Welfare Economics 9780195631036, 019563103X

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OXFORD IN INDIA READINGS

Themes in Economics G eneral E ditors

* Kaushik Basu * Prabhat Patnaik

WELFARE ECONOMICS

Edited by BHASKAR DUTTA

DELHI

OXFORD UNIVERSITY PRESS BOMBAY CALCUTTA MADRAS 1994

Oxford University Press, Walton Street, Oxford 0X2 6DP Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Kuala Lumpur Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland Madrid and associates in Berlin Ibadan

© Oxford University Press 1994 ISBN 019 563103 X

typeset by Urvashi Press, Meerut 250 001 Printed at Rekha Printers Pvt. L td, New Delhi 110 020 and published by Neil O ’Brien, Oxford University Press YMCA Library Building, Jai Singh Road, New Delhi IIP 001

Note from the General Editors As economics advances rapidly and becomes both more mathematical and statistically founded, the need arises to interpret its general prin­ ciples in the context of specific economies. In India, students are taught the latest models but it is usually left to them or the rare teacher to relate the models to the Indian context. The present series is an attempt to rectify this lacuna. Each book in this series presents the latest developments in a field and enunciates these in the context of the Indian economy. The series was conceived with senior undergraduate and post­ graduate students in mind. The aim is to provide accurate and interest­ ing books with contributions from leading economists. While each book has a volume editor, we—the general editors-^work with the volume editors in order to try and maintain some common norms and standards for the series as a whole. Initially there was a third general editor, the late Sukhamoy Chakravarty. He was actively involved in the planning of the first few books in this series; and was a great source of inspiration to us till the last days of his life. Kaushik Basil Prabhat Patnaik

Contents List o f Contributors Introduction B haskar D utta

Market Failure and Information D il ip M o o k h er jee

Efficient Resource Allocation under Increasing Returns Rajiv Vohra

Optimal Taxation and India: A Review of Theory and Applied Work M.N. M urty and Pulin N ayak Price and Quantity Controls: A Survey of Some Major Issues D ebraj R ay and A runava S en Some Non-Welfaristic Issues in Welfare Economics P rasanta K. P attanaik

Name Index Subject Index

Contributors B haskar D utta

Indian Statistical Institute, Delhi D ilip M o okherjee

Indian Statistical Institute, Delhi R a jiv V o h ra

Brown University, USA M.N. MURTY

Institute o f Economic Growth, Delhi P ulin N ayak

Delhi School o f Economics, Delhi D ebraj R ay

Boston University, USA A runava S en

Indian Statistical Institute, Delhi P rasanta P attanaik

University of California, Riverside, USA

Introduction B haskar D utta

Economics has always been concerned with prescriptions for public policy. Any prescription or recommendation of a particular policy must ultimately be based on an assertion that the proposed change will increase the ‘welfare of the society*. Assertions of this nature involve knowledge of two distinctly different kinds. First, how will the pro­ posed policy change affect ‘relevant’ economic variables? Second, how will changes in these economic variables affect social welfare? An answer to the first question is provided by the body of knowledge encompassing positive economics. Welfare economics, on the other hand, is concerned with various aspects of the second question. In particular, what aiy the components of social welfare? What is the meaning of maximizing or even increasing social welfare? Can one formulate (simple) sufficient conditions for an increase in social wel­ fare? A. Bergson’s notion of an (ordinal) social welfare function1 provid­ ed a framework within which various views on social welfare can be accommodated. Let a social state be a complete description of the amount of each type of commodity held by each individual, the amount of labour to be supplied by each individual, the amount of each productive resource invested in each type of productive activity, the structure of rights in society, and so on. In other words, the description of a social state must include eveiy variable which can conceivably affect the community’s welfare. Letting X denote the set of social states, a Bergson social welfare function W assigns a numeri­ cal social utility or welfare, W(x)9 to each social state x in X. The aim of society is then described by saying that it seeks to maximize social ‘See Bergsoo (1938).

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BHASKAR DUTTA

welfare subject to the relevant technological, resource, and institutional constraints.2 Bergson assumed that W(x), the value of social welfare in state x, would ‘depend on all the variables that might be considered as affect­ ing welfare’ (p. 417). Of course, this does not impose any constraint on the functional form of W. The construction of a particular social welfare function must be a normative procedure since it involves making value judgements. For each set of value judgements adopted, a different social welfare function will result. Hence, there is no sense in which the welfare economist can talk of a ‘unique’ or objective social welfare function. Is there a systematic way of choosing a particular Bergson-Samuelson social welfare function? The work of Arrow (1963) can be seen as an attempt at answering this question. Arrow defined a Social Welfare Function—henceforth SWF (to be distinguished from the BergsonSamuelson swf) as a functional relation / specifying one social order­ ing R for any n-tuple of individual orderings {/?,} defined over X.

R -/({*,})

(1)

Note that since the Bergson-Samuelson swf is an ordinal concept, it can be viewed as a numerical representation of a social ordering R. Hence, the Arrow SWF is a function the value of which is a BergsonSamuelson swf. Alternatively, the Arrow SWF is a method of ag­ gregating individual preferences into a social preference ordering. Arrow proceeded to impose seemingly mild conditions that a reason­ able SWF could be expected to satisfy. These conditions are defined below. In these definitions (and subsequently), N - { 1 ,2 ,..., n} is the society. Condition U (Unrestricted Domain). The domain of the SWF in­ cludes all logically possible /i-tuples of individual orderings over X. Condition D (Non-dictatorship). There is no individual i such that for 2Although Bergson introduced the concept of a social welfare function, it was really Samuelson (1947) who investigated the uses to which such a function can be put. Not surprisingly, this concept has come to be known as a Bergson-Samuelson social welfare function.

Introduction all preference n-tuples in the domain x,yEX,xPiy-+xPy.

3

SWF /, for each ordered pair

Condition P (Pareto). For all ordered pairs x , y E X , if for all in­ dividuals i E N 9x P i y - + x P y . Condition I (Independence of Irrelevant Alternatives). For all x ,y E X , for all /t-tuples {/?,} and {/?/}, if for all i E N , xRjy ++xRjy, then x R y ++x R ! y where R -/({/?*}) andR ' -/({/?/}). Arrow proved the following remarkable result. General Possibility Result. If X contains at least 3 distinct states, then there is no SWF satisfying Conditions U, I, P, and D. This basic result has given birth to the field of social choice theory. This literature has explored the possibility of evading the nihilistic conclusion of the General Possibility Result by relaxing the original Arrow conditions. Unfortunately, the basic impossibility result is rem­ arkably robust to such modifications within the traditional Arrovian framework.3 It has been suggested that the main reason for the plethora of impossiblity results in the Arrovian framework is that the framework fails to utilize a great deal of information. First, the traditional Ar­ rovian framework assumes that individual utilities are ordinal and interpersonally non-comparable. Of course, it has been pointed out by Sen (1970a) that allowing for cardinal but non-comparable utilities makes no differences to the basic impossibility result. However, as I will point out later, once the possibility of interpersonal comparability is introduced, several interesting SWFs satisfy suitably modified ver­ sions of the original Arrow conditions. Second, the Arrow framework involves welfarism, thereby ruling out the use of non-utility information. Welfarism means that the social welfare in state x is solely a function of the individual utilities in that state. Hence, social welfare must be identical in social states x and y if both result in the same individual utility distribution. In particular, the process by which individuals derive their utility can have no impact on social welfare. ^ o r excellent accounts of this literature, see Kelly (1978) and Sen (1986).

4

BHASKAR DUTTA

Arrow did not impose welfarism directly. However, Conditions /, P, and U imply a weak version of welfarism. The weaker version of welfarism requires that if individual preference rankings are strict, then any two social states must be ranked entirely on the basis of the individual utilities in the two states. Moreover, the Pareto indifference rule requiring that if all individuals are indifferent between any two states then so must society be, in conjunction with conditions U and / imply welfarism fully.4 The severity of the information restrictions in the Arrovian frame­ work makes it practically useless in analyses of many issues which are of obvious concern to the welfare economist. Consider, for instance, the problem of ranking income distributions in terms of equality. Let X be the set of all possible divisions of a cake of size 100 units between two persons 1 and 2. Individual preference orderings over X satisfy the usual assumption that each person prefers more of the cake to less. Suppose / is an Arrow SWF which in addition to satisfying Conditions / and P, also treats individuals symmetrically. Then, / must declare all divisions of the cake socially optimal so long as the entire cake is distributed.5 In particular, the 50-50 division is declared to be socially indifferent to the 0-100 division. Clearly, / is entirely inadequate in making distributional judgements. It is instructive to look at the role played by the various conditions (in the Arrovian framework) in eliminating the possibility of distribu­ tional judgements. Let x - (50,50), y - (0,100), and z - (49,51). Then the individual rankings must be x P \ zP ^y and yP^zP^x. We cannot say that preferences of 1 for x over y (or of 2 for y over jc) are stronger than l*s preferences for x over z (or of 2 for y over z) because of the ordinal framework. This, in conjunction with prohibition of interper­ sonal comparisons, eliminates the possibility of deriving that the utility gain of 1 in moving from y to x (that is, from 0 to 100) is much larger than the loss of 2 in moving from 100 to 50. Also, welfarism, which is implied by the conditions, means that only individual preferences matter in the social ranking of alternate distributions. As I remarked earlier, the use of interpersonally comparable utilities provides an escape route from the impossibility results. Before review­ 4Pattanaik’s paper in this volume contains a critique of welfarism. 5For a precise statement of a sharper result, see Sen (1973).

Introduction

5

ing some issues relating to the use of interpersonally comparable individual utilities, I will comment on the implication of the Arrow impossibility theorem on the existence of Bergson-Samuelson social welfare functions. It has been claimed by Little (1952) and Samuelson (1967) that impossibility results in the Arrovian framework have no relevance to the existence of Bergson-Samuelson swfs. The Little-Samuelson argu­ ment is based on the role of Condition /. Since the Bergson-Samuel­ son approach assumes that individual tastes are given, conditions of inter-profile consistency such as Condition I cannot be used However, the main contribution of Condition I in the derivation of the Arrow impossibility result is to precipitate welfarism. Note that the so-called ‘individualistic’ version of the Bergson-Samuelson swf makes social welfare a function o f the vector o f individual utilities. In other words, welfarism is almost automatic in the Bergson-Samuelson approach. Consider the following condition which essentially formalizes wel­ farism in the (single-profile) Bergson-Samuelson framework. Condition SPN (Single Profile Neutrality). For any given n-tuple {/?,} of individual preference orderings, for any xyy , z , w E X , if for all i x R i y ++ z R #*w and yR{X *» wRt z, then x R y z R w where

The effect of imposing condition SPN on a social welfare function satisfying the Pareto principle and having a domain with some diver­ sity of preferences is to precipitate a ‘single-profile’ dictatorship result. Thus, there will be some individual j such that all his strict preferences will be reflected in the social preferences for the profile.6 For some profiles, the single-profile dictatorship is not particularly disturbing since the dictator can have the same preferences as everyone else. However, in many other contexts, the nature of the domain may be such that preferences cannot be unanimous. This will be true, for instance, when X is the set of income distribution. And, of course, in all such cases the dictatorship result is just as disturbing in the Bergson-Samuelson framework. Indeed, Rubinstein (1981) contains an *Vbriants of this result have been proved by Parks (1976) and Kemp and Ng (1976), amongst others.

6

BHASKAR DUTTA

analysis of the logical correspondence between impossibility results in the multiple-profile and single-profile frameworks. In a welfarist framework,7 the only way out of the impossibility is to introduce interpersonal comparisons of utility. Robbins (1932), in an influential attack on the possibility of interpersonal comparisons, ar­ gued that such comparisons could not have any descriptive content. He believed that it was impossible to settle differences of views on interpersonal comparisons ‘in a purely scientific manner* and took interpersonal comparisons to be completely normative. Robbins’ criti­ que essentially inspired the belief that welfare economics (and ‘sensi­ ble* economists) should avoid interpersonal comparisons of utility. Indeed, this view persisted for almost 40 years. However, there has been some recent literature which makes systematic use of interper­ sonal comparisons, using various types of interpersonal comparisons to characterize interesting notions of social welfare and justice such as utilitarianism and the Rawlsian maximin role. In an illuminating discussion, Sen (1979a) points out that alternative formalizations of interpersonal comparability are possible, each for­ malization emphasizing different aspects of the problem and suggest­ ing subtle differences in interpretation. In what follows, I will follow the approach of Sen (1970a). Sen’s approach introduces interpersonal comparability within the Arrovian framework. This approach consists of identifying sets of /i-tuples of utility functions which are informationally identical and then insisting that the social welfare function generates the same social ordering for /i-tuples of utility functions which are informationally identical. Each individual has a family of utility functions, the family depending on the measurability assumption about individual utility. For instance, if individual utility is assumed to be ordinal, then each member of a family of utility functions of any person is a positive monotonic transformation of all other members, and the family must include all such transformations. If individual utility is cardinal, then a family of utility functions must be the set of all affine transformations of any member of the family. Given the measurabilty assumption on individual utility, let Lt denote the appropriate family of utility func­ 7Welfarism is a precursor of the Arrovian framework. Indeed, welfarism has been the dominant tradition in welfare economics since Bentham (1789).

Introduction

1

tions over X of individual i. The Cartesian product of the n-tuples of families of utility function {£,-} is the measurability set L - n ”_ iI,-. A comparability set L is a subset of L and represents the set of informa­ tionally identical /i-tuples of individual utility functions. As I have mentioned earlier, interpersonal comparability is introduced by im­ posing an invariance requirement of the social welfare function. The invariance condition requires that for any two /i-tuples {Uj} and {ifi} belonging to the same comparability set !,/({{/,})-/({££}), where / is the social welfare function. I describe below some of the more interesting comparability sets. Definition 1. The comparability set L satisfies each of the following restrictions if for any /i-tuple {l£} E l , it is the case that L consists of exactly all /i-tuples {£/,} such that for some /i-tuple of transformations {%} satisfying the following alternative restrictions, Ut for all i. Ordinal Non-Comparability (ONC). Each tp; is a positive, monotonic transformation. Ordinal Level Comparability (OLC). For all i, ip, - ip, a positive, monotonic transformation. Cardinal Unit Comparability (CUC). Each % is a positive, affine transformation, tp,{ •) - a, + b( •), with b > 0, the same for all i. Cardinal Full Comparability (CFC). Each is a positive, affine transformation, \p, - a + b( •) with b > 0, and a, b being the same for all i. The less precise is the information available, the bigger is the comparability set. And the bigger the comparability set, the more demanding is the invariance requirement. Of the 4 comparability sets defined here, the set corresponding to ONC is the biggest. ONC implies that individual utility is ordinal and interpersonally non-com­ parable. This, of course, is the original Arrovian framework. Since the invariance requirement is the most demanding in this case, the plethora of impossibility results is not surprising. If utilities are ordinal, but

8

BHASKAR DUTTA

utility levels are interpersonally comparable, then the relevant com­ parability set satisfies OLC. When utility levels are comparable, it makes sense to say that ‘individual i is better off in state x than individual j is in state y \ When the comparability set satisfies CUC, then utility gains and losses of different individuals can be compared. Comparability sets satisfying CFC are smaller than sets satisfying ONC, OLC, or CUC. CFC permits comparisons of utility levels as well as of utility gains and losses. The Rawlsian maximin criterion is an example of a social welfare function which satisfies suitably modified versions of Conditions U, I, P, and D if ordinal level comparability is introduced. Notice that the maximin (or its lexicographic version) criterion involves a rank dictatorship since the welfare of a social state can essentially be equated to the utility level of the worst-off individual. Similarly, the maximax (or leximax) involves the dictatorship of the most favourably placed individual. This naturally raises the question whether ordinal level comparability always involves the dictatorship of some rank. Indeed, Gevers (1979) and Roberts (1980) show that if the condition of non-dictatorship is strengthened to anonymity (i.e. symmetry across individuals), then the other Arrow conditions imposed in conjunction with ordinal level comparability will involve rank dictatorship. Thus, it might be argued that though OLC provides an adequate informational basis for avoiding the Arrow impossibility result, it does not really take us very far. The assumption of cardinal individual utilities, together with com­ parability of units (i.e. CUC), provides a richer informational basis. Indeed, utilitarianism, which was a dominant tradition in welfare economics from Bentham (1789) till the nineteen-thirties involves cardinal unit comparability. Under utilitarianism, social welfare in any state is simply the sum of individual utilities in that state. To Bentham, the utility of each individual was an objectively meaningful mag­ nitude. Being a welfarist and also believing that the social welfare function should be symmetric in individual utilities, Bentham arrived at the conclusion that it is the sum-of-utilities criterion which ought to determine social welfare. Of course, the additive form is only one example of a function which is symmetric in its arguments. For example, the Rawlsian

Introduction

9

social welfare function is also symmetric in individual utilities. How­ ever, Benthamite utilitarianism has been resuscitated in alternative ways. For instance, Vickrey (1945) suggested that the von NeumannMoigenstern theory of utility for risk bearing is applicable to the Bergson social welfare function. The criterion of impartiality or sym­ metry was interpreted to mean that the ethical judge should consider himself equally likely to have any position in society. Thus, one decision (social state) would be better than another if the expected utility of the first were higher. The utility function to be used in making the expected utility calculation is the ethical judge’s von Neumann-Morgenstem utility function. Now, since all positions are considered equally likely, expected utility is the same as average utility of all individuals. Hence, maximizing expected utility is the same as maximizing the sum of individual utilities. Harsanyi (1955) contains two essentially independent derivations of utilitarianism. One approach, which is very close to that of Vickrey, equates social welfare of any state as the ‘utility’ of a lottery assigning equal probability of being anyone in that state.8 In the alternative approach, Harsanyi assumes that (a) each individual has a family of cardinal utility functions, (b) the social welfare function is also car­ dinal, and (c) the Pareto indifference rule holds, so that Ut{x) - Ut{y) for all individuals i must imply W(x) - W{y). It then follows that social welfare is a linear weighted sum of individual utilities. n

W(x) - I aiU,{x) for all jc. i-l

(2)

Harsanyi goes on to argue that since each individual’s utility func­ tion is given by a class of positive affine transformations, the units of the individual utility functions can be chosen so that all the coeffi­ cients ai are unity. Equation (2) would then conform to the classical sum-of-utilities criterion. The utilitarian criterion has been used in many areas of public policy, including just taxation (Edgeworth, 1897) and measurement of inequality of income distributions (Dalton, 1920, Aigner and Heins, 1967). In this process, utilitarianism has been labelled an egalitarian *Diamood (1967) provides a critique of the moral acceptability of this approach.

10

BHASKARDUTTA

criterion. This is rather surprising since a criterion which is solely concerned with maximizing the sum of individual utilities is presumab­ ly unconcerned with the interpersonal distribution of utilities. The following argument due to Sen (1973) resolves the apparent paradox and also establishes that in general the utilitarian criterion is far from being an egalitarian criterion. First, note that the optimal distribution of a fixed sum of money according to the utilitarian welfare function must involve equating every individual’s marginal utility of money. In the special case in which everyone has the same utility function, this can only occur at the point where total utilities are equated as well. In general, there is no reason to assume that all individuals have the same utility function. That utilitarianism is not in general particularly egalitarian can be seen from the following example. Suppose we have a two person community consisting of individuals A and B. Assume that individual utilities are cardinal and fully comparable (CFC), so that utility gains and losses as well as levels can be compared. Suppose also that individual A gets twice as much utility as B from -each level of income. In this case, the utilitarian rule would require that person A be given a higher income than B. Clearly, this distribu­ tion of income accentuates the disparity in the utility levels of the two persons because even if income were equally divided, A would have received more utility than B. While strict utilitarianism ignores all considerations of equity, the Rawlsian maximin rule is at the other extreme since it is completely insensitive to the utility levels of anyone other than the worst-off individual. Is it possible to allow for some compromise between equity and the sum-of-utilities criterion? It is easy to incorporate a bias towards equality into the utilitarian-type social welfare function by making social welfare W a strictly concave function of individual utilities. This will then ensure that any averaging of utilities would at the same time reduce disparity and raise social welfare. One particular social welfare function which achieves this is the isoelas­ tic form.

