φi (v I +1 ) + λa (d I +1 )

(15)

In th is exp ression , th e n u m erator rep resen ts th e m on op olistic p rofits gen erated by th e in n ovation an d th e den om in ator rep resen ts th e own rate of discou n t for p rivate in vestm en ts in in n ovative activities. Th is is a com p osite rate m ade u p of th e op p ortu n ity cost of cap ital, th e rate of obsolescen ce becau se of (o t h ers’) t ech n o lo gical in n o vat io n , an d t h e rat e o f o b so lescen ce b ecau se o f b io lo gical in n o vat io n . In su m , t h e p rivat e firm valu es o n ly t h e m o n o p o ly ren ts th at m ay be acq u ired from a tech n ological in n ovation , an d it discou n ts an y fu tu re stream of su ch ren ts with regard to th e exp ectation of an y fu tu re tech n ological an d biological in n ovation .

Firm Decisionmaking Regarding Investment in R& D

Th e p rivate firm an alog to Eq u ation 10 is th e p rivate in cen tive for in vestm en t in reserves for R&D. Lan d is allocated by th e p aten t h older to eq u alize retu rn s in both th e fin al goods sector an d in R&D.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 311

p = As

F′(•) β

= φi ′(v s )V I +1

(16)

wh ere p is t h e p rice o f lan d an d F(• ) is F[β–1 (1 – (n – 1)v – g)]. Co n d it io n 16 p rovides th e in tertem p oral lin k between tech n ological stages. 26 Co m bin in g Eq u at io n 4 wit h Eq u at io n s 15 an d 16, so lvin g fo r t h e st ead y state, an d u sin g Eq u ation 5 to sim p lify, we derive th e op tim ality con dition for th e p rivate firm ’s allocation of lan d to th e reserve sector in th e steady state of a decen tralized econ om y.

[ F' (•)] γ

2

F′(•) β

= φi ′ ( v )

− F′′(•)

(

r + (n − 1)φi(v ) + λa (n − 1)v , g

)

(17)

As in Eq u ation 10, th e left-h an d side of Eq u ation 17 sh ows th e m argin al valu e of lan d allocated to p rodu ction an d th e righ t-h an d side of th e m argin al valu e of lan d allocated to reserve statu s. 27 Th e m argin al valu e of lan ds as reserves is eq u al t o t h e exp ect ed valu e o f m o n o p o ly ren t s accru in g t o t h e su ccessfu l in n ovator becau se of th e allocation of an addition al u n it of lan d to R&D, discou n ted at th e p rivate firm rate th at in clu des n ot on ly th e op p ortu n ity cost of cap ital bu t also th e an ticip ated effects of p aten t obsolescen ce (d erivin g from eith er th e p rocesses of creative or ad ap tive d estru ction ). In th e followin g section s, we will con trast th e p rivate in cen tives for in vestm en ts in biotech n ology with th e social op tim u m .

The Capacity for Patent-Based Incentives for R&D To Address Resistance Problems Now th at we h ave derived th e altern ative decision m akin g ru les for social an d paten t-based decision m akin g regardin g resistan ce problem s, it is possible to com pare h ow th ese altern ative decision m akin g system s respon d to th e fun dam en tal determ in an ts of resistan ce p roblem s. Th e followin g p rop osition s establish th e com parative statics of social an d decen tralized decision m akin g processes. P RO PO SITIO N 1: T he socially optim al am ount of investm ent in biotechnology increases with (a) a decrease in the discount rate r, (b) an increase in the m agnitude of the im pact of an innovation γ, (c) an increase in the arrival rate of technological innovations φ, and (d) an increase in the arrival rate of biological innovations λ. 28

312 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

PROOF: Take th e p artial derivatives of Eq u ation 10 with resp ect to th e variables sp ecified . Prop osition 1 states th at a h igh er d iscou n t rate lead s to a lower p resen t valu e o f t h e ben efit s o f in n o vat io n an d h en ce o f t h e in p u t s t h at gen erate th ese in n ovation s. Likewise, if th e m agn itu d e of th e im p act of a t ech n o lo gical in n o vat io n in creases, in n o vat io n b eco m es relat ively m o re p ro fit able, wh ich lead s t o in creased in vest m en t in reserves. Th is is co rresp o n d in gly t h e case wh en an in crease in t h e arrival rat e o f in n o vat io n s im p ro ves t h e p ro fit ab ilit y o f t h e R&D sect o r. Th is sh ift s allo cat io n o f reserves toward th e R&D sector as th e sacrifice in cu rren t con su m p tion is ou tweigh ed by th e gain s from a h igh er growth trajectory. Fin ally, an d p erh ap s m o st im p o rt an t ly, in vest m en t in R&D is so ciet y’s in st ru m en t fo r resp o n d in g t o bio lo gical in n o vat io n s, an d so t h e m argin al ben efit s fro m R&D will in crease as th e rate of biological in n ovation in creases.29 As in th e case of th e social p lan n er, we can m ake th e followin g statem en ts ab o u t Eq u at io n 17 t o d escrib e t h e resp o n se o f t h e in d ivid u al firm ’s in vest m en t in R&D in resp on se to ch an ges in th e basic p aram eters. PROPOSITION 2: The optim al level of investm ent by the individual biotechnology firm responding to patent-based incentives increases with (a) a decrease in the discount rate r, (b) an increase in the m agnitude of the im pact of an innovation γ, (c) an increase in the arrival rate of technological innovations φ, and (d) a decrease in the arrival rate of biological innovations λ. PROOF: Take th e p artial derivatives of Eq u ation 17 with resp ect to th e variables sp ecified. Th e in tu ition beh in d th e variou s assertion s with in Prop osition 2 is st raigh t fo rward . Th e n et p resen t valu e o f an y in vest m en t in R&D in creases with a lower d iscou n t rate, m akin g in vestm en ts m ore p rofitable at t h e m argin . Th e sam e is t ru e fo r an in crease in t h e m agn it u d e o f t h e im p act of in n ovation s. If tech n ological in n ovation s are less freq u en t, th en m o n o p o ly ren t s are likely t o accru e o ver lo n ger p erio d s, t h u s raisin g t h e ben efits associated with R&D, alth ou gh th e im p act is less straigh tforward becau se co m p et it o rs also gain fro m t h is in crease, wh ich affect s exp ect ed m on op oly ren ts in an ad verse m an n er. 30 Fin ally, wh en biological in n ovation s are m ore freq u en t, th en p aten ts becom e obsolete m ore q u ickly, th u s redu cin g in cen tives for in vestm en ts. Th e develop m en t of th e basic ch aracter of th e resp ective in cen tive system s allows u s to develop ou r m ain resu lt, stated in Prop osition 3. PRO PO SITIO N 3: A patent-based system of incentives is incapable of addressing the fundam ental problem of biological adaptation because the incentives to invest in solutions are weakened as the problem s becom e m ore serious.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 313

PROOF: Com p are (d) of Prop osition s 1 an d 2. Pro p o sit io n 3 st at es t h e o b vio u s im p licat io n fro m t h e co m p ariso n o f Pro p o sit io n s 1 an d 2. As t h e rat e o f b io lo gical ad ap t at io n in creases, t h e so cially o p t im al resp o n se is t o allo cat e m o re reso u rces t o t h e so lu t io n o f an in creasin gly th reaten in g p roblem . Prop osition 2 d em on strates, h owever, th at t h e in d u st ry m o t ivat ed b y a p at en t -b ased syst em o f in cen t ives will in fact resp on d in a p erverse m an n er. In creasin g rates of ad ap tation im p ly red u ced t im e h o rizo n s fo r p ro d u ct u sefu ln ess an d h en ce a t ru n cat ed flo w o f fu t u re ben efits. Th e in du stry will see redu ced in cen tives to in vestin g in th e solu tion of p roblem s if th e exp ected life of th at solu tion is red u ced , an d so a p aten tbased system is ill su ited to th e p roblem s of biotech n ology. How seriou s is th is p roblem ? Th at is, wh at wou ld cau se th e rates of biological in n ovation to in crease? Th e fu n dam en tal n atu re of adap tation p roblem s is su ch t h at an in creasin g rat e o f b io lo gical in n o vat io n is a given b ecau se it resu lts from an y attem p ts by society to m ake p rogress. Society p u rsu es growth in p rod u ction th rou gh eith er in creased allocation s of biological resou rces to th e p rodu ction sector or in creased rates of in n ovation . Eith er ap p roach resu lts in in creased rates of biological in n ovation . In creased areas of lan d d ed icated t o p ro d u ct io n resu lt in in creased p ro sp ect s fo r an y given bio lo gical in n o vat io n t akin g h o ld . In creasin g n u m bers o f t ech n o lo gical in n o vat io n s in crease th e n u m ber of d ifferen t p ath ogen s th at are im p licitly selected by society for p ossible trial. For th is reason , biotech n ological p rocesses are u su ally m od eled as a form of “arm s race”: an in creasin g rate of resp on se from th e com p etitor is in du ced by an y attem p t to gain an advan tage. In tellectu al p rop erty righ ts system s are very p oor m ech an ism s for p rovid in g in cen t ives in su ch co n t est s o f in n o vat io n . Th e in d u ced resp o n se fro m n at u re im p lies an exp ect at io n t h at an y in n o vat io n ’s life sp an will be sh o rt , an d th is redu ces th e in cen tives to in vest in in n ovation from th e ou tset. If, for som e reason , society d oes m ake an in itial attem p t to ach ieve growth in p rod u ction in th e biological sp h ere, th e in tellectu al p rop erty righ ts system p rovid es an in creasin gly d im in ish in g in cen tive to attem p t to rem ain with in th e co n t est o f in n o vat io n t h at resu lt s. Ju st as so ciet y b eco m es relian t o n t h e b io t ech n o lo gy sect o r t o ad d ress t h e resu lt in g p ro b lem s, t h e b io t ech n o lo gy sector becom es in creasin gly less m otivated to p u rsu e th ose p roblem s.

Comparing Private and Social Investment in the Biotechnology Sector We n o w h ave t h e b asic resu lt s n ecessary t o ad d ress t h e t h ird fu n d am en t al q u estion raised in th e in trodu ction of th is ch ap ter: h ow well does th e p aten tbased system p erform th e role of allocatin g biological resou rces between th e

314 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

p rod u ction an d reserve sectors? Weitzm an (2000) id en tified th is as a fu n d am en tal p roblem to be addressed with regard to th e in stabilities in th e biological world, an d we wish to kn ow h ow well a decen tralized in du stry will resolve th is issu e. 31 Th is is eq u ivalen t in ou r fram ework to th e gen eral q u estion of h ow well a p at en t -based syst em will m o t ivat e in vest m en t s in t h e bio t ech n o lo gy sect o r. Becau se we are varyin g on ly a sin gle factor of p rod u ction in ou r biotech n ology in d u stry (th e essen tial in p u t—lan d ), th e in cen tives to in vest in biotech n ology gen erally will be rep resen ted by th e level of in vestm en t in th is factor o f p ro d u ct io n . We wish t o kn o w h o w p at en t -b ased in cen t ives m o t ivat e in vestm en t in biotech n ology’s stability-en h an cin g fu n ction an d h ow th is will u ltim ately determ in e th e level of reserves retain ed for th is fu n ction .

The Externalities within the Patent-Based M anagement System

Th e o p t im al allo cat io n s o f lan d t o R&D b y t h e p rivat e firm an d t h e so cial p lan n er are cap t u red in Eq u at io n s 17 an d 10, resp ect ively. A co m p ariso n o f th ese allocation s sh ows six distin ct factors th at will determ in e th e relative size o f t h e reserve sect o rs u n d er t h ese d ifferen t regim es: t h e b u sin ess-st ealin g effect , t h e sin gle su p p lier effect , t h e ap p ro p riab ilit y effect , t h e d ifferen t ial in tern alization of extern alities, th e own discou n t rate effect, an d th e collateral cost effect. Th e first fact o r is wh at Agh io n an d Ho wit t (1992) t erm ed t h e “b u sin essst ealin g” effect . Th is effect cap t u res t h at t h e so cial p lan n er will accru e o n ly th e n et ben efits from its in n ovation s. Th is is becau se n ew typ es of tech n ology su p ersed e th ose d evelop ed p reviou sly by th e social p lan n er, d en oted by (γ – 1). In con trast, p rivate in cen tives for in n ovation are greater becau se in n ovatin g firm s ten d n ot to com p ete again st th eir own p aten ts (see also Tirole 1988) an d th u s receive th e total im p act of in n ovation (γ). In th is resp ect, th e in cen tives to in vest in biotech n ology are greater for p rivate in d u stry th an for th e social p lan n er. Th is is cou n terbalan ced by th e “sin gle su p p lier” effect th at resu lts becau se t h e so cial p lan n er faces o n ly t h e n et im p act o f b io lo gical in n o vat io n s (λa(v)/ γ), wh ereas th e p rivate firm faces th e fu ll effect (λa(v)). Th e social p lan n er is th e sole su p p lier of tech n ology, wh ereas in th e p rivate in d u stry case of o bso lescen ce t h ro u gh bio lo gical in n o vat io n , t ech n o lo gy (o f a p revio u s p ro d u ct ivit y st age) will b e su p p lied b y a co m p et it ive m arket wit h zero p ro fit s. Th e social p lan n er—in th e sam e circu m stan ce—will su p p ly its own tech n ology from an earlier stage. Th e th ird effect is th e “ap p rop riability” effect, wh ich reflects th at th e social p lan n er t akes in t o acco u n t t h e fu ll so cial welfare b en efit s d en o t ed b y F(• ), t h at is, all o f t h e so cial valu e resu lt in g fro m p ro d u ct io n an d co n su m p t io n .

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 315

Th e p rivate firm in stead will con sid er on ly th e m on op oly ren ts –[F′(• )]2 / F″(• ) th at it will ap p rop riate from its own ou tp u t.32 Th is sh ortfall in ren t ap p rop riat io n d ecreases t h e p rivat e in cen t ives fo r R&D act ivit ies an d h as a n egat ive effect on p rivate in vestm en t in to reserve lan ds.33 Th e fo u rt h effect is t h e “d ifferen t ial in t ern alizat io n ” o f ext ern alit ies: Th e social plan n er fu lly in tern alizes both of th e ben efits from h oldin g th e m argin al u n it of lan d as a reserve—th e direct ben efits from in creased rates of tech n ological in n ovation φi′(v) an d also th e in d irect ben efits from red u ced rates of biological in n ovation (i.e., –λ a′(v)). Th e firm con siders th e direct ben efit φi′(v) as t h e in d irect ben efit ext ern alit y d iffu ses o ver all m arket p art icip an t s. Th is is an oth er reason th at th e in cen tives for in vestm en t in reserve lan ds are redu ced u n der a decen tralized regim e. Th e fift h d ifferen ce is t h e “own discount rate” effect : Th e d en o m in at o r in Eq u ation 10 sh ows th at th e social p lan n er’s discou n t rate h as th e rate of tech n o lo gical in n o vat io n su b t ract ed fro m it , wh ereas in Eq u at io n 17 t h ese t wo rates are su m m ed . Th is is attribu table to an in creased rate of in n ovation th at gen erat es gro wt h t h at is valu ab le fro m t h e so cial p ersp ect ive b u t t h at t h e sam e ren d ers p rivat e in vest m en t in R&D less p ro fit ab le b y in creasin g t h e exp ected rate of tech n ological obsolescen ce. Th e last effect th at differen tiates th e p rivate firm from th e social p lan n er is th e “collateral cost” effect. Th is effect ap p ears in th e den om in ator of th e lefth an d side of Eq u ation s 10 an d 17: Th e social p lan n er takes in to accou n t th at th e exp an sion of in ten sive agricu ltu re req u ires an allocation of lan d to p rodu ce th e in term ediate good, th at is th e aggregate cost (in term s of lan d) is β + z. Th is im p lies th at th e loss of reserves from exp an din g in ten sive agricu ltu re is less th an th e gain in in ten sive lan d s. Th e p rivate firm d oes n ot con sid er th is extern ality, as th e left-h an d side den om in ator featu rin g on ly β sh ows. Th ree of th ese effects h ave been n oted in th e existin g in d u strial organ ization literatu re. Th e “bu sin ess-stealin g effect” h as p reviou sly been exp lored in Agh ion an d Howitt (1992). Th e p roblem of im p erfect ap p rop riation of ren ts from R&D is a well-kn own sou rce of su bop tim al p rovision of R&D wh en Ram sey p ricin g of in n ovation s is n ot feasible (see, for exam p le, Tirole 1988). Th e d ifferen ces in t h e im p act o f t ech n o lo gical p ro gress o n t h e d isco u n t rat e o f so cial p lan n er an d p rivat e firm s h ave been st u d ied by Rein gan u m (1989). 34 Th e rem ain in g th ree effects are p ecu liar to th e p roblem at h an d. Of th ese, th e fact th at th ere is a differen ce in in tern alization of extern alities between social p lan n er an d p rivate in du stry m u st be th e m ost sign ifican t on e. Th is is becau se it h igh ligh ts th e failu re of p rivate in d u stry to take in to accou n t th e n egative relat io n sh ip b et ween in t en sive u se o f t h e essen t ial reso u rce an d t h e rat e o f obsolescen ce of th e tech n ologies em p loyed in ten sively. Th is m ean s th at in all eco n o m ic set t in gs in wh ich su ch a class o f relat io n sh ip s exist s, ad d it io n al d eviat io n s o f t h e p rivat e in d u st ry allo cat io n o f reso u rces can be exp ect ed . 35

316 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

Th e “sin gle su p p lier” effect is im p ortan t in settin gs in wh ich im itation costs are low su ch th at gain s from in n ovation diffu se q u ickly across th e in du stry. In t h ese cases, t h e valu e o f sh elvin g in n o vat io n s is lo w, wh ich co n t rib u t es t o u n d erin vestm en t in to R&D relative to th e social op tim u m . Th e last sou rce of d ifferen ce b et ween t h e so cial p lan n er an d t h e p rivat e in d u st ry case is t h e p roblem of “collateral cost.” Th is is very sp ecific to th e agricu ltu ral settin g of th is m od el an d th erefore likely to h ave little ap p lication beyon d th e con text o f co n servin g bio d iversit y as an R&D in p u t . Ho wever, it p o in t s t o t h e m o re gen eral p roblem th at p rivate d ecision m akin g d oes n ot accou n t for collateral effects if th ey are n ot con veyed th rou gh m arket p rices. In total, th erefore, we fin d six reason s to believe th at th e in cen tives u n der a p at en t -b ased syst em vary fro m t h e so cial o p t im u m . Five o f t h ese effect s in d icat e t h at a p rivat e firm will u n d erin vest in t h e reserve sect o r. Th e o n ly effect t h at ru n s co u n t er is t h e “b u sin ess-st ealin g effect ,” wh ich allo ws o n e firm ’s in n o vat io n t o rep lace an o t h er’s before it s u sefu l life h as b een fu lly served. Of cou rse, th is is th e essen ce of th e p aten t race as an in cen tive m ech an ism , an d it s p recise effect varies sign ifican t ly o n t h e b asis o f assu m p t io n s an d exp ectation s (Kam ien an d Sch wartz 1982). In th e biotech n ology sector, th e in cen tives to overin vest bu ilt in to a p aten t race (if an y su ch exist) m u st be su fficien t to com p en sate for th e m an y clear ben efits th at th e p rivate decision m akin g extern alizes. 36 In an y even t , t h e p at en t -based syst em p erfo rm s p o o rly in gen erat in g t h e op tim al level of in vestm en ts in th e biotech n ology sector. It con tain s six clear extern ality p roblem s, five of wh ich in dicate th at th e p aten t-based system will ten d toward u n derin vestm en t in biotech n ology.

Comparing Social and Industrial Investments— A Simulation

Th e resu lt s o f a sim u lat io n exercise o f d ifferen ce b et ween cen t ralized an d d ecen tralized d ecision m akin g with regard to th e allocation of lan d s to R&D disp lay h ow th e u n derestim ation of th e valu e of reserves for th ese p u rp oses is n ot on ly system atic bu t also su bstan tial over a wid e ran ge of p aram eter valu es. To illu strate, we m u st first m ove from th e in dividu al firm level of an alysis to th at of th e aggregate in du stry. Th e in du stry eq u ilibriu m con cep t th at determ in es t h e o p t im al allo cat io n o f lan d d ep ict ed in Eq u at io n 17 is t h at o f a p aten t race in volvin g n – 1 firm s.37 Becau se in n ovation s are drastic by defin it io n , t h e p at en t race gen erat es a seq u en ce o f m o n o p o lies t h at rep lace o n e an oth er. In th is sen se, in d ivid u al m on op olies d o n ot p ersist, bu t th e m arket stru ctu re will rem ain m on op olistic. To assess n, we exam in e th e con d ition s u n d er wh ich firm s en ter th e race. En try is p rofitable so lon g as p ositive ren ts are associated with bein g en gaged in R&D. We restrict ou r atten tion to th e case in wh ich th e costs of R&D are

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 317

on ly th e cost of h oldin g lan d as a reserve. 38 Th en firm s will con tin u e to en ter in t o R&D as lo n g as t h e exp ect ed p resen t valu e o f R&D is n o t less t h an t h e cost of h oldin g th e op tim al am ou n t of lan d given by Eq u ation 17; th at is φi (v *)V I +1 − As

F′(•) β

v* ≥ 0

(18)

Makin g u se o f Eq u at io n s 17 an d 18 an d sim p lifyin g, t h is m ean s t h at t h e total n u m ber of firm s in th e m arket is determ in ed by th e con dition i ′( v *) =

i( v *)

(19)

v*

In th e absen ce of an y barriers to en try, th e op tim al level of reserves v* will be ch osen so th at th e m argin al p rodu ctivity of reserves eq u als average p rodu ctivity. Th is m ean s th at en try is occu rrin g u n til th e m on op oly ren ts are d issip ated across th e in du stry by virtu e of firm s en terin g R&D u n til average p rofits eq u al zero. Th is zero p rofit en try con dition will th en determ in e th e aggregate level of in vestm en t with in th e in du stry. To ad d ress t h e issu es raised at t h e b egin n in g o f t h is ch ap t er, we m ake a d irect com p arison of th e op tim al reserve d ecision s m ad e by a social p lan n er, b y a p rivat e in d u st ry, an d b y an in d ivid u al firm wit h in t h at in d u st ry. Th is req u ires u s t o lo o k fo r ways t o evalu at e Eq u at io n s 10 an d 17 exp licit ly, an d th is will req u ire th e selection of sp ecific fu n ction al form s. Table 11-2 lists th e exp licit fu n ct io n al fo rm s ch o sen fo r t h e vario u s an alyt ical fu n ct io n s co n tain ed in th e m odel. We assu m e t h at δ < 1. Th is m ean s we are assu m in g d ecreasin g ret u rn s t o scale in th e p rodu ction sector for both th e in term ediate in p u t an d—by virtu e of fixed p rop ortion s in p rod u ction —lan d . In th e R&D sector, we assu m e th at b o t h t ech n o lo gical an d b io lo gical in n o vat io n fu n ct io n s are lin ear in lan d in p u ts. 39 Th is allows u s to solve exp licitly for lan d allocation decision m akin g u n d er th e circu m stan ces of th e social p lan n er an d th e p rivate in d u stry. However, b ecau se t h e n u m b er o f firm s is in d et erm in at e in t h e case o f a lin ear in n o vat io n fu n ct io n , we will access m arket d at a t o d ep ict t h e level o f lan d dem an ded by an in dividu al firm .