(3)

Introduction

11

In this functional form, ------ is the constant elasticity of substitution 1 -a of an isowelfare contour. If a - 1, then we have the utilitarian form. Strict concavity of the welfare function is ensured for a < 1, while the Rawlsian maximin rule is obtained in the limit as a -* -oo. The class of welfare functions represented by equation (3) is certain­ ly a family of ‘reasonable’ welfare functions. This demonstrates clearly that once the Arrovian framework is enriched by allowing for interper­ sonal comparability, the impossibility theorems can be avoided quite comfortably. However, it should also be clear to the reader that a family of functions such as that represented by (3) is also an embar­ rassment of riches. Each value of a will represent a different social welfare function, and in several contexts, the actual policy prescription will be sensitive to the specific social welfare function. This is par­ ticularly true in the choice of the optimum linear income tax. Stern (1976) shows that the optimum linear tax rate rises markedly for higher values of a. Now, how should the welfare economist choose a specific value of a or a particular social welfare function? Since each social welfare function corresponds to a specific set of value judge­ ments, the choice of social welfare function implies recommendation of a set of value judgements. Unfortunately, there is no ‘objective’ basis for the choice of one set of value judgements in place of another. Not surprisingly, there is considerable support for the point of view that policy prescriptions should be based on value judgements which are widely accepted or non-controversial. Indeed, it is this viewpoint which has made Paretian welfare economics so popular. Paretian welfare economics is based on the (strict) Pareto criterion, which is a stronger version of Condition P. The criterion asserts that if everyone in the society considers social state x to be at least as good as y and at least one person strictly prefersx toy, then the society should declarex to be strictly preferred toy. The set of Pareto ‘optimal’ social states is now identified with those states which are not dominated according to the Pareto criterion. More formally, given any /i-tuple of utility functions u - (uh . . . , uH) the set of Paretooptimal states, P(Xj u) is defined as follows: PQ{, m)- { x E . X \ ^ y E.X such that ut{y) 2 u,{x) for all i E N and ufy) > ufx) for some j E N }

(4)

12

BHASKAR DUTTA ~

In a welfarist framework, it makes sense to insist on Pareto optimality as a necessary condition for social optimality. After all, if non-utility information is judged to be irrelevant in the welfare ranking of alterna­ tive states, then why should social state x be considered socially optimal if everyone prefers another state y to x? Any reasonable social welfare function must declare that social welfare is higher in y than in x. Hence, all welfarists will agree that the Pareto criterion as a rule of dominance involves a very weak value judgement—a value judgement which will be unanimously accepted. Unfortunately, it is the very weakness of the underlying value judgement that renders the criterion practically useless as a tool in the welfare analysis of different policies. This is because it is hard to conceive of a policy which will improve the position of all individuals. Almost all policies will generally make some individuals better off and others worse off, and the Pareto criterion alone can neither recommend nor reject such policies. Gearly, Pareto optimality is a very weak notion of optimality. A striking example of this is provided in the cake division problem where every allocation of the cake is Pareto optimal! The so-called compensation tests, first enunciated by Kaldor (1939) and Hicks (1939), were designed to supplement the Pareto criterion. Suppose a policy change is being contemplated which will mean a movement from state x to state y. If everyone gains from the move­ ment, then the Pareto criterion alone is sufficient to declare y to be better than x. Suppose, however, that some people gain while others lose as a result of the movement. The Kaldor criterion declares y to be socially preferred to x if the gainers can ‘compensate’ the losers and still remain better off. In other words, y is preferred to x according to the Kaldor criterion if it is hypothetically possible to undertake cost­ less or lump-sum redistributions in state y so as to achieve a new state z which is socially preferred to x according to the Pareto criterion. The Hicks criterion is similar but slightly different—y is socially preferred to x if it is not hypothetically possible to carry out lump-sum redistri­ bution in x so as to achieve a state which is Pareto superior to y. There are at least two difficulties with these criteria. First, Scitovsky (1941) pointed out that according to either criterion, one could have a pair of states x and y with x declared to be socially preferred to y and y to be socially preferred to x\ In order to resolve this kind of paradox,

Introduction

13

Sdtovsky suggested a double criterion—a state x should be declared preferred to another state y if both the Kaldor and Hicks criteria aie met. Unfortunately, while the Scitovsky double criterion avoids the paradox of preference reversals over pairs of social states, it does not generate a transitive social preference relation. The second difficulty with the compensation tests lies in the hypo­ thetical nature of the redistribution. Of course, if the redistribution is actually carried out, then the entire exercise would be a simple ap­ plication of the Pareto criterion. However, since the compensation to the losers does not actually have to be made, the equity aspect of the policy change is ignored completely. Suppose, for instance, that in a three-person, one-commodity society, states x and y represent the commodity distributions (3, 3, 3) and (0, 0, 10). Then, y must be socially preferred to x according to the Scitovsky test.9 But, welfare functions which are even slightly sensitive to distribution may well declare x to have a higher social welfare than y. This has prompted economists like Little (1952) to suggest that in order to be declared a welfare improvement, not only must the policy change pass the com­ pensation criteria, but the distribution of income must not have wor­ sened. But, how does one decide whether the distribution has not become more inequitable? For this, one needs a welfare ranking of income distributions. And if such a ranking was available, then there would be no need to use the compensation tests anyway. Moreover, as I have discussed earlier, in a framework where interpersonal utility com­ parisons are ruled out, reasonable welfare rankings do not exist. The central theme in Paretian welfare economics is the relationship between Pareto optimality and the equilibrium of an economy in which resources are allocated through a competitive market or price-guided mechanism. In competitive markets, all consumers and firms are pricetakers, that is, they take decisions on the assumption that their actions will not alter the market prices. A competitive equilibrium is a situation where the individual actions of the different agents are consistent in the sense that the supplies and demands of every commodity and factor match. The relationship between Pareto optimality and competi­ *1 am assuming that individuals prefer more of the commodity to less.

14

BHASKAR DUTTA

tive equilibria is known as the fundamental theorems of welfare economics. I will discuss these theorems in the framework of the classical Arrow-Debreu economy. Let us consider an economy with n consum­ ers indexed by i (i - 1 , . . . , it), m industries indexed by j(j - 1 , . . . , m) and / commodities indexed by k (k - 1 , . . . , I). Assume for conve­ nience that each industry consists of a fixed number of identical firms. Moreover, government policy does not discriminate between firms in the same industry. Therefore, without loss of generality, one can identify an industry with a single firm. The yth firm’s production possibilities are represented by its produc­ tion set Yj C R ;. An element of the set Y \ y J>will be referred to as a production plan for firm j. Some of the / commodities are inputs used by firm j. By convention the components of a production plan y J € YJ which refer to inputs used by the firm, have a negative sign. Assume that Y1 H R i - . In other words, it is impossible to produce any output without using some input. In addition, YJ is assumed to be closed and convex. The ith consumer is characterized by the four-tuple (X \ it, o', &). The set X 1 is the consumer’s consumption set. It is assumed that WtH+QX* C R 7 and that it is closed, convex and bounded from below. An element of the set X 1 will be referred to as a consumption plan of consumer i. The consumer’s preferences are defined by an ordering of the set X \ It is assumed that the ordering can be represented by a continuous, increasing, quasiconcave real valued utility function it \X l -*R . The vector co' is the consumer’s endowment vector. The vector 01E R+ denotes the ith consumer’s share in the profits of each industry. The jth component of & ,0*; is i’s share in the jth industry. Gearly, ? 0® - 1 for ally - 1 , , m. It should be emphasized that these assumptions are standard in traditional general equilibrium ana­ lysis (see e.g. Debreu, 1959). An allocation is a collection of consumption plans j and production plans (y7)/1. i such that

i-l

1

i-1

An allocation ((**)?. i, (y^/L i) is Pareto optimal or efficient if there

Introduction

15

docs not exist another allocation ((*')?. 1, (yOf- 1 ) such that ii(xl) * j ( x l) for all z, and the strict inequality holding for some i\ Loosely speaking, an allocation is efficient if any feasible reorganiza­ tion of production and consumption plans will make at least one consumer worse off. Let p E R ;+ be the prices faced by firms and consumers. The income of a consumer has two components—the value of his endow­ ments evaluated at consumer prices and his profit income. Thus, m

I 1-pw1+ 2 &jp.yj where y * is the production plan of firm j. The consumer solves the following problem: maxy e ^ ‘ U 'tf) subject to px! * I 1. Let (y;)7- 1 ) denote the consumption plan which solves the maximiza­ tion problem. Each firm chooses a production plan in order to maxi­ mize its technological constraints, i.e. firm j solves: maximize p •y J subject to y J E YJ. Let r\ J(p) denote the production plan which solves this problem. A competitive equilibrium is an allocation ((**)?-1, (y7))”- 1) and a price vector such that (i) y 1E r\*(p) for all j - 1 , . . . , m (ii) x l E |*(p, (y;)f. i) for all i - 1 , . . . , n n

A

m

n

(iii) 2 j c '- 2 ) ! i + 2w i. 1-1

1

|-1

At the competitive equilibrium price p, the production and consump­ tion plans chosen by profit-maximizing firms and utility-maximizing consumers ‘match’ perfectly in the sense that all markets clear simul­ taneously. Under the assumptions made here, a competitive equi­ librium always exists (see Debreu,1959 or Arrow and Hahn, 1971). The First Fundamental Theorem of welfare economics states that a competitive equilibrium is Pareto optimal or efficient. Given the per­ missiveness of the Pareto criterion, this is clearly not a very significant result. In particular, this result does not imply that a competitive equilibrium is socially optimal. A competitive equilibrium allocation

16

BHASKARDUTTA

reflects the existing distribution of endowments and profit shares which may be highly unequal. Consider the extreme case where one individual owns all the resources in the economy. The competitive equilibrium allocation must assign all the output in this economy to this individual, whereas an egalitarian government would typically wish to achieve a ‘more equal’ distribution of utilities than the one which obtains under the competitive equilibrium. Suppose the government’s objectives are specified by a (Bergson) social welfare function which satisfies the Pareto criterion. It follows immediately that the socially optimal allocation is efficient. Let this optimal allocation be {(**)?. j, 1 }* Can this allocation be sup­ ported as a competitive equilibrium? The answer to this question is provided by the Second Fundamental Theorem which states that, under the assumptions made so far, any efficient allocation can be supported as a competitive equilibrium provided that the government can levy lump-sum taxes (and subsidies). The following argument provides a heuristic explanation of this important result. Let Y - Y 1 + . . . +Ym. Since each of the W sets are closed and convex, the set Y is also closed and convex. The aggregate m

production plan y - 'Ey* must lie on the boundary of Y; otherwise it i-i would be possible to produce a little more output of some commodity without increasing the use of any input and this would contradict the assumption that the *bar’ allocation is efficient. Since y is on the boundary of Y, we can find a ‘supporting price’p such thatp ' y ' t p ' y for yEY. Observe that at the price p, firms maximize profits by producing ‘bar’ quantities, i.e. p my * p ' y * for all GKJ and all j - 1 , . . . , m. To simplify matters, let us assume that the boundary of Y is smooth, so that the price vector p is unique. Observe also that p must satisfy the following condition: for all i - 1 , . . . , n, U \jt) > U 'ffi implies that p •x 1> p •x \ In other words, if consumer i strictly prefers the consumption plan x l over x \ then the former must cost more than the latter, evaluated at prices p. Suppose that p does not satisfy this condition. This would imply that there exist consumption plans (x*)?. i arbitrarily close to (F)?_ j such that U \x ') > U'Qc') and p •x* * p • x 1

Introduction

17

for all i - 1 , . . . , n. Let y ■

- 2 co', so that p %y * p ' y . It follows i < that by choosing ( it ')?- i sufficiently close to (**)?. i, we can ensure that y E Y, which leads to a contradiction of the assumption that the ‘bar’ allocation is efficient. The argument outlined above is nothing more than a restatement of the classical necessary condition of ef­ ficiency that the marginal rate of substitution in consumption must equal the marginal rate of transformation in production. Suppose prices are p and firm j's production plan is y \ for j = 1, . . . , m. Consumer i ’s income is then p • co* + 2 •y. It is clear from j

earlier arguments that if his income was p •x 1, his optimal consump­ tion plan would in fact be ? . Suppose the government levied a lump-sum tax T* - p • to* + 2 &Jp •y J - p •x*. The consumer would then choose x % . Moreover, £ T' - 0, so that the government budget is / balanced. In other words, the ‘bar’ allocation is a competitive equi­ librium after the lump-sum taxes and transfers have been instituted. This completes the ‘proof’ of the Second Fundamental Theorem. This latter theorem is clearly more basic or fundamental than the First Fundamental Theorem. If real-world economies actually satisfy the conditions of the Arrow-Debreu model and if lump-sum transfers are possible, then it would appear that so long as the society’s ethical objectives are representable by a welfare function satisfying the Pareto criterion, there is very little scope for governmental intervention. The market outcome must be efficient, although not necessarily socially optimal (First Theorem). However, the government can levy appro­ priate lump-sum taxes to guide the economy to the socially optimal allocation (Second Theorem).10 Much of the theoretical debate on issues such as the desirability of planning or the extent of government intervention in the economy has been based on different interpretations of the Arrow-Debreu model and the two fundamental theorems. Proponents of the market mechan­ 10Of course, the applicability of these theorems is not restricted solely to the competitive market mechanism of private ownership economies. Socialist economies can also ‘mimic’ the market mechanism to achieve a social optimum. See, for instance, Lange (1938) and Lemer (1944).

18

BHASKARDUTTA

ism view the Arrow-Debreu model as a reasonably accurate descrip­ tion of real-world economies and then appeal to the fundamental theorems to justify their faith in laissez-faire. Other economists ques­ tion the validity of the Arrow-Debreu model, and hence conclude that the fundamental theorems are largely irrelevant to the ‘market versus government’ debate. This school emphasizes that markets may fail to achieve efficiency for a variety of reasons including externalities in consumption or production, non-convexities, missing markets, and im­ perfect competition. The phenomenon of market failure is then used as a justification for widespread intervention by the government.11 Clear­ ly, the fundamental theorems have been instrumental in promoting a great deal of research in theoretical welfare economics, and it is appropriate that the papers in this volume discuss some of the issues relating to the fundamental theorems and their implications for public policy. In a wide-ranging and elegant contribution, Mookheijee surveys some of the recent extensions of the standard Arrow-Debreu model which have been developed to accommodate externalities, incomplete markets, imperfect information, and transaction-cost based models of non-price institutions. I will mention very briefly a few of the issues discussed by Mookheijee. An important reason for the failure of the market to achieve efficien­ cy is the presence of externalities in production or consumption. Externalities cause a divergence between private and social costs and benefits. Since the agent creating the externality will only take private values into account in choosing his or her optimal action, this diver­ gence leads to market failure. Pigou (1920) suggested a tax or subsidy to bring about the equivalence of private and social values. Since then, several writers, including Arrow (1970) and Coase (1960), have point­ ed out the connection between externalities, incomplete markets, and property rights. Another important extension of the basic Arrow-Debreu model is the literature on markets with incomplete information. While various forms of informational imperfections have been studied, Mookheijee restricts his discussion to models of asymmetric information. Asymmetric innOf course, as Mookheijee points out in the following paper, the various instances erf market failure do not mean that markets fail relative to the government.

Introduction

19

formation can be further subdivided into one of two categories: (i) one side of a transaction has superior information about the ‘quality’ of the good exchanged—for example, the seller of a ‘lemon’ (used car)— usually referred to as adverse selection, (ii) the value of a transaction depends upon actions to be chosen by one of the two parties that are unobservable to the other—for example, output produced on a plot of land is a function of the effort put in by a sharecropper where effort is not observed or cannot be monitored by the landlord—the problem of moral hazard. Akerlof’s (1974) study of used car markets was instrumental in starting off the spate of papers on models of adverse selection. Akerlof produced examples where poor quality cars would drive out good ones from the market, whereas perfect information would ensure a distinct market for cars of any specific quality. A similar phenomenon can arise in other types of markets. Also, non-price features such as signalling and screening may be present in order to communicate information available to the better-informed agent to the other agent. Unfortunately, there has been no unified framework or model of competitive equilibrium with adverse selection. Different approaches have been employed and Mookheijee discusses several of them. In cases of moral hazard, first-best welfare levels cannot be achieved because additional risk has to be imposed on the agent (sharecropper) to ensure adequate effort levels. The problem, of course, arises because efforts cannot be observed by the principal, irrespective of whether the principal is a private firm or the government. Hence, Mookheijee argues that if the informational deficiency is correctly modelled, then government intervention may not achieve a Pareto improvement. Vohra discusses some implications of market failure caused by non-convexities in production. Suppose a firm has access to a technol­ ogy characterized by increasing returns. The firm will then become a natural monopoly, and efficiency requires that it be regulated. This also provides a rationale for introducing a public sector in the economy. Vohra analyses the resource allocation problem in a mixed economy in which government intervention is restricted to operating a public sector firm producing under increasing returns. Hotelling (1939) had shown that a necessary condition for Pareto optimality is that the market price of the commodity being produced

20

BHASKARDUTTA

under increasing returns be equated to marginal cost If differen­ tiability assumptions are made, then the first-order conditions of the constrained maximization problem of maximizing the utility of one consumer subject to given utilities of the others, and the technological and resource constraints yield marginal cost pricing. However, there has been some recent work which uses results from non-smooth analysis to drop the differentiability assumption. Vohra proves a ver­ sion of the generalized second welfare theorem for non-convex tech­ nologies using non-smooth analysis. Unfortunately, marginal cost pricing is not sufficient for efficiency and an equilibrium with marginal cost pricing is not necessarily Pareto optimal. In other words, the First Fundamental Theorem is not valid for non-convex technologies. What is more disturbing is that if there is some restriction on the ability of the government to redistribute in­ come, then none of the marginal cost pricing equilibria may be Pareto optimal. Vohra describes an interesting example in which this pheno­ menon occurs. He considers a two-consumer, two-good economy with a single firm which produces one of the commodities using the other as input. The technology is characterized by fixed costs and a constant marginal cost. Since marginal cost pricing is necessary for efficiency, the firm (under optimal regulation) must be operating at a loss. Suppose that the government can operate any tax scheme which does not involve subsidizing either consumer12 in order to cover the losses of the regulated firm. Vohra shows that no matter what may be the structure chosen by the government, all marginal cost pricing equi­ libria are inefficient. This demonstrates that unlike in the basic ArrowDebreu model, non-convex technologies imply that issues of income redistribution cannot be divorced from efficiency. The second welfare theorem requires that it is possible to redistri­ bute initial endowments. This, however, implies that the government must have complete information about individual consumers since the transfers must be independent of individuals’ behaviour. This makes lump-sum transfers infeasible since such information is unlikely to be available. The infeasibility of lump-sum transfers has given rise to the literature on optimal taxation. Murty and Nayak review some of the 12If some consumer can be subsidized while the other is taxed, then the tax structure can be explicitly used to redistribute inoomes.

Introduction

21

recent theoretical developments in this area and also discuss some applications with Indian data. Murty and Nayak start with a discussion of the optimum indirect tax. The classic paper in this area is Ramsey (1927). Ramsey was concerned with the problem facing a government which wants to maximize the utility of a representative consumer but has to raise a given amount of revenue through taxes on goods. Notice that maxi­ mization of a representative consumer’s utility essentially involves the assumption that all consumers are identical, so that considerations of equity are being ruled out. The basic Ramsey result is that the tax rates (*!,..., tn) must satisfy n

2 tjSi - -0 Xk for k - 1 , . . . , n i- 1 ‘

(5)

where Sk. is the derivative of the compensated demand curve, Xk is consumption of commodity k> and 0 is a constant. The left-hand side of (5) is the change in demand for good k following the tax change if the consumer is compensated to stay on the same indifference curve and the derivatives of the compensated demand curves are constant. So, the Ramsey rule states that the proportionate change in demand for all commodities along the compensated demand curve should be the same. Sharper conclusions can be obtained from the Ramsey rule if more specific assumptions are made about the utility function. The Ramsey rule has also been extended to a many-consumer economy by Diamond and Mirrlees (1971), Diamond (1975), and Mirrlees (1975) amongst others. This extension allows for redistribu­ tive considerations to be taken into account through the maximization of social welfare, where welfare can in principle be a concave function of individual utilities. As in the representative consumer case, one has to make specific assumptions about the nature of differences between individuals and the form of the utility function in order to get detailed results. Amongst other issues, Murty and Nayak also briefly discuss optimal income taxation. In his classic formulation of the problem, Mirrlees (1971) assumed that individuals’ utility depended on consumption and leisure. This introduced a trade-off between efficiency and equity since

22

BHASKAR DUTTA

high tax rates on the individuals with high skills are more equitable but have adverse effficiency implications since ‘more productive’ labour is withheld. It is worth pointing out that very few ‘general’ results are available in this area since the results are likely to be sensitive to the specification of the labour supply function, the level of revenue as well as the form of the social welfare function. Various causes of market failure as well as the inability of the government to levy lump-sum taxes imply that the government may have to intervene and guide the economy along the desired path. Ray and Sen discuss the issue of ‘quantities versus prices’ as alternative means of economic control. They point out that this issue is relevant only in a framework where the planner has incomplete information about the individual agents. Thus, only second-best policies are avail­ able in the form of policy instruments which are not individual specific. In the partial equilibrium framework, the authors review and extend the analysis of Weitzman (1974). The basic scenario involves an industry producing a single commodity. The society derives a benefit of B(x) from output level jc , while the cost is C(jc ). The planner wants to maximize net benefit B(x) - C(x) by a suitable choice of jc . The planner does not know the cost function of the producers, and so cannot command the producers to produce that level x* which maxi­ mizes net benefit. Instead, the planner must rely either on price controls which involve specification of appropriate producer price or tax leaving the actual choice of output to producers, or quantity controls which involve direct restrictions on levels of output. Even in this simple framework, it turns out that there may be interesting cases where the planner may be better off by using quantity signals. Sup­ pose, for instance, that there is a single monopolistic producer of the commodity. Then quantity controls are relatively more efficient than price controls if the benefit function has a high curvature. The analysis of the ‘prices versus quantities’ issue in a general equilibrium framework is conducted in the Arrow-Debreu model. Suppose the government’s policy options are quotas {qfi and linear tax rates {tj} on outputs of industry j. Now, the set of efficient allocations constitutes the first-best frontier, and, from the Second Fundamental Theorem, we know that all allocations on this frontier can be attained provided the government can use lump-sum taxes and subsidies. The

introduction

23

second-best frontier is the set of allocations that can be attained if the policy instruments available to the government are the quota vector q and the tax vector t. Clearly, the second-best frontier is contained in the first-best frontier. Ray and Sen also define the third-best frontier as the set of allocations that can be attained if the government only uses price controls. They also construct examples in which the third-best frontier is a strict subset of the second-best frontier. These examples, therefore, demonstrate that even in a general equilibrium framework, , there may be instances where the government may have to take recourse to quantity controls. The debate on the significance of the two fundamental theorems and their implications for the role of the state, that is the discussion of govemnment failure versus market failure, has always been conducted in the traditional framework of welfarism in which social welfare depends only on the individual utilities. How compelling is this frame­ work? Should issues like individual rights and freedom affect or influence the welfare ranking of social states? These issues are dis­ cussed by Pattanaik. In particular, Pattanaik surveys some of the recent literature on individual rights and liberty and also on the non-welfarist approach to the measurement of the standard of living. Why should non-utility information be considered an essential in­ gredient for the social evaluation of alternatives? The following ex­ ample from Sen (1979b) answers this question. Let N - {1, 2} and x ,y and z be three alternatives. The distribution of utilities is given below. X

y

l ’s utility

30

60

z 60

2’s utility

100

90

90

In social state x, individual 1 is poor while 2 is rich. A redistribution of income from 2 to 1 leads us from x to y. Now, suppose that individual 1 is a sadist. In state z, the distribution of income is the same as in x, but the change in utilities is due to the fact that in z, 1 tortures 2, while there is no torture in x. Notice that the distribution of utilities in y and z is identical, so that a welfarist must declare y and z to be socially indifferent. If any welfarist believes that y is socially

24

BHASKAR DUTTA

preferred to x> he or she must also admit that z is socially preferred to x , even though he or she may condemn torture! The basic reason for the conflict between one’s ethical values about torture and the necessity to declare that z is socially preferred to x is that welfarism renders irrelevant the non-utility differences between states y and z. Almost everyone will agree that in this case the non-utility differences between y and z should affect the social evalua­ tion of these states. Similarly, there are other contexts in which relatively non-controversial value judgements appeal to information other than individual utilities. An important context in which it is natural to go beyond the consideration of individual utilities is the issue of individual and group rights. Sen (1970a, 1970b) was the first to provide a formal treatment of rights in social choice theory. Sen’s basic idea was that for every individual, there are some matters which are ‘private’ to himself. Sen’s notion of Liberalism essentially meant that the preferences of the individual with respect to these matters should prevail irrespective of what the others may feel about them. Suppose (x,y) are two social States which are identical in every respect except that in x> individual i’s bedroom wall is blue whereas in y it is white. It then seems reasonable to argue that individual i*s preferences over the pair (x> y) should ‘dictate’ the social preference over (x, y). Sen’s Liberal Paradox showed that this notion of Liberalism is incompatible with Condition JP. Several writers have subsequently explored different issues con­ nected with individual and group rights. One of the earliest was Gibbard (1974) who showed that individual rights may even conflict with each other. There has also been a huge literature on various resolutions of the Liberal Paradox. There have also been several alternative formulations of individual (and group) rights. These have moved away from Sen’s formulation of individual rights in terms of restrictions on social choices imposed by the individual’s preferences over certain distinguished pairs of alternatives, and have sought to formulate rights in terms of game-theoretic frameworks. As I mentioned earlier, welfarism has been the dominant theme in welfare economics for two centuries. The need to give up welfarism in various contexts has been stressed only recently. Not surprisingly, much of this discussion has focused on conceptual issues, and the use

Introduction

25

of non-utility information is not at all widespread in applied welfare economics. However, readers of Pattanaik’s insightful survey will clearly recognize that policy prescriptions should not always be based on the welfarist approach to welfare economics. REFERENCES A igner , DJ. and A J . H eins (1967), A Social Welfare View of the Measurement

of Inequality, Review o f Income and Wealth, 13. A k e rlo f, G. (1974), The M arket for Lemons, Quarterly Journal o f Economics, 8 4 ,4 8 8 -5 0 0 . A rrow , K.J. (1963), Social Choice and Individual Values, 2nd edition, New York:

Wiley. ___ (1970), The Organization of Economic Activity: Issues Pertinent to the Choice of Market versus Non-Market Allocations, in R. Haveman and J. Margolis (^ds.), Public Expenditures and Policy Analysis, Chicago: Markham. ARROW, K J. and F.H. H ah n (1971), General Competitive Analysis, San Francisco: Holden-Day. Bentham , J. (1789), An Introduction to the Principles o f Morals and Legislation, London: Payne. B e rg so n , A. (1938), A Reformulation of Certain Aspects of Welfare Economics, Quarterly Journal o f Economics, 5 2 ,3 1 0 -3 4 . C oase , R. (1960), The Problem of Social Cost, Journal o fLaw and Economics, 3, 1-44. D alton , H. (1920), The Measurement of the Inequality of Incomes, Economic Journal, 30. D eb reu , G. (1959), Theory o f Value: An Axiomatic Study o fEconomic Equilibrium, New York: Wiley. D iamond , P. (1967), Cardinal Welfare, Individualistic Ethics and Interpersonal Comparisons of Utility, Journal o f Political Economy, 75. ___ (1975), A Many-Person Ramsey Tax Rule, Journal o f Public Economics, 4, 335-42. D iam ond, P. and J. M irrle e s (1971), Optimal Taxation and Public Production. I—II, American Economic Review, 61, 8-27, 261-78. E dgew orth , F.Y. (1897), The Pure Theory of Taxation, Economic Journal, 7, 46-70, 226-38, 550-71. G evers , L. (1979), On Interpersonal Comparability and Social Welfare Orderings* Econometric^ 47, 75-90. G ibbard , A. (1974), A Pareto-Consistent Libertarian Claim, Journal o f Economic Theory, 1 ,388-410.

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H a rs a n y i, J. (1955), Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility, Journal o f Political Economy, 6 3 ,3 0 9 -2 1 .

Hicks, J.R. (1910), The Valuation of Social Income, Economica, 7,105-24. _ (1939), The Foundations of Welfare Economics, Economic Journal, 49, 696-712. H otelling , H. (1939), The General Welfare in Relation to Problems of Taxation and of Railways and Utility Rates, Econometrics 6,224-69. K aldor , N. (1939, Welfare Propositions in Economics and Interpersonal Com­ parisons of Utility, Economic Journal, 49, 549-52. K elly , J. (1978), Arrow Impossibility Theorems, New York: Academic Press. Remp, M.C. and Y.K. Ng (1976), On the Existence of Social Welfare Functions, Economica, 43,59-66. Lan ge , O. (1938), On the Economic Theory o fSocialism, Minneapolis: University of Minnesota Press. L erner , A.P. (1944), The Economics o f Control, New York: Macmillan. L ittle , I.M.D. (1952), Social Choice and Individual Values, Journal o f Political Economy, 60,422-32. M irrlees , J A . (1971), An Exploration in the Theory of Optimal Income Taxation, Review o f Economic Studies, 38, 1975-2008. ___ (1975), Optimal Commodity Taxation in a Two-Class Economy, Journal o f Public Economics, 4, 27-33. Parks , R.P. (1976), An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Social Welfare Function, Review o f Economic Studies, 43,447-50. P igou , A.C. (1920), The Economics o f Welfare, London: Macmillan. Ramsey, F.P. (1927), A Contribution to the Theory of Taxation, EconomicJournal, 37,47-61. Robbins , L. (1932), An Essay on the Nature and Significance of Economic Science, London: Allen and Unwin. Roberts , K.W.S. (1980), Possibility Theorems with Interpersonally Comparable Welfare Levels, Review o f Economic Studies, 47,421-39. R ubinstein , A. (1981), The Single Profile Analogue to Multiple Profile Theorems: Mathematical Logic’s Approach, mimeographed, Murray Hill: Bell Labo­ ratories. S amuelson , P.A. (1947), Foundations o f EconomicAnalysis, Cambridge: Harvard University Press. ___ (1967), Arrow's Mathematical Politics, in S. Hook (ed.), Human Values and Economic Policy, New York: New York University Press. Scitovsky , T. (1941), A Note on Welfare Propositions in Economics, Review o f Economic Studies, 9,77-88.

Introduction

27

Sen, A.K. (1970a), Collective Choice and Social Welfare, San Francisco: HoldenDay and Edinburgh: Oliver and Boyd. ___ (1970b), The Impossibility of a Paretian Liberal, Journal o f Political Economy, 72, 152r-7. ___ (1973), On Economic Inequality, Oxford; Clarendon Press. ___ (1979a), Interpersonal Comparisons of Welfare, in M. Boskin (ed.), Econo­ mics and Human Welfare, New York: Academic Press. ___ (1979b), Personal Utilities and Public Judgements: Or What’s Wrong with Welfare Economics?, Economic Journal, 89, 537-58. ___ (1986), Social Choice Theory, in KJ. Arrow and M.D. Intrilligator (eds.), Handbook o f Mathematical Economics, 3, Amsterdam: North Holland. S tern, N.H. (1976), On the Specification of Models of Optimum Income Taxation, Journal o f Public Economics, 16, 123-62. V ickrey , W. (1945), Measuring Marginal Utility by Reaction to Risk, Econometrica, 13, 319-33. W eitzman , M. (1974), Prices versus Quantities, Review o f Economic Studies, 41, 477-91.

Market Failure and Information D ilip M o o k h er jee *

i . in t r o d u c t io n

The relative role of markets and the government is a question that has preoccupied economists for over the past two hundred years at the very least. During this century, this question acquired renewed interest in Western developed countries following the Great Depression of the 1930s, and in developing countries since the Second World War. The advent of Keynesian thinking, the perceived role of the War in finally eliminating the shackles of the Depression in the West, and the ap­ parent success of Soviet-style centralized planning—all these factors led to governments occupying a more important role in developed and underdeveloped countries alike in the postwar period. In recent years the market failure question has resurfaced as many Eastern Bloc countries as well as developing countries prepare for a reverse transi­ tion toward private property and decentralized market mechanisms, and most developed Western industrial democracies experiment with reducing the scale and scope of centralized government programs. Most traditional treatments of the question pose it at a normative level: what ought to be the relative roles of centralized planning and the market, or of the private and the public sector? Most economists also tend to focus on purely economic aspects of this comparison, e.g. on the efficiency and equity of associated resource allocation mechan­ isms, rather than broader political and cultural facets of alternative systems.1 The purpose of this essay is to provide an overview of some *1 would like to thank Bhaskar Dutta, Peter Funk, and Jim Mirrlees for detailed comments on an earlier draft of this essay. ‘By and large, the literature also tends to ignore the important question of successful modes of transition from one system to another, an issue of considerable contemporary relevance.

Market Failure and Information

29

recent developments in mainstream neoclassical economic theory that bear on the issue of market failure. The model of a Walrasian competitive equilibrium of a market economy forms the cornerstone of this analytical approach, particularly in the development of this model by Arrow and Debreu in the fifties. This model has formed the traditional basis for the view that market mechanisms serve to adequately achieve societal goals of equity and efficiency. Economists typically vary widely in their views regarding the usefulness of this theoretical approach, and with respect to their interpretations of the model. Some view the model as descriptively realistic of modem developed as well as underdeveloped economies (e.g. the ‘freshwater’ approach to modem macroeconomics; and Town­ send, 1987, 1988, 1991). Others interpret it as an elaboration of conditions under which markets would lead to socially desirable out­ comes: while these conditions may be satisfied in certain sectors of the economy, they may be violated in certain other sectors (e.g. Arrow, 1965, 1970, 1971, 1973, 1974; and Hahn, 1973, 1974). According to this view, the discrepancy between certain aspects of real-world econo­ mies and the conditions of the Arrow-Debreu model is useful for delineating areas of a market economy where governments may have a role in improving efficiency or equity. Other economists (usually more favourably inclined toward government intervention) question the positive and normative connotations of the Arrow-Debreu model at a broader level: these include Dobb (1969), Galbraith (1958, 1967), Komai (1971), Kaldor (1972), and Robinson (1974). Development economists have also traditionally believed the ArrowDebreu model to be essentially irrelevant to the market versus govern­ ment question in underdeveloped countries. This is particularly true of the writings of Young (1928), Nurkse (1953), Rosenstein-Rodan (1943), Scitovsky (1954), as well as the orthodox viewpoints articu­ lated in most development textbooks. The reasons are various: in LDCs many important markets (especially in the financial sector) are either missing, fragmented, or monopolistic; production and exchange in many sectors are characterized by non-price ‘institutional’ mechan­ isms; problems of capital formation involve indivisibilities and scale economies; pecuniary externalities and coordination problems (under­ lying ‘Big Push’ arguments for centralized planning) abound owing to

30

DILIP MOOKHERJEE

missing markets and imperfect competition; common property and intergenerational externalities as well as problems of unemployment, overpopulation, and unequal income distribution assume an important role. Nevertheless, it is a complete non sequitur to infer from the inap­ plicability of the Arrow-Debreu model that widespread intervention by governments is justified. Nothing at all can be inferred from the irrelevance of the model, apart from the fact that its arguments in favour of market mechanisms do not apply. This is very distinct from the inference that markets necessarily fail, relative to governments, whenever the conditions underlying the Arrow-Debreu model fail to apply. An intellectual argument for government intervention must then be based on some variant or substitute for the Arrow-Debreu model which accommodates ‘non-neoclassical’ features of missing markets, non-price institutions, increasing returns, imperfect competition, and externalities. In addition, it must be able to pose the ‘markets versus government* in a cogent and analytically tractable manner. In recent years the theory of competitive equilibrium has been extended to accommodate a variety of these non-neoclassical features. This essay concentrates on some of these developments, dealing espe­ cially with externalities, incomplete markets, imperfect information, and the related area of transaction-cost based models of non-price institutions. I exclude discussion of the literature on increasing returns (partly because this area is discussed by Vohra in this volume), as well as of the literature pertaining to government policy and oligopolistic industries. Moreover, I discuss models which extend the ArrowDebreu approach, and which thereby retain certain elements of the Arrow-Debreu model such as maximizing behaviour by atomistic (though not necessarily price-taking) agents. Nevertheless, the models include a rich variety of alternative ways of modelling strategic self-interested behaviour by economic agents, including both non-cooperative and co-operative game-theoretic formulations that accord institutional factors a more important role than the fiction of the Walrasian auc­ tioneer. If anything, as I will try to explain in the essay, the literature is characterized by an ‘embarrassment of riches’: there are simply too ^ o r an introductory survey of the latter area, see Krugman (1989).

Market Failure and Information

31

many alternative ways of modelling market mechanisms that yield disparate answers once the comfortable environment of the ArrowDebreu model is left behind. In addition to providing an overview of the relevant literature, this essay elaborates at length on a number of important weaknesses and lacunae of the theory of market failure. In part these difficulties derive from the intrinsic nature of the topic itself. Some may infer from this discussion that the question of ‘markets versus government’ or ‘private versus public sector’ is intrinsically unanswerable. Others may be more optimistic about the future of the subject, viewing the weaknesses of the current theory as providing an important indication of the directions that future research ought to take. My own prejudice is to side with the Jatter camp. It is easy to overlook the many useful insights thrown up by the literature: in my opinion these are extremely important to economists generally, both in the context of developing and developed countries. If it is believed that the analytical apparatus of economics is useful primarily as providing a useful framework for discussing important economic problems, rather than providing universally valid, general theories—then this literature must be judged as enormously successful. As I will try to explain in succeeding sections, this literature has succeeded in providing a set of analytical tools to discuss a large range of phenomena that could not be accommodated by the Arrow-Debreu model, and in overturning many of the traditional presumptions concerning welfare analysis of market outcomes, and of government policies. The essay is organized as follows. The remainder of this section discusses the overall framework within which the question of market failure is usually framed, and some of the important limitations of this framework. Section 2 discusses issues relating to equity, in particular the implications of informational constraints on the role of govern* ments in effecting redistribution of economic welfare. Succeeding sections focus on the role of governments in enhancing efficiency of market outcomes under alternative non-neoclassical settings. Section 3 deals with externalities and public goods, Section 4 with incomplete markets, and Section 5 with imperfect information. Based on the discussion of the previous three sections, Section 6 reviews some of the controversies concerning the appropriate definition of a private market economy in non-neoclassical environments. Section 7 describes

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one approach of dealing with this ambiguity: of attempting to obtain more abstract notions of decentralized and centralized resource alloca­ tion mechanisms (in the tradition pioneered by Hurwicz, 1960, 1972, 1973). Section 8 briefly discusses the newly emeiging literature on transaction-cost-based theories of property rights and resource alloca­ tion. Both Sections 7 and 8 deal with literatures that are far from being settled in any definitive sense, and will probably form the basis of important future research. Finally, Section 9 concludes with some remarks on what developing countries may learn from this literature. Basic framework o f market failure theory A well articulated theory of the relative roles of market and govern­ ment should ideally specify the following ingredients explicitly: (a) Definition o f social objectives, such as efficiency, equity, the securing of different kinds of rights and entitlements, as well as trade-offs between these different objectives. (b) Theory o f market behaviour, which involves a definition of a market economy, and a description of the outcomes generated by it. (c) Theory o f government behaviour, involving a definition of a state-controlled economy, or a mixed economy with substantive state intervention, and a description of the outcomes generated by it. (d) Comparison o f market outcomes with outcomes o f substantive state intervention, in terms of expressed social objectives. Differences between alternative views on the role of the state can usually be traced back to differences on one or more of these issues. Requiring different schools of thought to articulate these components is therefore useful in focusing the debate better, and narrowing the differences between them. Nevertheless, existing theories of market failure typically fall short of articulating all four of the above components satisfactorily in a common analytical framework. To appraise the achievements of the theory, as well as to chart out useful research directions for the future, it is important to be aware of these shortcomings. One of the most important shortcomings refers to item (c) above: a theory of government behaviour. Most existing theories of market failure usually formulate a model of a market economy quite explicitly, but then proceed to compare it with an idealized notion of what a government could

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achieve via command-and-control. Hie government is represented by a single entity, a benevolent social planner pursuing a well-defined set of social objectives (captured by a social welfare function). In more recent theories, some care is devoted to the question of what informa­ tion is available to the idealized social planner; and whether this is comparable with information available to private agents in a market3 Apart from this aspect, the idealized social planner in market failure theories bears no resemblance at all to actual governments. Excluded are all the ingredients of a positive theory of government behaviour, the topic of public choice theory (for a survey of this area, see Mueller, 1989): political institutions that influence the nature of collective choices by a community of voters or elected representatives; the behaviour of bureaucrats and the organization of bureaucracies; the nature of regulatory processes; the formation and influence of special interest groups, and related activities of lobbying and rent-seeking. While public choice theory deals with many of these issues in an interesting way, there is little prospect yet of an overarching theory jthat marries market failure theory with public choice theory. Two distinct literatures therefore deal with possible failures of the two alternative modes of resource allocation in isolation from one another. In evaluating the lesser of two evils, market failure and government failure, one is therefore forced to combine the partial insights of the two literatures in a piecemeal fashion.4 A less ambitious though more useful approach is to interpret market failure theory in the following manner. The outcomes that could conceivably be achieved by a benevolent social planner in the absence of any pressure group influence are to be viewed as a normative benchmark, an expression of what the government can ideally, though not realistically, achieve. To the extent that an ideal social planner cannot improve upon market outcomes, there is a powerful presump­ tion against government intervention. And if the social planner can

3The purpose is to ensure that the theory does not accord the state an ‘unfair' advantage, comparable to the implications of allowing the state to operate with a superior production technology than is available to private agents. Note, however, that there is considerable controversy about what exactly ‘comparable’ information limitations on the state is: this issue will be discussed more extensively in Section 5. 4See Wolf (1988) for an attempt along these lines.