TABLE 11-2. Assumed Functional Forms

Agricu ltu ral p rodu ction fu n ction Tech n ological in n ovation fu n ction Biological adap tation fu n ction

Analytical

Explicit

F(x) φi(v) λa(v)

xδ φiv λa(1 – v)β/ (β + z)

318 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

Solvin g Eq u ation 10 for th e op tim al level of reserves ch osen by th e social p lan n er RS, we get

RS = 1 −

⎞ ⎛ r δ⎜ − φi ⎟ ⎠ ⎝ γ −1

(

)

λ β β2 − δ + β2 φi − δφi a γ β+z

(20)

Eq u at io n 20 co n fo rm s t o t h e t en et s o f Pro p o sit io n 1, an d it exh ib it s o t h er ch aracteristics we wou ld exp ect, su ch as th e con d ition s u n d er wh ich it p rovides valu es less th an on e.40 Solvin g Eq u ation 17 for th e level of reserves ch osen by th e in du stry as a wh ole RI, we get RI = 1 −

r + φi (β − z )φiγβ2 − λβa + φi (1 − δ)(β + z ) β + z

(21)

Again , Eq u ation 21 con form s to th e ten ets of Prop osition 2 an d exh ibits th e ch aracteristics req u ired for ou r sim u lation s. 41 We are n o w ab le t o p ro vid e so m e sim u lat io n s o f t h e ch o sen levels o f reserves u n d er varyin g assu m p t io n s abo u t in n o vat io n , ad ap t at io n , an d d isco u n t rat es. Tab le 11-3 su m m arizes t h e ch o ices fo r t h e b aselin e p aram et ers th at gen erate th ese p lots an d th e literatu re from wh ich th ey derive. Th e results from th ese sim ulation s are depicted in Figures 11-2 to 11-4. Th ey un derlin e th e basic poin t set forth earlier. Th e private valuation of reserve lan ds for R&D is a very poor estim ator of th e social value of th ese lan ds for th ese purp oses. Th e sim u lation s d em on strate th is p oin t over a wid e ran ge of p lau sible param eter values. Th ey furth er illustrate th e direction an d th e m agn itude of th e bias. Over alm ost th e en tire ran ge of p aram eter valu es, th e p rivate m etric system atically un derestim ates th e social value of reserves for purposes of R&D. Th e m agn itude of th e un derestim ate depen ds on th e specific param eter values, but it can vary from a sm all am oun t to a differen ce of several orders of m agn itude. Several fu rth er im p ortan t d ifferen ces between social d ecision m akin g an d p rivate decision m akin g are illu strated in th ese figu res. Figu re 11-2 sh ows h ow variation s in th e rate of tech n ological in n ovation affect th e op tim al reserve levels. Private in du stry allocates con sisten tly less to reserves, an d its op tim u m declin es m ore p ron ou n cedly th an th at of th e social p lan n er. At very low rates o f t ech n o lo gical in n o vat io n , R&D b eco m es u n p ro fit ab le. In co n t rast , t h e social p lan n er is willin g to p reserve lan d even if th e in n ovation rate is zero. Th e reaso n fo r t h is lies in t h e fact t h at reserves n o t o n ly serve as an R&D in p u t bu t also act as an ep id em iological bu ffer. Th is d ifferen ce in in vestm en t levels reflects th e differen tial rate of in tern alization of th is extern ality.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 319

TABLE 11-3. Baseline Simulation Parameters and Sources Param eter Description

Sym bol

Value

Discou n t rate Produ ctivity in agricu ltu re of in term ediate good

r

0.01

δ

0.35

In n ovation rate

φi

0.0019

Adap tation rate In term ediate good p er lan d ratio in fin al goods sector

λa

0.0025

β

3

In term ediate good p er lan d ratio in in term ediate sector Magn itu de of in n ovation s

z γ

0.2 1.5

Nu m ber of firm s in in du stry

N

25

Source

Even son 1998 Con tribu tion of gen etic resou rces to global rice p rodu ction Cartier an d Ru iten beek 1999 “Hitrate” of 10 –6 tim es th ree sam p les p er sp ecies tim es sp ecies rich n ess p er h ectare 42 Heisey an d Bren n an 1991

Relative p rodu ctivity of fin al an d in term ediate goods sector. In agricu ltu re between 1:0.003 to 1:0.2. Here 1:0.06 (Sm ith 1998).

Legal req u irem en t of “sign ifican ce” Market data (RAFI 1997)

Th e sim u lat io n in Figu re 11-3 illu st rat es h o w t h e gen eral in cen t ives fo r in vestm en t in reserves d im in ish as th e d iscou n t rate in creases. Of cou rse th e p rivate in cen tives to in vest lie everywh ere ben eath th e social in cen tives an d , to su ch an exten t th at th e discou n t rate at wh ich it becom es u n p rofitable for in du stry to con du ct R&D, lies below th at at wh ich th e social p lan n er ceases to in n ovate by a factor of 5. However, it is also worth n otin g th e differen ce h ere t h at t h e rat e o f d isco u n t will vary fo r in d u st ry an d so cial p lan n er, wit h t h e in d u st ry o p erat in g u n d er a rat e t h at is great er t h an o r eq u al t o t h at o f t h e p lan n er. Th is st an d ard d ifferen ce wo u ld aggravat e t h e alread y exist in g t en den cy of p rivate in du stry to u n derin vest in reserves. Fin ally, t h e resp o n se t o ch an ges in t h e rat e o f b io lo gical in n o vat io n d ep icted in Figu re 11-4 d em on strates th e m ost p ron ou n ced d ifferen ce in th e t wo d ecisio n m akin g p ro cesses, as d iscu ssed earlier. In t h e co n t ext o f rap id rates of biological in n ovation , th e social p lan n er resp on ds with in creased levels of in vestm en ts in reserves for R&D. Th is is in d icative of th e fu n d am en tal role of su ch reserves as th e gen erators of th e in form ation req u ired to resp on d t o t h ese recu rrin g p ro b lem s. In co n t rast , t h e p rivat e in d u st ry resp o n d s t o

320 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

0.8 Social Planner 0.6 Private Industry 0.4

0.2

Private Firm 0

0.2 φ

0.4 φ

0.6 φ

0.8 φ

1φ

FIGURE 11-2. Share of Reserves for Varying Rate of Technological Innovation

1.0

0.8 Social Planner 0.6

0.4

0.2 Private Industry 0

r

2r

3r

FIGURE 11-3. Share of Reserves for Varying Discount Rate

4r

5r

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 321

1.0 Social Planner 0.8

0.6

0.4

0.2

Private Industry Private Firm

0

λ

2λ

3λ

4λ

FIGURE 11-4. Investments in R&D for Varying Rate of Biological Innovation

in creasin g rat es o f b io lo gical in n o vat io n in a p erverse m an n er. Th e p rivat e in d u stry actu ally red u ces its R&D activity in resp on se to in creased p ath ogen act ivit y. Th is resp o n se sh arp en s as t h e ad ap t at io n rat e in creases wh ich , in tu rn , widen s th e gap between th e social op tim u m an d th e in du stry resp on se.

Conclusion Th e dyn am ics of th e biological world gen erate certain p redictable an d destabilizin g resp on ses to attem p ts to m ake p rogress with in th at world . Attem p ts to exp an d th e p rod u ction sector are m et au tom atically with biological ad ap tat io n s t h at n eu t ralize t h o se effo rt s. In creasin g t h e rat es o f in t erven t io n also in creases th e rates of arrival of su ch ad ap tation s. An d , on ce in terven tion h as occu rred, th e op tion of retain in g th e statu s q u o is n o lon ger available. Society is th en en gaged forever with in a con test of in n ovation an d adap tation . Th e bio t ech n o lo gy sect o r is t h e bran ch o f R&D t h at u n d ert akes so ciet y’s cau se with in th is con test. As described in Weitzm an (2000), we view th e fu n dam en tal determ in ation to be m ade by th is sector as th e op tim al relative size an d exten t of th e biological resou rces d ed icated to p rod u ctive as op p osed to “reserve” u ses. Becau se th ese reserves serve an im p ortan t role with in th e R&D p rocess, th e decision is also related to th e decision con cern in g th e am ou n t of in vestm en t to allocate to th e stabilizin g role of biotech n ology. In vestm en ts in

322 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies

biotech n ology m ay be seen as in vestm en ts in m ain tain in g su stain able growth with in th ese p arts of th e econ om y. Th e n o vel q u est io n we h ave ad d ressed h ere is wh et h er a d ecen t ralized in du stry m otivated by a paten t-based in cen tive m ech an ism is able to approxim at e t h e so cially o p t im al o u t co m e in t h is co n t est o f in n o vat io n . We h ave d em on strated th at in th e m ost fu n d am en tal sen se, th e in cen tives facin g p rivate firm s m otivated by p aten ts sim p ly d o n ot accord with th e objectives of so ciet y. Th e basic so ciet al o bject ive in t h is aren a is t o m an age t h e gro wt h cap acity of th e econ om y by in vestin g in th e cap acity to resp on d to biological in n ovation s. Ou r an alysis of th e p aten t-based in cen tives facin g p rivate firm s in dicates th at th ese firm s are wh olly in differen t to th e growth cap acity of th e econ om y (as op p osed to th e cyclical p u rsu it of tech n ological in n ovation ), 43 an d th at th e in cen tives for in vestm en ts in respon se m ech an ism s are positively perverse. Hen ce, at th e m ost fu n dam en tal level, th e decen tralized biotech n ology in du stry is n ot pu rsu in g th e objectives society wou ld set ou t for it. In ad d ition , th e in cen tives th at d o exist u n d er th e p aten t system con tain n u m ero u s ext ern alit ies t h at gen erally cu t in t h e d irect io n o f u n d erin vest m en t . To t h e ext en t t h at t h e b io t ech n o lo gy in d u st ry d o es in vest , it in vest s dem on strably less th an th at wh ich is socially efficien t. Th is resu lts in a biological wo rld t h at is in su fficien t ly in vest ed in t h e reserve fu n ct io n o r, eq u ivalen tly, too h eavily in vested in to th e p rodu ction fu n ction . Th e p roblem h ere is th e in stitu tion al on e cau sed by th e in tersection of two d yn am ic p h en o m en a: t h e p at en t -b ased in cen t ive syst em an d t h e b io lo gyb ased ad ap t at io n syst em . Pat en t syst em s req u ire wid ely d em an d ed in n o vat io n s wit h reaso n ab le life sp an s t o b e effect ive. Bio lo gical syst em s co n t ain in h eren t ad ap tation s th at au tom atically resp on d to an d sh orten th e life sp an o f an y in n o vat io n t h at is ap p lied ext en sively. Th e d yn am ics o f t h e t wo system s are in com p atible. Th is is becau se p aten t-based in cen tive m ech an ism s are b ased o n a sin gle view o f t ech n o lo gical p ro gress, t h at is, t h e view t h at p rogress con sists of a con tin u in g clim b u p a on e-way ladder. In th is view, th e coin cid en ce between th e p aten t-based in cen tives an d th e social objective are p erfect. Th is is becau se th e p aten t-based reward is awarded for an y step u p th e lad d er, an d each st ep rep resen t s a p erm an en t ach ievem en t . In t h e case o f b io t ech n o lo gy, h o wever, p ro gress is m o re o f t h e n at u re o f t h e race u p t h e escalat o r. Each st ep in t h is co n t est is n ecessarily im p erm an en t , an d it m ay ach ieve n oth in g in th e lon g ru n . In th is in stan ce, awardin g p aten ts for “step s” p ro vid es in cen t ives fo r firm s wit h o u t p o in t in g in t h e d irect io n o f real “p ro gress.” Th is m ay be seen by t h e fact t h at firm s resp o n d in g t o su ch system s wou ld be able to ach ieve m axim u m ren ts sim p ly by tim in g th eir step s to coin cide with th e exp iration of th eir p aten ts. In gen eral, a p aten t system p rovid es t h e b io t ech n o lo gy sect o r wit h in cen t ives t o t ake st ep s rat h er t h an t o m ake real p rogress.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 323

Acknowledgements We th an k ou r discu ssan t David Sim p son , an d th ree an on ym ou s reviewers for h elp fu l co m m en t s an d su ggest io n s o n t h e ch ap t er. Th e au t h o rs t h an k Ph ilip p e Agh ion an d Gardn er Brown for com m en ts an d discu ssion s. We h ave ben efited from th e com m en ts of sem in ar p articip an ts at th e Sch ool of Pu blic Policy an d th e Dep artm en t of Econ om ics, Un iversity College Lon d on , at th e In stitu te of Advan ced Stu dies, Vien n a, an d at th e Eu rop ean Econ om ic Association Meetin g in San tiago. Tim o Goesch l ackn owledges su p p ort from th e Eu rop ean Com m ission , DG XII, u n der its Fellowsh ip Sch em e.

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324 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies Heisey, P.W. 1990. Accelerating the Transfer of W heat-Breeding Gains to Farm ers: A Study of the Dynam ics of Varietal Replacem ent in Pakistan. CIMMYT Research Rep o rt No . 1. Mexico City: CIMMYT. Heisey, P.W., an d J.P. Bren n an . 1991. An An alyt ical Mo d el o f Farm ers’ Dem an d fo r Rep lacem en t Seed. Am erican Journal of Agricultural Econom ics 73(4): 1044–52. Kam ien , M., an d N. Sch wartz. 1982. Market Structure and Innovation. Cam brid ge, U.K.: Cam bridge Un iversity Press. Kiyosawa, S. 1989. Breakd own of Blast Resistan ce in Rice in Relation to Gen eral Strategies of Resistan ce Gen e Dep loym en t to Prolon g Effectiven ess of Disease Resistan ce in Plan ts. In Plant Disease Epidem iology, Volum e 2: Genetics, Resistance, and Managem ent, edited by K. Leon ard an d W. Fry. New York: McGraw-Hill, 251–83. Laxm in arayan , R., an d G. Brown . 2001. Econ om ics of An tibiotic Resistan ce: A Th eory of Op tim al Use. Journal of Environm ental Econom ics and Managem ent 42(2): 183–206. Mason , R., an d T. Swan son . 2002. Th e Costs of Un coordin ated Regu lation . European Econom ic Review 46(1): 143–67. May, R.M., an d R. An d erson . 1983. Ep id em iology an d Gen etics in th e Coevolu tion of Parasites an d Hosts. Proceedings of the Royal Society London B 219: 281–313. Mayn ard Sm ith , J. 1976. A Com m en t on th e Red Qu een . The Am erican Naturalist 110: 325–30. Mu n ro , A. 1997. Eco n o m ics an d Evo lu t io n . Environm ental and Resource Econom ics 9: 429–49. Myers, N. 1997. Biodiversity’s Gen etic Library. In Nature’s Services: Societal Dependence on Natural Ecosystem , edited by G.C. Daily. Wash in gton , DC: Islan d Press. O erke, E.C., H.W. Deh n e, F. Sch ön beck, an d A. Weber. 1994. Crop Production and Crop Protection: Estim ated Losses in Major Food and Cash Crops. Am st erd am , Th e Net h erlan ds: Elsevier. RAFI (Ru ral Advan cem en t Fou n dation In tern ation al). 1997. The W orld’s Top 10 Seed Corporations. RAFI Com m u n iq u é 28, Novem ber 1997. Rau sser, G., an d A. Sm all. 2000. Valu in g Research Leads: Biop rosp ectin g an d th e Con servation of Gen etic Resou rces. Journal of Political Econom y 108(1): 173–206. Rein gan u m . 1989. Th e Tim in g of In n ovation : Research , Develop m en t, an d Diffu sion . In Handbook of Industrial Organization, Volum e 1, ed it ed b y R. Sch m alen see an d R. Willig. Am sterdam , Oxford, an d Tokyo: North -Hollan d, 849–908. Sch effer, R. 1997. The Nature of Disease in Plants. Cam bridge, U.K.: Cam bridge Un iversity Press. Sch u m p eter, J.A. 1942. Capitalism , Socialism and Dem ocracy. New York: Harp er an d Bros. Sim p son , R.D., R.A. Sedjo, an d J.W. Reid. 1996. Valu in g Biodiversity for Use in Ph arm aceu tical Research . Journal of Political Econom y 104(1): 163–85. Sm ith , S. 1998. Person al com m u n ication with th e au th ors, October 12, 1998. Swan son , T. 1995. The International Regulation of Extinction. Lon don : MacMillan . ——— (ed .). 2002. T he Econom ics of Managing Biotechnologies. Do rd rech t , Th e Net h erlan ds: Klu wer. Swan so n , T., an d T. Go esch l. Fo rt h co m in g. Search in g fo r So lu t io n s: Ren ewab le Resou rces, IPR an d Problem s Resistan t to Resolu tion . Research in Law and Econom ics. Swan son , T., an d R. Lu xm oore. 1998. Industrial Reliance on Biodiversity. Cam bridge, U.K.: W CMC. Tirole, J. 1988. The Theory of Industrial Organization. Cam bridge, MA: MIT Press.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 325 Weitzm an , M. 2000. Econ om ic Profitability versu s Ecological En trop y. Quarterly Journal of Econom ics 115(1): 237–63. Zad o ks, J., an d R. Sch ein . 1979. Epidem iology and Plant Disease Managem ent. O xfo rd , U.K.: Oxford Un iversity Press.

Appendix: Derivation of Equation 9 From Eq u ation 1 an d settin g A 0 F(x) = 1, we can rewrite th e u tility fu n ction as ∞

U=

+∞

−rt Π( s, t )γ s dt ∫ e s∑ =−∞

(A1)

with s = I − D

(A2)

t =0

an d wit h t h e h ist o ries o f I an d D gen erat ed b y t h e p ro cesses d escrib ed in Eq u ation s 6 an d 7, Π( I , t ) =

Π( D , t ) =

I − φi ( v )]t 1 φi(v )t e [ I!

[

]

[

1 λa (v )t D!

]

[

(6)

]

D − λa ( v ) t

e

(7)

su ch th at ⎛ I in n ov. h ave occu rred by tim e t | D ad ap t. ⎞ Π( s, t ) = Pr ⎜ ⎟ ⎝ h ave occu red by tim e t ⎠

(A3)

Th en , ∞

U = ∫ e −rt t =0

∞

∞

1

1

∑ ∑ I ! (φit ) e− φit × D! (λat ) I

D

e − λat × γ I − D dt

(A4)

I =0 D =0

∞

wh ich is U =

∞

∞

−rt ∑ ∫e ∑ I =0 D =0

t =0

(γφit )I e − φit I!

⎞ ⎛1 ⎜ λat ⎟ ⎠ ⎝γ × D!

D

e − λat dt

(A5)

Makin g u se of th e in fin ite series of th e factorial an d th e exp on en tial fu n ction , we can rewrite Eq u ation A5 as

326 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies ∞

U=

∫

t =0

e −rt − φit − λat × e γφit × e

λa t γ

dt =

1 r − φi( γ − 1) + λa

γ −1 γ

(A6)

Th e den om in ator of Equ ation A6 gives th en th e effective discou n t rate applied to th e ou tpu t fu n ction . Reform u latin g A6 for som e arbitrary A 0 F(x), we arrive at Equ ation 9.

Notes 1. In th e rem ain der of th is ch ap ter we will u se “lan d” as th e base, lim itin g factor th at m u st be allocated between th e p rodu ction an d su stain ability fu n ction s. Lan d th en rep resen ts th e in stru m en t by wh ich all biological resou rces can be allocated between th ese t wo co m p et in g fu n ct io n s. Th e m o re gen eral q u est io n wo u ld o f co u rse d evo lve t o t h e allocation of th e su m of society’s resou rces between th e objectives of p rodu ction versu s su stain ability. 2. Th e t erm o rigin at es fro m Lewis Carro ll’s Alice in W onderland in wh ich t h e Red Q u een p roclaim s to Alice th at “arou n d h ere, we m u st ru n faster an d faster, m erely to stan d still ….” 3. It is p ossible to claim “p lan t breed ers righ ts” in n ew p lan t varieties u n d er th e socalled Co n ven t io n o f t h e In t ern at io n al Un io n fo r t h e Pro t ect io n o f New Variet ies o f Plan ts or p aten t righ ts in gen etically m odified seeds an d an im al varieties. 4. A 1998 su rvey fou n d th at p lan t breeders cited p est resistan ce as th e p rim ary focu s of th eir activities (Swan son an d Lu xm oore 1998). 5. Th e lit erat u re o n seed rep lacem en t cycles in agricu lt u re d o cu m en t s a cycle o f th ree to seven years between in trodu ction s of n ew p est-resistan t p lan t varieties on com m ercially m ean in gfu l scales (Heisey 1990; Heisey an d Bren n an 1991). 6. In t h e co n t ext o f agricu lt u re, t h is o n ly im p lies a p ro p o rt io n al in crease in t h e am ou n t of h igh -yieldin g seed x req u ired with an in crease in th e am ou n t of in ten sively cu ltivated lan d d. 7. Th is is a close ap p roxim ation to reality with in th e seed in du stry, in wh ich th ere is a crop -sp ecific, bu t n everth eless lin ear, relation sh ip between th e lan d u sed in seed p rodu ction an d th e lan d sown u sin g th is seed. Th e relative size of β an d z is on th e order of 100:0.1 to 100:5 dep en din g on th e crop (Sm ith 1998). 8. Th e “sign ifican ce” o f a t ech n o lo gical in n o vat io n is a legal req u irem en t fo r t h e acq u isit io n o f p ro p ert y righ t s in t h e in n o vat io n . Becau se t h is is an issu e t h at we will in trodu ce in th e section on th e social objective of biotech n ology, we will n orm alize th e m agn it u d e o f an y t ech n o lo gical in n o vat io n t o b e eq u ivalen t t o t h e m agn it u d e (γ) req u ired for th e acq u isition of a p rivate p rop erty righ t in th at in n ovation . 9. Th e in d u strial organ ization literatu re d efin es in n ovation s as “d rastic” if th e tech n ological advan tage con ferred by th e in n ovation is of su ch a m agn itu de th at th e in n ovatin g firm cap tu res th e en tire m arket wh en settin g th e m on op oly p rice (Tirole 1988). Th is is sim p ly th e “su bstan tial im p rovem en t” req u ired u n d er p aten t law to q u alify for t h e issu an ce o f a p at en t an d h en ce t h e est ab lish m en t o f a n ew m o n o p o ly righ t . We

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 327 stan dardize th e con cep t of a relevan t in n ovation in th is m an n er to com p are th e system (fo r gen erat in g su ch in n o vat io n s) t h at wo u ld exist u n d er a p at en t syst em wit h o t h er system s. 10. Th is assu m p tion follows th e stan d ard literatu re in crop ep id em iology in wh ich th e em ergen ce of viru len ce is assu m ed to follow a Poisson p rocess (see also Zadoks an d Sch ein 1979; Kiyosawa 1989). 11. Th is assu m p tion is con sisten t with both th e th eory of selection (becau se th ose p ests with a m atch in g gen e for x h ave a relative advan tage th at in creases with th e u se of x) an d t h e em p irical o b servat io n t h at t h e wid esp read u se o f HYVs is asso ciat ed wit h redu ced p eriods of com m ercial viability. 12. We can rewrit e t h is as λ a(d) m akin g u se o f Eq u at io n 3 wh ere λ is a p aram et er th at m easu res su ccessfu l m u tation or recom bin ation of th e p ath ogen p op u lation an d a, a′ < 0 m easu res th e ad ap tive resp on se rate of biological com p etitors relative to size of in ten sive agricu ltu re on ce a su ccessfu l m u tation h as occu rred. 13. For an an alysis of th e situ ation in wh ich ad ap tation m ay be d am p en ed by th e sim u lt an eo u s u se o f m an y d ifferen t p ro d u ct io n m et h o d s, see Go esch l an d Swan so n (2000). 14. Modelers of th e dyn am ics of evolu tion ary gam es view resistan ce as th e accu m u lation of “m atch in g gen es” with in th e p est p op u lation , wh ere su ch m atch es en able th e p est t o p rey o n t h e h o st . A b io lo gical in n o vat io n in t h is co n t ext wo u ld co n sist o f a ch an ge from a p au city to th e relative p revalen ce of su ch a m atch in g gen e th rou gh ou t th e cu rren t p est p op u lation . 15. Th is assu m p tion rep resen ts a u n iform m etric of a con tin u ou s p rocess of dep reciation . Th e u n it of an alysis is fixed with in th e tech n ological sector (by th e req u irem en t th at a p aten table in n ovation be a sign ifican t im p rovem en t. See Note 9.). 16. In t h is ch ap t er we assu m e t h at t h e resp o n siven ess o f p est s is “st age in d ep en den t”; th at is, th e p ests do n ot react differen tly to differen t levels of tech n ological in terven tion . Of cou rse, it m igh t be th at system s resp on d very differen tly to differen t levels o f t ech n o lo gical in t erven t io n . An o t h er assu m p t io n m igh t b e t h at n at u ral syst em s attem p t to retu rn to p reviou s states of eq u ilibriu m , an d h en ce greater levels of in terven tion gen erate m ore drastic reaction s from th e n atu ral system (i.e., m ore in n ovation s by t h e p est s an d p at h o gen s). It also m igh t be p o ssible t h at great er levels o f in t erven t io n h ave t h e cap acit y t o t ake t h e syst em o u t sid e o f t h e area o f at t ract io n t o it s p revio u s eq u ilibriu m , an d th en th ere is n o resp on sive in n ovation from p ests an d p ath ogen s (i.e., t h e h yp o t h esis o f win n abilit y). Th ese vario u s assu m p t io n s an d t h eir im p licat io n s fo r th e m odel are in vestigated in a sep arate work (Goesch l an d Swan son 2002). 17. It is im p ortan t to n otice a su btlety h ere in th at th e discrete n atu re of th e Poisson p rocess in trodu ces two “tim e scales” in to th e system . On e is n atu ral tim e, den oted by t, wh ereas s den otes th e p rodu ctivity stage of th e econ om y. 18. On e ben efit of ch oosin g th is fu n ction al form for th is p roblem is th at it im p lies n o bias in favor of in tergen eration al tran sfers of u tility (see Barrett 1992 for a discu ssion in th e con text of biodiversity). 19. Th is red u ces th e own d iscou n t rate becau se n ew tech n ologies sh ift th e p rod u ction set ou tward an d relax th e bu dget con strain t. 20. In th is in stan ce, th e in n ate growth capacity of th e biological resou rce—pests an d path ogen s—detracts from available con sum ption an d so in creases th e own discoun t rate.

328 • Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies 21. A station ary solu tion to th e p roblem is to be exp ected becau se of th e lin earity of th e objective fu n ction . 22. Recall th at a′ < 0. 23. Th e resu lt is d iscu ssed in m ore d etail in com p arison to th e p rivate m arket solu tion in th e section on com p arin g p rivate an d social in vestm en t in th e biotech n ology sector. 24. Th is assu m p tion is n ot essen tial to th e argu m en t, bu t it sim p lifies th e an alysis. It is also n o t an u n realist ic assu m p t io n in t h e co n t ext o f agricu lt u ral lan d s wh en it is h igh ly likely th at th ere is a sin gle m ost p rodu ctive u se of m ost arable lan ds an d a sin gle m on op olist of th e in term ediate goods (HYVs) req u isite for th at u se. 25. Oth er p ap ers cover th e issu e of strategic sh elvin g of p aten ts in situ ation s wh ere t ech n o lo gies d egrad e o ver t im e (Go esch l an d Swan so n 2000, Maso n an d Swan so n 2002). 26. Th ere is a su b t let y in Eq u at io n s 14, 15, an d 16: Becau se s = I – D, t h e p ayo ff from d eliverin g th e n ext in n ovation d ep en d s on th e h istory of biological ad ap tation s t h at h ave o ccu rred sin ce t h e last t ech n o lo gical in n o vat io n . St rict ly sp eakin g, t h e n et p resen t valu e o f t h e n ext t ech n o lo gical in n o vat io n , V I + 1 , is t h e exp ect ed valu e o f m on op oly ren ts based on a p robability d istribu tion over s. Th is is becau se th e flow of p ro fit s p is d irect ly affect ed b y t h e cu rren t level o f p ro d u ct ivit y A s, wh ich is a jo in t o u t co m e o f b o t h t ech n o lo gical an d b io lo gical p ro cesses. Th e p resen t valu e t h u s d ecreases if p ath ogen ad ap tation s h ave occu rred . Bu t if th e p rice of lan d is allowed to ch an ge wit h in t ech n o lo gical st ages, t h en t h e fact t h at m argin al p ro d u ct ivit y will d ecrease at exact ly t h e sam e m o m en t at wh ich a bio lo gical ad ap t at io n o ccu rs m ean s th at th e relation sh ip between lan d p rices an d p rivate R&D is u n affected by p ath ogen ad ap tation becau se th e real cost of R&D (m easu red in term s of th e cost of lan d ) d oes n ot ch an ge. 27. Becau se th e left-h an d side is in creasin g in v an d th e righ t-h an d side is decreasin g in v fo r F′≤ ≤ 0 (su fficien t co n d it io n ), t h e eq u ilib riu m will b e u n iq u e assu m in g t h is restriction on F′″. 28. Th e effect of th e rate of biological in n ovation req u ires a q u alification in th at it h olds on ly as lon g as th e discou n t rate exceeds th e n et m argin al p rodu ctivity of lan d for in n ovation s, th at is, for

⎤ ⎡ ⎛ i ′( v ) ⎞ r > ( γ − 1) ⎢ φ ⎜ i ( v ) − + λ 1 − a ( v ) γ −1 ⎥ ⎟ a ′( v ) ⎠ ⎥⎦ ⎢⎣ ⎝

(

)

If th is con d ition d oes n ot h old , it wou ld m ean th at lan d in R&D is th e m ost com p etitive op p ortu n ity to gen erate welfare available in th e econ om y. We wou ld th erefore gen erally exp ect th is con dition to h old. 29. Th e o n ly q u alificat io n o n t h is resu lt is t h at if t h e reserve sect o r h as a h igh er in trin sic growth rate th an all oth er sectors in th e econ om y th at h ave im p act on con su m p tion , th en a h igh er arrival rate of biological in n ovation s frees u p resou rces to be p u t to fin al goods p rodu ction . 30. In fact, th ere are two effects at work, on e as m en tion ed earlier, th e oth er decreasin g t h e exp ect ed valu e o f in n o vat io n s. Bu t t h e lat t er is o n ly a seco n d -o rd er effect , wh ich is dom in ated by th e first as th e p artial derivatives sh ow.

Chapter 11: The Interaction of Dynamic Problems and Dynamic Policies • 329 31. Tan gen tially we n ote th at th e p rivate valu ation of reserve lan d s for p u rp oses of R&D system atically u n d erestim ates th e social valu e of th ese lan d s for th ose p u rp oses. Th is is an im p o rt an t p ro b lem in t h eo ry as well as p ract ice. Th e p rivat e valu at io n o f reserve lan d s h as b een u sed as a su ggest ive m easu re fo r t h e valu at io n o f reserves fo r R&D p u rp oses (Goesch l an d Swan son forth com in g; Sim p son et al. 1996). 32. Of cou rse th is resu lt h olds on ly if th e m on op olist is n ot able to Ram sey p rice its ou tp u t. 33. Th e fact th at th e m on op olist at an y p oin t will on ly be con cern ed with th e op tim al ou tp u t severs th e lin k between ou tp u t an d con servation decision s. We wou ld th erefo re n o t exp ect t h e m o n o p o list t o exh ib it t h e co n servat io n ist effect s in t erm s o f resou rce extraction observed in m in in g m odels of th e Hotellin g typ e. 34. Th e sp ecific m an ifestation of biological obsolescen ce in th is m odel adds a n ovel p ersp ective to th e an alysis of th e differen t discou n t rates, h owever. 35. Su ch settin gs can arise gen erally wh ere th ere is a scale-related risk to tech n ological b reakd o wn . Su ch sit u at io n s m ay b e q u it e co m m o n . We are grat efu l t o Ph ilip p e Agh ion for stressin g th is p oin t. 36. We can th erefore con clu de th at th e u se of th e p rivate firm ’s valu ation of reserve lan d s is a h igh ly p ro blem at ic est im at o r o f t h e so ciet al in t erest in su ch lan d s. Sp ecifically, it is very likely th at th is estim ator will u n d erestim ate th e social valu e of reserves sign ifican t ly. Th e reaso n lies in t h e fu n d am en t al d ifferen ce bet ween t h e valu at io n o f reserves as an in p u t in to a p aten t race between p rivate firm s wh ose p aten ts are th reaten ed both by econ om ic an d biological com p etitors, an d th e valu ation of reserves as an in p u t in to a race of con tin u ou s in n ovation (tech n ological an d biological) between society an d adap tin g p ath ogen s. 37. Becau se o n e o u t o f n firm s will h o ld t h e p at en t o f t h e p referred t ech n o lo gy at an y p oin t in tim e an d becau se th is firm h as n o in cen tive to in vest in R&D (as it wou ld rep lace it s o wn p at en t ), n – 1 firm s will b e en gaged in a race t o p ro d u ce t h e n ext p aten table in n ovation . 38. Th is elim in at es issu es o f su n k an d fixed co st s an d creat es co n d it io n s in wh ich th ere are n o barriers to en try in to th e R&D sector. 39. O t h er sp ecificat io n s are p o ssib le an d h ave b een at t em p t ed . Th e fu n d am en t al resu lts are robu st over m an y p lau sible sp ecification s. 40. Eq u ation 20 sh ows th at th e level of reserve lan d s ch osen by th e social p lan n er will gen erally be less th an on e so lon g as th e discou n t rate is greater th an n et p rodu ctivity in creases in th e fin al sector at th e m argin . Th is m ean s th at as lon g as th ere are oth er co m p et it ive o p p o rt u n it ies available in t h e eco n o m y t o gen erat e welfare, n o t all lan d will be u sed for R&D. We wou ld gen erally exp ect th is con dition to h old. 41. It is ap p aren t t h at t h e p rivat e in d u st ry level o f reserves will b e less t h an o n e in dep en den t of th e discou n t rate. 42. We assu m e t h at t h e exp o n en t h as t h e st an d ard valu e o f 0.25 an d t h e sp ecies rich n ess p aram eter th e (com p aratively low) valu e of 200. 43. See Swan son an d Goesch l forth com in g an d Mason an d Swan son 2002 for related an alyses.

Chapter 12

Industrial Organization and Institutional Considerations in Agricultural Pest Resistance M anagement Jennifer Alix and David Zilberman

This chapter demonstrates the complexity of the relationship among incentives, pesticide applications, and resistance buildup. First, analysis of the im pacts of pesticide use m ust consider both the dynamics of the overall pest and the resistance buildup. Farmers may overapply chem icals if they ignore resistance dynam ics but m ay underapply chem icals if they ignore population dynam ics. Furtherm ore, other factors (e.g., including alternative chem icals, integrated pest m anagem ent, crop rotation) m ust be considered in assessing the im pact of pesticide use on resistance. Second, pest resistance is significantly affected by the structure of the industry, property rights, and patent considerations. M anufacturers w ill likely have a monopoly on the production of new pesticides during the life of the patent, which will provide the incentive to underapply them relative to the optimal solution. Furthermore, manufacturers are concerned with the negative side-effects of resistance buildup because of the im pact on future sales and their reputation. Thus, they may be actively involved in activities to reduce resistance buildup. Indeed, w e present evidence of m anufacturer involvem ent in resistance m anagem ent and resistance prevention. We also show that m anufacturers’ incentives to control resistance m ay be w eaker than what is socially desirable because of the limitation of a patent’s life. Third, manufacturers’ incentives and choices will likely lead to overapplication of pesticides by m yopic farm ers as the chem icals get older and the supply network becomes more competitive. There are several old pesticides (m ostly organophosphates or carbonates) that have long been used

• 330 •

Chapter 12: Industrial Organization and Institutional Considerations • 331 because of a lack of significant resistance buildup potential or the existence of effective resistance m anagem ent schem es. Pest m anagem ent agencies should be especially aware of potential problems with fairly new chemicals once the initial patent period lapses, if the provision of the chem icals increases, or if the initial m anufacturer does not get very involved in the product stewardship. Finally, in addition to the manufacturers and users of the pesticides, other econom ic agents, in particular pesticide advisors and extension specialists, are involved in pest control decisions. Extension and especially individual consultants have the incentive to reduce resistance buildup and improve the performance of pest control agents. Our analysis suggests that the network of econom ic agents concerned about and involved in decisions regarding pest management and control of resistance buildup is quite complex. Even if individual growers may not be concerned with resistance and population dynamics issues when applying pesticides, other agents affecting their decisions may have these issues in mind.

P

esticide u se is th e resu lt of a web of decision s con n ectin g th e farm er to th e research ers, m an u fact u rers, regu lat o rs, an d co n su m ers. Given it s wid e ran ge of im p acts an d its im p ortan ce in th e seq u en ce of even ts th at determ in e agricu ltu ral su p p ly, it is n o su rp rise th at p esticides h ave in sp ired a large literatu re in th e field of econ om ics. Of growin g im p ortan ce with in th is literatu re is th e top ic of p est resistan ce to p esticides. Acco rd in g t o t h e Fo o d an d Agricu lt u re O rgan izat io n , t h e n u m ber o f p est sp ecies with resistan ce to p esticid es h as in creased from alm ost n on e 50 years ago t o m o re t h an 700 t o d ay (FAO 2001). As t h e n u m ber o f resist an t sp ecies in creases, so d o losses in cu rred by farm ers. Th e In secticid e Resistan ce Action Co m m it t ee st at es t h at “in sect icid e resist an ce in t h e Un it ed St at es ad d s $40 m illio n t o t h e t o t al in sect icid e bill in ad d it io n al t reat m en t s” (2001). It also cites th e case of Mich igan p otato p rod u cers wh o in 1991 su ffered a $16 m illion crop loss cau sed by resistan ce in th e Colorad o p otato beetle. In th e case of p yreth roid s, in wh ich seriou s resistan ce h as been en cou n tered am on g cotton p ests, a 50% rep lacem en t of it by altern atives wou ld ap p roxim ately d ou ble th e con trol costs an d redu ce yield by 11% (Riley 1990). Th ere is a rich b o d y o f lit erat u re o n p est resist an ce sp aw n ed b y Regev an d H u et h ’s (1 9 7 4 ) sem in al w o rk (see su rveys b y C arlso n an d Wet zst ein 1 9 9 3 ; Pan n ell an d Zilb erm an 2 0 0 0 ). Th e m ajo rit y o f t h e lit erat u re view s resist an ce in t h e co n t ext o f ren ewab le o r n o n ren ewab le reso u rces. A m ain resu lt o f t h is vein o f research is t h at co m m o n -p o o l p ro b lem s, m yo p ic b eh avio r, o r b o t h lead t o t h e o veru se o f p est icid es. Th e lo gical p o licy resp o n se t o t h is p ro gn o sis w as a call fo r co llect ive act io n o r go vern m en t in t erven t io n t o red u ce p est icid e ap p licat io n an d b u ild u p o f resist an ce.

332 • Chapter 12: Industrial Organization and Institutional Considerations

Clearly, ad ap t in g t h e fram ewo rk o f ren ewab le an d n o n ren ewab le reso u rces t o exist in g p ro blem s h as gen erat ed valu able in sigh t . Mo reo ver, a n ew wave o f st u d ies o n resist an ce em erged recen t ly in resp o n se t o co n cern ab o u t resist an ce bu ild u p t o p est co n t ro l agen t s em bo d ied in gen et ically m o d ified cro p s (Secch i an d Bab co ck, Ch ap t er 4; Laxm in arayan an d Sim p so n , 2002; an d Hu rley et al., fo rt h co m in g) an d h as been ap p lied fo r p o licy ch o ices, fo r ex am p le, t h e d esign o f refu ge. Perfect co m p et it io n , h o w ever, is a cen t ral assu m p t io n o f t h is lit erat u re, wh ich p o t en t ially o b scu res feat u res essen t ial t o u n d erst an d in g t h e d yn am ics o f resist an ce in a m o re co m p lex realit y. In t h is ch ap t er, we at t em p t t o p o in t o u t so m e o f t h ese feat u res, an d we in t ro d u ce em p irical evid en ce o n t h e co st an d m agn it u d e o f resist an ce p ro blem s in agricu lt u re. In th e first section , we will set u p a con cep tu al fram ework to an alyze resistan ce th at in clu d es two d yn am ic p h en om en a—th e bu ild u p of resistan ce an d t h e d yn am ics o f t h e p est p o p u lat io n . Th is fram ewo rk will be u sed t o d erive som e of th e m ajor resu lts abou t resistan ce m an agem en t. We will th en adap t it t o co n sid er t h e em ergin g issu es o f in t egrat ed p est m an agem en t (IPM) an d crop rotation , am on g oth er tech n ologies im p ortan t to p est m an agem en t, an d an alyze t h eir im p act o n resist an ce b u ild u p . Th e fin al t wo sect io n s o f t h is ch ap ter will address en viron m en tal regu lation an d in stitu tion al p roblem s th at h ave b een ab sen t fro m t h e lit erat u re; in p art icu lar, t h e fo u rt h sect io n will ad d ress t h e ro le m an u fact u rers p lay in d ealin g wit h resist an ce p ro b lem s th rou gh p rod u ct d evelop m en t an d steward sh ip . We con sid er h ow in d ivid u al farm er in cen tives in teract with m an u factu rer con cern s an d p resen t evid en ce regardin g m an u factu rer p articip ation in resistan ce m an agem en t.

Factors Affecting the M anagement of Resistance We n o w sket ch o u t a fram ewo rk fo r m o d elin g t h e im p act o f resist an ce o n farm ers’ p esticid e d ecision m akin g p rocesses over tim e. For in terested read ers, t h e m at h em at ical d et ails can b e fo u n d in Alix an d Zilb erm an (2001). Th e farm er solves h is or h er p roblem by m axim izin g d iscou n ted exp ected p rofit, wh ich in clu d es reven u e m in u s ap p lication costs an d d eclin es with p est d am age. Dam age, in tu rn , is con trolled by th e effectiven ess of p esticid e ap p licat io n s, an d resist an ce is t h e key fact o r in co n t ro llin g t h e im p act o f p est icid e ap p lication . We m odel resistan ce as a stock variable, wh ich is m easu red by th e fraction of th e p est p op u lation n ot vu ln erable to ch em ical treatm en ts. However, we also exp licit ly in t ro d u ce an o t h er st o ck variab le, p est p o p u lat io n . With ou r sp ecification s, we d istin gu ish between two p est p op u lation s: p ests th at are vu ln erable to th e p esticide an d p ests th at are resistant. Th is fram ework is con sisten t with th e work of Regev an d Hu eth (1974) an d Laxm in arayan an d Sim p son (2002).

Chapter 12: Industrial Organization and Institutional Considerations • 333

Ou r farm er u n dertakes h is or h er op tim ization p roblem su bject to two con strain ts: • Growth of resistance: Resist an ce gro wt h is affect ed b y t h e gro wt h rat es o f vu ln erable an d resistan t p op u lation s an d th e p esticid e kill fu n ction . Pesticide ap p lication s in crease resistan ce, alth ou gh th e m argin al effect of sp rayin g on resistan ce in creases for som e resistan ce ran ge an d th en decreases. • Pest population growth: Th e seco n d co n st rain t , p est p o p u lat io n gro wt h , is affect ed b y t h ree fact o rs: t h e kill fu n ct io n (wh ich d ep en d s o n p est icid e ap p lication ), th e growth of th e resistan t p op u lation , an d th e growth of th e vu ln erable p op u lation . We exp ect p est p op u lation growth to decrease with ch em ical ap p lication s. Th e solu tion to th is p roblem leads to th e con clu sion th at th e op tim al p esticid e ap p licat io n at an y given t im e is at a level at wh ich t h e farm er eq u at es im m ed iate m argin al an d fu tu re m argin al ben efits from red u ced p est p op u lation s to th e p rice of p esticides p lu s m argin al resistan ce cost. Th e eq u ation is V MPxt + V MFt = W + V Rt wh ere th e left-h an d side of th e eq u ation rep resen ts th e m argin al ben efits th at com e from red u cin g p esticid e d am age. V MPx t is th e p rivate m argin al ben efit of redu ced p est dam age associated with p esticide ap p lication s in p eriod t, an d V MFt is t h e m argin al valu e o f red u cin g t h e p est p o p u lat io n b y ap p licat io n , th u s red u cin g fu tu re d am age. Th e righ t-h an d sid e is th e p rivate cost of p u rch asin g p esticid es p lu s th e m argin al social cost of resistan ce from th e p esticide ap p lication . W is th e p esticide cost, an d V Rt is th e m argin al cost of resistan ce fro m p est icid e ap p licat io n . Farm ers m ay n o t b eh ave acco rd in g t o t h e socially op tim al beh avior for two m ain reason s: (a) th ey m ay be m yop ic, an d (b) th e p est p op u lation p ool is a com m on -p rop erty resou rce. Myo p ic d ecisio n m akers ign o re t h e fu t u re im p licat io n s o f t h eir d ecisio n s. As in t h e b asic m o d elin g case, t h e farm er will ch o o se a p ro fit -m axim izin g level of p esticid es; th e d ifferen ce is th at h e con sid ers on ly th e sh ort term . At th e m yop ic op tim u m , th e valu e of m argin al p rodu ct of p esticide ap p lication s is eq u al to th e cost, wh ere V MPx t m rep resen ts th e valu e of m argin al p rodu ct of u sin g x am o u n t o f p est icid e an d w is t h e p rice. Th e eq u ation d escribin g th e eq u ilibriu m is as follows: V MPxtm = W Th is con dition ign ores th e im p act of p esticide u se on resistan ce an d on fu tu re levels of th e p est p op u lation . We assu m e th at th e resistan ce effect d om in ates t h e p o p u lat io n ’s gro wt h su p p ressio n effect o f p est icid e u se. Th e sit u at io n is

334 • Chapter 12: Industrial Organization and Institutional Considerations

d ep ict ed in Figu re 12-1. If t h e co n cern abo u t resist an ce d o m in at es t h e gain fro m su p p ressio n o f p est p o p u lat io n b u ild u p , m yo p ic b eh avio r will lead t o overu se of p esticid e. Th is is exactly th e con clu sion th at resu lts from com p arin g p o in t s A an d B. If, h o wever, t h e gain s fro m su p p ressio n o f p o p u lat io n growth overcom e th e gain s from slowin g resistan ce bu ildu p , m yop ic beh avior resu lts in u n derap p lication . Figu re 12-2 describes th is case. Com m on resou rce p ool p roblem s in p est m an agem en t occu r becau se p est p op u lation s are m obile, an d farm ers’ p lots m ay be sm all relative to th e p ests’ ran ge. Un d er th ese circu m stan ces, farm ers m ay believe th at th eir activity h as little im p act on resistan ce bu ild u p of th e p est p op u lation , an d th at m ay lead to th e tragedy of th e com m on s. O n e im p licat io n o f t h e co m m o n -reso u rce p ro b lem is t h at farm s large en ou gh to con tain m u ch of th e p est m ovem en t are likely to be su p erior p est m an agers. In oth er words, “big is beau tifu l” from a p est m an agem en t p ersp ect ive. Alt ern at ively, in regio n s wh ere p lo t s are fragm en t ed , co llect ive act io n an d go vern m en t in t erven t io n are req u ired t o co o rd in at e p est m an agem en t act ivit ies. In d eed , in m an y regio n s, m ajo r ext en sio n act ivit ies h ave im p le-

W + VR

B

•

C

W

D

A

•

VM Px

+ VM F

VM Px

xt *

xt

m

FIGURE 12-1. Resistance Effect Dominates Population Growth

xt

Chapter 12: Industrial Organization and Institutional Considerations • 335

W + VR B

• A •

W

• VM Px + VM F VM Px

m

xt

xt*

xt

FIGURE 12-2. Population Growth Dominates Resistance Effect

m en ted in tegrated strategies to address p esticide p roblem s. Th e im p ortan ce of n eigh bors’ activities in th e su p p ression of p est p op u lation s is freq u en tly m en tion ed in th e p est con trol literatu re. With som e effort, activities m ay h elp to edu cate farm ers to u n deru se ch em icals to slow th e bu ildu p of p est resistan ce. However, in oth er cases, m ost n otably in som e sou th ern states p lagu ed by th e cotton boll weevil, collective action in clu des extra ap p lication aim ed to eradicate th at p est. To su m m arize, alth ou gh m u ch of th e econ om ic literatu re recogn izes th at eith er m yop ic beh avior or com m on resou rce p roblem s m ay lead to overap p lication of p esticid es by farm ers wh o ign ore th e d yn am ics of resistan ce, oth er stu d ies su ggest th at sim ilar situ ation s m ay actu ally lead to u n d erap p lication of p esticides. Several oth er factors th at m ay affect resistan ce m an agem en t an d th at h ave n ot gain ed m u ch atten tion are ad d ressed in th e rem ain d er of th is ch ap ter.