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improve upon market outcomes, there is merely the potential for an actual government to effect economic improvements. Whether or not an actual government will be able to realize this potential is then left as a problem that belongs to a different area of expertise: public choice or political economy of the state. It is also worthwhile to point out a related strength of market failure theory: by forcing the analyst to be explicit about the primitives of the economy that do not vary with the resource allocation mechanism chosen (i.e. markets or government) such as technology, tastes, trans­ action costs, and informational constraints, one ensures a ‘fair’ com­ parison between the two economic systems. In particular, the theory has to ensure parity between the information available to a social planner, and information that is common knowledge among private agents. If some information is known privately by some agent in a market setting (such as personal creditworthiness, or ability to produce output, or consumption needs), and not available to other agents in the markets, then it is reasonable to require that this information is also not available to a social planner. To the extent that some problems with a market economy (such as incomplete markets, or certain forms of non-price institutions) arise from the absence of perfect information among market agents, the theory also forces the same informational constraints on the social planner. This restricts substantially the range of feasible policy tools available to the planner, and therefore restricts the ability of the planner to effect improvements upon second-best market outcomes. This is true particularly of contexts where market outcomes are deemed inequitable, or where certain imperfections (such as rationing, price stickiness, or missing insurance and futures markets) of market processes arise from underlying informational costs. Constrained by informational limitations (e.g. with respect to the endowments and consumption needs of specific people, or with respect to their creditworthiness, their abilities, and efforts), a government is also severely restricted in its ability to implement desired redistribu­ tions, or to generate efficiency-enhancing economic activity. So far as informational constraints are concerned, the theory does succeed in posing the question of comparing second-best market outcomes with second-best government policies. Indeed, as I shall argue, one of the main contributions of the theory is to alert economists to a more

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realistic view of what government policies are truly feasible in the face of informational costs, before inferring the necessity of government intervention. A second major source of disagreement concerns item (a), i.e. statement of social objectives. The analytical framework of tradition­ al neoclassical economics concentrates on consequentialist objectives such as Pareto-efficiency and equity, thus excluding deontological concerns such as rights and freedoms. Yet many economists would be unwilling to deny the importance of the latter. Important problems arise partly with the difficulty of ensuring consensus on issues such as (i) what kinds of rights are important, (ii) the relative importance of rights and consequentialist objectives, and (iii) the relative effective­ ness of markets and governments in securing the rights deemed to be important. Friedman (1953) and Nozick (1974) phrase their argument for a minimal state in terms of the importance of ‘negative’ freedoms and the difficulty of securing such freedoms in societies with activist states. Other philosophers such as Dworkin (1977) and Sen (1985) emphasize ‘positive’ freedoms such as the satisfaction of minimum needs that can only be assured by active state intervention. Despite the importance of these issues, we shall not review these philosophical arguments. Indeed, subsequent to Section 2 dealing with equity and redistribution, we shall be concerned with the sole criterion of efficiency. With reference to item (b), i.e. specification of a theory of market behaviour, there are also significant differences of opinion on the appropriate way to model the functioning of a market economy. The traditional depiction has been in terms of a Walrasian price-theoretic model, with the formalization of Arrow and Debreu representing its most definitive version. From a theoretical standpoint, this model is unsatisfactory in the respect that it lacks an explicit model of price formation: the latter typically necessitates a game-theoretic formula­ tion. In the context of atomistic (i.e. where individual agents are of negligible size relative to the rest of the economy) economies that are ‘neoclassical’, i.e. those not characterized by externalities, increasing returns, transaction costs, incomplete markets, or imperfect informa­ tion, there is little disagreement that this model accurately depicts the outcomes of a competitive market. For instance, explicit game-theoredc models of competitive economies of both co-operative and non­

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cooperative variety, typically generate Walrasian allocations in 'neoclassical* environments.5 However, this pleasing consensus breaks down in ‘non-neoclassical’ environments. This issue, and its attendant implications, will be discussed in further detail. I shall also argue that the theory says little about the implications of private versus public ownership of property. It is concerned primarily with the potential of decentralized market modes of resource alloca­ tion, compared to more centralized modes. As Oskar Lange and others in the debate on market socialism pointed out in the thirties, there is no reason why a socialist economy should not be able to use marketbased methods. Some scholars of comparative economic institutions, such as Lindblom (1977) or Wiles (1977), have also expressed the view that the fundamental issue is the comparison of market and non-market modes of resource allocation, rather than alternative forms of ownership. Private ownership economies can embrace non-market hierarchical modes (witness, for instance, large corporations in capitalist economies), while socialist economies can employ shadowprice-guided decentralized mechanisms. Yet, one feels that there are fundamental issues relating to the implications of alternative patterns of ownership of property that need to be addressed by a satisfactory theory of market failure. The contemporary wave of privatizations of govemment-owned property all over the world attests to the practical importance of this issue. Theories of the implications of alternative ownership struc­ tures for resource allocation theory are still in their infancy; and will be briefly reviewed in Section 8. These theories have been developed in connection with issues of vertical integration in the theory of industrial oiganization; applications and extensions to the question of private versus public ownership are yet to be systematically addressed. To summarize, theories of market failure usually develop an explicit model of a market economy, and compare its outcomes with what can be achieved by an ideal social planner (rather than a real government), in terms of the objectives of economic efficiency, and occasionally, equity. Nevertheless, it still provides, in my opinion, useful insights into some of the strengths and weaknesses of market outcomes. In so far as market sFor an overview of the co-operative approach to perfect competition, see Hildenbrand (1974,1962); for the non-cooperative approach, see the symposium issue of the Journal of Economic Theory (1980) on the foundations of the theory of perfect competition.

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outcomes are judged to achieve the same performance as an idealized social planner, there is a strong presumption against intervention by an actual government on efficiency grounds. And if markets fall short of this standard, the question of whether a real government will be able to effect improvements, will be answered depending on one’s assessment of the nature of political institutions and constraints, as well as the competence and incorruptibility of government officials. These assess­ ments may well depend on historical and cultural circumstances of a given society, and may thereby lack any kind of universality. 2. REDISTRIBUTION As the introductory chapter by Dutta has exposited, the two principal theorems of welfare economics in the Arrow-Debreu model succinct­ ly express the conditions under which competitive market equilibria achieve the twin societal goals of Pareto-efficiency and equity. While Pareto efficiency requires no governmental intervention (under the assumptions of the first welfare theorem), equity objectives do, how­ ever, typically require the government to engage in lump-sum redis­ tribution of endowments. Moreover, to the extent that a government can engage in lump-sum redistributions, the achievement of efficiency and equity objectives can be neatly separated from one another. Thus, if the presence of certain externalities cause the failure of efficiency, the government needs to devise its corrective policies with the sole objective of ensuring efficiency, since any adverse equity effects of these policies can be 'neutralized’ at zero efficiency cost by suitable lump-sum redistributions. The assumption that a government can costlessly engage in lump­ sum redistributions has come under considerable attack in the recent literature on optimal tax theory and incentive-compatible planning procedures.6 The fundamental point of this critique is that the above prescription assumes the availability of far more information (to the government) than is realistic. Most ethical notions of equity relate the deservingness of individuals for asset redistribution to attributes such as their endowments, abilities, and market opportunities, since these 6Scc, for example, Mirrlees (1974,1986) and Hammond (1979,1987).

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help determine the level of consumption and well-being that they will achieve in a market economy. Reliable information regarding such personal attributes of individual citizens is notoriously difficult to obtain. Witness, for instance, the frustrated attempts of many LDC governments in implementing land reforms, or in ensuring that welfare programmes benefit those for whom the programme is intended. The fundamental implementational obstacle in such programmes is undoubtedly the lack of information about which people truly need assistance. It would be ob­ viously self-defeating for the government to ask individuals to disclose their private attributes, as they would all have an incentive to hide their true endowments. Even if the government has reasonably accurate infor­ mation concerning the statistical distribution of these attributes over the population at large, such aggregate information would serve little purpose in designing redistributions across the population. Given such informational constraints, it can be shown (see Ham­ mond, 1979) that the optimal combination of efficiency and equity is quite generally unachievable by any governmental resource-allocation mechanism. And under certain conditions (if there is sufficient vari­ ability in endowments of different agents, and if individual demand functions are 'smooth’), the only resource allocation mechanism that results in Pareto-efficient outcomes is the Arrow-Debreu equilibrium without lump-sum redistribution. This implies that equity improve­ ments (relative to the market outcome) that can feasibly be achieved by governments must be at the expense of Pareto efficiency. In other words, redistributions must be inherently distortionary or non-lumpsum: somewhat paradoxically, the presence of informational limita­ tions on governments argues for a more activist role for them. In particular, a large number and variety of forms of state intervention can conceivably be justified on redistributive grounds.7 The strict can be shown that under certain ‘smoothness’ assumptions, whenever the laissez-faire outcome is not a local welfare optimum (i.e. if lump-sum transfers were feasible then a small amount of redistribution would be welfare improving), then even in the absence of lump­ sum transfers it is desirable for the government to engage in some (efficiency-reducing) redistribution. That is, the relevant issue is not whether the government ought to engage in redistributive policies, but the extent to which it should. The intuitive justification for this result is that, starting from the laissez-faire situation, a small dose of a distortionary, redistributive policy imposes zero first-order efficiency losses. For further discussion of this result, see Mookheijee and Ray (1991).

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separation between efficiency and equity objectives breaks down: policies have to be evaluated simultaneously in terms of their impact on both social objectives. In view of the general theory of the second-best in welfare economics,8 this might be thought to imply that economists have little to say in general about the forms of state intervention that can or cannot be justified on redistributive grounds. Can almost any policy be defended on the basis of a possibly benign redistributive impact? The literature on optimal taxation and public production deals with this question, and fortunately there are some general insights regarding the structure of optimal redistributive policies. Since the theory of optimal taxation is reviewed by Murty and Nayak in this volume, it is appropriate for me to mention the results of Diamond and Mirrlees (1971, 1976) concerning governmental policies relating to private and public sector firms, as well as to international trade. In developing countries, private firms are frequently subject to myriads of regulations that are partly motivated by redistributive considerations. In addition, investment decisions in the public sector, as well as restrictive trade policies, are also justified in a similar manner. Against the spirit of such a policy approach, Diamond and Mirrlees establish what has come to be known as the Production Efficiency Theorem. In its original form, this theorem states that in the absence of pure rents in the private sector (e.g. stemming from decreasing-retums technologies), if the government has sufficient con­ trol over the formulation and enforcement of linear taxes and subsidies (that separate producer and consumer prices), it is not desirable for the government to choose policies that distort the pattern of production in the economy.9 The government’s redistributive objectives are tackled

*This theory states that in the absence of simultaneous fulfilment of all the Paretian conditions for efficiency, the satisfaction of more rather than fewer Paretian conditions does not necessarily enhance efficiency. See Lipsey and Lancaster (1956). 9In the presence of pure profits, the result can be extended if the government can optimally tax die profits of different firms at different rates, provided certain technical conditions are satisfied by production sets (e.g. Inada conditions): see Dasgupta and Stiglitz (1972) and Mirrlees (1972). Restrictions on differential profit taxes may, however, cause the result to fail. However, distortionary production policies aimed at indirect lump-sum redistributions do require the government to be able to identify the deservingness of owners of different kinds of firms.

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more directly and efficaciously through the fiscal system: distortionary direct and indirect taxes. In particular, this theorem rules out distortionary tax-subsidy policies for firms, or any form of quantitative controls on production or investment. Furthermore, in the context of trade policy, it allows the government to interfere with free trade only in so far as the country in question commands monopoly (or monopsony) power in the world market, exactly as recommended by the traditional theory of optimal tariffs. For small countries facing fixed terms of trade, in particular, it recommends free trade.10 It is important to note that these conclusions apply irrespective of the redistributive preferences of the government—the argument is simply that production or trade distor­ tions are not a particularly efficacious mode of redistribution, and are dominated by purely fiscal redistributive policies. It is important to remember that the Production Efficiency theorem does use a number of strong assumptions.11 One such assumption is that the government can enforce any tax or subsidy rate it likes over any transaction between any firm and any household in the economy, as well as distinguish such transactions from inter-firm transactions. Such an assumption is particularly untenable for many LDCs whose governments struggle to enforce income and commodity taxes against informational, administrative, and corruption constraints. The calcula­ tion of the 'right’ level of indirect taxes requires the government to possess sufficient knowledge about industry cost and supply condi­ tions: in the presence of uncertainty regarding these conditions quan­ titative controls may be superior. The theorem also relies on assumptions of a complete set of perfectly competitive markets without chronic excess supply or demand.12 Nevertheless, the result 10This result is also not robust to the presence of pure profits. Trade taxes and restrictions can be justified if they succeed in promoting profits of enterprises owned by deserving individuals, since such forms of redistribution are essentially lump-sum in character. “ For an extended discussion of the possible role of quantitative controls on private producers on redistributive grounds when the assumptions of the Diamond-Mirrlees model are violated, see Mookheijee and Ray (1991). 12Mention should be made of the recent developments in the theory of trade policy under conditions of imperfect competition (for a survey, see Krugman (1989)). These theories recommend interventionist policies that mainly serve to transfer rents from foreign producers to domestic producers. However, the ‘right’ policies require the government to have rather intimate knowledge of the nature of the oligopolistic interaction between foreign and domestic producers, as well as demand and cost parameters.

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does justify treating non-inteiventionism in production and trade as the benchmark (particularly for the substantial part of the manufacturing and service sector that produces intermediate goods), departures from which ought to be justified in terms of violation of one or more assumptions of the Diamond-Mirrlees model. Concerning shadow prices that ought to form the basis for evaluating investment proposals in the public sector, Diamond and Mirrlees (1976) show that the border price rule recommended by Little and Mirrlees (1974) is quite generally valid, provided the government pursues welfare-optimiz­ ing fiscal policies (that may be constrained in a large variety of ways). The border price rule recommends the use of marginal foreign exchange costs as shadow prices for goods that are traded at the margin. Governments of small countries with fixed terms of trade therefore must only adopt projects that break even at world prices. This result applies irrespective of the government’s redistributive preferences. Rirther, the result is robust to the assumption that the government pursues welfare-optimizing fiscal policies: all that is required is that the shadow price of foreign exchange in the economy is positive, and that demand-supply balances are restored follow­ ing adoption of public projects (see Mirrlees, 1978; Bell and Devarajan, 1983; Diewert, 1983; Hammond, 1986; and Mookheijee, 1986).13 Summarizing, markets may fail to generate equitable distributions of welfare among different members of an economy, thereby creating the potential for an equity-minded government to adopt interventionist policies. However, this does not necessarily provide justification for arbitrary forms of distortionary policies on redistributive grounds: the Diamond-Mirrlees model alerts one to the possibility that some forms of distortionary policies may achieve similar degrees of redistribution at lower efficiency costs than others. For instance, if the government can feasibly enact redistributive policies through a wide range of direct and indirect excise taxes, there may be little need to interfere with market forces in large parts of production and trade sectors.

The work of Bulow and Summers (1986) on trade policy in the presence of unemployment should also be mentioned. A merit of their approach is that unemployment and wage rigidity is endogenously derived from considerations of imperfect information in labour markets. ^However, the shadow price rules for goods not traded at the margin are substantially altered if the government fails to pursue welfare-optimizing fiscal policies.

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3. EXTERNALITIES AND PUBLIC GOODS The efficiency of competitive equilibrium as embodied in the first fundamental theorem of welfare economics depends critically on the assumption that externalities and public goods are absent. Since public goods can be viewed as a limiting form of an externality, we shall hereafter (mainly) refer to the latter alone. It has been well known since the work of Pigou that externalities cause a divergence between private and social valuations; consequently goods with negative exter­ nal effects tend to be overproduced and overconsumed in a competi­ tive market economy, with the opposite true for goods with positive external effects. Most conventional arguments for efficiency-enhancing government intervention involve an externality argument, the typical remedy being the imposition of a Pigouvian tax or subsidy to bring private and social valuations in line. In the context of public goods, it is typically presumed that such goods will have to be provided by the government and financed out of compulsory taxation. Indeed, even the most laissez-faire economists and philosophers (such as Friedman or Nozick) concede the necessity of a government to provide public goods such as law and order, and defence from external aggression. So, subject to an important qualification to be discussed below, there is little disagreement on the principle that market economies may fail in the context of externalities, and that governments have an important role to play in this respect. Disagreements over the range of pheno­ mena qualifying as externalities in any given economy, and the capacity of an actual government to effect improvements, are however pervasive. It is important, however, to emphasize the distinction between ‘tech­ nological’ and ‘pecuniary’ externalities (see Scitovsky, 1954, who stressed this in the context of developing countries). The former represent instances where utility or production functions of given economic agents depend directly on consumptions or productions of others. Pecuniary externalities, on the other hand, are interdependen­ cies in achieved welfare levels that are mediated by prices. Interdepen­ dencies of the latter kind are, of course, all pervasive in market economies; for instance, virtually any change in consumption or pro­ duction of one agent will have a (perhaps small) impact on market

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prices, and thereby affect the consumption or profit opportunities available to other agents. Under the neoclassical assumptions (perfect competition, complete markets, and perfect information), pecuniary externalities do not generate efficiency failures. Indeed, this is precise­ ly the conclusion of the First Welfare Theorem. Intuitively, an ArrowDebreu equilibrium is characterized by equality between marginal rates of substitution and marginal rates of transformation; small pertur­ bations in the allocation will thereby have no first-order efficiency effects. This is no longer the case with ‘technological’ externalities where the marginal rates corresponding to different agents differ, consequently only these externalities matter from an efficiency stand­ point. It follows from this, however, that pecuniary externalities will have first-order efficiency implications in contexts of imperfect com­ petition, incomplete markets, or imperfect information (since those contexts will not be characterized by equality of marginal rates be­ tween different agents).14 Nevertheless, many important problems in LDCs have an aspect of ‘technological’ externality: common property resources (such as air, water, fisheries, firewood, or agricultural topsoil), health and sanita­ tion, the spread of technical innovations, and overpopulation, to name only a few. It is also important to recognize the close connection between the phenomena of externalities, incomplete markets, and imperfect infor­ mation. As Arrow (1970) pointed out, externalities may be viewed as a phenomenon of missing markets. The problem would disappear if there were markets that mediated the interdependence between dif­ ferent agents. For instance, pollution problems could be solved with perfect markets for pollution rights, where polluters and pollutees would trade these rights at parametric prices. Since polluters would have to pay a price for polluting, which equalled the marginal cost imposed upon pollutees, the divergence between private and social valuations would disappear. This is formally represented by a Lindahl equilibrium, which is essentially an Arrow-Debreu equilibrium applied to an economy with an extended commodity space (for a definitive treatment, see Foley, 1970). l4See Greenwald and Stiglitz (1986) for an elaboration.