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Farm-Level Factors Influencing Resistance Ignorance about Resistance

An o t h er p lau sib le cau se o f su b o p t im al p est icid e ap p licat io n is ign o ran ce abou t resistan ce. Resistan ce p roblem s vary am on g an d with in p esticid e categories. Narrowly targeted ch em icals, wh ich attack on e system in th e body th at are con trolled by a sm all n u m ber of gen es, are m ore likely to d evelop resistan ce p ro blem s t h an bro ad -u se ch em icals t h at h ave several m o d es o f o p eration . Joh n Dam icon e, an exten sion ist for th e Un iversity of Oklah om a, argu es th at m u lt isit e fu n gicid es, wh ich in terfere wit h m an y m etabolic p rocesses of fu n gu s, are m u ch less likely to resu lt in bu ild u p of resistan ce th an fu n gicid es with a site-sp ecific m ode of action (2001). Ben om il, a fu n gicide th at was able to both p reven t an d cu re p lan t diseases cau sed by fu n gi, is a site-sp ecific fu n gicide th at h as en cou n tered sign ifican t resistan ce p roblem s sin ce its in trodu ct io n in t h e 1970s. Dam ico n e su ggest s lab o rat o ry exp erim en t s can id en t ify fu n gicid es t h at will m o re likely en co u n t er resist an ce an d t h u s lead t o t h e design of strategies to avoid th ese p roblem s. To com p licate th e m atter fu rth er, it takes tim e before th e existen ce of su ch p roblem s is discovered, a p h en om en on exacerbated by th e fact th at in form ation is n ot always tran sferred very q u ickly across region s. Let u s con sider a situ at io n in wh ich a farm m ay be large en o u gh t h at co m m o n reso u rce p o o l is n ot a p roblem , an d th u s farm ers take in to accou n t th e d yn am ic p est p op u lat io n su p p ressio n effect o f p est icid e u se bu t n o t resist an ce bu ild u p . Pest icid e u se in th is case is th erefore determ in ed by solvin g V MPxt + V MFt = W In th is case, th ere will be overu se of p esticides. Note, h owever, th at own ers of large farm s are likely to h ire p est con trol p rofession als. Pest con trol sp ecialists h ave develop ed th e cap acity to iden tify th e circu m stan ces u n der wh ich in trodu ction of a n ew p est con trol agen t is likely to resu lt in th e bu ildu p of resistan ce. In d eed , gu id elin es by Du Po n t an d o t h ers fo r t h e ap p licat io n o f h erbicides su ggest th at freq u en t ap p lication of an y h erbicide will likely lead to th e bu ild u p of resistan ce, an d th ey su ggest h erbicid e m an agem en t strategies th at will overcom e or m in im ize th ese p roblem s.

Fixed Cost of Application

Featu res of crop system s affect ap p lication s of p esticide an d, h en ce, resistan ce. On e of th em is fixed ap p lication costs. Ap p lication of ch em icals in a field m ay be rath er costly. Ru n n in g a tractor th rou gh on e acre of lan d can cost between

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$10 an d $20. In m ost cases, th e ap p lication cost m ay be m ore exp en sive th an th e cost of th e ch em ical. Fu rth erm ore, th e freq u en t ru n n in g of m ach in ery on a field leads to com p action of th e soil, wh ich , in tu rn , redu ces yield. Ap p licat io n co st co n sid erat io n s are cru cial t o d evelo p in g t h e eco n o m ic t h resh o ld . Carlson an d Wetzstein (1993), in p articu lar, su ggest th at farm ers sh ou ld m on itor p est p op u lation s to d eterm in e th e tim in g of ap p lication s wh en th e p op u lation is su fficien t, so th at th e gain from redu cin g th e p est exceeds th e cost of ap p licat io n . O f co u rse, t h e t h resh o ld level also can be ad ju st ed t o t ake in t o accou n t th e cost of resistan ce bu ildu p an d p op u lation growth . Ap p lication cost con sid eration s m ay lead to red u ced p esticid e u se on ly in cert ain sit u at io n s. Th ey will also likely red u ce resist an ce b u ild u p . Th is is b ecau se t h e vu ln erab le p o rt io n o f t h e p o p u lat io n gro ws fast er, an d , wit h redu ced p esticide levels, its sh are will in crease.

Integrated Pest M anagement

As t h e n am e su ggest s, IPM is a bro ad co n cep t t h at in t egrat es d ifferen t t o o ls an d a variet y o f available in fo rm at io n t o m an age p est p ro blem s an d red u ce th e relian ce on an d u se of ch em ical p esticides. A key com p on en t of IPM is th e m on itorin g of p est p op u lation s, followed by resp on sive rath er th an p reven tive ch em ical ap p lication s. Pest ap p earan ce is ran dom , dep en din g on weath er sit u at io n s, t h e relat io n sh ip bet ween t h e p o p u lat io n s o f vario u s sp ecies an d p est con trol activities by n eigh borin g farm ers, an d oth er variables. Freq u en t p reven t ive ap p licat io n s t h at release a large vo lu m e o f ch em icals at a t im e wh en t h e arrivin g p est p o p u lat io n is sm all o r wh en it is t o o early fo r t h e ch em ical to be effective m ay actu ally in crease th e resistan ce. In addition , p reven tive ap p lication s m ay h ave a n egative en viron m en tal effect. Th e resp on sive ap p licat io n , h o wever, m ay b e exp en sive in t h e sen se t h at it req u ires a h igh m on itorin g cost an d th at th e p est m ay d estroy crop s if th e resp on se is slow; h owever, it m ay save both m aterials an d ap p lication costs. Som e stu dies actu ally argu e th at IPM m ay be cost-effective in a wide variety o f sit u at io n s (see Carlso n an d Wet zst ein 1993). Resp o n sive ap p licat io n s in m ost cases will lead to a redu ction in p esticide u se an d better tim in g of ch em ical ap p lication s, wh ich togeth er m ay d ecrease resistan ce bu ild u p . Em p irical resu lts regard in g th e effects of IPM on p esticid e u se h ave been m ixed . In on e p ap er, h o wever, Fern an d ez-Co rn ejo an d o t h ers (1998) rep o rt ed an u n weigh ted average of 44 stu d ies, wh ich sh owed th at p esticid e u se d eclin ed 15% with th e adop tion of IPM tech n iq u es. Several biologists h ave n oted th at resp on sive ap p lication s m ay n ot always b e p referab le t o p reven t ive o n es. In t h e case o f fu n gicid es, fo r exam p le, research by exten sion agen ts at Oklah om a State Un iversity (Dam icon e 2001) su ggest s t h at ap p licat io n in t h e early seaso n wh en in fect io n levels are lo w

338 • Chapter 12: Industrial Organization and Institutional Considerations

m ay be m ore effective th an waitin g for a bu ildu p of fu n gu s. Th e sam e m ay be tru e for th e ap p lication of h erbicid es. In th ose situ ation s, u n certain ty abou t th e em ergen ce of p est p roblem s is low, an d ap p lyin g relatively sm all levels of ch em icals m ay p reven t th e n eed to ap p ly larger volu m es of m aterials later in th e season .

Agricultural Practices

Ap p lyin g ch em icals is on ly on e way th at farm ers h ave to treat p est p roblem s. Ad d it io n ally, farm ers rely q u it e ext en sively o n m ech an ical m ean s su ch as weed in g, p lo win g, an d p h ysically killin g p est s by o t h er m et h o d s. Alt h o u gh so m e o f t h ese t ech n iq u es are co m p o n en t s o f an IPM st rat egy, t h e fact t h at m an y n on -IPM farm ers u se th em su ggests th at th eir im p acts sh ou ld be con sid ered sep arat ely. Mech an ical m ean s p ro vid e a very go o d su b st it u t e fo r ch em ical st rat egies. Fo r exam p le, t o ad d ress t h ese p ro b lem s p ru n in g t rees, esp ecially d u rin g th e p ostseason , m ay sign ifican tly red u ce p esticid e u se, d isease in ciden ces, an d bu ildu p of resistan ce. W h en m ech an ical altern atives for p est con trol exist, th e farm er m ay view th em as backstop tech n ologies th at can overcom e fu tu re p roblem s of resistan ce as well as p op u lation bu ildu p over tim e. Th at m ay lead to m yop ic beh avior closer to th e social op tim u m . Th is m ay actu ally cau se lower p esticid e u se in som e cases an d in crease ap p lication wh en resistan ce bu ildu p is oth erwise a m ajor con cern .

Crop Rotation

Farm ers th rou gh ou t th e world en gage in crop rotation for several reason s: soil fertility bu ild u p , risk d iversification , p rod u ctivity m an agem en t, an d p op u lat io n co n t ro l. Th e p ract ice o f cro p ro t at io n m ay lead t o u n d erem p h asis o f d yn am ic con sid eration s, esp ecially relative to crop -sp ecific p ests. Man y d ecision s abou t p ests are taken with in th e con text of a field, an d, if th e crop is n ot grown in th e sam e field season after season , th en som e of th e dyn am ic im p lication s of p esticid e m an agem en t becom e m u ch less relevan t. Th e effect ren ders th e op tim al p esticide-u se decision s to be closer to th e m yop ic on es. Carefu l con sid eration of th e im p act of crop rotation on p est m an agem en t suggests som e basic flaws in th e m odelin g of th e dyn am ics of pest population s. To m ake com p u tation clean er, we ten d to assu m e th e existen ce of region al stocks of p est p op u lation s an d p est resistan ce. Th is assu m p tion , h owever, is overly sim plistic. In reality, th e m ovem en t of som e pests, for exam ple, weeds or fu n gi, is lim ited , esp ecially for som e sp ecies. Progen ies of a p articu lar p est are m ore likely to reside close to its origin al location th an farth er away. More realistic m od elin g m ay req u ire h avin g a large n u m ber of location al stocks of both

Chapter 12: Industrial Organization and Institutional Considerations • 339

p est p op u lation an d p est resistan ce d escribed in a way th at recogn izes th eir in terd ep en d en cies. A farm er en gagin g in crop rotation d rastically affects th e pest population in h is own field, wh ich m ay affect n eigh borin g population s. Th e overall im pact of crop rotation on global pest population an d resistan ce is qu ite com plex. On th e on e h an d, crop rotation m ay lead to a drastic redu ction of p est p op u lation in th e field s wh ere it occu rs. On th e oth er h an d , th e m yop ia su ggested earlier m ay en cou rage larger ap p lication s of ch em icals th at could in crease resistan ce in oth er fields. Alth ough th e an swer is un clear, th e fact th at crop rotation is bein g prom oted as an an tiresistan ce strategy suggests th at th e overall effect is p ositive. For exam p le, “Accord in g to Nebraska exten sion offices, Un iversity of Nebraska, Lin coln , m ore th an 35% of Nebraska’s corn acreage was rotated to soybean s in [19]96, reducin g th e n eed for in secticides to con trol corn rootworm s. Use of crop rotation h as resulted in a reduction of over on e m illion lbs. of active in gredien t per year, an d an an n ual savin gs in production costs of at least $10 m illion ” (Pure Foods Cam paign 2001).

Precision Technologies

Loosely defin ed, p recision tech n ologies m on itor th e state of relevan t variables o ver sp ace an d t im e, b e it p est p o p u lat io n , t em p erat u re, o r so il co n d it io n . Th ey also con tain a d ecision m akin g elem en t th at d eterm in es an ap p rop riate resp on se an d an ap p lication com p on en t to im p lem en t it. To a certain exten t, IPM can be viewed as a p recision tech n ology, as can m od ern irrigation tech n ology com bin ed with an irrigation sch ed u lin g system . Th e term “p recision tech n ology,” for m ost com m ercial agricu ltu re, is a m ore n arrowly d efin ed set o f t ech n o lo gies t h at t akes ad van t age o f d evelo p m en t s in rem o t e sen sin g, co m m u n icat io n , an d co m p u t ers. Th ese t o o ls h ave t h e p o t en t ial t o p lay im p ortan t roles in alertin g farm ers, wh o m ay n ot en ter a field for m on th s at a tim e, to im p ortan t ch an ges in p est p op u lation s. Precision tech n ologies are still in th eir in fan cy, even th ou gh th e evolu tion of data gath erin g h as im proved over tim e. Th ere is a n eed to develop both software t o in t erp ret d at a an d in exp en sive in t erven t io n m ech an ism s. Precisio n tech n ologies provide th e m ean s to collect th e data n eeded for large-scale statistical an alysis. Th ese an alyses are essen tial to im p rovin g cu rren t econ om etric stu dies th at attem pt to qu an tify th e relation sh ips between en viron m en tal con d ition s an d p rod u ctivity. Th e tech n ologies rem ain in th e early stages of th eir evolu tion , alth ou gh eq u ip m en t is n ow bein g in trodu ced to m on itor en viron m en t al variables. Even t u ally, d ecisio n m akin g will be d o n e u sin g t o o ls t h at closely resem ble th e con ceptu al m odel th at we presen ted earlier. Th ere is evid en ce, h owever, th at th e availability of m ore p recise in form ation m odifies p est con trol strategies, redu ces ap p lication s, an d m in im izes p est d am age an d bu ild u p of resistan ce. For exam p le, th e im p act of th e Californ ia

340 • Chapter 12: Industrial Organization and Institutional Considerations

Irrigat io n Man agem en t In fo rm at io n Syst em d et ailed b y O sgo o d an d o t h ers (1997) su ggested th at on e of th e m ost im p ortan t ap p lication s (valu ed at $10 m illion an n u ally) was to p rovide weath er in form ation to p est con trol advisors wh o u se t h em t o t im e p est icid e ap p licat io n s. Im p ro ved in fo rm at io n will en able tran sition away from gen eralized p reven tive ap p lication s. Th e ad van tage of m ovin g away from th is tradition al strategy is m ore p recise an d less freq u en t ap p lication s an d p ossibly in larger dosages. Th is redu ces th eir im m ediate im p acts an d th e likelih ood of resistan ce bu ildu p . Th e in tegration of m on itorin g tech n ologies, like rem ote sen sin g with geograp h ic in form ation system s, are esp ecially im p ortan t in tracin g th e evolu tion of d iseases an d p est p roblem s over sp ace. Th ey m ay be u sed to id en tify weed in festation an d trigger in terven tion . Even tu ally, sp ecial sen sors m ay id en tify in sect in festation . Geograp h ic in form ation system tech n ology is u sed to trace th e sp read of p est p roblem s.

New Pesticides

W h en resist an ce is m o d eled as a ren ewable o r n o n ren ewable reso u rce, t h en th e develop m en t of altern ative or n ew ch em icals can be treated as a backstop tech n ology. As th e literatu re on ren ewable resou rces su ggests, th e availability of backstop tech n ology redu ces th e sh adow cost of th e stock. Th e p rosp ect of h avin g an altern ative is likely to red u ce th e in cen tive for farm ers to d evelop resistan ce con trol strategies. Th e discovery, develop m en t, an d in trodu ction of altern ative ch em icals are affected both by sp ecific kn owled ge an d by in stitu tion al an d econ om ic con dition s, som e of wh ich we will discu ss in th e section on ch em ical com p an ies an d con su ltan ts.

The Value of M aintaining Pest Control Alternatives

As was m en tion ed earlier, resistan ce p roblem s are om n ip resen t. Recen t statistics su ggest th at m ore th an 700 p est sp ecies h ave develop ed resistan ce to on e p ro d u ct o r an o t h er. Th at , in sp it e o f all t h e co n st rain t s, n ew ch em icals are bein g in trod u ced an d th at m an y p roblem atic p esticid es h ave su bstitu tes m ay raise th e q u estion , wh y worry abou t p esticide resistan ce or ability to m ain tain ch em icals an d p est co n t ro l agen t s? Th e an swer m ay n o t b e fo u n d in resist an ce p er se bu t in a bro ad er view o f p est co n t ro l. Alt h o u gh m o st ch em icals h ave su bstitu tes th at are u sefu l, th ere is som e evid en ce th at som e agen ts are difficu lt to rep lace. O n e o b vio u s exam p le is t h e u se o f Bacillus thuringiensis (Bt) in o rgan ic farm in g. In th is case, th e set of “n atu ral” p est con trols is sm all, an d losin g an y cru cial elem en t m ay be very costly. Even with ch em ical p esticides, m an y p est icid es h ave su rvived d esp it e regu lat o ry p ressu re an d exp en sive at t em p t s t o

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fin d su bstitu tes. On e exam p le is m eth yl brom id e, a fu m igan t u sed to ad d ress soilborn e diseases. Meth yl brom ide ap p lication s are relatively exp en sive ($100 to $300 p er acre) an d cau se severe en viron m en tal p roblem s (d ep letion of th e ozon e layer). Yet, farm ers figh t to m ain tain th eir u se, even in a lim ited cap acit y. U.S. farm ers in Califo rn ia an d elsewh ere h ave u sed a wid e variet y o f m ean s t o d elay p h ase-o u t s o f ch em icals u n t il an ap p ro p riat e alt ern at ive is fo u n d . Ho wever, fin d in g alt ern at ives is st ill n o t easy. A sign ifican t b o d y o f research o n t h e im p o rt an ce o f m et h yl b ro m id e t o U.S. agricu lt u re fin d s it s an n u al valu e to be several h u n dred m illion dollars (Yarkin et al. 1994; Carp en ter et al. 2000). Diseases th at can n ot be treated are very costly to agricu ltu re. For exam p le, Pierce’s d isease is n ow wreakin g h avoc in Californ ia agricu ltu re, th e n u m ber of strategies available to com bat it is lim ited, an d th eir vu ln erability to resistan ce m ay p rove to be costly. Th erefore, wh en an alyzin g th e cost of resistan ce an d efforts to com bat it, em p h asis sh ou ld be on cases in wh ich th ere are few altern atives an d in wh ich d am age, on ce p est p roblem s are con trolled , is su bstan tial.

Institutional Factors Influencing Resistance: Environmental Regulation

Co n cern ab o u t en viro n m en t al sid e-effect s fro m p est icid e u se—in clu d in g p roblem s of worker safety, food safety, an d en viron m en tal h ealth —h as led to t h e d evelo p m en t o f a wid e array o f p est icid e p o licy p rescrip t io n s, each o f wh ich h as im p act s o n resist an ce b u ild u p . Eco n o m ist s h ave su ggest ed so lu tion s su ch as p esticide taxes as p olicy tools to redu ce extern alities (see Zilberm an et al. 1991). Som e western Eu rop ean cou n tries, n otably Norway an d Sweden , h ave relied on p esticide taxes. Practical realities often in tercede, h owever, an d im p lem en tation of op tim al taxes m ay be difficu lt becau se of variability of extern alities over sp ace (Zilberm an an d Millock 1997). Op tim ality p roblem s th at d eterm in e p esticid e u se h ave to be m od ified to in clu d e t h e ext ern alit y co st wh en ever p est icid es cau se ext ern alit y p ro blem s in clu d in g h arm t o farm wo rkers, fo o d co n su m ers, n o n t arget sp ecies, an d water an d air q u ality. Som e extern ality costs h ave a d yn am ic d im en sion ; for exam p le, accu m u lation of p esticide residu es in a body of water over tim e m ay reach satu ration levels th at are h arm fu l to fish . Oth er p esticides are a sou rce of ch ron ic risks an d m ay cau se can cer after lon g, freq u en t exp osu re. Becau se of sp ace lim itation s, we will n ot cover op tim al resou rce m an agem en t p roblem s of extern alities in great detail. However, let MECx t den ote th e m argin al extern alit y co st asso ciat ed wit h ap p licat io n o f x t , an d t h en t h e o p t im al p est icid e allocation ru le at tim e t will be determ in ed by solvin g V MPxt + V MFt = W + V Rt + MECxt

342 • Chapter 12: Industrial Organization and Institutional Considerations

If all oth er factors are taken in to con sid eration (resistan ce, p est d yn am ics) an d a tax eq u al to MECx t is in trodu ced, it will lead to op tim al resou rce allocat io n . In t ro d u ct io n o f a t ax will lead t o a red u ct io n in p est icid e u se an d , in som e cases, adop tion of m ore p recise p esticide ap p lication tech n ologies, th u s lead in g t o red u ct io n o f resist an ce b u ild u p . W h en t h e valu e o f t h e im p licit ben efits from a tax th at red u ces resistan ce p roblem s becom es larger or wh en farm ers are m yop ic or ign oran t abou t resistan ce p roblem s, p esticid e taxation th u s m ay p rovide an extra dividen d in redu cin g resistan ce dam age. In t h e Un it ed St at es, h o wever, t h e m ajo r t o o l fo r co m b at in g p est icid e extern ality p roblem s is ban n in g th eir u se an d can celin g th eir registration . In th is case, th e im p act on resistan ce is m ore com p lex. Th e 1996 Food Qu ality Pro t ect io n Act aim ed t o p h ase o u t t h e o ld er cat ego ries o f p est icid es su ch as o rgan o p h o sp h at es. So m e o f t h ese ch em icals, fo r exam p le, p arat h io n an d m alat h io n , u sed a b ro ad ran ge o f ap p licat io n s an d h ad b een effect ive fo r a lon g tim e with ou t en cou n terin g m u ch resistan ce. Th ey were rep laced by m ore n arro wly fo cu sed ch em icals t h at ad d ressed sp ecific p ro b lem s b u t t h at were m ore vu ln erable to resistan ce bu ild u p . In ad d ition , on e of th e m ost effective ways of redu cin g resistan ce is to u se m u ltip le ch em icals with differen t m odes of op eration or to rotate ch em icals. Ban n in g ch em icals, rep lacin g th em with m ore targeted ch em icals, an d red u cin g op tion s, as d on e by th e Food Qu ality Protection Act, m ay red u ce th e strategies available to con trol p ests an d th u s in crease resistan ce. Govern m en t p olicies also in clu d e restriction s on p rod u ction activities for th e sake of safety. On e exam ple is reen try regu lation wh ich sets a restriction on th e m in im u m am ou n t of tim e workers can begin workin g in a field after sprayin g. Lich t en berg an d o t h ers (1993) argu ed t h at reen t ry regu lat io n m ay lead farm ers to switch from respon sive to preven tive application s. Th is is tru e especially before h arvestin g; in stead of waitin g to sp ray u n til th e first ap p earan ce of pest popu lation , farm ers m ay spray ah ead of tim e to en su re th at h arvestin g will be feasible at t h e righ t t im e. Th u s, in m an y cases, sp rayin g o ccu rs even th ou gh th e pest popu lation is very sm all, an d in oth er cases, early application of th e pesticides redu ces th eir effectiven ess wh en th e pest actu ally arrives. Th e im p act of a strict regim e of registration an d testin g on ch em ical com p an ies’ efforts to p rod u ce n ew ch em icals sh ou ld n ot be u n d erestim ated . On e stu dy fou n d th at in creased regu lation led to a 7–9% declin e in p esticide registration (Fern an d ez-Corn ejo et al. 1998). Th e testin g aim s to red u ce th e likelih ood of en viron m en tal sid e-effects an d u n in ten d ed con seq u en ces. Fin an cial an d in stitu tion al cap acity to in trod u ce an d m arket ch em icals is an ed ge th at ch em ical com p an ies h ave over n ew en tran ts. Several au th ors su ggested th at th e oligop olistic stru ctu re of th e ch em ical in d u stry is cau sed by registration req u irem en ts an d m arketin g costs rath er th an p rod u ction con sid eration p er se (see Carlson an d Wetzstein 1993).

Chapter 12: Industrial Organization and Institutional Considerations • 343

If th e regu latory req u irem en ts are effective an d gen erally red u ce en viron m en t al sid e-effect s, an o t h er serio u s p ro b lem asso ciat ed wit h p est icid e u se, th en th e p rice p aid in term s of resistan ce bu ild u p an d con trol is worth wh ile. If, h owever, as som e su ggest, m an y of th e regu latory req u irem en ts are aim ed at m ain tain in g th e oligop olistic stru ctu re, th en th ey m ay im p ose an extra cost in term s of resistan ce. Research th at will lead to m ore realistic assessm en t of th e regu latory fram ework an d its im p rovem en t is on e of th e m ost ch allen gin g asp ects of research an d p est con trol.

Chemical Companies’ Choices and Resistance

In exam in in g th e ch oices th at lead to pesticide u se, on e can h ardly ign ore th e in flu en ce of agroch em ical p rod u cers an d d istribu tors on th e p rocess. Most an alyses of resistan ce h ave been m icroecon om ic in n atu re an d , as su ch , h ave ign ored in dustrywide con sideration s. However, th e dyn am ics of pesticide use is d eterm in ed by m an u factu rers. Man u factu rers con trol p rod u ct d evelop m en t, pricin g, prom otion , an d m ost in form ation al use guidan ce; th us, th eir self-in terest affects th e evolu tion of resistan ce. Th e ap p en d ix con tain s th e d etails of a m ath em atical m od el of ch em ical p rod u cers’ ch oices, takin g in to accou n t th e effects of resistan ce. Here we sketch out th e assum ption s an d m ain con clusion s. Con sider a case in wh ich th e p est p op u lation is ren ewed every season , an d resist an ce is t h e o n ly d yn am ic variab le t h at ch an ges o ver t im e. We also assu m e th at th e farm in g in d u stry con sists of m an y sm all farm s so th at resistan ce co n t ro l d o es n o t affect farm er beh avio r. Th e in verse d em an d fu n ct io n fo r p est icid es in creases in t h e p rice o f o u t p u t an d d ecreases wit h aggregat e p esticide u se an d resistan ce. W h en p est icid es are relat ively n ew, t h e m an u fact u rer’s p at en t gives it m on op oly p ower, wh ich also dep en ds on availability of su bstitu tes (ch em ical, biological, or agron om ical). Ch em icals m ore th an 20 years old are p rod u ced b y co m p et it ive (o r sem ico m p et it ive) in d u st ries. Th e p resen ce o f p at en t s allo ws u s t o m o d el a m o n o p o list ic m an u fact u rer wh o m axim izes exp ect ed p ro fit s su b ject t o a resist an ce co n st rain t t h at d ep en d s o n b o t h resist an ce bu ild u p an d t h e reco very rat e o f t h e vu ln erable p o p u lat io n . Th e co n st rain t in creases with ch em ical u se. At t h e o p t im al p est icid e p ro d u ct io n level o f t h e m an u fact u rer, m argin al reven u e (MRt ) is eq u al t o m argin al co st o f p ro d u ct io n (MC t ) p lu s resist an ce cost (MRC t) MRt = MCt + MRCt Th is situ ation is dep icted in Figu re 12-3. Th e m an u factu rers’ op tim u m occu rs at A an d resu lts in u se p rice W A an d q u an tity X A . If th e m an u factu rers ign ore

344 • Chapter 12: Industrial Organization and Institutional Considerations

WA

M Ct + M Cr

•

WD

•

WE D

E

•

M Ct

• •

A

C

• B

••

F D Dt = Wr

Rt XA

XB XE

XC

Xt

FIGURE 12-3. Optimal Determination of Pesticide Products

resistan ce, th e op tim al ou tcom e cou ld be X B > X A . If th ey are com p etitive an d ign ore resistan ce, th e ou tcom e is at C. Th e d yn am ics o f t h e sh ad o w p rice o f resist an ce µt ch an ges t h e valu e o f MRC t o ver t im e. Th e d et ails o f t h e d erivat io n are co vered in t h e ap p en d ix. W h en th e valu e of th is sh ad ow p rice d eclin es over tim e, we exp ect MRC t to d ecrease, an d t h e red u ct io n in p est icid e p ro d u ct io n b y t h e m o n o p o list becau se of resistan ce con sid eration s also will d eclin e over tim e. Th is su ggests th at th e m on op olistic resistan ce con trol effort in gen eral will d eclin e as th e p rodu ct m atu res. To com p are th is case with th e social op tim u m , con sid er th e social welfare op tim ization p roblem , in wh ich a welfare fu n ction describin g th e gross ben efit to farm ers from ch em ical u se is m axim ized su bject to th e resistan ce con strain t. Th e op tim ality con dition for th is p roblem is W t D = MCt + MSRt

Chapter 12: Industrial Organization and Institutional Considerations • 345

wh ere W t D is th e dem an d p rice, MC t is th e m argin al cost of p rodu ction , an d MSRt is th e m argin al social sh ad ow cost of resistan ce, wh ich is d istin ct from t h e m o n o p o list ’s MRC t . Th u s, it fo llo ws t h at t h e o p t im al so cial q u an t it y is sm aller t h an X C bu t m ay be great er t h an X A u n less at X A so ciet y’s m argin al resistan ce cost is m u ch h igh er th an th e m on op oly’s, an d th e social op tim u m is at D. Th is is described by th e followin g eq u ation :

W

D

+ MRSt < W

D

−

∂W D X t + MRCt ∂X t

Th is eq u ation sh ows th at th e m on op oly will likely p rodu ce less p esticide an d farm ers will likely u se less p esticide th an is socially optim al. We su ggest t h at if resist an ce is t h e o n ly d yn am ic bio lo gical p ro cess t h at affects p esticid e p rod u ctivity, p rod u ction of ch em icals u n d er m on op oly m ay be below th e social optim al level; fu rth erm ore, th e ch em ical com pan y will take resistan ce in to accou n t in both th e p rod u ction an d p ricin g of ch em icals. Th e m ath em atical m odel on ly sketch es som e of th e key featu res of real-life beh avio r, bu t it s m ain in sigh t is t h at ch em ical co m p an ies care abo u t resist an ce redu ction , esp ecially wh en th ey own th e p aten ts of a p rodu ct. However, even aft er t h e p at en t lap ses, t h e ch em ical co m p an y st ill h as it s bran d n am e, an d th at gives th em an edge. Oth er com pan ies will produ ce an altern ative gen eric p ro d u ct , bu t t h e o rigin al co m p an y wit h t h e co m m ercial bran d n am e m ay ch arge a p rem iu m . Fu rth erm ore, th e com p an y m ay ch arge gen eric p rod u cers for registration data. In su m , a produ ct th at h as less resistan ce an d a better repu tation will be easier to m arket, an d m an u factu rers will be willin g to p ay for th e righ ts to produ ce th e produ ct an d to obtain in form ation related to it. Ou r an alysis ign ores issu es of p rod u ct m arketin g an d in trod u ction to variou s u ser grou p s. As th e su rvey article by Su n d in g an d Zilberm an (2001) su ggests, it m ay take several years before agricu ltu ral p rod u cts reach a fu ll ran ge of u sers. Ad op tion p rocesses are lon g an d req u ire sign ifican t in vestm en t for ch em ical co m p an ies t o gen erat e awaren ess o f t h e p ro d u ct , d em o n st rat e it s p o t en t ial, an d ed u cat e in d ivid u als ab o u t it s valu e an d u se. Th is t h eo ret ical argu m en t su ggests th at m an u factu rers (a) will in vest in research abou t resistan ce, (b ) m ay h elp effo rt s in co llect ive act io n t o co n t ain it , an d (c) m ay b e active in th e efforts to deal with it. We will in trodu ce som e eviden ce th at ju stifies ou r argu m en t. Ou r argu m en t also in d icates th at m an u factu rers’ con cern abou t resistan ce varies th rou gh ou t th e d ifferen t stages of a p rod u ct’s life. From th e m an u factu rer’s p ersp ective, th e valu e of resistan ce bu ildu p declin es th rou gh ou t th e life of a p rod u ct. Th e origin al m an u factu rer m ay be less in terested in com batin g resistan ce as th e p rodu ct ages, esp ecially wh en it does n ot exp ect a large m arket sh are after p aten ts exp ire or in m arkets wh ere it does n ot ben efit from p ro-

346 • Chapter 12: Industrial Organization and Institutional Considerations

tection of IPM. Gen eric p rod u cers in m ore com p etitive m arkets d o n ot en joy m o n o p o list ic p o wer an d are less likely t o wo rry ab o u t resist an ce. W h en p aten t righ ts are n ot resp ected, th e origin al m an u factu rer is less com m itted to red u cin g resist an ce p ro b lem s. It fo llo ws t h at m an u fact u rers in d evelo p in g cou n tries are less likely to figh t resistan ce th an th ose in develop ed on es. Th e resu lt s o f o u r an alysis are su p p o rt ed by t h e beh avio r o f several large ch em ical m an u fact u rers. Fo r exam p le, p est icid e co m p an ies are liab le wh en p esticid e u se resu lts in crop d am age. In d eed , Du p on t recen tly p aid $750 m illio n t o u sers o f Ben o m yl in co m p en sat io n fo r d am age resu lt in g fro m resist an ce bu ild u p (www.p an -u k.org/ actives/ ben om yl.h tm ). As m en tion ed earlier, even in th e absen ce of legal rep ercu ssion s, m an u factu rers are in th e bu sin ess of sellin g th eir p rodu ct, an d if th eir p rodu ct is fou n d to be in effective, p rofits p lu m m et. Th is alon e p rovides a stron g in cen tive to m an age resistan ce. It is often argu ed th at ch em ical com p an ies ign ore th e resistan ce issu e, p articu larly becau se th ey h ave scores of in creasin gly exp en sive an d toxic su bstitu tes available wh en on e of th eir p rodu cts p roves n ot to be viable. Ou r discu ssio n su ggest s t h at p ro d u cin g a series o f fau lt y p ro d u ct s is n o way t o at t ract m o re cu st o m ers. In d eed , o n e in d u st ry sp o kesp erso n claim ed t h at a sin gle n on p erform an ce com p lain t can cost 10 to 1,000 in d ivid u al sales (Th om p son 1997). Fu rt h erm o re, t h e en o rm o u s research an d d evelo p m en t co st s t o p ro du ce ju st on e p esticide, in addition to th e 7 to 10 years sp en t u n dergoin g th e fed eral regu latory ap p roval p rocess, are su fficien t d isin cen tives to creatin g a wid e gam u t of su bstitu table p esticid es. Accord in g to th e Am erican Crop Protection Association (ACPA), on average, on ly on e in 20,000 ch em icals em erges from th e ch em ist’s laboratory an d is ap p lied on th e farm er’s field. Th is develo p m en t co st s m an u fact u rers bet ween $35 m illio n an d $50 m illio n fo r each p rodu ct (ACPA 2001). Oth er estim ates of th ese costs ru n between $15 m illion an d $30 m illion . In ad d ition , as was p oin ted ou t by Gary Th om p son , a rep resen tative from Dow AgriServices, “Wh ile it is true th at th e failure of existin g tech n ology due to resistan ce or oth er reason s can in crease research efforts an d allow m ore selective products to com pete, it is also true th at selective products h ave sm aller m arkets, n eed lon ger m arket life, an d con sequen tly, protection from resistan ce developm en t to be fin an cially viable” (Th om p son 2001). In terestin gly, h owever, th e cases in wh ich farm ers en tirely cease to dem an d a product because of resistan ce h ave been rare. Even in th e extrem e case of p yreth roid s in th e Un ited States, th eir m arket valu e d rop p ed by on ly 50%, an d th ey rem ain on th e sh elves of agricultural supply stores. In fact, pyreth roids h ave rem ain ed in h igh dem an d; Fern an d ez-Corn ejo an d oth ers (2001) estim ated th at th e im p act of its loss on corn producers would be in excess of $172 m illion per year. Th ere is con sid erable evid en ce th at th e ch em ical in d u stry in vests h eavily in d evelop in g strategies for resistan ce m an agem en t. As Bayer-Pflan zen sch u tz

Chapter 12: Industrial Organization and Institutional Considerations • 347

(2001) p u t it, “If resistan ce is likely to arise, fu rth er develop m en t of th e p rodu ct can be p ractically exclu ded.” In dividu al com p an ies fin an ce scien tists both with in an d ou tsid e of th eir corp oration s. Mon san to, a m ajor p rod u cer of Bt crop s, collaborates d irectly with th e NC-205 research com m ittee on research regard in g th e Eu rop ean corn borer, an im p ortan t p est for Bt corn . Mon san to also h as ext en sive p ro ject s am o n g en t o m o lo gist s wo rkin g o n resist an ce am on g cotton p ests (Sach s 2001). Bayer Corp oration em p loys 68 scien tists in its In stitu te for In sect Con trol, wh ose m ajor focu s is th e stu d y of in sect biology. Am on g th e p rojects listed on th eir website are stu d ies of ap h id s, beetles, sp ider m ites, th e codlin g m oth , an d n em atodes an d th eir variou s in teraction s with m aize, rice, cotton , soy, an d vegetables. Overall, sp en d in g on resistan ce m an agem en t b y co m p an ies is su b st an t ial an d in creasin g, p art icu larly sin ce 1995, wit h larger am o u n t s sp en t by co m p an ies o fferin g t ran sgen ic p ro ject s (Th om p son 2001). Du rin g t h e lat e 1970s, a h o st o f in t ern at io n al o rgan izat io n s were creat ed by agroch em ical com p an ies to h elp coordin ate research an d to gen erate in form ation exch an ge regardin g resistan ce. In itially, efforts were crop - or p rodu ctsp ecific, su ch as th e Au stralian W h eat Broad Workin g Party on Grain Protect an t s an d t h e Pyret h ro id Efficacy Gro u p . Th e early 1980s saw t h e creat io n , u n der th e u m brella of th e Global Crop Protection Federation (GCPF), a series of in terin d u stry com m ittees ad d ressin g h erbicid e, in secticid e, fu n gicid e, an d roden ticide resistan ce. Th e In sect icid e Resist an ce Act io n Co m m it t ee (IRAC), fo rm ed in 1984, states its m ission as follows: “to p rovide a coordin ated crop p rotection in du st ry resp o n se t o t h e d evelo p m en t o f resist an ce in in sect an d m it e p est s. Th e m issio n o f IRAC is t o d evelo p resist an ce m an agem en t st rat egies t o en ab le growers to u se crop p rotection p rodu cts in a way to m ain tain th e efficacy. Th e o rgan izat io n is im p lem en t in g co m p reh en sive st rat egies t o co n fro n t ” (see IRAC 2001). Th e IRAC organ izes several con feren ces a year regardin g th e m an agem en t of in secticide resistan ce an d p u blish es exten sive gu idelin es regardin g in secticid e u se. It fu n d s sp ecific resistan ce p rojects an d coord in ates cou n try gro u p s in t h e Un it ed St at es, Brazil, In d ia, Pakist an , Au st ralia, So u t h Africa, Sp ain , an d Ch in a. Cu rren t p ro ject s in clu d e m o n it o rin g resist an ce t o p yret h ro id s o f co t t o n p est s in West Africa an d Asia (an in cip ien t p ro ject t o u n d erstan d th e reaction of th e cod lin g m oth ), a variety of p esticid es, an d an on goin g effort to d evelop resistan ce m an agem en t strategies for th e Colorad o p otato beetle in Polan d. Th e Herbicide Resistan ce Action Com m ittee (HRAC), fou n ded in 1989, h as a m ission sim ilar to th at of th e IRAC, an d its m em bersh ip in clu des rep resen tatives from 13 m ajor agroch em ical com p an ies: AgrEvo, BASF, Bayer, Am erican Cyan am id , Do w AgriServices, Du Po n t , FMC, Mo n san t o , No vart is, Rh o n ePo u len c, Ro h m & Haas, To m en , an d Zen eca (Nevill et al. 1998). A m ajo r

348 • Chapter 12: Industrial Organization and Institutional Considerations

com p on en t of th e HRAC’s resp on sibilities is th e dissem in ation of in form ation am o n g farm ers an d research ers. Like IRAC, HRAC fu n d s an o n go in g glo b al resistan ce su rvey stu d y. In ad d ition , it h as su p p orted sp ecific p rojects in th e m on itorin g wild oats in th e Un ited Kin gd om , gen e flow in Ru ssian th istle in t h e Un it ed St at es, m an agem en t o f u rea-resist an t Pharalis in In d ia, an d t h e eco n o m ics o f h erb icid e-resist an t b lackgrass. It s m o st recen t fo cu s h as b een d eterm in in g th e fin an cial im p acts of h erbicid e resistan ce in th e agricu ltu ral in d u stry. Du rin g th e 1990s, HRAC sp en t m ore th an $300,000 fu n d in g scien tific stu dies on h erbicide resistan ce (Ju tsu m an d Grah am 1995). Th e Fu n gicid e Resist an ce Act io n Co m m it t ee (FRAC), d evelo p ed fro m an in d u st ry sem in ar in 1980, h as sin ce fo rm ed a variet y o f wo rkin g gro u p s fo cu sed o n p art icu lar fu n gicid es. Th e cu rren t gro u p s in clu d e scien t ist s research in g an ilin o p yrim id in es, b en zim id azo les, d icarb o xim id es, p h en ylam ides, sterol biosyn th esis in h ibitors, an d strobilu rin typ e action an d resistan ce (see FRAC 2001). Th e GCPF, th e u m brella over th e action com m ittees (form erly th e In tern ation al Grou p of Nation al Association s of Man u factu rers of Agroch em ical Produ cts), h as a stron g region al focu s. It is com posed of six region al crop protection association s: Africa an d th e Mid d le East, Latin Am erica, Asia an d th e Pacific, Japan , North Am erica, an d Eu rope. Man y of th e region al organ ization s h ave a lon g h istory; th e North Am erican bran ch , for exam p le, was fou n d ed in 1933 an d boasts a m em bersh ip of firm s ran gin g from Aven tis to Zen eca (see ACPA 2001). Alth ou gh th e region al organ ization s are respon sible for a m u ch broader ran ge of issu es th an ju st p esticid e resistan ce, th eir p articip ation in th e resistan ce m an agem en t p rocess is cru cial becau se th ey allow for th e collection an d d issem in at io n o f in fo rm at io n acro ss regio n s. Th eir m ajo r effo rt in t h is area in clu d es t h e co o rd in at io n o f t h e act io n co m m it t ees. In fo rm at io n regard in g total spen din g by th e GCPF an d its com m ittees on research an d con tribu tion s of in du stry to th e organ ization s is, u n fortu n ately, n ot available. Desp ite th is in form ation al barrier, th e evid en ce su ggests th at ou r m od el describes an im portan t an d un derstudied piece of th e pesticide resistan ce puzzle.

Pesticide Use Advisors An oth er area of research th at h as been alm ost com p letely ign ored by th e tradition al an alysis of resistan ce m an agem en t is th e role of p esticide con su ltan ts, p articu larly in th e Un ited States. Su ch con su ltan ts p lay a role an alogou s to a d octor, id en tifyin g th e cu lp rit d isease an d p rescribin g a treatm en t. Alth ou gh in d ep en d en t con su ltan ts h ave p rovid ed services to farm ers for m ore th an 40 years, th eir p articip ation was p reviou sly lim ited to fru it an d vegetable p rodu ction . Presen ce in oth er food an d feed grain p rod u ction is a m ore recen t p h en om en on (Wolf 1998). In 1993, con su ltan ts were fou n d to h ave p layed a role

Chapter 12: Industrial Organization and Institutional Considerations • 349

in th e p rodu ction of 53% of cotton acres, 53% of vegetable acres, 21% of corn acres, an d 13% of soybean acres. Th e sam e stu dy estim ated th at, overall, diagn o st ic services were p ro vid ed b y co n su lt an t s o n 16% o f U.S. farm lan d (Nowlin 1993). Th e p ast 10 years h ave seen a bu rst o f act ivit y in t h is field . Th e Nat io n al Allian ce of In dep en den t Crop Con su ltan ts, a p rofession al society rep resen tin g in d ep en d en t con su ltan ts an d research ers, was fou n d ed in 1978. In 1985, th e organ ization h ad m ore th an 150 m em bers, a n u m ber th at h as sin ce in creased to m ore th an 500. It was n ot u n til 1991 th at it fou n d ed th e Certified Profession al Crop Con su ltan t Program , wh ich com p etes with th e Am erican Society of Agron om y’s Certified Crop Advisor Program . Both are in ten ded to raise th e st an d ard s o f t h e in d u st ry, alt h o u gh t h e Cert ified Pro fessio n al Cro p Co n su ltan t Program is seen as m ore rigorou s, req u irin g a bach elor’s degree in agricu ltu re, p est m an agem en t, or biology; exten sive exp erien ce; an d con tin u ed edu cat io n (Wo lf 1998). Th e gro win g im p o rt an ce o f co n su lt an t cert ificat io n is illu st rat ed b y t h e fact t h at b et ween Feb ru ary 1993 an d Feb ru ary 1995, t h e Am erican So ciet y o f Agro n o m y ad m in ist ered alm o st 12,000 Cert ified Cro p Advisor n ation al exam in ation s. Wo rk by Wiebers (1992) su ggest s t h at rep u t at io n is t h e key elem en t t h at d eterm in es th e su ccess of con su ltan ts. If th ey switch from p rivate p ractice to wo rkin g fo r a co m p an y, o ft en t h ey t ake t h eir clien t s wit h t h em . Given t h at co n su lt an t s m ay wo rk fo r a large n u m b er o f firm s in a regio n , t h ey p lay a p oten tially im p ortan t role in affectin g region al resistan ce. Th e fact th at large farm s are m o re likely t o h ire co n su lt an t s p ro vid es fu rt h er exp lan at io n as t o wh y large farm s are m ore likely to u se lower levels of p esticides. Ho wever, Wiebers’s st u d y (1992) also sh o ws t h at co n su lt an t s m ay ad ju st ch em ical u se in stru ction accord in g to farm ers’ p ercep tion of effectiven ess in u sin g a ch em ical. Farm ers wh o are less effect ive m ay b e p rescrib ed m o re ch em ical ap p lication s to red u ce th e likelih ood of p est d am age. Th is p ractice p rovid es fu rth er su p p ort for th e d octor–p atien t an alogy. On e m igh t also su sp ect t h at , like m an y p at ien t s, farm ers m ay eit h er ign o re t h e ad vice o f t h eir con su ltan ts an d “self-m edicate,” a p rocess sim ilar to th at of th e ram p an t an d u n n ecessary u se o f an t ib io t ics fo r m an y d iseases in t h e Un it ed St at es. Th e o p p o sit e effect m igh t also h o ld t ru e—farm ers m ay n o t fin ish t h eir cycle o f p est icid e ap p licat io n s (sim ilar t o t wo year o ld s wh o will n o t t ake t h eir last dose of am oxicillin )—th u s con tribu tin g to resistan ce bu ildu p cau sed by ch em ical u n d eru se, an effect th at m ay be exacerbated by both en viron m en tal an d p rice con cern s. In eit h er case, agricu lt u ral co n su lt an t s h ave an im p o rt an t ro le t o p lay in th e m an agem en t of p esticide resistan ce, an d on e cou ld easily im agin e ben eficial co o rd in at io n effo rt s t aken acro ss farm s an d regio n s t h at m igh t sign ifican tly lower th e resistan ce bu ildu p .