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Apart from the problem that certain externalities may generate nonconvexities in this world with an extended commodity space, causing Lindahl equilibria to fail to exist in general (see Starrett, 1972), a more substantive problem concerns the enforcement of property rights in such contexts. For instance, in the context of en­ vironmental pollution, separate property rights of different individuals to a common environment would be infeasible to enforce. Yet this is what would be required to implement a Lindahl equilibrium in situa­ tions where more than one individual suffered the effect of a given act of pollution, as the polluting agent would have to purchase pollution rights from each affected party separately. In other contexts, property rights cannot be enforced owing to the difficulty of monitoring exter­ nality-causing activities (as in Meade’s, 1952, famous example involv­ ing a beekeeper and a neighbouring orchard owner). One of the questions that may be raised about the capacity of redistribution, concerns the availability of requisite information to identify an externality, as well as choose corrective measures. For instance, how easy is it for a government to measure private and social valuations? From a theoretical standpoint, there is the much-studied free-rider problem: since social valuations cannot often be inferred from market data, one way for a government to estimate social valua­ tions is via questionnaires or public surveys administered to the public. However, private individuals would have the incentive to bias their stated valuations in the hope of manipulating public decisions. The practical significance of this problem, at least in the context of national rather than local governments, is probably less severe (see, for ex­ ample, the arguments of Johansen, 1977, as well as the experimental evidence of Bohm, 1972). Of greater practical significance is that private individuals rarely have enough reliable information to estimate how they are affected by certain kinds of atmospheric pollution or other environmental risks, or how they benefit from general education and health programs in their vicinity. There are also the hopelessly complicated problems associated with the valuation of human lives.15 Nevertheless, these problems do not necessarily constitute, in my

uFbra discussion ofsome ofthese practical problemsin costbenefit analysis, see Gramlich (1981).

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opinion, strong arguments against governmental interventions. To the extent that scientific research helps assess some of these costs and benefits, it may be argued that such research itself constitutes an important public good. The government then has the respon­ sibility of investing in the acquisition of information regarding the prevalence and magnitude of different kinds of externalities, and thereafter developing corrective measures on the basis of the infor­ mation obtained. And the unreliability of external cost and benefit estimates does not constitute a good argument for inaction, but rather policy initiatives based on the best possible information available to a government. A more significant theoretical criticism of the recommendation that governments have a natural role in treating externality problems is owed to the important paper of Coase (1960). Coase argued that in certain situations it was plausible that those private agents that respec­ tively create and are affected by an externality would themselves have an incentive to ‘correct’ the inefficiency in their mutual interest. This may occur through a situation where the externality recipients bribe creators to reduce their activities to efficient levels, or where the latter pay the former to earn the right to create the externality (in which case they internalize the cost of the externality). Which of the two situations arises depends on the initial assignment of property rights. In the context where one firm exerts a significant externality on another firm, the two firms have a strong incentive to merge into a single firm which would ‘internalize’ the externality. A related point often made in the context of common resource problems, as well as in connection with the need for a state to enforce law and order and avoid Hobbesian anarchy (e.g. Axelrod, 1984), is that communities may evolve social norms such as reciprocity and third-party sanctions in order to avoid mutually unsatisfactory outcomes in a decentralized fashion.16 To the extent that these arguments are valid in any given externality situation, the need for a centralized state to intervene with coercive restrictions and punitive sanctions is mitigated. One way of interpreting the Coasian criticism is that in externality situations the appropriateness of an Arrow-Debreu formulation of 16See Qstrom (1990) for numerous examples in the context of common property resources.

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behaviour of private agents in market situations is questionable. It is afgued that it is unreasonable to suppose that agents will be content to choose production and trading plans at parametric prices. In the pres­ ence of an externality, they have an obvious incentive to bypass the price mechanism and enter into bilateral or multilateral contractual arrangements that are mutually welfare improving. Thus, for instance, a co-operative game theoretic formulation of the competitive market process would yield outcomes considerably different from the ArrowDebreu price-theoretic model.17 When phrased in this fashion, the efficiency of market outcomes (i.e. modelled as a core-like solution) is a tautology: it is a byproduct of the definition of the equilibrium concept employed. Core outcomes must be invulnerable to blocking by any coalition, including the ‘grand’ coalition, so core outcomes are necessarily Pareto efficient. Of course, Coase did not assert that a core solution was necessarily the correct one in every externality situation: this was true only in the absence of ‘transaction costs’. These costs may be incurred by different parties in the act of negotiating with one another, and in the institution and execution of an ‘enforceable’ contract. Of course, if these transaction costs are large enough, the private parties will not be able to correct the externality on their own in a decentralized fashion, and the poten­ tial need for a government stands resurrected. It is difficult to expect that large-scale environmental problems such as deforestation and topsoil erosion, acid rain, and depletion of the ozone layer can be solved entirely through voluntary processes of negotiation and bargain­ ing between all involved parties. In some contexts involving renewable or exhaustible resources, the actions of current generations affect the welfare of future generations that will be born after the death of the current one: such intergenerational externalities cannot be solved in Coasian fashion for the simple reason that the two ‘parties’ do not inhabit the planet at the same time! Other reasons for the possible failure of ‘voluntary negotiations’ in resolving externality problems have been discussed above. In some contexts, it is physically impossible or prohibitively costly to define

17For a discussion of core-theoretic treatments of externalities, see Foley (1970), Starrett (1973), and Roberts (1974).

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and assign property rights over common resources to separate in­ dividuals.18 The enforceability of contracts entered into by the parties to the externality requires sufficient monitoring of subsequent actions of these parties, so that transgressions can be suitably punished. Thirdparty authorities such as governments may conceivably have a com­ parative advantage in monitoring actions, as well as in the adminis­ tration of punitive measures for transgressors. Moreover, negotiation between different parties may lead to inefficient outcomes in the presence of incomplete information about each other’s costs and benefits from the externality: for example, haggling over the level of appropriate compensation to the victim may prevent the parties from reaching an agreement. In general, there exist a variety of alternative institutional mechan­ isms for the resolution of externality problems, varying from voluntary negotiation between the parties directly involved at one extreme, to coercive controls administered by third-party government authorities. To a certain extent, all these mechanisms have to confront similar sources of ‘transaction costs’: acquisition of information pertaining to individual costs and benefits that allows a decision on the level of ex­ ternality activities to be tolerated (or induced), monitoring actions of externality creators, and subsequent administration of suitable rewards and punishments. The relative efficacy of these mechanisms depends on their relative ‘transaction costs’, i.e. the effectiveness with which these functions can be carried out. Evaluation of these transaction costs requires one to leave the tradi­ tional analytical contexts of perfect frictionless markets (as assumed by the Pigouvian approach), or simple core-like solutions (as assumed by the Coasian approach). It necessitates the develop­ ment of theories of incentives, bargaining, and of enforceable con­ 18The insightful analysis of Chari and Jones (1991) illustrates a point made by Arrow (1970): simultaneous assignment of property rights over a common resource, such as air or water, generates monopoly and consequent market-thinness problems. Suppose a factory emits smoke, thereby reducing the well-being of neighbouring households. Requiring the factory owner to negotiate separately with every concerned resident will not generate efficient outcomes, since each resident has monopoly power over the sale of its pollution rights. As the number of residents in the vicinity grows, the eventual outcome will be for the factory to reduce its pollution level to zero (failing which, to close down), even if the efficient outcome requires the factory to operate with moderate pollution levels.

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tracts under conditions of imperfect information. Recent years have witnessed substantial research on these topics, though a definitive theory is yet to emeige; we shall return to a discussion of these issues in Section 6. Despite the unavailability of a satisfactory theory of ‘transaction costs’, casual empiricism suggests that externalities involving a small­ er number of parties are more likely to be satisfactorily resolved between the parties themselves. Intuitively, the costs of negotiation and coordination among members of small coalitions are likely to be small, partly because such arrangements are less complicated with fewer parties, because there is better information about true preferen­ ces, while monitoring individual actions is easier within small groups. Ostrom (1990) describes a number of case studies involving common property resources of irrigation water and fisheries in small com­ munities that appear to have been satisfactorily resolved via institu­ tional arrangements devised, monitored, and sustained by the local users themselves. On the other hand, it is difficult to visualize prob­ lems of large-scale environmental damage or overpopulation being resolved via a Coasian process of voluntary negotiation and decentral­ ized enforcement. Nevertheless, one of the main intellectual contributions of the Coase critique is to force attention of theorists to ‘organizational’ issues—ir­ respective of whether we examine ‘private’ or ‘public’ solutions to externality problems, the focus is on alternative institutional forms that such solutions may take. Not only does it shift theoretical discourse from prices and market-clearing towards bargaining, contracts, and informational issues, it also causes economists to embrace a wider range of ways in which a government may deal with externality problems. For instance, while some government intervention may be considered necessary in some contexts, the form of such intervention need not be the traditional Pigouvian tax-subsidy route. Some com­ mon resource problems may be most effectively tackled by a mixed approach, wherein the government assigns property rights in a certain way, or it initiates a negotiation process designed to institute a ‘con­ tract’ which is subsequently enforced by the affected parties themselves in a decentralized fashion.

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4. INCOMPLETE MARKETS The Arrow-Debreu theory posits the existence of a complete set of markets at the given point of time where trading occurs. Taken literal­ ly, this has a number of clearly unrealistic implications. Markets open only once, and so there is no role for expectations formed by agents about future prices. There is also no need for agents to trade shares owned in different firms, since the value of a firm is unambiguously defined by the prevailing commodity price vector. Indeed, there is little role for financial assets of any kind in the Arrow-Debreu formulation, since such assets are principally useful as a store of value, i.e. in transferring purchasing power across markets that open at different dates.19 Real-world market economies are usually characterized by a limited set of credit and insurance markets: agents can rarely borrow all they want, or obtain unlimited amounts of insurance against arbitrary con­ tingencies, at parametric prices. Similarly, firms can rarely buy or sell commodities forward for arbitrary dates in the future, or contingent on arbitrary contingencies. The reasons are various. One is asymmetric information: some agents may have better information than others about the likelihood or occurrence of different states of nature (the problem of adverse selection). Alternatively, these likelihoods may depend on actions opportunistically chosen by certain agents that are unobservable to other parties (the problem of moral hazard). These will be discussed explicitly in the next section. Another reason for market incompleteness is the prohibitive transaction cost of organizing trades for delivery of every physical commodity in every conceivable date-contingency specification (these may include the costs of quoting prices, specifying contracts, monitoring delivery commitments, in ad­ dition to the costs to agents of computing their optimal strategies in such a complicated environment). Finally, it may not be possible for all agents in the economy to trade with one another at a given point of time for the simple reason that they cannot all be physically present at ‘’However, as we shall discuss below, there may be economies with a sequence of commodity and asset markets, with resulting allocations that could have been achieved in an Arrow-Debreu economy. The latter could then be defended as a simple ‘as if’ model of the true economy.

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a given point of time: current generations cannot trade with genera­ tions to be bom in the future. Given the lack of a complete set of forward contingent markets, the ability of agents to smooth consumption across different dates, or insure against risks, is severely limited. Market allocations will typi­ cally fail to be Pareto efficient, as marginal rates of substitution across different dates and contingencies will not be equated across agents. Morever, with a sequence of markets, price expectations will begin to play an important role in determining market allocations. Agents will also begin to demand financial assets in order to transfer purchasing power across markets. Consequently, a rather substantive extension of the Arrow-Debreu theory is required to accommodate these pheno­ mena. The last two decades have witnessed substantial research on these topics. While the theory is by no means settled, this literature has generated results that depart from those of the Arrow-Debreu model in a variety of novel ways. One literature attempts to retain the price-theoretic character of the Arrow-Debreu approach: with a given specification of the set of markets that are active, agents are presumed to choose production, consumption, and trading plans that maximize their objective functions at given prices. The other literature pursues a more foundational, game-theoretic approach, where the underlying sources of incomplete­ ness (imperfect information or transaction costs) are explicitly modelled. In this section, we review some of the results of the former strand, while the next section will examine game-theoretic models with asym­ metric information. One immediate difficulty the price-theoretic approach runs into is the specification of price expectations. The traditional approach, fol­ lowing Hicks’ Value and Capital, is the so-called theory of temporary equilibrium, where agents’ expectations regarding future price move­ ments are related to current prices in a specific fashion. Equilibrium is represented by a price vector on the currently open market, which induces price expectations that generate optimal trade offers and re­ quests that clear the (current) market.20 Clearly, the existence and 20This refers to the case of an economy with two dates, and may be extended in an obvious fashion to the case where there are multiple dates. Relatively recent important contributions to this literature indude Grandmont (1974) and Green (1973).

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nature of equilibrium outcomes will depend upon the process by which agents form expectations. Within this framework, one can explore the implications of restricting the nature of these expectations, on the ground that in stationary environments rational agents may ‘learn’ something about future prices from observing past prices. The polar opposite assumption is one of rational expectations, where agents are presumed to have self-fulfilling expectations. Some effort has been devoted to the question of conditions under which ‘rational’ agents will indeed iearn’ the ‘true’ price function in the long run (e.g. Bray, 1982; Blume and Easley, 1982; and Bray and Kreps, 1987). Even if agents manage to learn enough to have the ‘correct’ expecta­ tions, market-clearing equilibria with incomplete markets may possess properties far removed from Arrow-Debreu equilibria. Before we discuss these, it is appropriate to mention that there are also some fundamental difficulties in defining these equilibria for economies with production. Specifically, in the absence of a complete set of prices available for the commodities produced by a firm, the profits of a firm are no longer well-defined. Moreover, shareholders of a firm need not agree on the objectives of the firm. To the extent that the production plans of the firm affect the profits resulting in future contingencies that cannot be directly insured against, different shareholders with different risk preferences or beliefs may prefer the firm to choose different production plans. With incomplete markets, production decisions of firms have implications not only for the current incomes of their owners, but also the riskiness of their future incomes. Consequently, even the definition of a competitive equilibrium is no longer clear-cut. The interested reader is referred to Diamond (1967), Radner (1972), Dreze (1974), Ekem and Wilson (1974), and Grossman and Hart (1979) for discussion of the theory of the firm with incomplete mar­ kets. In what follows, we abstract from this problem by concentrating on exchange economies. We now list a set of distinctive and striking properties of competi­ tive equilibria of exchange economies with incomplete markets. The concept of equilibrium is based on Radner (1972), who termed it an ‘equilibrium of plans, prices and price expectations’. Specifically, there is a sequence of markets corresponding to different ‘date-event’ pairs, on which agents trade commodities and assets. Assets may be ‘finan-

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rial’ or ‘real’. A real or indexed asset has a given return denominated in terms of commodities in future date-event pairs. In contrast, a financial or non-indexed asset pays off in terms of a nominal unit of account in future date-event pairs. An equilibrium involves a price vector for spot commodities and assets in the market at each dateevent pair, corresponding to which agents form optimal trade and portfolio plans that clear all markets. The interpretation is that when this price vector (as a function of the date-event pair) is expected by market agents, the corresponding optimal responses are such as to make these prices self-fulfilling. (a) Existence o f equilibrium. Hart (1975) showed that with real assets, competitive equilibria need not exist. Intuitively, this arises from the fact that the distribution of purchasing power across different date-event pairs allowed by a given asset depends on the vector of spot prices of the commodities paid off, in a possibly discontinuous fashion. Alterna­ tively, there is no natural upper or lower bound on portfolio holdings of assets, and the demand for assets cannot be bounded in general. However, this problem arises only in so far as assets pay off in multiple commodities: Geanakoplos and Polemarchakis (1986) show that if assets pay off in terms of a single numeraire commodity then equilibria exist and are locally unique, just as in the Arrow-Debreu theory. Moreover, the non-existence is not robust to certain perturbations of the parameters of the economy, as demonstrated in the generic existence theorems of Duffie and Shafer (1985) and others. However, if assets are financial, then Cass (1984), Duffie (1987), and Werner (1987) have shown that equilibria typically exist. Non-existence problems do not arise in the same fashion as in the case of real assets since the problem of discontinuity of asset returns with respect to the price vector no longer arises. (b) Indeterminancy o fequilibria. However, with financial assets, there may be ‘too many’ equilibria. This is demonstrated most strikingly by Geanakoplos and MasColell (1985). In a model where there are two dates: 0 and 1, and S states of nature at date 1, they show that if the number of assets is less than S, the dimensionality of the set of equilibrium allocations is S - 1. In other words, there are a continuum of equilibria, and there are S - 1 degrees of freedom in selecting

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equilibria! In contrast, generic Arrow-Debreu equilibria are locally unique and finite in number. Note also that when there are as many assets as states of nature, the market structure is effectively complete, and equilibria coincide with Arrow-Debreu equilibria (as originally demonstrated by Arrow (1964)). So there is a striking "discontinuity* in the dimensionality of the set of equilibria with respect to the number of assets: even if the number of assets falls just one short of the number of states S, the dimensionality of the equilibrium set jumps from 0 to S - 1! One intuitive explanation of this result is the following. Financial assets are not valued for their own sake, but for the purchasing power they confer (i.e. use value is zero, exchange value is positive). More­ over, in any state an asset generates a redistribution of purchasing power between agents, i.e. it has the characteristic of inside money with an aggregate endowment of zero. Consequently, the aggregate excess demand for the asset (money) is zero, irrespective of the price of money in that state (relative to other commodities). Nevertheless, variations in this price (or, equivalently, the rate of inflation) have real (wealth) effects, since they affect creditors and debtors differently. The introduction of financial assets thus introduces an additional relative price (which reflects the inflation rate) without adding a non-redundant market-clearing condition. Since there are S states, S - 1 such relative prices or rates of inflation can be arbitrarily chosen: equilibrium conditions do not pin them down. (c) Inefficiency o f equilibria. With incomplete markets, it is evident that competitive equilibria will not typically be Pareto efficient. Never­ theless, this is not necessarily tantamount to market failure. Whatever constrains the set of available markets (information or transaction costs) presumably also constrains a social planner. The normative benchmark with which to evaluate market outcomes must also, in all fairness, reflect these constraints. However, the absence of explicit modelling of these informational or transaction costs prevents an accurate derivation of the suitable notion of constrained efficiency. The first person to confront this question was Diamond (1967). In the context of a special model (two dates, a single commodity, and Multiplicative* separability), he showed that market equilibria were