350 • Chapter 12: Industrial Organization and Institutional Considerations

Conclusion Ou r ch ap ter su ggests th at th e m ain lin e of research on th e econ om ics of p esticide resistan ce h as been rath er n arrow an d too h eavily dep en den t on th e logic an d m ain an alysis o f t h e eco n o m ics o f n o n ren ewab le an d ren ewab le resou rces. It ch allen ges th e m ain resu lt of th is literatu re, n am ely, th at resistan ce p ro vid es in cen t ive t o o verap p ly p est icid es, wh ich creat es resist an ce bu ild u p . Th u s, th e p olicy im p lication of th e trad ition al an alysis is th at in terven t io n is n eed ed t o red u ce ap p licat io n levels t o slo w p est icid e resist an ce bu ildu p . We in trodu ce a n ew con cep tu al fram ework an d in stitu tion al eviden ce from th e field to dem on strate th e com p lexity of th e relation sh ip am on g in cen tives, p esticid e ap p lication s, an d resistan ce bu ild u p . Fu rth erm ore, we in d icate th at in m an y sit u at io n s, t h ere m ay b e an u n d erap p licat io n o f p est icid es. It is im p ortan t for p olicym akers to be able to d istin gu ish between circu m stan ces an d to focu s th eir effort again st resistan ce bu ildu p th at occu rs wh en th ere are in cen tives to overap p ly p esticides. We in trod u ce n ew con sid eration s in evalu atin g resistan ce bu ild u p at th ree levels. First , at t h e field level, we argu e t h at t h e d yn am ics o f p est icid e u se m u st take in to accou n t both th e dyn am ics of th e overall p est p op u lation s an d th e dyn am ics of resistan ce bu ildu p . Th e existin g literatu re con siders on ly th e dyn am ics of resistan ce bu ildu p , wh ich ten ds to bias th e resu lts toward th e trad ition al con clu sion of overap p lication of p esticid es. Plau sible situ ation s can exist in wh ich ign orin g th e dyn am ics of p op u lation bu ildu p m ay actu ally lead to u n derap p lication of ch em icals. Th u s, to assess th e overall effect of growers wh o m ay ign ore dyn am ic im p lication s of p esticide ap p lication , th e im p act of th eir ch oices on resistan ce an d overall p op u lation s m u st be in corp orated. Fu rth erm ore, we argu e th at farm ers’ p esticide ch oices are affected by oth er factors beside resistan ce con sideration s. W h en exam in in g th e im p act of in divid u al beh avior on p esticid e resistan ce an d p est p op u lation d yn am ics, oth er factors, in clu din g altern ative ch em icals, IPM, crop rotation , an d th e like, m u st be taken in to accou n t Ou r ch ap ter fu rth er su ggests th at a correct an alysis of p est resistan ce p roblem s m u st con sider aggregate decision s regardin g p esticide p ricin g an d overall su p p ly an d th at th ese d ecision s are affected by th e stru ctu re of th e in d u stry, p ro p ert y righ t s, an d p at en t co n sid erat io n s. Man u fact u rers will likely h ave a m on op oly on th e p rod u ction of n ew p esticid es d u rin g th e life of th e p aten t, wh ich will p rovid e th e in cen tive to u n d erap p ly th em relative to th e op tim al solu tion . Fu rth erm ore, m an u factu rers are con cern ed with th e n egative sid eeffect s o f resist an ce b u ild u p b ecau se o f it s im p act o n fu t u re sales an d t h eir rep u tation . Th u s, th ey m ay be actively in volved in activities to red u ce resistan ce bu ild u p . In d eed , we p resen t evid en ce o f m an u fact u rer in vo lvem en t in

Chapter 12: Industrial Organization and Institutional Considerations • 351

resistan ce m an agem en t an d resistan ce p reven tion . We also sh ow th at m an u factu rers’ in cen tive to con trol resistan ce m ay be weaker th an is socially desirab le b ecau se o f t h e lim it at io n o f a p at en t ’s life an d b ecau se m an u fact u rers con sider on ly th e im p act on th eir sales rath er th an on social welfare. In ad d ition , we su ggest th at m an u factu rer’s in cen tives th at resu lt in p esticid e su p p ly an d p ricin g, as well as actu al in volvem en t in resistan ce con trol, will likely lead t o o verap p licat io n o f p est icid es b y m yo p ic farm ers as t h e ch em icals get older an d th e su p p ly n etwork becom es m ore com p etitive. Th ere are several old p esticid es (m ostly organ op h osp h ates or carbon ates) th at h ave lon g been u sed becau se of a lack of sign ifican t resistan ce bu ildu p p oten tial or th e existen ce of effective resistan ce m an agem en t sch em es. Pest m an agem en t agen cies sh o u ld b e esp ecially aware o f p o t en t ial p ro b lem s wit h fairly n ew ch em icals on ce th e in itial p aten t p eriod lap ses, th e p rovision of th e ch em icals in creases, or th e in itial m an u factu rer d oes n ot get very in volved in th e p rod u ct stewardsh ip . We also argu e th at, in addition to th e m an u factu rers an d u sers of th e p esticid es, o t h er eco n o m ic agen t s, in p articu lar p esticid e ad visors an d exten sion sp ecialist s, also are in vo lved in p est co n t ro l d ecisio n s. Ext en sio n an d esp ecially in d ivid u al con su ltan ts h ave th e in cen tive to red u ce resistan ce bu ild u p an d im p ro ve t h e p erfo rm an ce o f p est co n t ro l agen t s. O u r an alysis su ggest s th at th e n etwork of econ om ic agen ts con cern ed abou t an d in volved in d ecisio n s regard in g p est m an agem en t an d co n t ro l o f resist an ce bu ild u p is q u it e co m p lex. Even if in d ivid u al gro wers m ay n o t b e co n cern ed wit h resist an ce an d p op u lation dyn am ics issu es wh en ap p lyin g p esticides, oth er agen ts affectin g th eir decision s m ay h ave th ese issu es in m in d. In addition to con cep tu al m odels an d sim p le econ om etric an alysis of p esticid e u se levels, m o re em p irical st u d ies are n eed ed . Th ese st u d ies sh o u ld b e based o n u n d erst an d in g t h e basic st ru ct u ral an d in st it u t io n al relat io n sh ip s, t h e at t it u d es o f vario u s agen t s t o p est co n t ro l ch o ices, an d t h e ext en t t o wh ich t h ey h ave in feren ce o n t h ese ch o ices. Fu rt h erm o re, p o licy an alyses affectin g resistan ce sh ou ld be in tegrated an d com bin ed with p olicy an alyses ad d ressin g oth er sid e-effects of p esticid es, in p articu lar, h u m an an d en viron m en tal h ealth .

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Appendix: Chemical Companies’ Choices and Resistance Th is ap p en dix p rovides th e m ath em atical detail of th e m odel described in th e secon d h alf of th e ch ap ter. We con sider a case in wh ich th e p est p op u lation is ren ewed every seaso n an d resist an ce is t h e o n ly d yn am ic variab le t h at ch an ges over tim e. We also assu m e th at th e in du stry con sists of m an y sm aller farm s an d th u s resistan ce con trol does n ot affect farm er beh avior. At p eriod t, th e in verse dem an d fu n ction for p esticides is W t = W t D ( Pt , X t , Rt )

(A1)

wh ere Pt is th e price of th e crop to be grown , X t is pesticide u se, an d Rt is resistan ce in p eriod t. W t is dem an d at tim e t. Th is dem an d cu rve in creases in ou tp u t p rice, ∂W D / ∂Pt > 0; d ecreases with aggregate p esticid e u se, ∂W t D / ∂X t < 0; an d decreases with resistan ce, ∂W D / ∂Rt < 0. W h en p est icid es are relat ively n ew, t h e m an u fact u rer’s p at en t gives it m o n o p o ly p o wer, wh ich also d ep en d s o n t h e availab ilit y o f su b st it u t es. Ch em icals m ore th an 20 years old are p rodu ced by com p etitive (or sem icom p etitive) in du stries.

354 • Chapter 12: Industrial Organization and Institutional Considerations

We will con sider th e beh avior of a m on op olistic m an u factu rer. It will m axim ize exp ected p rofits su bject to resistan ce con strain t, Rt +1 − Rt = g ( X t , Rt ) − ψ ( Rt )

(A2)

wh ere g(X t , Rt ) is t h e resist an ce bu ild u p fu n ct io n t h at in creases in ch em ical u se ∂g/ ∂X > 0 an d th e p est vu ln erability recovery is ψ(Rt ). For sim p licity, we assu m e lin earity, bu t p op u lation gen etics m ay req u ire a m ore com p lex stru ctu re (see, for exam p le, Laxm in arayan an d Sim p son , 2002). However, th is sp ecification will n ot affect th e resu lts h ere. Th e cost fu n ction of th e m an u factu rer is given by C(X t ), an d m argin al cost C′(X t ) is p ositive an d in creases, C ′( X t ) > 0 , C ′′( X t ) > 0 Th u s, th e op tim al p rodu ction ch oice p roblem is

∑ βt [W t D (Pt , X t , Rt )X t − C ( X t )] T

m ax Xt

(A3a)

t =0

wh ere th e tim e h orizon T den otes th e en d of th e p aten t’s life, su bject to Rt +1 − Rt = g ( X t , Rt ) − ψ ( Rt ), t = 0 ,1 ... T

(A3b)

Th e Lagran gian for th is p roblem is T

L = m ax X t ,µt

[

∑ βt [W t D (Pt , X t , Rt )X t − C ( X t )]

t =0

]

+ µt R t +1 − Rt − g ( X t , Rt ) + ψ ( Rt )

(A4)

wh ere µt is th e tem p oral sh ad ow cost of resistan ce. Th e first-ord er con d ition s to th is op tim ization p roblem are ∂L ∂W t D ∂C ∂g = − µt = 0,t = 0,T Xt + W tD − ∂X t ∂X t ∂X t ∂X t ⎡ ∂W t D ⎡ ∂L ∂g ∂ψ ⎤ ⎤ t −1 X t − µt ⎢1 + = βt ⎢ − ⎥ ⎥ + µt −1 β = 0 , for t = 0 , T ∂Rt ∂ ∂ ∂ R R Rt ⎦ ⎥⎦ ⎢⎣ t t ⎣

(A5)

(A6)

an d R0 = 0. We also assu m e µT = 0 b ecau se, aft er p erio d T , t h e p at en t h as lap sed an d m on op oly p ower an d extra p rofit disap p ear. Con dition A5 su ggests th at at th e op tim al p esticide p rodu ction level, m argin al reven u e,

Chapter 12: Industrial Organization and Institutional Considerations • 355

MRt =

∂W t D Xt + W tD ∂X t

is eq u al t o t h e m argin al co st o f p ro d u ct io n p lu s resist an ce co st , MRC t = µt [∂g(X t , Rt )/ ∂X t ], th at is, MRt = MCt + MRCt

(A7)

Figu re 12-3 d ep icts op tim al d eterm in ation of p esticid e p rod u ction by th e m an u factu rers as well as oth er ou tcom es. Th e m an u factu rers’ op tim u m occu rs at A an d resu lts in u ser p rice W A an d q u an tity X A . If th e m an u factu rers ign ore resist an ce, t h e o p t im al o u t co m e co u ld be X B > X A . If t h e m an u fact u rers are co m p et it ive an d ign o re resist an ce, t h e o u t co m e is at C. Th e eq u at io n o f m otion of th e sh ad ow p rice µt is d erived from Eq u ation A6 to sh ed ligh t on th e beh avior of MRC t . From Eq u ation A-6 an d β = 1/ (1 + r), on e obtain s µt − µt −1 =

⎡ ∂g ∂W t D ∂ψ ⎤ − X t − µt ⎢ ⎥ + r µt −1 R Rt ⎦ ∂Rt ∂ ∂ t ⎣

(A8)

Th e differen ce in µt – µt – 1 is th e ch an ge in cost from delayin g th e m argin al expan sion of resistan ce from period t – 1 to period t. Th e delay h as several effects: • ∂W / ∂Rt rep resen ts red u ction in cost becau se of lower resistan ce d am age in p eriod t. • –µt [(∂g/ ∂Rt ) – (∂ψ/ ∂Rt )] rep resen ts th e effect of d elay from exp an d in g resistan ce or resistan ce growth . It is n egative if th e m argin al growth of resistan ce ∂g/ ∂Rt is greater th an th e m argin al growth in p est vu ln erability ∂ψ/ ∂Rt . • rµt – 1 rep resen ts th e adju stm en t from u sin g tem p oral sh adow p rices. It is an in t erest gain asso ciat ed wit h d elay co st . W h en resist an ce b u ild u p is fast an d t h e first effect is d o m in an t , t h e sh ad o w co st o f resist an ce st o ck d eclin es. Th is is reason able becau se µT = 0, wh ich reflects ou r assu m p tion th at n o extra p rofits are earn ed on ce th e p aten t exp ires. As t h e valu e o f µt d eclin es o ver t im e, an d assu m in g t h at ∂g/ ∂Rt d o es n o t drastically in crease, we exp ect MRCt to declin e over tim e, an d th e redu ction in p esticid e p rod u ction by th e m on op olist (relative to X B) becau se of resistan ce con sid eration s will also d eclin e over tim e. Th at su ggests th at th e m on op olist resistan ce con trol effort in gen eral will declin e as th e p rodu ct m atu res. To assess th e m on op olist’s ch oice again st th e social op tim u m , let u s derive t h e so cial o p t im alit y co n sid erat io n . If t h ere are o t h er ext ern alit y co n sid eration s, th e social welfare op tim ization p roblem is

356 • Chapter 12: Industrial Organization and Institutional Considerations

m ax Xt

∞

⎡Xt

⎤

t =0

⎣0

⎦

∑ βt ⎢⎢ ∫ W t D (Pt , xt , Rt )dx − C ( X t )⎥⎥

(A9)

su bject to Eq u ation A3b an d given R0 , wh ere Xt

D ∫ W t ( ⋅ ) dx 0

is t h e gro ss ben efit o f farm ers fro m u sin g t h e ch em ical. If t h e o p t im izat io n p roblem can be solved by a Lagran gian tech n iq u e, let th e sh adow p rice of th e eq u ation of m otion be den oted by µt 0 . Th e optim ality con dition determ in in g ou tpu t u n der th e optim al solu tion is W tD −

∂C ∂g − µt0 =0 ∂X t ∂X t

(A10)

wh ich can be rewritten as W t D = MCt + MSRt

(A11)

wh ere MSRt is th e m argin al social sh adow cost of resistan ce, wh ich is differen t t h an MRC t , t h e m o n o p o list ’s sh ad o w co st o f p o llu t io n . Th u s, at t h e so cial op tim u m , th e d em an d p rice is eq u al to th e m argin al cost of p rod u ction p lu s resistan ce cost. It follows th at th e op tim al social q u an tity is sm aller th an X C bu t m ay be greater th an X A if at X A

W

D

+ MRSt < W

D

−

∂W D X t + MRCt ∂X t

(A12)

As Eq u ation A12 su ggests, u n less society’s m argin al resistan ce cost is m u ch h igh er t h an a m o n o p o ly’s an d so cial o p t im u m is at D, t h e m o n o p o ly will likely p rodu ce less p esticide th an is socially optim al.

Commentary

Strategic Issues in Agricultural Pest Resistance M anagement R. David Simpson

B

o t h “Th e In t eract io n o f Dyn am ic Pro blem s an d Dyn am ic Po licies: So m e Eco n o m ics o f Bio t ech n o lo gy” b y Tim o Go esch l an d Tim o t h y Swan so n (Ch ap ter 11) an d “In du strial Organ ization an d In stitu tion al Con sideration s in Agricu ltu ral Pest Resistan ce Man agem en t” by Jen n ifer Alix an d David Zilberm an (Ch ap t er 12) d eal wit h wh at o n e m igh t call “st rat egic” asp ect s o f p est resist an ce m an agem en t . Th ey co n sid er h o w t h e act io n s o f firm s p ro vid in g n ew p ro d u ct s an d t h e in t eract io n s b et ween firm s seekin g t o d evelo p n ew p rod u cts affect th e n atu re of p rod u cts d evelop ed , th eir u se, an d th e role for p u blic regu lation of su ch p rodu cts. Th e two con tribu tion s take differen t exp osit io n al ap p ro ach es, h o wever. Go esch l an d Swan so n st ru ct u re t h eir ch ap t er arou n d a m ath em atical m od el of n ew biotech n ology p rod u ct d evelop m en t. Alt h o u gh Alix an d Zilberm an p resen t so m e fo rm al m o d elin g in a t ech n ical ap p en dix, th e m ain th ru st of th eir exp osition is m ore discu rsive. Th ey p resen t an exten sive discu ssion of a n u m ber of scien tific, in stitu tion al, an d econ om ic factors th at affect th e u se of p esticid es an d th e con seq u en t evolu tion of p est resist an ce. In t h is resp ect , t h e ch ap t ers are co m p lem en t ary. Go esch l an d Swan son d elve d eep ly in to th e sp ecifics of a sp ecialized , bu t n on eth eless illu m in at in g, m o d el. Alix an d Zilb erm an p resen t a wealt h o f “o n -t h e-gro u n d ” detail. Th e Goesch l an d Swan son con tribu tion m igh t best be su m m arized by referen ce to its term in ology of “creative” an d “adap tive” destru ction . Th e form er refers to th e ten d en cy of on e in n ovation to d isp lace an oth er as rivals in th e tech n ology sector seek to in trodu ce n ew p rodu cts an d p rofit from th e m on op oly ren ts th e p ossession of a su p erior p rodu ct p rovides. Th is p h en om en on h as • 357 •

358 • Commentary: Strategic Issues in Agricultural Pest Resistance M anagement

been m u ch stu d ied in econ om ics, from th e sem in al con tribu tion s of Josep h Sch u m p eter (1943), wh o coin ed th e term “creative d estru ction ,” th rou gh th e m o re recen t ad van ces o f Ph ilip p e Agh io n an d Pet er Ho wit t (1992). Go esch l an d Swan son layer a con cern with “adap tive destru ction ” wrou gh t by biological ad ap tation on top of th e “creative d estru ction ” occasion ed by in d u strial com p etition . Adap tive destru ction arises from selection . Th e in trodu ction of a n ew p esticide, for exam p le, p laces selection p ressu re on th e organ ism s again st wh ich it is targeted. Th ose few th at are gen etically favored su rvive in disp rop ortion ate n u m bers, cau sin g resistan t organ ism s to becom e in creasin gly com m on in th e gen eral p op u lation . Th e ren ts th e su p p lier of a n ew p esticide earn s are eroded as th e p rodu ct’s effectiven ess declin es an d in cen tives rise for oth er research ers to su p p ly m ore effective p rod u cts. Th e au th ors, borrowin g a p h rase from th e biological literatu re, ch aracterize th e situ ation as a “Red Qu een ” gam e. As in Alice in W onderland, on e m u st ru n faster an d faster to rem ain still becau se th e biological lan dscap e is itself racin g by. Two im p o rt an t im p licat io n s can b e d rawn fro m Go esch l an d Swan so n ’s an alysis. Th e first is t h at t h e p at en t syst em m ay be in effect ive in p ro vid in g in cen tives for ad van ces in biotech n ology. Th e p rotection of a 17-year p aten t is of little valu e for a p rod u ct wh ose effective life sp an m ay be con sid erably sh orter. Th e in ad eq u acies of th e p aten t system h ave lon g been th e su bject of eco n o m ic in vest igat io n (Sch u m p et er 1943). It is n o t su rp risin g t h e au t h o rs con clu d e th at it is in ad eq u ate in th is con text—alth ou gh th ey d o id en tify in “adap tive destru ction ” a n ovel m ech an ism . W h ile th e au th ors em p h asize th e sh ortcom in gs of p aten ts in th eir an alysis an d co n clu sio n s, I fin d a p o in t o ver wh ich t h ey glo ss rat h er q u ickly m o re co m p ellin g. Th e su p p ly o f in n o vat io n s is n o t fixed . It d ep en d s o n t h e resou rces allocated to th e research sector. Th ese resou rces m ay in clu d e th in gs su ch as m an u fact u red cap it al an d t rain ed research ers, bu t t h ey also in clu d e n atu ral p rototyp es. Th e p rod u cts of biotech n ology are, alm ost by d efin ition , d erived fro m n at u ral bio t a. It st an d s t o reaso n , t h en , t h at t h e m o re n at u ral b io t a are m ain t ain ed , t h e m o re o p t io n s t h ere are fo r n ew p ro d u ct d evelo p m en t. Th is su bject h as been th e top ic of som e p rior in vestigation (Sim p son et al. 1996; Rau sser an d Sm all 2000), bu t Goesch l an d Swan son offer a n ew an d im p ortan t p ersp ective on th e m atter. Previou s in vestigation s h ave p resu m ed th at th e d em an d for n ew p rod u cts arises exogen ou sly. As Goesch l an d Swan son sh owed, h owever, th e dem an d for n ew p rodu cts m ay dep en d im p ortan tly on th e m an agem en t of existin g on es. (In th is resp ect, th e au th ors’ referen ce to recen t work by Martin Weitzm an [2000] is also germ an e. Weitzm an relates th e likelih ood of catastrop h ic failu re to th e diversity of th e agricu ltu ral base). Th e Alix an d Zilb erm an ch ap t er co n t rib u t es a n u m b er o f in t erest in g in sigh ts. Let m e begin with a few th at com p lem en t th e Goesch l an d Swan son

Commentary: Strategic Issues in Agricultural Pest Resistance M anagement • 359

an alysis n icely. First, Alix an d Zilberm an p resen t an exten sive an d en ligh ten in g d iscu ssio n o f several st rat egies availab le fo r resist an ce m an agem en t . Alt h o u gh Go esch l an d Swan so n fo cu s o n t h e d evelo p m en t o f p ro d u ct s d e n ovo, an d m u ch of th e existin g literatu re con cen trates on refu ge areas (largely b ecau se t h is is t h e st rat egy ad o p t ed b y t h e U.S. En viro n m en t al Pro t ect io n Agen cy (EPA) in its m an agem en t of bioen gin eered Bt crop s (see Hu rley et al. 1997; Laxm in arayan an d Sim p son 2000, 2002), Alix an d Zilberm an also d iscu ss p ractices su ch as in tegrated p est m an agem en t, crop rotation , an d p recision tech n ologies th at can accom p lish th e sam e goal. Th is reviewer feels con sid erab le sym p at h y 1 wit h Go esch l an d Swan so n in t h e n eed t o st rip an an alytical m od el d own to its bare essen tials to obtain tractable resu lts. Even Alix an d Zilberm an h ave faced th is n ecessity in con stru ctin g th e m od el p resen ted in th eir ap p en dix. Havin g said th is, h owever, on e wou ld su rely wan t to con sid er th e broad er m an agem en t strategies Alix an d Zilberm an d iscu ssed in m akin g p olicy ch oices. Th eir ch ap ter p rovid es an excellen t overview of th ese op tion s. A secon d com m on th em e in th e two ch ap ters con cern s th e role of p aten ts. Goesch l an d Swan son focu s on th e lim itation s of p aten t p rotection in p rovidin g in cen tives for n ew biotech n ology p rod u ct d evelop m en t. Alix an d Zilberm an co n sid er t h e ro le o f p at en t s in t h e m o re gen eral co n t ext o f resist an ce m an agem en t. Th ey p oin t to a straigh tforward bu t very im p ortan t in sigh t: a m an u factu rer’s in cen tive to m an age resistan ce to its p rod u ct d ep en d s on its m ain t en an ce o f a m o n o p o ly p o sit io n in t h at p ro d u ct . Nat u rally en o u gh , th en , th e p u rveyor of a bran d-n ew p esticide wou ld h ave a stron g in cen tive to m ain tain its fran ch ise by p reven tin g th e evolu tion of resistan ce. Con versely, as p aten t exp iration loom s, th e m an u factu rer m ay care little for m ain tain in g th e lon g-term efficacy of its p rod u ct. As Alix an d Zilberm an n oted , h owever, p aten t exp iration d oes n ot n ecessarily im p ly th e aban d on m en t of all in vestm en t s in co n t in u ed efficacy. Even t h e m an u fact u rer o f a p ro d u ct wh o se ch em ical com p osition will soon p ass in to th e p u blic d om ain m ay h ave som e in cen tive to m ain tain th e valu e of its bran d an d , m ore gen erally, th e rep u tation of its com p an y, by m ain tain in g th e efficacy of th e p rodu ct. Alix an d Zilberm an ask th e righ t q u estion s con cern in g th e basis for p u blic p olicy in terven tion regardin g resistan ce. In a world in wh ich th e adop tion of Bt crop s rem ain s far from u n iversal, critics m igh t take excep tion to th e refu ge req u irem en ts th at EPA h as an n ou n ced. Alix an d Zilberm an raise cru cial issu es of tim in g an d m obility (on th e latter q u estion , see also Secch i an d Babcock, Ch ap ter 4). If farm ers can ch an ge crop s wh en resistan ce d evelop s, or largely “reap wh at th ey sow” from p ests th at rem ain close to h om e, th e extern ality argu m en t th at p resu m ably m otivates regu lation is at least redu ced. Perh ap s th e m ost com p ellin g argu m en t th at th e costs of resistan ce will be in t ern alized wit h in t h e p rivat e sect o r is, as Alix an d Zilb erm an co n sid er in

360 • Commentary: Strategic Issues in Agricultural Pest Resistance M anagement

som e detail, th at a m on op olist in a p esticide h as an in cen tive to p reserve th e valu e of its m on op oly. Th e m on op olist can , th en , by settin g th e p rice of th e p ro d u ct o r t h e co n d it io n s o f it s u se, d et erm in e it s ad o p t io n an d h en ce, t h e rate at wh ich resistan ce d evelop s. As th e au th ors n ote, th ese m otives m ay be atten u ated by th e im p en din g exp iration of th e p aten t. As th ey also n ote, h owever, th e m on op olist h as a sort of “bu ilt-in ” con servation ist ten den cy. Becau se a m on op olist ch arges a p rice in excess of m argin al cost (h owever th e m argin al cost m ay be con stitu ted between cu rren t p rodu ction an d distribu tion an d discou n ted resistan ce costs), it will su p p ly less to th e m arket th an wou ld a com p etitor. Th is is th e essen ce of Bu ch an an ’s classic (1969) argu m en t, alth ou gh work don e on exh au stible resou rces dem on strates th at on e m u st be carefu l in its ap p lication to dyn am ic settin gs (Stiglitz 1976). Alix an d Zilberm an h ave don e a won derfu l job of layin g ou t th e issu es, an d in th e p rocess, th ey h ave sketch ed a rich agen d a for fu rth er research . An y or, on e m igh t h op e, all of th e top ics th ey h ave in trodu ced m ay be th e su bject of m ore in ten sive exp loration . Th ere are clear an d im p ortan t p olicy im p lication s o f su ch research . Th e cen t ral issu e rem ain s t h e ro le o f p u b lic regu lat io n o f biotech n ology an d resistan ce, bu t su bjects su ch as in n ovative activity, m arket p ower, firm s’ ability to d eterm in e th e u se of th e p rod u cts th ey sell, m obility am on g p est p op u lation s, refu ges, an d th e role of in tegrated p est m an agem en t an d p recision tech n ologies are cen tral to th e resolu tion of th at issu e.