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constrained-efficient in the sense that a social planner constrained to reallocate through the existing set o f markets would not be able to achieve Pareto improvements. The seminal paper of Hart (1975) showed that this result did not generalize. Specifically, it is possible that given an incomplete market structure, one competitive equilibrium may Pareto-dominate another! The example runs as follows. Suppose there are two traders, two dates, two commodities, and no uncertainty. The traders have concave utility functions that are additively separable in consumption across the two dates. At date 1 there is no forward market for delivery at date 2. Hence there is no connection between the markets at the two dates: an equilibrium in one market can be determined independently of what happens in the other market. An equilibrium in the two-date economy thus consists of a conjunction of two independent spot equilibria. Now suppose that the spot market at date i (= 1, 2) has at least two equilibria A,- and B„ where agent 1 is better off in the former, and agent 2 better off in the latter. The economy then has at least four possible equilibria, obtained by any combination of two spot equilibria, and these are independent of the time discount rates of the two traders. Consequently, if agent l ’s discount rate is sufficiently high and agent 2’s discount rate sufficiently low, the equilibrium (Bh A2) will be Pareto-dominated by (Alf B£. Hart’s example demonstrates the strongest possible sense in which market equilibria may fail to be constrained-efficient: a planner con­ strained to reallocate through the existing set of markets (but without using lump-sum transfers) can effect Pareto improvements. Later work by Grossman (1977) and Grossman and Hart (1979) attempted to obtain a characterization of the efficiency of incomplete market equi­ libria (i.e. a representation of the social planner’s problem that would generate extensions of the two Welfare Theorems). However, the usefulness of such characterizations is limited in view of Hart’s result. To elaborate, the characterization involves the notion of a Social Nash Optimum (SNO) which requires that the social planner not be able to reallocate in any date-event pair to effect Pareto improvements, ^given the allocations in other date-event pairs. This reflects a certain lack of coordination in allocations across different date-event pairs. Grossman (1977) and Grossman and Hart (1979)

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show that incomplete market equilibria are SNO allocations, and any SNO allocation can be achieved as an incomplete market equilibrium with state-contingent lump-sum transfers. Note that the set of SNO allocations includes the set of Pareto-efficient allocations, as well as many inefficient allocations. In particular, one SNO allocation may Pareto-dominate another (this is how the first result ties up with Hart’s example). Consequently, given the weakness of the SNO criterion, the usefulness of the first result is questionable. The second result states that any SNO allocation, including efficient allocations, can be decentralized. This may appear surprising, as there are many incom­ plete market models where no equilibrium is efficient. The clue lies in the fact that the decentralization requires lump-sum transfers that are state-contingent: in effect the planner is allowed to spread risks in a manner that the market is not allowed to (see Stiglitz, 1982, for an elaboration of this criticism). (d) Effects o f opening new markets. Hart (1975) examined the welfare effects of opening new markets, when starting with an incomplete set. If the resulting set of markets continues to be incomplete, he showed that the result of opening the new markets may be to make all agents in the economy worse off. Of course, this is not possible if the result of opening the markets is to make the market structure complete, as the equilibria of complete market structures are Pareto efficient. Hart demons­ trated an example in which a new market caused a Pareto-inferior outcome: the intuition for the result is not easy to communicate. Below we shall describe a more intuitive example due to Newbery and Stiglitz (1984). The foregoing results may be viewed as vindicating the notion that markets ‘fail’ in essential ways in the absence of a complete set of markets. Before reviewing this judgment, it is perhaps illuminating to provide specific illustrations of these results in a variety of concrete contexts. Price destabilizing speculation. It has often been argued that specula­ tion necessarily stabilizes price, since speculators buy when the price is low, and sell when it is high. A number of counterarguments to this have been advanced in the literature, but many of them rely on imperfect competition or irrational expectations of speculators. Hart and Kreps

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(1988), however, show that speculation can be destabilizing even when speculators are competitive, and both speculators and nonspeculators have rational expectations. This, however, leaves open the question whether price stabilization is necessarily desirable from a welfare standpoint. Many policy discus­ sions of price support schemes for farmers implicitly assume the desirability of price stabilization. However, with incomplete markets, this intuition may be seriously flawed: this is demonstrated by the following example due to Newbery and Stiglitz. Pareto-inferior trade. Newbery and Stiglitz (1984) generate an example in which free trade results in Pareto-inferior outcomes com­ pared to autarky, essentially because free trade stabilizes prices 4too much*. They consider two economies, each of which can grow a risky crop and a safe crop. The economies are identical in every respect, except in that the climactic "shocks’ to production of the risky crop are perfectly negatively correlated. Each economy consists of a set of farmers and consumers, and the demand for the risky crop has unit price elasticity. Fanners are risk-averse, and there are no futures or contingent com­ modity markets in either economy: only spot markets open. In this world, autarky results in price fluctuations (of the risky crop, relative to the safe crop) that perfectly insure incomes from cultivation of the risky crop. The effect of free trade is to perfectly stabilize the price of the risky crop, since the aggregate supply of this crop across the two economies is constant. This implies that the incomes from the risky crop fluctuate considerably with free trade. This makes farmers worse off, and induces them to shift production toward the safe crop. The resultant increase in the average price of the risky crop may make all consumers worse off as well. The crucial point is that price stabilization often (but not necessarily) implies substantive income risk: the link between the two depends on relevant elasticities. In the absence of a complete set of markets that enable income risks to be diversified away, the effect of opening new markets may be to increase income risks, and thereby cause welfares “ Sec Diamond (1980) for an exploratory attempt to examine conditions under which government price or demand stabilization policies may be welfare-improving: these typically involve elasticities in an essential and complicated way.

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of risk-averse agents to decrease. The example also serves to illustrate the point made by Hart (1975) about the possible effects of opening new markets. Inefficient growth, sunspots, and Keynesian effects. Following Malinvaud (1953), it has been well known that competitive equilibrium growth paths generated in infinite horizon economies may fail to be efficient, since they may violate a 'transversality’ condition. Such economies typically exhibit a continuum of competitive equilibria, only some of which are efficient. In particular, some equilibria may Pareto-dominate others. In similar vein, infinite horizon models of overlapping genera­ tions have been demonstrated to possess a continuum of equilibria with different welfare properties. These indeterminacies may be viewed as arising from the essential "open-endedness’ of expectations in an infinite horizon context, or equivalently from market incompleteness: see Geanakoplos and Brown (1982) for an interpretation of indeterminacy arising from "lack of market clearing at infinity*. The basic reason for the indeterminacy is that market behaviour of short-lived agents determines relative prices across a finite number of successive dates. The level of prices is thus left undetermined, though it affects real allocations (e.g. it determines whether or not the transversality condition is satisfied; alternatively the resulting inflation or deflation generates wealth effects). For instance, in an economy where each successive generation lives for two periods, and where there is a single consumption good (in addition to money), the price of the commodity at any date (relative to money) depends upon the expectations consumers have at this date about the price at the next date. But the price at the next 22The simplest illustration of this failure is in the context of the extraction of an exhaustible resource, as described by Dasgupta and Heal (1979, pp. 155-63). Suppose at a certain date there is a given stock of an exhaustible resource, and a riskless asset which earns an interest rate of r for ever. The resource can be costlessly extracted; however, resource owners live for a finite number of periods and maximize their personal lifetime utility. With competitive markets, equilibrium requires merely that there be no arbitrage opportunities unexploited, so the resource must be extracted at a rate such that the price appreciation of the resource equals r (the Hotelling rule). The market merely determines the rate of price appreciation, however, not the level of the price. If the initial price of the resource is ‘too high’, then some amount of the resource will never be used, an inefficient outcome. Efficiency specifies the level as well as the rate of change of price to be at particular levels, whereas a sequence of competitive markets with (relatively) myopic traders will only ensure the latter.

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date depends upon the price at the date following iht next date, and so on. Given the absence of a last date, rational expectations and marketclearing conditions do not pin down the level of the price at any date. Clearly, this indeterminacy will vanish in an Arrow-Debreu economy with a finite number of dates (though, as the Geanakoplosr-MasColell paper demonstrates, inflation rates in finite-horizon incomplete market equilibria with financial assets will also be indeterminate). It has often been argued that the essence of the Keynesian criticism of the Walrasian model is that the latter misses the crucial importance of expectations in determining real economic activity, and that these expectations are essentially arbitrary and indeterminate in a market economy. The preceding results may therefore be viewed as a rigorous formulation of some of these ideas. What is particularly interesting is that this indeterminacy may exist despite the postulate of rational expectations. Combined with the possibility that some equilibria may be Pareto-dominated by others, there may also appear to be a role for governments in steering economies away from inefficient equilibria. This may be related to the Keynesian notion that market expectations are susceptible to sudden and considerable fluctuations, with con­ comitant effects on real levels of activity; consequently governments may have a role in neutralizing the effects of such fluctuations via fiscal and monetary policies. The recent literature on sunspots has developed some of these themes: for a recent evaluation see Wood­ ford (1987). We end this section with some words of caution regarding inferences about market failure that may be drawn from the literature on competi­ tive equilibria with incomplete markets. This literature has certainly succeeded in overturning many classical properties of market out­ comes in the Arrow-Debreu model, and in generating a number of new insights. It also seems to be emerging as a unified theory of what has for long appeared to be disparate subjects: models of equilibria in financial assets, overlapping generations models, alternative theories of corporate finance, infinite horizon growth models, and sunspots. But many of the results, especially pertaining to the welfare properties of equilibria, are of the character of examples and possibilities. There are few simple and general results that indicate conditions under which specific forms of government intervention will yield welfare ihi prove-

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ments: a specific policy may result in welfare reductions in some contexts, and improvements in other contexts.23 More importantly, the theory suffers from a number of ad hoc features. It exogenously specifies the set of markets that are available to agents for trading, without specifying the underlying reasons for incompleteness. The choice of the kinds of markets and securities is itself an important aspect of market behaviour.24 For instance it may be argued that if the absence of a particular kind of market or security causes substantial welfare losses, economic agents would have a powerful incentive to introduce just such markets and assets. Further­ more, by failing to specify the underlying informational and transaction-cost considerations that prevent market completeness, the theory is devoid of the ‘right’ efficiency benchmark. This criticism has been voiced recently by Dixit (1987,1989). In the context of the Newbery-Stiglitz model elaborated above, he argues that if the incompleteness of markets arises from informational imper­ fections that are explicitly modelled, then the prescriptions for optimal trade policy may differ substantially from an analysis (such as New­ bery-Stiglitz’s) which assumes in an ad hoc manner that such markets are missing. For instance, if crop insurance markets are missing or limited owing to adverse selection or moral hazard factors, and if the government is also subject to these informational problems, then Dixit shows that in many situations laissez-faire continues to be an optimal policy. In others, the optimal trade policy is to depress domestic prices below world prices of a risky crop, i.e. subsidize imports or tax exports. This is in sharp contrast to the protectionist arguments of Newbery and Stiglitz. Dixit also argues that direct public insurance programs may be simpler and just as effective as distortionary trade policies combined with income tax policy. As outlined above, the general methodological im­ plication of Dixit’s criticism is that the nature of optimal government policies is complex, and depends on the precise source of market incom­ pleteness: no simple and general rules can be enunciated This important point raises the need to consider models where ®For example, see Diamond (1980) for an analysis of welfare-optimal prioe-stabilization policies when forward markets we missing. MFor recent attempts to endogenize the selection cf markets and assets, see Allen and Gale (1968,1989)r

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informational imperfections that generate market incompleteness are explicitly analysed. What does the presence of imperfect information imply for market failure? What is the appropriate efficiency bench­ mark with which to evaluate market outcomes? The latter question requires, in particular, analysis of planning problems where govern­ ments are restricted by informational problems on par with market agents. These topics are discussed in the following section. 5. IMPERFECT INFORMATION The last two decades have witnessed an explosion of theoretical literature on markets with imperfect information. Various forms of informational imperfections and related phenomena have been studied, including asymmetric information, differential information, models of prices revealing information, and search models. In this section, I will confine myself to models of asymmetric information; see Grossman (1981) and Admati (1989) for surveys of the literature on revelation of information via prices, and Diamond (1987) for a survey of the literature on equilibrium search models. By asymmetric information is meant either of the following two situations: (a) one side of a given transaction has superior information about the ‘quality’ of the good exchanged, usually referred to as the problem of adverse selection, or (b) the profitability of the transaction depends upon certain actions to be chosen by one of the two parties that are unobservable to the other, the problem of moral hazard. These terms are borrowed from the insurance literature, where adverse selec­ tion arises from insurees having better information than insurance providers about the odds of an accident, and moral hazard from the dependence of accident probabilities on unobservable choices of care or effort in preventing the accident. If insurees are risk-averse, and insurance companies risk-neutral, then an Arrow-Debreu equilibrium would require the issuance of perfect insurance at prices that reflect actuarially fair odds. This outcome is no longer supportable in the presence of these informational problems. Adverse selection means that insurance companies can no longer distinguish high-risk cus­ tomers from low-risk ones, and the former would pretend to be low-risk in the hope of obtaining insurance at lower prices. With moral

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hazard, full insurance would leave insured individuals with no incen­ tive to exercise due care in preventing accidents, and insurance com­ panies would consequently lose money. We alternately consider the literature on these two kinds of asym­ metric information. Adverse Selection The literature on adverse selection was sparked off by the paper of Akerlof (1970), which provided the example of used cars whose sellers had better information about the quality of their car than potential buyers. He argued that this would cause the market for used cars to disappear, or be exceedingly ‘thin’. The reasoning was based on the fact that those sellers with better quality cars would have higher reservation prices. Consequently, a given price would elicit only those sellers with lower reservation prices. When compared to a situation without adverse selection, rational buyers would be aware that the prices they offer affect the average quality of cars that are supplied, and therefore might wish to lower their offers. This, in turn, would adversely affect the quality elicited still further, and the process may unravel to the point where the market either disappeared, or only the worst grades of cars were traded. Effectively, poor quality cars would drive out good ones from the market. With perfect information, on the other hand, there would be a distinct market for cars of any given quality. Akerlof provided examples of many other sectors of the economy where similar phenomena might arise; the literature has studied many other examples since. These include credit and insurance markets (where borrowers have better information about the profitability of projects that need financing, and insurees know better the risks of accidents that are sought to be insured against); labour markets (where workers or job applicants have better knowledge of their productive potential than prospective employers) and markets for services or other products for which quality is an important attribute unobservable to buyers at the time of purchase. As Myerson (1987) has remarked, in all such instances of adverse selection, the traditional notion of a com­ modity which provides utility or profit opportunity independent of the identity of the suppliers, is fundamentally altered. Instead, the value of a given transaction depends as much on (the buyer’s perceptions of)

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what is being exchanged, as well as the personal characteristics of the seller. Attention must thereby shift away from anonymous commodity exchanges to relation-specific transactions. The subsequent literature has demonstrated that market thinness need not be the only consequence of adverse selection. Instead, trading may be accompanied and supported by a variety of non-price mechanisms, usually referred to as signals and screening devices.25 Examples include education levels and other forms of certification, warranties and long-term contracts, collateral, financial policies of public limited companies (such as capital structure or dividend policy), quantity premiums or discounts—aH of which serve the purpose of credibly communicating the information about the seller’s characteristic to buyers. In addition, certain markets (such as labour or credit) may be characterized by rationing and sticky prices.26 The prevalence of agrarian institutions such as sharecropping, dual labour markets, and interlinked transactions can be explained by similar informa­ tional asymmetries.27 The theory is thus rich in terms of capturing a variety of non-price institutions that are commonly observed in real economies. Nevertheless, there have been substantial difficulties in constructing a definitive model of competitive equilibrium with adverse selection. Different approaches employed include: (a) Price-theoretic models, such as Prescott and Townsend (1984), Gale (1987), and Hammond (1989). Prescott and Townsend define the set of commodities to be pieces of randomized, individually incentive-compatible trade contracts, each of which carries a linear price. This construction enables them to ensure that executed trades will respect the limited information about preferences and opportunities of individual agents, in addition to allowing ‘effective* purchases to determine the ‘effective* price paid (i.e. alternative forms of non-linear pricing). Randomizations over incentive contracts are necessary to eliminate problems of nonconvexities. Despite this elaborate, abstract construc­ tion, the Arrow-Debreu theorems on existence and welfare properties of competitive equilibria can be extended by Prescott and Townsend only in the case where informational asymmetries arise at a stage following “ See Spence (1973) for a pioneering analysis of signalling in a market context. “ See Stiglitz and Weiss (1981,1963). 27See Bardhan (1989) for an overview as well as samples of this literature.

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the contracting process. In the case where information is asymmetric at the time that contracts are being traded, Hammond (1989) has developed the Prescott-Townsend construction further (by increasing the space of tradeable commodities) to achieve an extension of the Arrow-Debreu theorems. Nevertheless, some critics of this approach (such as Hahn, 1988) argue that it is hard to interpret what these results really mean, i.e. whether such commodity and trading structures can be identified with any real economy. Hammond points out that the construction requires the existence of some rather sophisticated option markets, which are also vulnerable to certain arbitrage opportunities. Gale’s model deals with a simpler commodity structure: every con­ ceivable contract (i.e. bundle of commodities traded) is treated as a separate commodity, with a separate price (a transfer of money that must accompany the trade). Buyers and sellers treat these prices as parametric. Nevertheless, owing to adverse selection, the formation of profit* or utility-maximizing net demands necessitates specification of beliefs on the part of buyers regarding the (average) identity of agents offering to sell different contracts at the going price. Despite requiring these beliefs to be self-fulfilling, there remains significant indeter­ minacy of market-clearing equilibria. Gale consequently applies a game-theoretic refinement of the beliefs (called stability) to single out a unique equilibrium. Moreover, this equilibrium can be achieved in a non-cooperative, decentralized game-theoretic model of the trading process. Gale does not, however, describe welfare properties of his equilibrium notion. (b) Non-cooperative game-theoretic models. Most of the literature has adopted this approach, following Rothschild and Stiglitz (1976) who studied non-cooperative equilibria of a competitive insurance market with free entry of (risk-neutral) insurance firms, and a large number of (risk-averse) insurance customers. The customers are identical in all respects, except in terms of the likelihood of occurrence of an accident. In particular, they consider the simplest possible case where there are just two risk classes in the population. Every customer knows his own risk level, but insurance firms cannot identify high-risk customers from low-risk customers. Rothschild and Stiglitz modelled the insurance market as follows:

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there is a two-stage process where firms move first in offering in­ surance contracts, and customers move second by selecting their most preferred contracts from those offered. Competition is ensured by free entry of firms. The approach of Spence (1973) is related to this by reversing the sequence of moves: informed agents (workers) move first, and the uninformed agents (firms) move second.28 Rothschild and Stiglitz demonstrated in this model that for a large class of cases, Coumot-Nash equilibria fail to exist.29 This problem arises essentially due to a phenomenon called 'cream-skimming’ which is fundamental to competitive markets with adverse selection. Briefly, 'cream-skimming* arises to undermine a contract which 'pools’ agents of different qualities. If a firm offers a contract which is meant to attract agents of varying qualities, and which must earn zero profits (due to competition) as a whole, it must be the case that high quality agents subsidize low quality agents (in the sense that the firm earns positive profits on the former, which enables it to cover its losses on the latter). This contract is vulnerable to competition: another firm can 'cream-skim’ away the high quality clients by offering them a contract which appeals only to the high quality agents (e.g. in the insurance setting, this contract could provide restricted coverage at a more attractive price). On the other hand, it is often the case that Pareto-effi­ cient contracts necessarily involve pooling i.e. every non-pooling incentive-compatible contract (where the trade with every distinct quality type of agent breaks even separately) can be Pareto-dominated by some pooling contract (this point is elaborated below). Then a non-pooling contract cannot survive under competition either, since some firm could attract away customers on a non-pooling contract with a competitive pooling contract. Faced with this non-existence problem, subsequent literature (Wil­ son, 1977; Miyazaki, 1977; Riley, 1979; and Engers and Fernandez, 1987) has explored alternative non-Coumot-Nash equilibrium con­ cepts. For instance, Wilson introduces a notion called 'anticipatory equilibrium’, where cream-skimming is thwarted owing to the belief held by 'invading* firms that if they steal the high quality clients from “ For an elaboration of this point, as well as of other related models discussed in this section, see Kreps (1990, Chapter 17). 29The same discovery was made independently by Wilson (1977).