References Agh io n , P., an d P. Ho wit t . 1992. A Mo d el o f Gro wt h t h ro u gh Creat ive Dest ru ct io n . Econom etrica 60(2): 323–51. Bu ch an an , J.M. 1969. Extern al Disecon om ies, Corrective Taxes, an d Market Stru ctu re. Am erican Econom ic Review 59: 174–77. Hu rley, T.M., B.A. Babcock, an d R.L. Hellm ich . 1997. Biotechnology and Pest Resistance: An Econom ic Assessm ent of Refuges. Am es, IA: Cen ter for Agricu ltu ral an d Ru ral Develop m en t, Iowa State Un iversity. Laxm in arayan , R. an d R.D. Sim p son . 2000. Biological Lim its on Agricu ltu ral In ten sification : An Exam p le from Resistan ce Man agem en t. Discu ssion Pap er 00-43. Wash in gton , DC: Resou rces for th e Fu tu re. ———. 2002. Refu ge Strategies for Man agin g Pest Resistan ce in Tran sgen ic Agricu ltu re. Environm ental and Resource Econom ics 22: 521–36. Rau sser, G.C., an d A.A. Sm all. 2000. Valu in g Research Lead s: Bio p ro sp ect in g an d t h e Con servation of Gen etic Resou rces. Journal of Political Econom y 108(1): 173–206. Sch u m p et er, J. 1943. Capitalism , Socialism , Dem ocracy. Lo n d o n : Un win Un iversit y Books. Sim p son , R.D., R.A. Sedjo, an d J.W. Reid. 1996. Valu in g Biodiversity for Use in Ph arm aceu tical Research . Journal of Political Econom y 104: 163–85. St iglit z, J. 1976. Mo n o p o ly an d t h e Rat e o f Ext ract io n o f Nat u ral Reso u rces. Am erican Econom ics Review 66(4): 655–61.

Commentary: Strategic Issues in Agricultural Pest Resistance M anagement • 361 Weitzm an , M.L. 2000. Econ om ic Profitability vs. Ecological En trop y. Quarterly Journal of Econom ics 115(1): 237–63.

Note 1. Th is co m m en t at o r also sh o u ld ackn o wled ge t h at h e h as m o t ivat ed t h e h igh ly sch em at ic m o d els h e an d h is co lleagu e h ave p ro d u ced (Laxm in arayan an d Sim p so n , 2000, 2002) with th is argu m en t.

Index

Abatem en t fu n ction s, dam age con trol agen ts, 139–40, 142 refu ge zon es as “care” in m odel, 263–64, 273–82, 283–85, 289–92 See also Refu ges Adap tation (biological), 295–99, 302, 304–8, 312–13, 321–22 See also Biological in n ovation Adap tive destru ction , 299, 306, 357–58 Addition al n et ben efits, 214–15, 219–21, 231–32 op tim al levels, 222, 224f, 226–30, 235–36 Agricu ltu ral con su ltan ts, 331, 348–49 Agricu ltu ral in n ovation . See Biotech n ology in n ovation Agricu ltu re. See Farm in g; Pesticides; Produ ctivity Agrobiotech n ology. See Biotech n ology in n ovation Alleles, su scep tible vs. resistan t p ests, 105–8, 187 Allergic reaction s, Bt crop s, 212–13 Allocation of resou rces com p etitive vs. op tim al, 268–70, 288–92 im p act of p esticide taxation , 341–42 for p rivate vs. social in vestm en ts, 311–22

for p rodu ction vs. reserves, 293–95, 300–301, 307–14, 358 Am oxicillin , 64, 126–27, 128t An im al feed, u se of an tibiotics, 11 An tibiotics in an im al feed, 11, 135 for ear in fection s, 125–31 effectiven ess, as a n atu ral resou rce, 4–5, 34–35, 43–44 h eterogen eity of treatm en t, 65–68, 69–74 m ath em atical an alysis of u se, 45–61 resistan ce, 9, 295–96 ben efit–cost an alysis, 3–4, 6, 44–46, 48–50, 76–82, 90–92 caused by tran sgen ic crops, 216, 217 fitn ess costs of, 17–19, 20, 23–25, 26, 29, 77 im p act of m arket stru ctu re, 283 im p act on dem an d, 119–25, 127–31 m easu rin g costs, 134–36 m odel of en dogen ou s resistan ce, 67–69 See also Gen etic resistan ce; Resistan ce “Ap p rop riability” effect (biotech n ology in n ovation ), 314–15 Assu m p tion s abou t p est resistan ce variables, 113–15, 244, 246–47

• 363 •

364 • Index Atrazin e, xv, 172–75 Bacillus thuringiensis (Bt). See Bt crop s Bacteria, 21–25, 28–29, 78–79 Ban n in g p esticides, 172, 174–75, 342 Bayer Corp oration , 346–47 Bellm an ’s Prin cip le of Op tim ality, 30–31 Ben eficial organ ism s, dep letion from p esticide u se, 142–43, 145, 212 Ben efit–cost an alysis, 182, 308 com m ercialization of Bt corn , 201t, 211–13 estim atin g an tibiotic ben efits, 135–36 GMOs, 146, 149, 150–54 in fection con trol, xiii, 6 irreversible costs an d ben efits, 215–29, 231–32 p olicy im p act, 226–30, 232 of op tion th eory, 184–86, 195–96, 200–203, 214 resistan ce m an agem en t strategies, 162–63 tran sgen ic crop s, 214–32, 238–47 treatm en t an d an tibiotic resistan ce, 3–4, 6, 44–46, 48–50, 76–82, 90–92 See also Costs; Treatm en t (an tibiotics), costs Ben om il (fu n gicide), 336 Bias, 123–24, 150 Bioen gin eered Bt corn seeds, as p rodu ction in p u ts, 263–64, 273–82, 283–85, 288–92 Biological in n ovation , resistan ce as, 293–300, 304–5, 308–9, 311–14, 317–19, 321–22 See also Adap tation (biological); Biotech n ology in n ovation ; Tech n ological in n ovation Biologists an d econ om ists, 113, 115, 238–40, 247, 257 Biotech n ology in n ovation im p act assessm en t of, 145–54 in term ediate goods sector in , 299–303, 309–10 m arket m odel lim itation s, 145–47 m arket stru ctu re effects, 263–85, 357–60

p rodu ction (fin al goods) sector in , 299–304, 306–8 su rp lu s, 145, 147, 191–93, 201t u tility fu n ction s, 305–6 welfare effects, 294–95, 305–9, 311–22 See also Biological in n ovation ; Bt crop s; Firm s; Gen etically m odified organ ism s (GMOs); Tech n ological in n ovation ; Tech n ology; Tran sgen ic crop s Bipolaris m aydis (fu n gu s) in vasion (U.S., 1970), 248–49 Birds, im p act of p esticides, 212 Black–Sch oles form u la, 190–91, 198 Bon h oeffer m odel, 20–21 Broad-sp ectru m an tibiotics, 120, 126, 128t, 129 Brown ian m otion , 189, 190, 193–94, 221–22 Bt crop s bioen gin eered Bt corn seeds, 263–64 con trol altern atives, 340 corn com m ercialization decision s, 184–86, 191–203 econ om ic stu dies, 147–48, 191–203, 211–13 p est refu ges, xiv–xv, xvi, 11–12, 94–110 resistan ce to Bt, 151, 186–88 U.S. distribu tion of Bt corn , 98f, 99f See also Biotech n ology; Corn ; Gen etically m odified organ ism s (GMOs); Tran sgen ic crop s “Bu sin ess-stealin g” effect (biotech n ology in n ovation ), 314, 315 Care. See Abatem en t Certification of agricu ltu ral con su ltan ts, 349 Ch ildren , ear in fection s, 119–20, 125–29 Ch oice m odels, an tibiotic dem an d, 122–23 Ch oice of an tibiotics. See Dem an d, for an tibiotics Ch oke p rices, resou rce dep letion , atrazin e, 173–74 Civil society, con cern s abou t GMO risks, 138–39, 148–49, 215

Index • 365 Clin ical treatm en t gu idelin es, 64–67 Cobb–Dou glas (C–D) fu n ction s, p rodu ctivity m easu rem en t, 139–40 “Collateral cost” effect (biotech n ology in n ovation ), 315, 316 Collective action . See Regu lation Com m ercialization of Bt corn , econ om ic an alysis, 184–86, 191–203, 211–13 Com m on p rop erty an tibiotics, 7 gen etic resistan ce, 263–85, 288–92 p est su scep tibility, 143, 145, 166, 333–35 Com m u n ication am on g discip lin es econ om ists an d biologists, 113, 115, 238–40, 247, 257 sim u lation m odels as aid to, 88–89 Com p arative statics for decision m akin g p rocesses, 311–13 for firm s, 275–77 See also Static an alysis Com p etition between in du stries, 294–95, 298–99, 330–31, 343–46 See also Con tests Com p etition , im p erfect, 289–90 Com p etitive allocation , 268–69 Com p etitive eq u ilibriu m . See Eq u ilibriu m Com p lem en tarity of in p u ts, 276–77 Com p lian ce, as factor in resistan ce m an agem en t, 110 Com p u ter sim u lation m odels for in terdiscip lin ary com m u n ication , 88–89 Con fiden ce in tervals, an tibiotic m arket sh are, 130 Con gestion an alogy, 85–87 Con servation of resou rces an d decision m akin g, 163–67, 175–76 See also Reserves (biological) Con stan t varian ce rate, 221 Con su ltan ts, agricu ltu ral, 331, 348–49 Con su m er su rp lu s. See Su rp lu s Con tests biological vs. tech n ological in n ovation , 293–99, 302, 304–8, 311–13, 318–22

See also Com p etition ; In n ovation , rates Con tin gen t claim an alysis, release of tran sgen ic crop s, 231–32 Con tractin g over, m on op oly, 271–72, 279–80, 282 Con trol agen ts, Darwin ian selection , 1–2 Con trols (treatm en t regim es), 26–29, 32–36 Con ven ien ce yield, as discou n t rate, 225–27 Corn Bt vs. con ven tion al p rodu ction , 193–203 p est m an agem en t, 94–110, 172–75, 187 Sou th ern corn leaf bligh t (U.S., 1970), 248–49 See also Bt crop s Cost–ben efit an alysis. See Ben efit–cost an alysis Cost-effectiven ess an tibiotics, 64–67, 72–73 See also Effectiven ess, of an tibiotics an d p esticides Costate variables. See Sh adow p rices Costs of crop p rotection , 4, 158–60, 165, 167–75, 181 of in trodu cin g n ew p rodu cts, 3–4, 9 irreversible, 248–49 in ben efit–cost an alysis, 214–32, 242 in regu latory decision m akin g, 184–85, 188–90 p esticide ap p lication , 336–37 See also Ben efit–cost an alysis; Extern alities; In cen tives; Margin al costs (MC); Prices; Treatm en t (an tibiotics), costs; Welfare effects Creative destru ction m odel, 294, 298–99, 302, 304, 306, 357–58 Critical valu es, release of tran sgen ic crop s, 240, 243 Crop advisory certification p rogram s, 349

366 • Index Crop p rotection costs. See Costs, of crop p rotection Crop rotation , 113–15, 172–75, 338–39 Cu m u lative p robability distribu tion , GMO ben efits, 152–54 Dam age con trol factors, 139–40, 143, 145, 148, 153–54 Dam age fu n ction s, Eu rop ean corn borer, 101–2 Darwin ian selection , 1–2 Data collection GMO stu dy gu idelin es, 150–51 p recision tech n ologies for p est con trol, 339–40 DDT, resistan ce as added in cen tive to ban , 182 Decision m akin g com m ercialization of Bt corn , 184–86, 192–203 op tion th eory, 188–91, 192–203 p esticide p rodu ction , 354–56 p esticide u se, 163–67, 331–40, 350–51 R&D in vestm en ts, 309–13, 316–19, 321–22 release of tran sgen ic crop s, 218–25, 231–32 Degradation of n atu ral resou rces. See Natu ral resou rces, dep letion from p esticide u se Dem an d for an tibiotics, im p act of resistan ce, 119–25, 127–31 elasticity, agricu ltu ral in n ovation , 145 See also Factor dem an d Dep reciation of Bt corn effectiven ess, 195–96 “Differen tial in tern alization ” of extern alities, 315, 318 Dim in ish in g retu rn s, treatm en t ben efits, 32 Discou n ted p resen t valu e. See Presen t valu e (PV) Discou n tin g atrazin e resistan ce, 174, 175t con ven ien ce yield, 225–27 cu re vs. in creased resistan ce, 50–51 disease in ciden ce, 33–34

own discou n t rate, 307–8, 310, 315 p rivate vs. social in vestm en ts, 319–20 risk-free rate of retu rn , 230 Disease ecology, 77–81, 248–52 Distribu tion al effects. See Welfare effects Doctors. See Op tim al treatm en t; Ph ysician s; Treatm en t (an tibiotics) Drift rate, 221, 226–28 Dru g p rices, 120, 124, 126–29 Dru g treatm en t regim e sch em atic, 22f Dyn am ic an alysis of an tibiotic treatm en t, 30–32, 87–90 farm p rodu ction m odels, 100–105 Ear in fection s (otitis m ed ia), xv, 119–20, 125–31 Econ om ic m odels vs. ep idem iological m odels, 6–7 an tibiotics, 32–33, 44, 79–80 tran sgen ic crop s, 238–40, 253–54, 257 Econ om ics ap p lication to GMOs, 145–54 ap p lication to p olicy design , xvii–xviii, 1–12 n atu ral resou rces an d p esticides, 142–45 p rodu ctivity m easu rem en t, 137, 139–40, 149–51 risk redu ction in p est con trol, 141–42 th resh olds for u sin g GMOs, 160 th resh olds for u sin g p esticides, 101, 337 See also Resou rce econ om ics Econ om ists an d biologists, 113, 115, 238–40, 247, 257 Ecosystem com p lexity, an d GMOs, 158–60 Effectiven ess of an tibiotics an d p esticides, 2, 7–9, 65, 216, 217, 265–66 See also Cost-effectiven ess of p esticides in Bt corn , 194–96 an d firm in cen tives, 343–46 in flu en ced by u sage, 349 refu ges, 94–110 Efficien cy of factor m arkets, 280–82

Index • 367 Elasticity of dem an d, agricu ltu ral in n ovation , 145 Em p irical m odels an tibiotic dem an d, 123–25 com m ercialization of Bt corn , 199–202 En dogen ou s an tibiotic resistan ce, 65–69, 72, 74 En viron m en tal extern alities. See Extern alities EPA. See U.S. En viron m en tal Protection Agen cy (EPA) Ep idem iological m odels Bon h oeffer m odel, 20–21 “ecological” vs. in terven tion ist strategies, 21–25 vs. econ om ic m odels, 6–7 an tibiotics, 32–33, 44, 79–80 tran sgen ic crop s, 238–40, 253–54, 257 SIS (su scep tible→in fected→ su scep tible) m odel, 42–43, 77–81 Eq u ilibriu m of bacteria p op u lation s, 23–25, 29, 35 com p etitive vs. op tim al, 269–70, 277–82, 291–92 valu e of treatm en t rate, 38–41 Escalator an alogy (tech n ological p rogress), 296, 322 Eu rop ean corn borer, 94–110, 113, 115, 147, 187, 191 Exp ectation s of decision m akers, 166 of tech n ology, 176 Exp en se ratios, fertilizer vs. p esticides, 168–71 Exp en sive treatm en ts as social ben efit, 65–67 Exp ort m arket, gen etically m odified organ ism s (GMOs), 97 Extern alities dep letion of ben eficial organ ism s, 142–43, 145 dru g resistan ce costs, 43–44, 70–72 gen etic resistan ce, 267–68, 277–79, 283–85, 289–92 of GMOs, 149, 151–53 an d p aten t system s, 314–16

of p est m an agem en t, 5, 96–97, 100, 138, 162–64, 341–43 treatm en t h om ogen eity, 63–67, 73–74 See also Costs; Private vs. social costs; Risk; Welfare effects Factor d em an d , 268–72, 276, 279, 282, 284 Factor p rodu ctivity, bioen gin eered Bt corn , 291–92 Factor su p p ly m arket, for bioen gin eered seeds, 278–82 Farm accou n tan cy n etwork database (Germ an y), 167–72 Farm size, 334, 336, 349 See also Field size; Patch size Farm in g Bt crop s an d resistan ce m an agem en t, 94–110 organ ic, im p act of Bt crop s on , xvi, 95, 186 p esticide u se an d resistan ce, 5, 11–12, 172–76, 289–91, 330–43, 348–49 p rodu ctivity of tran sgen ic crop s, 217, 219–20 su stain able agricu ltu re, 162 Fertilizer, u se tax, 160 Fertilizer, vs. p esticides, exp en se ratios, 168–71 Field size, 166–67 See also Farm size; Patch size Fin al goods (p rodu ction ) sector, 299–304, 306–8 Firm s com p arative statics for, 275–77 m argin al reven ues (MR) of, 271–72, 275 op tim ization for, 274–75 Pigovian taxation of, 270, 272, 277–79, 280, 284 p rofit fu n ction s of, 268, 271, 274–76 resistan ce m an agem en t in cen tives for, 343–48, 350–51, 353–56 See also Biotech n ology in n ovation ; In du strial organ ization ; Tech n ological in n ovation Fitn ess costs of an tibiotic resistan ce, 17–19, 20, 23–25, 26, 29, 77

368 • Index op tim al p ath s with an d with ou t, 30f, 31f Fu n ction al form s in du ced evolu tion fu n ction , 304–5 in n ovation , 317–18 p rodu ctivity m easu rem en t of p esticide u se, 140 Fu n gicide Resistan ce Action Com m ittee (FRAC), 348 Fu n gicides, 336, 337–38 Fu n gu s in vasion by Bipolaris m aydis (U.S., 1970), 248–49 Gam e th eory. See Con tests; “Red Qu een ” con tests (tech n ological p rogress) Gen e flows, tran sgen ic crop s, 215–16 Gen etic resistan ce as com m on p rop erty, 263–64, 266–67, 288–92 extern alities, 267–68 h istory, 264–66 m odel with abatem en t, 273–82 m on op oly effects, 279 See also Resistan ce Gen etically m odified organ ism s (GMOs) an d ecosystem com p lexity, 158–60 exp ort m arket, 97 lesson s of p esticide econ om ics, 137–39, 145–54 resistan ce, 151–52, 184–86 risk, 141–42, 145, 153–54, 158–60, 184–88, 191–203 risk p ercep tion , 138–39, 148–49, 215 See also Biotech n ology; Bt crop s; Resistan ce; Tran sgen ic crop s Geograp h ic in form ation system s (GIS), 340 Geom etric Brown ian m otion , 189, 190, 193–94, 221–22 Germ an y, case stu dies in econ om ic p esticide resistan ce, 161–76 Global Crop Protection Federation (GCPF), 347, 348 GMOs. See Gen etically m odified organ ism s (GMOs) Govern m en t in terven tion . See Regu lation

Grids, Bt an d n on -Bt crop s, 104–5 Gross m argin s, tran sgen ic crop s, 216–17, 219–20 Ham ilton ian , 26, 36–37, 47–50, 51 Han d-wash in g by m edical staff, as in fection con trol, xiii, 6, 35 Hardy–Wein berg p rin cip le, 96, 100 Health services. See An tibiotics; Op tim al treatm en t; Treatm en t (an tibiotics) Herbicide Resistan ce Action Com m ittee (HRAC), 347–48 Herbicides vs. in secticides, cost in creases, 181 Hessian fly, p est m obility, 114 Heterogen eity in p est resistan ce, 248–54 of treatm en t (an tibiotics), 65–68, 69–74 High dose strategies, p est con trol, 95–96, 187, 340 High way con gestion an alogy, 85–87 Hom ogen eity, treatm en t (an tibiotics), 9, 63–67, 73–74 Hosp ital-acq u ired in fection s, costs, 3–4 Hu m an allergen icity, Bt crop s, 212–13 Hu rdle rates, release of tran sgen ic crop s, 225, 226–27 Im p erfect com p etition , 289–90 In cen tives, 176 for develop in g n ew p rodu cts, 2, 7–10 for doctors an d p atien ts, 10, 65–66 for farm ers to m in im ize resistan ce, 11–12, 175–76, 330–43, 350–51 to m axim ize valu e of existin g p rodu cts, 2, 4–7 of p aten t system s, 293–95, 309–22, 330–31, 343–46, 350–51, 354–56 for tech n ological in n ovation , 293–95, 301, 311–16, 322 See also Costs; Ren ts In du ced evolu tion fu n ction , 304–5 In du strial in n ovation . See Biotech n ology in n ovation ; Tech n ological in n ovation In du strial organ ization im p act on an tibiotic resistan ce m an agem en t, 283