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an existing pooling contract, then the incumbent firms will go out of business (since they will be left serving only the low quality cus­ tomers), following which the low quality customers will also flock to the new firm. In cases where the Coumot-Nash equilibrium does not exist, this concept singles out the break-even pooling contract (which is always Pareto efficient among the class of incentive-compatible contracts). Miyazaki explores this concept further to the context where firms may offer a whole set of contracts rather than just a single one, and argues that resulting outcomes can be interpreted as the emergence of firms with ‘internal labour markets*. In a related vein, Riley introduces the notion of 'reactive equili­ brium* characterized by a different kind of conjectural belief held by invading firms (i.e. the possible entry of other firms in the future which may undermine the profitability of the invading contract). These beliefs serve to protect non-pooling contracts from being undermined by a pooling contract, even if the latter Pareto-dominates the former. Consequently, this equilibrium concept picks out the non-pooling con­ tract where the low quality customers obtain their first-best trades, and high quality customers obtain less insurance than their corresponding first-best level (though at the same price). Such an outcome can be interpreted as an instance of rationing, where the amount of insurance that can be purchased by any given customer is restricted, unless the customer is willing to pay a high price corresponding to the actuarially fair odds for low quality customers. An alternative interpretation is that insurance is priced non-lineaiiy: the price generally increases with the extent of coverage sought. Engers and Fernandez extend Riley’s analy­ sis in a number of interesting directions. On the other hand, Spence’s model (where the sequence of moves is reversed, relative to the Rothschild-Stiglitz model) generates a con­ tinuum of equilibria that are Pareto-ranked, somewhat akin to incom­ plete market models. The Pareto-dominating equilibrium happens to coincide with the equilibrium selected by Riley’s equilibrium—this is quite different from that selected by Wilson’s equilibrium. Neverthe­ less, Spence’s analysis permits other non-pooling contracts to also arise. Clearly, the alternative approaches give rise to a plethora of alternative outcomes that differ from one another in important ways. The lack of consensus between alternative ways of modelling competi­

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tive markets with adverse selection is disturbing, and in sharp contrast to contexts with perfect information where most reasonable models of competition yield Walrasian outcomes. The game-theoretic status of the Wilson or Riley equilibrium con­ cepts, however, is not well established, as they involve agents conjec­ turing about reactions of other agents to their own moves, despite the fact that the formal model involves them moving simultaneously. Clearly, however, these solution concepts have to be viewed as reduced form solutions to some dynamic model of interaction between compet­ ing agents. Recent papers by Cho and Kreps (1987) and Hellwig (1986) have explored these adverse selection models more carefully from the game-theoretic point of view. Cho and Kreps demonstrate that the multiplicity in Spence’s model disappears with the application of certain refinements of the notion of Nash equilibrium: the Paretodominating equilibrium turns out to be singled out by such techniques. Hellwig shows that the addition of a third move restores equilibria in the Rothschild-Stiglitz style models where uninformed firms move first (the third move involves firms accepting or rejecting applications made by informed agents at the second stage). However, reversing the sequence of the first two moves generates the Cho-Kreps equilibrium (with a suitable refinement), which is substantially different from the outcome without the moves reversed. In other words, the outcomes are very sensitive to the specification of the sequence of moves. To the extent that detailed information about the exact sequence of moves in any given market is not available, the theory fails to emerge with any definite predictions. What are the implications of these models for the role of a govern­ ment in enhancing efficiency of market outcomes? Given a setting involving fundamental asymmetries of information, a natural efficien­ cy benchmark is the notion of optimality where a social planner is constrained by the same informational constraints as are uninformed firms facing informed customers. This notion of constrained efficiency is well-defined as the solution to a planning problem subject to a set of incentive-compatibility constraints (whereby it must not be the case that agents of any particular quality type envy the contract offered to any other). As mentioned in the introduction, a sensible comparison between markets and government must be based on equal endowments

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of information between private firms and the social planner. Conse­ quently, efficient govement insurance programs must also respect informational constraints, and may thereby involve 'institutional* ele­ ments similar to those observed in the private market, such as signall­ ing or screening via certification, collateral requirements, non-linear pricing, and rationing. The mere presence of these practices, however unpleasant their consequences may be, does not constitute prima-facie evidence that a government can realistically achieve better outcomes by public provision of credit and insurance, or by corrective tax-subsidy policies. This is why it is essential to explicitly spell out a model of the market which enables this comparison to be made. In comparing market outcomes with this standard of informationconstrained efficiency, the conclusions again depend sensitively upon the specification of the specific non-cooperative model (and associated equilibrium notion) employed. For instance, Rothschild-Stiglitz equi­ libria, when they exist, or Riley’s reactive equilibria, are typically cqnstrained-inefficient. The reason is that constrained-efficient out­ comes usually involve'some cross-subsidization (i.e. pooling). Intui­ tively, it pays the high quality agents to subsidize the low quality agents since this relaxes the incentive-compatibility constraint (where­ by high quality agents must be given a contract which is not envied by low quality customers following the subsidy). Yet, as argued above, such forms of cross-subsidization cannot be sustained in competitive settings permitting cream-skimming: passive firms would be tempted to cream-skim the high quality customers away with a contract that would not appeal to the low quality ones. On the other hand, the anticipatory equilibrium of Wilson and Miyazaki typically yields constrained-efficient outcomes (see Crocker and Snow, 1985), as such an equilibrium concept does not permit cream-skimming. Similarly, the Hellwig model suggests that con­ strained efficiency of outcomes will depend importantly on whether informed or uninformed agents move first in offering a contract. (c) Co-operative game-theoretic models. A criticism of the preceding set of non-cooperative models is that in order* to be tractable they postulate a given sequence of moves that restricts the ability of market agents to enter into flexible contract forms or organizational arrange­

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ments (see, especially, Boyd, Prescott, and Smith, 1988). Imperfections in information and missing markets are often believed to induce the creation of contracts, non-market organizations, or ‘institutions*—a process with an undoubted co-operative flavour. To the extent that models of the Rothschild-Stiglitz variety restrict the ability of groups of customers and firms to make proposals to one another regarding choice from a sufficiently flexible set of trading arrangements, they are an unsatisfactory representation of the emergence of market institutions. In particular, they presuppose a given institutional framework, rather than letting the institutions emerge endogenously. Boyd, Prescott, and Smith therefore adopt an approach which modi­ fies the traditional model of the core to an imperfect information setting. Other papers in this genre also include Boyd and Prescott (1986), Kahn (1987), Marimon (1988), and Berliant (1990). The mod­ ification entails imposition of incentive-compatibility restrictions on the set of feasible allocations, as well as on the process by which coalitions form in order to ‘block* proposed allocations. These con­ straints have a non-cooperative flavour (since they require no single agent to derive an advantage from masquerading as some type dif­ ferent from its true type); strictly speaking, therefore, the theories are semi-cooperative. Not surprisingly, resulting core allocations (when they exist) are constrained-efficient. However, Kahn and Mookheijee (1991) argue that the ‘private information* core approach makes a set of implicit assumptions about the institutional framework within which proposals and counter­ proposals can be made, and about the degree to which deviations by coalitions can be monitored by others. These assumptions are tan­ tamount to ruling out ‘cream-skimming*. They develop an alternative model of a process which does not impose any artificial restrictions on the coalitions that can form, nor on the kinds of proposals for co­ ordinated trades that can form the basis of a contract. Nevertheless, they employ a different set of informational assumptions, pertaining for instance to the observability of trades between any pair of agents by other agents in the economy. The lack of such observability is a natural aspect of a decentralized trading environment. It, however, reduces the set of contracts that are enforceable: since, for instance, enforceable contracts have to be invulnerable to possible deviations by sub-coali­

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tions (i.e. cream-skimming). This kind of a trading process is modelled naturally by the game-theoretic notion of Coalition-Proof Nash equi­ librium of an underlying simultaneous-offer trading game. This for­ mulation yields a different outcome from the private information core approach: specifically the outcome selected by the Riley equilibrium emerges as the unique Coalition-Proof equilibrium. As described above, this outcome is often constrained Pareto-inefficient, as it is characterized by lack of cross-subsidization. Consequently, the out­ comes of a ‘co-operative’ approach also depend sensitively on the specified institutional structure within which bargaining and trade take place, and on the extent to which actions of coalition members can be monitored by one another. To conclude the discussion of adverse selection models, different formulations of the process by which market participants bargain and trade with one another generate strikingly distinct ‘solutions’. Conse­ quently, one loses faith in the ability of theorists to say something reasonably general regarding the welfare properties of market out­ comes, i.e. the possible role of governments. This merely reiterates the theme of the previous section on incomplete markets. Moral hazard Examples of moral hazard also abound in modem economies: in addition to credit and insurance markets, instances include tenancy, labour, and service markets. A moral hazard situation arises whenever a principal (such as employer, landlord, or customer) cannot monitor the level of effort exerted by an agent (such as worker, tenant, or seller) in producing a satisfactory outcome. What can be observed is an imperfect proxy for this effort, such as the level of output or product quality. The latter depends not only upon the effort by the agent, but also on some uncertain environmental factors (such as weather, soil quality, breakdown of machinery, erratic input supply and so on). Contractual payments from the principal to the agent must perforce depend only on observed output or quality, rather than under­ lying effort. These payments must balance the need to share the burden of environmental risks between principal and agent, with the need to provide the agent with adequate effort incentives. In particular, the agent’s compensation must depend on observed output for the latter

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reason, no matter how disparate the abilities of the principal and agent in bearing risks. Equivalently, the agent can only be partially insured from the environmental risks, and the principal must be able to prevent the agent from acquiring supplemental insurance from other sources. That is, the agent must be rationed in terms of the amount of insurance acquired. In such contexts, first-best welfare levels (which correspond to the hypothetical world where efforts are publicly observable) cannot be achieved because of the need to impose additional risk on the agent to ensure adequate effort incentives. However, the relevant efficiency benchmark should impose a similar informational constraint if the agent were to be given a contract by a social planner. If a private firm cannot monitor the effort chosen privately by the agent, it is reasonable to suppose that neither can the social planner. If private principals or firms can enter into exclusive contracts with agents (i.e. ensure that the latter are not transacting simultaneously with other firms),"and if the market for contracts is competitive, then the market outcome will coincide with the solution to the social planner’s problem (see Shavell, 1979). For if this were not the case, some new firm could enter the market by offering the agent a contract generating higher expected utility, as well as positive expected profit, while continuing to satisfy the agent’s effort-incentive compatibility constraint. This result recurs in alternative formulations of the mar­ ket process: price-theoretic (Prescott and Townsend, 1984), noncooperative (Shavell, 1979), and co-operative (Kahn and Mookheijee, 1990a) game-theoretic models. What happens if exclusive contracts cannot be enforced? Then the agent will have an incentive to circumvent the restriction imposed on the amount of insurance that he or she can acquire, by purchasing supplemental insurance from another firm. This point was first made by Pauly (1974), and reiterated by Helpman and Laffont (1975), and Amott and Stiglitz (1986a, 1988). Most of these authors infer that the market outcome is then constrained-inefficient. Pauly, for instance, argues that if side-contracts cannot be prevented, then in effect, the agent can purchase unlimited quantities of insurance at a given price, and will thereby lose any incentive to apply any effort at all. Amott and Stiglitz argue that the government can enhance welfare in this

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situation by imposing taxes on insurance trades; moreover, taxes or subsidies on commodities that are respectively complements or sub­ stitutes for effort will also be welfare-improving. Essentially similar aiguments are made by Greenwald and Stiglitz (1986) to claim that market equilibria in imperfect information contexts are beset with fundamental inefficiencies; Stiglitz (1988) bases an overarching argu­ ment for an activist role for governments in these terms. The argument, however, continues to apply the same (second-best) efficiency benchmark to evaluate market outcomes when exclusive contracts cannnot be enforced. Nevertheless, the lack of enforceability of exclusive contracts stems from an additional information problem: the unobservability of side-trades of one’s clients with other firms. Once this is explicitly recognized, it is natural to impose a similar informational constraint on the relevant social planning problem as well. Kahn and Mookheijee (1990a, b) develop the corresponding third-best planning problem, where the planner is constrained from observing side-trades of the agent, as well as the chosen effort level. It turns out that there always exist market equilibria (where the solution concept employed is Coalition-Proof Nash equilibrium of an underly­ ing trading game) which achieve the third-best welfare level (which thereby extends the Second Fundamental Theorem of welfare econo­ mics). So viewed from this perspective, there is no fundamental inefficiency that is necessarily associated with market outcomes under conditions of moral hazard. A similar criticism could be made of any argument which purports to demonstrate constrained inefficiency of market outcomes by show­ ing the existence of distortionary taxes or subsidies that generate Pareto improvements. The ability of a government to enforce such taxes implies that it has the ability to monitor all transactions in the economy. If information about all trades is publicly available, then private exclusive contracts should be enforceable (since firms can then credibly threaten to stop trading with a customer if the latter engages in side-trades), and in such cases competitive market outcomes are known to be second-best. Even if the government has a comparative advantage over private agents in monitoring transactions, markets should achieve constrained-efficient welfare levels as long as the government acts as a contract enforcer.

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Concluding, asymmetric information models have been successful in explaining the possible roles of a range of phenomena and market institutions that could not be understood in terms of the Arrow-Debreu theory. However, they have not succeeded in generating an unambiguous depiction of competitive market equilibria. Different formulations have yielded radically different predictions concerning equilibrium allocations and their welfare properties. Market equilibria rarely achieve first-best welfare levels, but it was argued that the relevant efficiency criterion must involve similar informational constraints on the corresponding so­ cial planning problem as well. The solution to such informationally-constrained planning problems also yield welfare losses relative to the first-best world of perfect information, and generate resource allocation mechanisms with similar features as observed in the market (such as non-linear pricing, rationing, collateral). Moreover, there is substantial disagreement between different formulations of the functioning of com­ petitive markets: in most contexts there exist formulations which yield the conclusion that markets generate constrained-efficient outcomes, while others reach different conclusions. It is difficult to agree on a priori grounds which is ‘the’ right formulation: specific institutional features of trading processes play an important role, and these typically vary substan­ tially across different contexts. Consequently, it is premature to draw any general inferences regarding the ‘failure’ of markets with asymmetric information: somewhat like the case of externalities, details of relevant ‘transaction cost’ features of alternative institutional mechanisms (private and public) involve a mass of details that vary considerably from one context to another. 6. A DILEMMA We have seen in the previous section that there is no unambiguous notion of a ‘competitive market equilibrium’ under conditions of asymmetric information. In particular, co-operative approaches yield considerably different outcomes than do non-cooperative approaches, unlike the case of ‘neoclassical’ environments. To a large extent, this owes to the fact that imperfect information generates important pecu­ niary externalities. The presence of informational constraints creates a gap between marginal rates of substitution and transformation. Small

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perturbations in the allocation, induced for instance by tax policy changes, can then induce first-order efficiency effects (see Greenwald and Stiglitz, 1986, and Kahn and Mookheijee, 1988, for further elabo­ ration). These externalities create a strong incentive for associated parties to meige, or coordinate their actions in a way to ‘internalize’ the externality. Such forms of coordinated behaviour are not allowed by most non-cooperative formulations which restrict the strategy spaces and sequence of moves in the formulation of a market game in an arbitrary fashion. However, co-operative formulations permit ar­ bitrary coalitions to form and coordinate trade and action plans con­ strained only by informational and other resource constraints. This ambiguity may cause the reader to recall the point raised by Coase in connection with the suitability of the Arrow-Debreu formula­ tion of market behaviour in the presence of ‘technological’ exter­ nalities. It is also similar to the criticism of price-theoretic models of equilibrium with a given set of incomplete markets, whereby inef­ ficiencies arising from the incompleteness of markets are argued to create a strong incentive for economic agents to create such markets. In all cases, the presence of an inefficiency resulting from a given formulation of market behaviour is argued to create economic incen­ tives for new forms of behaviour that ‘correct’ the inefficiency. In some contexts it involves the creation of new markets and securities, in others the merging and coordination of different agents in the economy through the institution of explicit or implicit contractual mechanisms. This leaves theorists of market failure with a substantive dilemma. Any theory that generates the possibility of market failure will by its own logic create private (individual and collective) incentives for the formation of new institutions and arrangements that remedy the origi­ nal failure. The extent to which the market system will succeed in evolving such efficiency-enhancing institutional changes depends on the ‘transaction costs’ associated with the formation of the requisite coalitions and institutions. These transaction costs remain nebulous, and indeed almost tautological: a proper definition is difficult to offer, and verges on ‘whatever inhibits the formation of efficiency-enhancing coalitional arrangements’. Nevertheless, there is little doubt that market economies do exhibit

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substantive institutional changes designed to overcome failures of the price system (see, for instance, Arrow, 1974; Williamson, 1975,1985; and especially Chandler, 1977 for an interpretation of the historical emergence of large private corporations in advanced market economies along these lines). But there is no theory or evidence to suggest that the institutional changes have been ‘optimal’ responses to evolving economic necessities. To the extent that they reflect evolutionary forces, there is no presumption of their ‘optimality’, at least in the short run. But there is no commonly agreed upon theory of the evolution of institutions either, and it is difficult to make such claims rigorous. An implication of the preceding discussion is that there may be a substantive divergence between the notions of ‘private sector' eco­ nomic activity, and ‘decentralized’ economic activity. To the extent that we identify the Arrow-Debreu model or non-cooperative formula­ tions of markets with a certain form of anonymous, ‘decentralized’ activity, one may interpret the market failure results in non-neoclassical environments as failures of such decentralized economic mechan­ isms. These failures could be ameliorated by the private sector via the evolution of appropriate markets, contractual mechanisms, and or­ ganizational frameworks that appear more ‘centralized’. Alternatively, they could be resolved via governmental interventions that resemble such ‘centralized’ mechanisms. The current state of theory has little to offer in distinguishing between these alternative ‘private’ and ‘public’ solutions.31 Nevertheless, the theory may be interpreted as clarifying a different distinction: that between ‘centralized’ and ‘decentralized’ resource allocation mechanisms, where the latter is identified with Arrow-Debreu-Iike contexts of the interaction of a large number of anonymous market agents in response to impersonal price signals. ‘Centralized’ mechanisms may involve either private or public forms of non-market organizations: private or public corporations that make important production and investment decisions in a centralized or

30See the introductory essay in Bardhan (1989) for an elaboration of this point. 31Datta Chaudhuri (1990) argued that the market failure literature is too ‘sterile* in terms of foiling to accommodate forms of constructive co-operation between private and public sectors of the kind in evidence in post-war Japan, Korea, or Taiwan. This view can be interpreted as pointing to the inability of the literature to throw light on the comparative advantage of alternative forms of 'non-market' organizational structures.