Index • 369 im p act on gen etic resistan ce m an agem en t, 263–64, 273–82, 288–92 im p act on p est resistan ce m an agem en t, 330, 342–51, 353–60 m arket stru ctu re com p arison , 273f, 281 th eory, 298–99 See also Firm s; Mon op oly In eq u ity. See Welfare effects In fection con trol, xiii, 6, 35 In fection dyn am ics, 44–45 econ om ic m odels, 26–30, 45–54, 55–61 ep idem iological m odels, 21–25, 252–54, 256f sin gu lar an d op tim al p ath s, 51–53 SIS m odel, 42–43 In form ation gath erin g. See Data collection In n ovation , 244 an d adap tive destru ction , 304–5 an d creative destru ction , 302, 304 rates, 311–13, 318–22 See also Biological in n ovation ; Biotech n ology in n ovation ; Con tests; Tech n ological in n ovation In sect release an d recap tu re stu dies, 109–10, 115 In secticide Resistan ce Action Com m ittee (IRAC), 347 In secticides, vs. h erbicides, cost in creases, 181 In stitu tion s. See Regu lation In tegrated p est m an agem en t (IPM), 337–38 In tellectu al p rop erty righ ts. See Paten t system s In terdiscip lin ary com m u n ication econ om ists an d biologists, 113, 115, 238–40, 247, 257 sim u lation m odels as aid to, 88–89 In terior solu tion s, op tim al dru g com bin ation s, 69–70 In term ediate goods sector, 299–303, 309–10

In tern alization of extern alities, 315, 318, 359–60 In tern ation al Grou p of Nation al Association s of Man u factu rers of Agroch em ical Produ cts. See Global Crop Protection Federation (GCPF) In trin sic valu e of op tion to release tran sgen ic crop s, 219 In vasion , by p ests, 248–56 In vestm en ts. See Allocation of resou rces; Decision m akin g Iowa, fertilizer u se tax, 160 IPM. See In tegrated p est m an agem en t (IPM) Irreversibility in ben efit–cost an alysis, 214–32, 242 p est resistan ce n ot in evitable, 248–49 in regu latory decision m akin g, 184–85, 188–90 Liberalization of m arkets an d farm p rice risk, 230 Life cycle of p rodu cts, 345–46 Lim itation s of m arket m odels, 145–47 Lin ear con trol p roblem s, 26–27, 36–41 Log-lin ear econ om etric m odels, growth rate of p esticide u se, 168–69 Logit m odels, 120–25, 127–29 Maize. See Bt crop s; Corn Man u factu rers. See Firm s Margin al costs (MC), 343–45, 354–55 allocation to R&D, 308 in m on op oly p ricin g, 278–79, 282, 283–85, 289–92 of p esticide resistan ce, 333 See also Costs Margin al p rodu ctivity, 274, 276–77, 279, 281, 290–92 Margin al reven u es (MR), 271–72, 275, 279, 280, 343–45 Margin al social dam age (MD). See Welfare effects Marker gen es, in tran sgen ic crop s, 216 Market m odels, lim itation s, 145–47 Market p en etration . See Market sh are Market sh are of an tibiotics, 120–25, 129–30

370 • Index of Bt crop s, 94–110 Market stru ctu re. See In du strial organ ization ; Mon op oly Marku p , m on op oly p ricin g, 278–79, 281, 284 Marsh allian op tim ality, 222–24 Math em atical disease m odels. See Ep idem iological m odels Math em atical m eth ods ap p lied to an tibiotic u se, 45–61 Maxim al tolerable irreversible costs, 225–29, 230–32, 242 Maxim ization strategies in crop p rotection , welfare effects, 167–72, 175–76 Maxim u m likelih ood estim ation , an tibiotic dem an d, 125, 129 Mean -revertin g p rocess, for m odelin g addition al n et ben efits, 222, 244 Measu rem en t of an tibiotic resistan ce costs, 134–36 of crop p rotection costs, 167–72 of p rodu ctivity with p esticide u se, 137, 139–40, 149–51, 167–68 Mech an ical p est con trol p ractices, 338 Medical treatm en t. See Op tim al treatm en t; Treatm en t (an tibiotics) Metap op u lation . See Pop u lation dyn am ics Meth yl brom ide, 341 Mixed m u ltin om ial estim ates, 127–29 Mixed-p olicy of an tibiotic u se. See An tibiotics, h eterogen eity of treatm en t Mobility, Eu rop ean corn borer, 94–110 Models. See specific types of m odels Mon itorin g pest population s, 337, 339–40 Mon ocu ltu re an d p est in vasion , 248–49 Mon op oly, 357–60 bioen gin eered seeds, 263–64, 278–82, 283–85, 288–92 con tractin g over, 271–72, 279–80, 282, 285 con trol of in p u ts, 270–72 extern alities, 267–68 h ealth care, 283 p aten t righ ts, 309–12, 316, 343–46, 354–56

p ricin g, 288–92 m argin al costs (MC), 278–79, 282, 283–85, 289–92 m arku p , 278–79, 281, 284 See also In du strial organ ization Mon san to, 285, 347 Mu ltin om ial m odels, an tibiotic dem an d, 122–23, 124–25, 127–29 Mu ltip liers, p recau tion ary. See Precau tion ary p rin cip le Mu ltip liers, u ser costs of dru gs, 70 Myop ic beh avior. See Private vs. social costs Nation al Allian ce of In d ep en d en t Crop Con su ltan ts, 349 Nation al Am bu latory Medical Care Su rvey (NAMCS), 125–27 Natu ral resou rces dep letion from p esticide u se, 142–45, 158–60, 165, 168–76 See also Resou rce econ om ics Net ben efits (release of tran sgen ic crop s). See Addition al n et ben efits Net p resen t valu e. See Presen t valu e (PV) Non ren ewable resou rces. See Natu ral resou rces; Resou rce econ om ics Op tim al allocation , 269–70 Op tim al eq u ilibriu m . See Eq u ilibriu m Op tim al levels addition al n et ben efits, 222, 224f, 226–30, 235–36 refu ges, 107, 109 Op tim al treatm en t an tibiotic h eterogen eity, 65–67, 69–74 ben efit–cost an alysis, 44–45, 80–82 ep idem iological vs. econ om ic m odels, 44, 79–80 for m an agin g an tibiotic resistan ce, 25, 26–30, 32–36, 39–41 m ath em atical an alysis, 45–61 p olicy vs. im p lem en tation , 84–87 See also Ph ysician s; Treatm en t (an tibiotics) Op tim ality con dition s, 220, 222–24, 343–45, 356

Index • 371 See also Marsh allian op tim ality Op tim ization of an tibiotic an d p esticide u se, 19–21 for farm ers, 332–35 for firm s, 274–75, 343–45, 354–56 real op tion s, 189–91 software, 88–89 of treatm en t cost p aram eters, 34 of treatm en t regim es, 35–36 Op tion th eory, 184–86, 188–91, 192–203 See also Ration al op tion s; Real op tion s Op tion valu e defin ed, xvi in release of tran sgen ic crop s, 217–24, 230, 235–36, 240–43 Organ ic farm in g, im p act of Bt crop s on , xvi, 95, 186 Otitis m edia (ear in fection s), xv, 119–20, 125–31 Own discou n t rate, 307–8, 310, 315 Param eters, ben efit–cost an alysis, tran sgen ic crop s, 244, 246t Patch size an d p est in vasion , 253 See also Farm size; Field size Paten t system s, xvii, 7–9, 288, 354–56, 358–60 in cen tives of, 293–95, 309–22, 330–31, 343–46, 350–51 See also In du strial organ ization ; Resistan ce m an agem en t Path dep en den ce, ch em ical p esticides, 142–43 Path ogen s. See Bacteria; Pests Patien ts. See Ch ildren ; Op tim al treatm en t; Treatm en t (an tibiotics) Pen icillin resistan ce, 120 Percep tion of GMO risk, 138–39, 148–49, 215 Persisten ce (p est in vasion ), 248–49, 254 Pest con trol costs. See Costs, of crop p rotection Pest refu ges. See Refu ges Pest su scep tibility to p esticides. See Su scep tible vs. resistan t p ests Pesticides, 184–86 efficacy, 101, 105–8

vs. fertilizer, exp en se ratios, 168–71 in teraction with n atu ral resou rces, 142–45, 158–60, 165, 168–76 m easu rem en t of p rodu ctivity with p esticide u se, 137, 139–40, 149–51, 167–68 regu lation , 95, 159–60, 174–76, 341–43 an d risk redu ction , 141–42 Pests alleles, 105–8, 187 con trol altern atives, 337–41 m obility, 94–110, 113–15, 338–39 sim u lation m odels, 100–105 resistan ce as biological in n ovation , 293, 295–300 in Bt corn , 186–88, 194–99 econ om ic stu dies, tran sgen ic crop s, 240–47 ep idem iological p ersp ective, 238–40, 247–57 farm -level factors, 336–41 as irreversible cost, 215–18 regu latory factors, 341–43, 359–60 resou rce econ om ics ap p lied to, 161–76, 331–32, 340 as stock variable, 332–35, 338–39 See also Gen etic resistan ce; Resistan ce Ph arm aceu tical in du stry, 295–96, 298 Ph ase sp ace diagram s, 23–25, 28f, 29, 33f Ph ysician s ch oice of treatm en t, 63–67, 73–74, 119–31 en forcin g p olicy, 87 See also Treatm en t (an tibiotics) Pierce’s disease, 341 Pigovian taxation , 270, 272, 277–79, 280, 284 Plan n in g, tim e h orizon s, 197–99 Plan t breedin g, 296, 298, 299–300 Poisson p rocesses freq u en cy of in n ovation , 302, 304 p est resistan ce, 195–96 selection p ressu re, 304–5 Policy design , 225–27, 242–43

372 • Index ap p lication of econ om ic p rin cip les to, xvii–xviii, 1–12 an d ben efit–cost an alysis of tran sgen ic crop s, 226–30, 242–43 an d op tim al treatm en t, 84–87, 91–92 an d resou rce con servation , 175–76 See also Decision m akin g; Regu lation Pon tryagin op tim ality, 26, 37–38, 88 Pop u lation dyn am ics of p ests, 100–108, 239, 248–49, 252–57, 332–35, 336–39 Precau tion ary p rin cip le, 150–54, 190–91, 242 defin ed, 185 m u ltip liers, 193–96, 202 Precision tech n ologies for p est con trol, 339–40 Preferen ce for an tibiotics. See Dem an d, for an tibiotics Prescrip tion s. See Ph ysician s Prescrip tive u se of GMOs, 159 Presen t valu e (PV), 79–80 in allocation of resou rces, 307 eq u ation derivation , 325–26 ben efit–cost an alysis, 188–90 Bt an d n on -Bt crop s, 105, 193–96, 200–203 of costs of resistan ce, 174 “Crystal Ball” sim u lation s, 211–13 op tion th eory, 193–96, 197–99 Prices, an tibiotics, 120, 124, 126–29 Pricin g, m on op oly. See Mon op oly, p ricin g Private vs. social costs in cen tives, 2, 309–19, 321–22, 333–35, 343–48, 350–51 of m edical treatm en t, 66–67, 68–69, 73–74, 87, 88 p esticide resistan ce, 162–64, 167–72, 174–75, 288–92, 331 See also Extern alities; Welfare effects Probability den sity, p est resistan ce, 195–96 Probability distribu tion , in n ovation an d adap tation , 306 Produ cer op tim ization , 274–75 Produ cer su rp lu s. See Su rp lu s

Produ ct life cycle an d firm in cen tives, 345–46 Produ ction (fin al goods) sector, 299–304, 306–8 Produ ction fu n ction s, 139–40, 142–44, 300–301 Produ ction in p u ts, 268–73 bioen gin eered Bt corn seeds, 273–82 Produ ction vs. reserves, allocation of resou rces, 293–95, 307–11 Produ ctivity an d tech n ological p rogress, 305 See also Factor p rodu ctivity; Margin al p rodu ctivity; Welfare effects Produ ctivity m easu rem en t an d GMOs, 147–48, 149–51 m odelin g of crop yields an d p rices, 221 with p esticide u se, 137, 139–40, 142–45, 167–68 Profit fu n ction s, 268, 271, 274–76 Prosp ect th eory, 141 PV. See Presen t valu e (PV) Pyreth roids, 331, 346 R&D (research an d d evelop m en t), 295–96, 298–304, 306–7, 309–19, 346–48 Ran dom -effect regression m odels, determ in an ts of p esticide u se, 169–72 Ran dom n u m bers, p esticide resistan ce, 100–101 Ran dom -p aram eters m u ltin om ial logit m odels, 124–25 Rate of in n ovation . See Con tests; In n ovation Rate of retu rn , release of tran sgen ic crop s, 227f, 228, 229f Ration al op tion s, 189, 190–91 an d tran sgen ic crop p olicy, 196–99, 241f with u n certain ty variables, eq u ation s, 207–10 See also Op tion th eory Real op tion s, 188–90 an d tran sgen ic crop p olicy, 193–96, 217–18, 222–23, 231–32, 241f

Index • 373 with u n certain ty variables, eq u ation s, 206–7 See also Op tion th eory “Red Qu een ” con tests (tech n ological p rogress), 296, 298, 307, 358 Referen ce system s, for GMO ben efits, 138, 147, 148, 149, 154 Refu ges, 94–110, 187, 212 op tim al levels, 107, 109 as p rodu ction in p u t in m odel, 274–82 regu latory p olicy, xiv–xv, xvi, 11–12, 94–97, 110, 229–30 See also Abatem en t; Reserves (biological) Regression an alysis, determ in an ts of p esticide u se, 169–72 Regu lation GMOs, 184–86, 191–203 p est con trol, 95, 174–76, 334–35, 359–60 See also Policy design Ren ewable resou rces. See Natu ral resou rces; Resou rce econ om ics Ren ts im p act of m arket stru ctu re, 270–71, 280, 283–85, 288–92 in n ovation in cen tives, 299, 310–12, 316–17 See also In cen tives Research an d develop m en t. See R&D (research an d develop m en t) Reserves (biological), 295–96, 298, 302–3, 311–14, 316–21 See also Con servation of resou rces an d decision m akin g; Refu ges; Su stain ability Resistan ce as biological in n ovation , 293–300, 304–5, 308–9, 311–13, 317–19, 321–22 as dep reciation , 195–96 tim e for th e ap p earan ce of, 297t See also Adap tation (biological); An tibiotics, resistan ce; Gen etic resistan ce; Gen etically m odified organ ism s (GMOs), resistan ce; Pests, resistan ce; Resistan ce m an agem en t

Resistan ce m an agem en t, 175–76, 244 Bt crop s, 94–110 Crop rotation , 113–15, 172–75, 338–39 econ om ic strategies, 152–53, 161–76, 180–82 farm er op tim ization , 332–35 im p act of in du strial organ ization , 263–64, 273–82, 288–92, 330, 342–51, 353–60 an tibiotic resistan ce, 283 in cen tives in biotech n ology, 293–95, 311–14, 343–48, 350–51, 353–56 p est con trol altern atives, 337–41 tim e h orizon s, in p lan n in g, 197–99 See also Paten t system s Resou rce econ om ics ap p lied to an tibiotic resistan ce, 18–19, 21, 29, 30–32, 43–44 ap p lied to p est resistan ce, 161–76, 266–85, 331–32, 340 See also Econ om ics; Natu ral resou rces Resou rces, con servation , an d decision m akin g, 163–67, 175–76 Resou rces, degradation . See Natu ral resou rces, dep letion from p esticide u se Reven u e cu rves, fertilizer an d p esticide u se, 143–44 Rh izom an ia (disease) sp read (U.K.), 249–52 Risk, 186 an d decen tralized decision m akin g, 66 of GMOs, 141–42, 145, 153–54, 158–60, 184–88, 191–203 See also Extern alities; Welfare effects Risk-free rate of retu rn , release of tran sgen ic crop s, 228, 230 Risk n eu trality, 190–91, 197–99, 243 Risk p ercep tion of GMOs, 138–39, 148–49, 215 Risk redu ction in p est con trol, 141–42 Rotation of crop s, 113–15, 172–75, 338–39 Sad d le p oin t, social valu e of red u cin g in fection , 50–51 Selection bias. See Bias

374 • Index Selection , p est resistan ce, 1–2, 295–96, 304–5 Sen sitivity an alysis, lim itation s for GMO ben efit calcu lation s, 154 Set-aside p olicies. See Refu ges Sh adow p rices, 26, 48–49, 53–54, 150, 344–45, 354–56 Sh ocks, Eu rop ean corn borer, 100–101, 193–96 Sh owers exp erim en t, p est m obility, 109–10, 115 Side-effects. See Extern alities Sim u lation m odels for in terdiscip lin ary com m u n ication , 88–89 of p est m obility, 100–105 of treatm en t p olicy ch an ges, 90 “Sin gle su p p lier” effect (biotech n ology in n ovation ), 314, 316 Sin gu lar p ath , in fection , 51, 52–53 SIS (su scep tibleÆin fectedÆsu scep tible) m odel, 21, 42–43, 77–81 Size of farm s, 334, 336, 349 of fields, 166–67 p atch size, 253 Social costs. See Extern alities; Presen t valu e (PV); Private vs. social costs; Welfare effects Social discou n t rate. See Discou n tin g Software for op tim ization , 88–89 Sou th ern corn leaf bligh t (U.S., 1970), 248–49 Sp atial grids, Bt an d n on -Bt crop s, 104–5 Sp atial h eterogen eity in p est resistan ce, 248–54 Stabilization (biological resou rces). See Reserves (biological); Su stain ability StarLin k (Bt strain ), 212–13 State eq u ation s, for op tim al treatm en t rate, 38–41 Static an alysis, 84–87, 191–92 See also Com p arative statics Steady state an tibiotic u se, 46–47 level of in fection , 50–53 p est resistan ce, 195–96 stock of an tibiotic resistan ce, 29

stock of in fected in dividu als, 23–25 Stoch astic p rocesses Bt corn , 194–95, 198–99 determ in istic vs. stoch astic m odels, 254–57 Eu rop ean corn borer p op u lation s, 100–101 n et ben efits of tran sgen ic crop s, 220–21 p est in vasion an d p ersisten ce, 248–49 sim u lation m odels, 138, 152–54 Stru ctu re (in du strial). See In du strial organ ization Su bstitu tion of in p u ts, 277, 278–79 Su rp lu s, 280 biotech n ology in n ovation , 145, 147, 191–93, 201t U.S. corn p rodu ction , 211 Su rveys, ear in fection diagn osis an d treatm en t, 125–27 Su scep tible bacteria. See Bacteria; SIS (su scep tibleÆin fectedÆsu scep tible) m odel Su sceptible vs. resistan t pests, 95–96, 216 corn p ests, 187 Hessian fly, 114 as a n atu ral resou rce, 4–5, 100, 137, 142–45, 151 Germ an case stu dies, 161–76 tran sgen ic crop s, 216, 230–32 p op u lation dyn am ics, 100–108, 164–65, 248–49, 332–35, 336–39 Su stain ability, 162, 293–95, 306–9, 321–22 See also Reserves (biological) Switch in g fu n ction s, 26–27, 37–41 Taxation of fertilizer, 160 of p esticide u se, 159–60, 341–42 of tran sgen ic crop s, 230 Tech n ological in n ovation an d biological adap tation , 302, 304–8 com p etition between in du stries, 294–95, 298–99 GMOs an d p esticides, 138–39 in cen tives for, 293–95, 301, 311–16, 322

Index • 375 in R&D, 295–96, 298–300, 302, 304, 307–19 See also Biological in n ovation ; Biotech n ology in n ovation ; Firm s Tech n ology, 319–20 in crop p rotection , 165, 176, 191–92 an d p rodu ctivity, 171, 305, 306–8 Tem p oral h eterogen eity in p est resistan ce, 248 Tim e-attribu te in teraction s, in an tibiotic dem an d m odels, 124 Tim e h orizon s, in p lan n in g, 197–99 Tim in g of in n ovation , 302, 304 of p esticide ap p lication , 337–38, 340 release of tran sgen ic crop s, 214–15, 219–22, 224–32 Tragedy of th e com m on s. See Com m on p rop erty Tran sgen ic crop s, 191–92, 214–15 irreversible costs an d ben efits, 215–29, 231–32 m eth odological ap p roach to ben efit–cost an alysis, 218–24, 238–47 p olicy im p act on decision to release, 226–30, 232, 242–43 an d u n certain ty, 225–29, 240, 242–44, 247, 249 See also Biotech n ology; Bt crop s; Gen etically m odified organ ism s (GMOs) Treatm en t (an tibiotics) costs, 34, 48–51, 69–72, 79–80, 119–25, 130–31 m easu rem en t, 134–36 with m u ltip le dru g resistan ce, 43 p rivate vs. social op tim u m , 65–67 See also Costs; Op tim al treatm en t h om ogen eity, 9, 63–67, 73–74 strategies, 21–25, 32–36 Un certain ty abou t ben efits of resistan ce strategies, 162

abou t GMOs, 138–39, 225–29, 240, 242–44, 247, 249 with op tion s, eq u ation s, 206–7 in regu lation , 184–85, 187–203 U.S. En viron m en tal Protection Agen cy (EPA), refu ges, xiv–xv, xvi, 11–12, 94–97, 110 User costs, resistan ce an d treatm en t, 70–71 Utility, an tibiotic dem an d m odels, 123–24, 129 Utility fu n ction s biotech n ology in n ovation , 305–6 gain s vs. losses, 141 Valu ation , p u blic h ealth , 79–80 Valu e. See Presen t valu e (PV) Variables, ben efit–cost an alysis, tran sgen ic crop s, 243–44, 245t Varian ce rate, release of tran sgen ic crop s, 226–28 Volatility, op tion th eory, 193–96 Water p ollu tion , from atrazin e, 172, 174–75 Weeds, 215–16 Welfare effects of biotech n ology in n ovation , 294–95, 305–9, 311–22 m argin al social dam age (MD), 269–70, 277–79, 281 of m arket stru ctu re, 281–82, 283–85 of m axim ization strategies in crop p rotection , 167–72, 175–76 of p esticide resistan ce m an agem en t, 174–76, 182 of tran sgen ic crop s, 191–92, 211–13, 219–20 See also Extern alities; Margin al social dam age (MD); Presen t valu e (PV); Private vs. social costs; Risk Wien er p rocess, 221, 244

About the Editor

Ramanan Laxminarayan is a fellow at Resou rces for th e Fu tu re. His research on resist an ce eco n o m ics fo cu ses o n u sin g eco n o m ic an alysis t o d evelo p p o licy resp o n ses t o su ch p ro b lem s as b act erial resist an ce t o an t ib io t ics an d p est resistan ce to p esticides. He is cu rren tly a m em ber of th e Nation al Academ y of Scien ces/ In stitu te of Med icin e Com m ittee on Th e Econ om ics of An tim alarial Dru gs. He h as wo rked wit h t h e Wo rld Healt h O rgan izat io n o n evalu at in g m alaria t reat m en t p o licy in Africa an d was a m em b er o f t h e Wo rld Healt h Organ ization Task Force on Dru g Resistan ce an d Policies in 2000 an d 2001. His o t h er research in t erest s in t egrat e en viro n m en t al q u alit y an d p u b lic h ealth . Cu rren t stu dies in clu de an an alysis of th e h ou seh old econ om ic im p act of tobacco u se in Vietn am , an d an exam in ation of social an d en viron m en tal factors th at in flu en ce th e sp read of in fectiou s diseases with in h ou seh olds an d villages in Cam bodia. Train ed in both econ om ics an d p u blic h ealth , h is research on th e econ om ics of resistan ce h as ap p eared in th e Annals of Pharm acotherapy, Journal of Environm ental Econom ics and Managem ent, Am erican Journal of Agricultural Econom ics, an d Journal of Health Econom ics.

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