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semi-centralized fashion; long-term contractual arrangements where signalling, reputations, and third-party monitoring play an important role; and forms of decision-making relying upon social norms, and on coordination achieved through verbal communication and persuasion. One may then interpret market failure theory as a rigorous formulation of the importance of economic ‘institutions': a theme that has recurred in recent literature in a variety of contexts involving developed and developing countries alike (such as the organization of firms and industries, as well as agrarian institutions in LDCs). The following section describes a literature that may be viewed as developing this theme in a more rigorous manner, i.e. which puts forward an explicit and general notion of a decentralized resource allocation mechanism, and then proceeds to explore the extent to which such mechanisms generate ‘satisfactory’ outcomes. The notion of decentralization is not necessarily linked to the notion of a privateownership market economy, nor to a planned economy—on the contrary, it could apply to either context equally well. Moreover, a decentralized process need not be price-based, though prices form one possible way of coordinating decisions of different agents in a decentralized mechanism. This literature develops an analysis of the strengths and weaknesses of decentralized processes in different kinds of economic environments (including externalities and increasing returns). The fact that the notion of decentralization in this literature has no necessary connection with the structure of ownership is both a strength and virtue. The strength lies in developing an ‘institution-free’ notion of decentralization, thereby enabling one to focus on this aspect of resource allocation mechanisms in a general manner, in isolation from alternative aspects such as the structure of ownership. It may be viewed as the natural generalization of the Arrow-Debreu theory to non-neoclassical, non-price-theoretic contexts. The weakness of the theory is that it does not throw any light on the important topic of choice between private and public forms of ownership. Section 8 goes on to discuss an alternative literature pertaining to the efficient allocation of property rights, inspired largely by the work of Oliver Williamson (1975, 1985). Though this literature mostly deals with the organization of vertical relations in the private industrial sector, it has the potential for generating a theory of the efficient

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allocation of ownership rights between the private and the public sector. 7. DECENTRALIZED RESOURCE ALLOCATION MECHANISMS Through a series of papers, Leo Hurwicz has pioneered the approach of developing suitable notions of decentralized resource allocation mechanisms that generalize the relevant features of an Arrow-Debreu model. His approach is undoubtedly inspired by the literature on ‘market socialism* developed in the thirties and the forties by Taylor, Lange, and Lemer. This literature developed in response to the scep­ ticism voiced by von Mises and Hayek concerning the feasibility of ‘rational economic calculation’ in socialist economies. Specifically, it was argued that it would be impossible for a single planning agency to acquire all the information relevant to important economic decisions, and that even if such information were available such a planning agency would lack the computational ability to process the available information to solve for the ‘correct’ allocations. In response to these arguments, Taylor, Lange, and Lemer argued that a planning agency could resort to a ‘decentralized’ mechanism that mimicked a Walrasian tatonnement process. Such a mechanism would involve itera­ tive exchanges of information concerning prices and proposed allocations between economic agents and the planning agency; such mechanisms would not involve communicational or computational burdens more onerous than required by a Walrasian mechanism. Moreover, these mechanisms might be able to overcome problems caused by the presence of increasing returns, unlike the Walrasian process. Note, however, that the central point of literature in this tradition is that there is no inevitable connection between the public sector and ‘centralized’ modes of resource allocation, since the latter is being argued to be capable of employing a ‘decentralized’ market-like process. Hence, one would not expect this literature to deliver a theory that distinguishes between ‘private’ and ‘public’ allocation mechanisms. Hurwicz formalizes the notion of abstract resource allocation mecha­ nism (hereafter referred to as RAM), and of ‘informationally decen­ tralized’ resource allocation mechanisms. A RAM involves: (a) a message space, which specifies for each agent a language or set of

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allowable messages, (b) a response rule, which specifies for each agent a message response to messages previously received from other agents, and (c) an outcome rule, which associates a chosen allocation with a given message configuration. The chosen message spaces in conjunction with the response rules define a difference equation in message configurations. Given a stationary point of this iterative pro­ cess, the outcome rule selects an allocation. To the extent that relevant information is dispersed among different agents, such mechanisms enable information to be exchanged, and used as a basis in selecting production, consumption, and trading activities for the economy. A Walrasian tatonnement mechanism is a special form of such a RAM, where agents communicate prices and quantities of different com­ modities; response rules are formed by agents (myopically) optimizing production or consumption plans corresponding to prices announced at the last round (for the auctioneer they are formed by some rule adjusting prices depending upon announced excess demands). Similarly, quantitybased ‘command’ mechanisms may involve exchange of information concerning production or utility functions from agents to a centre, which responds by issuing production and consumption allocations to different agents. There are a large number of alternative RAMs which ‘mix’ elements of such price and quantity-guided mechanisms. While a large literature (surveyed by Heal, 1973) has been con­ cerned with the study of specific RAMs or ‘decentralized planning procedures’ in different environments, Hurwicz (1960, 1972) intro­ duced the general notion of an ‘informationally decentralized’ RAM. This definition seeks to capture those features of a Walrasian mechan­ ism that represent its informationally decentralized character, i.e. that each agent has no information concerning the characteristics or deci­ sions of other agents, and concerns itself solely with the effects of its actions (or those of others) on itself. The former notion is expressed by the property that the response rule specified for any agent expresses a message response to previous messages received, solely as a function of the information possessed by that agent alone. The latter notion is expressed by the condition that the agent’s message concerning the suggested allocation should express only that component of the eco­ nomy-wide allocation that pertains to itself (e.g. aggregate net trades of this agent with the rest of the economy).

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Having defined decentralized mechanisms, Hurwicz proceeds to define a required performance standard for RAMs, that of Pareto satisfactoriness. This requires that the mechanism: (a) yield (essential­ ly) unique stationary message configurations in every conceivable state of the economy, (b) the chosen allocation should be Pareto efficient corresponding to the state of the economy, and (c) every Pareto-efficient point should be achievable by the mechanism with suitable lump-sum redistributions. Hurwicz then poses the question whether in a given class of environ­ ments or possible states of the economy, there exist informationally decentralized RAMs that are Pareto satisfactory. In this way, he seeks to examine if the two classical welfare theorems can be extended to the more abstract notion of a decentralized RAM, and to non-neoclassical environments (e.g. including increasing returns or externalities). Apart from the question of Pareto satisfactoriness, questions relating to the convergence of the mechanism can also be posed in this framework. The main results of this approach are as follows. First, there exist decentralized mechanisms that are Pareto satisfactory in the absence of externalities, but not necessarily otherwise. This means that decentral­ ized mechanisms do not ‘fail’ in the presence of indivisibilities or increasing returns, but they might in the presence of externalities. Second, in neoclassical environments, there do not exist any Paretosatisfactory decentralized RAMs that are informationally more effi­ cient than the Walrasian price-guided mechanism (in the sense of lower dimensionality of the message spaces used by the agents to exchange information). However, in the presence of increasing returns, no decentralized mechanisms may achieve Pareto satisfactoriness with finite-dimensional message spaces. The first result may be interpreted as expressing the need for certain forms of centralized coordination in the presence of externalities, in the sense that some agent(s) need to concern themselves with com­ ponents of the economy-wide allocation that do not concern themsel­ ves directly (in conjunction with the component that does matter to them directly), or with the characteristics of other agents. The second result deals with choices between different forms of decentralized RAMs, when more than one may achieve Pareto satisfactoriness. They may be compared in terms of their respective communicational re­

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quirements: under neoclassical environments price-guided mechanisms are shown to be informationally-efficient in this sense (see Mount and Reiter, 1974 for an elegant derivation of similar results). These results undoubtedly advance our understanding of the choice between centralized and decentralized planning mechanisms. They do not, of course, have direct implications for the question of markets versus governments: the theory may just as well apply to the internal organization of a large private firm as they might to the planning process of a socialist economy. In what follows, we shall discuss some recent extensions and criticisms of this literature. (a) The theory deals with the stationary outcomes of iterative adjustment processes, that may require a large number of iterations to achieve desired standards of convergence. To the extent that these iterations are time-consuming, there would be interest in looking at the outcomes of mechanisms that are constrained to operate only for an arbitrary, finite number of rounds. In general, there may be interesting trade-offs between decision-making delays and the size of the message spaces. For example, the main advantage of a centralized mechanism could be that it requires less time to arrive at a decision, while requiring higher communicational and computational cost. (b) In contexts (such as externalities) where Pareto-satisfactory decentral­ ized mechanisms do not exist, it may be interesting to compare the second-best performance achieved by different kinds of RAMs. In general, there may be important trade-offs between informational/com­ putational requirements of a mechanism and achieved performance standards. These trade-offs are difficult to analyse, owing to the lack of satisfactory measures of informational and computational costs. In fact, there always exist (trivial) centralized mechanisms with 'large’ message spaces that are Pareto satisfactory: the advantage of a decentralized mechanism is its economy of information, communication, and computa­ tional costs. When Pareto-satisfactory decentralized mechanisms exist, there is a clear argument for them on these grounds. But when they do not exist (as in the presence of externalities) the theory does not seem able to say very much about the trade-off between centralized and decentralized mechanisms.

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(c) The question of incentives of agents participating in the process is also an important one. One of the attractive features of the Walrasian mechanism is that response rules for active agents are formed on the basis of self-interested behaviour. Hurwicz (1972) extended his approach to incorporate the question of incentive compatibility of a RAM with the personal objectives of participating agents. This led to a large literature on the 'implementation* of a given performance standard by a RAM, where implementation required that messages sent by agents form a noncooperative equilibrium of the game induced by the mechanism. There are differences of opinion, however, on what the suitable equilibrium concept is for such games. The implications of alternative concepts for the implementability of different performance standards have been worked out quite systemati­ cally in recent years. For instance it is known that with the Nash equilibrium concept, Pareto-satisfactory mechanisms generally exist (see Maskin, 1977, 1985 for instance), while they do not for the dominant-strategy equilibrium concept (Hurwicz, 1972). Some authors have also examined whether the positive results of Nash implementation survive if additional restrictions are imposed on the outcome functions. For example, Chari and Jones (1991) argue that an appropriate notion of decentralization requires the outcome func­ tion to satisfy certain continuity conditions. This expresses the notion that no single individual should be able to exert a dispropor­ tionate influence on the economy-wide allocation. They show that in the presence of externalities, there do not exist Nash-implementable Pareto-satisfactory mechanisms satisfying this continuity condition, and interpret this as an instance of the failure of decentralized mechanisms with externalities. (d) Finally, one may argue that the definition of informational decen­ tralization does not include some important aspects of the general notion of decentralization. Hurwicz’s notion allows all agents to participate in a centralized communication process, where agents communicate with a central allocation authority. One of the important features of a market economy is that agents communicate and transact only with a small number of other agents. Such ‘communicationaT and ‘transactional* forms of decentralization are not captured by the notion of informational

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decentralization. Even within large private firms, there is substantial reliance on hierarchical forms where certain agents are assigned to manage ‘responsibility centres’, wherein they are given sole respon­ sibility to communicate and contract with subordinates. For recent analyses of such hierarchical mechanisms, see Marschak and Reichelstein (1990) and Melumad, Mookheijee, and Reichelstein (1990). 8. THEORIES OF PROPERTY RIGHTS Theorists interested in explaining the phenomenon of vertical integra­ tion in modem industries have also grappled with the problem of developing a theory of property rights. Following the pioneering work of Coase (1937), Simon (1951), Williamson (1975, 1985) and others, the problem has been to explain the boundaries between firms and markets. For instance, what is accomplished by a merger between two firms that could not have been achieved with separate ownership? In other words, how does a change in the ownership structure affect the range of feasible resource allocation mechanisms? A satisfactory theory of this would have important implications not only for under­ standing the historical emergence of large corporate hierarchical firms in advanced market economies, but also the impact of the transfer of ownership of assets from the public to the private sector. In his seminal paper, Coase (1937) posed this question for the first time, and argued that it depended on the relative ‘transaction costs’ of organizing production and exchange through the alternative forms of a market or a hierarchical mechanism. Williamson (1975, 1985) has attempted to provide more content into the notion of transaction costs. According to Williamson, transaction costs of organizing through the market tend to be large when: (a) the number of traders involved are small, (b) when there ‘is' a need to develop a long-term relationship between buyers and sellers, (c) when ‘bounded rationality’ does not allow the relationship to be mediated by a long-term contract with various contingencies foreseen and written into it, and (d) when there is scope for one party to opportunistically exploit another at the time of renegotiations of the contract (as would be the case when one party was required to make upfront investments in relation-specific assets). On the other hand, the transaction costs of organizing through hierar­

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chies depend on the costs of ‘bureaucratization’, which may comprise ‘control loss’ resulting from loss of information and incentives across multiple vertical layers of management. Williamson’s theories reflect features that describe many observed features of market and non-market relationships, respectively. They have also received a certain amount of empirical support (e.g. see Joskow, 1988). However, it is difficult to develop a rigorous formula­ tion of many of these ideas on the basis of conventional tools of economic theory. For instance, a generalization of the so-called ‘Reve­ lation Principle’ (see Myerson, 1979, 1982) implies that if long-term comprehensive contracts (or resource allocation mechanisms) can be instituted^ if opportunistic renegotiations of this contract can be pre­ vented, and if there are no computational or communicational con­ straints, then a particular kind of resource allocation mechanism dominates all others. This mechanism resembles in some respect Hurwicz’s notion of a resource allocation mechanism: all agents communicate their private information to a centre, which processes this information and issues instructions to agents about production, consumption, or trade activities. Rewards of different agents are condi­ tioned on observed performance variables, and are designed in such a way as to provide them with incentives to communicate their private information truthfully, and obey instructions issued by the centre. Note that there is nothing to prevent organizations with different ownership structures from employing such mechanisms. The implication of this result is that the absence of contractual incompleteness (and concomitant strategic renegotiations) and of com­ putational or communicational costs implies that ‘organizational struc­ ture’ or ‘structure of ownership of assets’ is irrelevant. Any economic context, irrespective of whether it happens to be a market relationship between two private agents, or a hierarchical relationship within a private sector firm, or within a public sector firm, can organize production, consumption, and exchange via a particular kind of res­ ource allocation mechanism. In particular, there is no reason why any of these organizational forms cannot imitate the resource allocation mechanism employed by another. To illustrate the last point, Williamson does not describe why the problems of small-number bargaining or strategic renegotiation charac­

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teristic of market relationships do not occur within a hierarchical firm. If it is argued that hierarchical superiors within firms have better access to audits of private information of subordinates, or are better able to arbitrate disputes, one wonders why contracts governing market relationships cannot share the same features (e.g. one party voluntarily surrenders the right to be audited by the other, or both agree to refer to third-party arbitrators in the event of a dispute). Conversely, one may ask the question why hierarchical firms suffer the costs of bureau­ cratization, instead of replicating a market-like process for their vari­ ous departments. Besides, the notion of 'bureaucratic costs’ is very nebulous: instead of the two-layer mechanism singled out by the Revelation Principle, why do large firms opt for organizational struc­ tures with a larger number of layers that are the sources of 'control loss’? Part of the difficulty, as the Revelation Principle suggests, is that a meaningful theory of property rights would have to rely on notions of bounded rationality or communication costs. An alternative is to retain the assumptions of complete rationality and costless communication, and examine the consequences of incomplete contractual mechanisms, i.e. those that are subject to renegotiation. Of course, such an approach would have to leave open the question of why contracts or resource allocation mechanisms are incomplete in the first place: as Williamson argued, bounded rationality is perhaps an important reason. Grossman and Hart (1986) have initiated a theory along these lines, that formalizes some of Williamson’s ideas. Suppose that a buyer and a seller are involved in a two-period market relationship which is governed by a sequence of two single-period contracts. Exogenous reasons prevent the relationship from being governed by a comprehen­ sive long-term contract. The seller can invest in early periods in ways that are desirable from their mutual point of view; however these are relation-specific investments that are worthless to anyone outside this particular relationship. At the end of the first period, the second-period contract is negotiaied on the basis of the bargaining strengths of the two parties at that stage. In such a context, the seller will underinvest in the first period, as part of the returns from this investment will be captured by the buyer when they negotiate the second-period contract. The buyer will be unable to prevent this because of the relation-

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specificity of the assets he has invested in: he cannot credibly threaten to withdraw from the relationship and obtain a better deal elsewhere. Moreover, there is no way that the buyer can commit at the first period to offer the seller the full value of the return on his investment: once this investment is made, it will be in his self-interest to obtain a second-period bargain that captures some of this return for himself. An alternative mode of organization is for one agent to purchase the assets of the other, and form a hierarchical merged firm. Grossman and Hart define ownership as 'residual rights of control*, i.e. as the right to decide what is to be done with the asset in question when a contingen­ cy arises that was not written into the original contract. With this definition, the implication is that if one party purchases the assets of the other, he has the sole right to decide the second-period allocation, subject to satisfying a participation constraint for the other agent. In the example described above, efficient investments are ensured if the party making the investment 'buys out’ the other firm, for he then has the hierarchical authority to ensure that the entire return on his invest­ ment accrues to him. In more complicated scenarios where both parties may invest in relation-specific investments, a purchase of firm B by firm A would boost the investment incentives of the latter, but reduce the incentives of the former. Consequently, some non-trivial trade-offs emerge between separate ownership and different forms of vertical integration. For an extension of these ideas to the case of more than two agents, to the idea of ownership of human as well as non-human assets, and to alternative forms of ownership such as co-operative firms, see Hart and Moore (1990). The Grossman-Hart approach is notable for providing a notion of asset ownership with non-trivial implications for the range of resulting resource allocation mechanisms. However, it rests on a rather ad hoc assumption of incompleteness of contracts that was assumed rather than explained. Subsequent literature (e.g. Hart and Moore, 1988) has attempted to fill this gap by exploring the idea that relevant contingen­ cies may not be written into contracts because they are not verifiable by third-party contract enforcers such as courts (though they may be observable to the two parties concerned). However, this has met with a number of important criticisms (e.g. see Green and Laffont, 1988; and Aghion, Dewatripoint, and Rey, 1989). It seems that alternative ex­

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planations for incomplete contracts (such as bounded rationality or communication costs) would be useful to pursue in future research, but this is undoubtedly a difficult venture. Further, the 'costs of bureau­ cratization’ in hierarchies would also seem to require more serious analysis than has been witnessed in past literature. Finally, extension of this approach to study distinctions between private and public ownership would be equally important to study. 9. CONCLUDING COMMENTS The theory of general equilibrium, welfare economics, and planning has progressed considerably in recent years to encompass non-neoclassical phenomena of externalities, incomplete markets, and imperfect informa­ tion. The theory has succeeded both in broadening as well as complicat­ ing the depiction of 'market' as well as 'government' behaviour. For instance, the literature on incomplete markets incorporates models of financial and real assets, and the impact of future price expectations on economic activity. In so doing, it has overturned many classical presump­ tions about the efficiency and determinacy of competitive equilibrium outcomes. The literature on imperfect information and game-theoretic models of trade encompasses strategic behaviour in small-number situa­ tions (e.g. bargaining), and a large number of non-price market institu­ tions.32 Informational considerations have also provided a deeper and more complicated picture of what governments can accomplish via interventionist policies. This is illustrated by elucidation of informational and incentive considerations in the design and implementation of redistributive policies, of policies regulating private firms, and in the organization of production and exchange within the public sector.33 In

32The latter indude quality signals (such as warranties, certification, collateral, etc.), quantity constraints (e.g. credit rationing, unemployment, and sticky prices), intermediaries, information-generating (e.g. accounting firms) and information-exchanging (e.g. credit bureaus) institutions, as well as different forms of contractual, incentive, and organizational mechanisms (such as auctions and procurement mechanisms, subcontracting, piece-rates, promotion schemes, and corporate hierarchies). 33We did not, however, adequately survey these literatures, partly because other chapters in this volume deal more directly with these topics. Difficulties in implementing lump-sum redistributions were discussed in Section 2 while Section 7 bore on some issues in designing planning mechanisms. For a survey of the literature on regulation, see Baron (1989).

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particular, discussions regarding ‘planning’ mechanisms are now more sensitive to the problems of gathering information dispersed among dif­ ferent agents before formulating a comprehensive ‘plan’, and of attendant communicational, coordination, incentive, and enforcement costs. I have attempted to argue that comparisons between outcomes achievable via markets or governments under non-neoclassical condi­ tions are complicated by ambiguities regarding the depiction of market behaviour, and about the appropriate benchmark in terms of govern­ ment behaviour. The literature substantiates the intuitive view that anonymous, decentralized modes of interaction of the kind embodied in the Walras-Arrow-Debreu model will ‘fair in the presence of externalities and imperfect information. Whether these failures will be more successfully resolved via governmental interventions, or via private processes of conglomerate organization or non-price contrac­ tual mechanisms, is a fundamental open question. In particular, the connection between patterns of ownership (private versus public) and resource allocation mechanisms has proved elusive, though some emerging literature on property rights (reviewed in Section 8) may shed light on this in the future. A major shortcoming of the literature is the lack of a rich theory of government behaviour. Just as recent theoretical developments have attempted to grapple with realistic imperfections of market processes, there is a need for theories that confront market imperfections with realistic imperfections of government behaviour such as incentives of politicians, pressure group influences, and bureaucratic inefficiencies. Moreover, there is a need for theories that throw light on the question whether inefficiencies traditionally associated with markets and gov­ ernments, respectively, are in some sense inevitable concomitants of private property and socialistic systems, respectively, or whether it is possible for the public sector to ‘reform’ itself by imbibing private sector practices whenever these appear to be superior. In other words, is privatization essential to reform an inefficient public sector? What do less developed countries have to learn from the literature on market failure? I conclude this essay with some remarks on this issue. Since obtaining independence from colonial powers a few decades ago, many underdeveloped countries embarked on ambitious prog­

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rammes of state-led industrialization. The intellectual underpinnings of these programmes were provided by ideas of the 'big push’ and balanced growth associated with Rosenstein-Rodan and Nurkse. The theoretical basis for these ideas was the notion of 'pecuniary externalities’ and their relevance to underdeveloped economies (Scitovsky, 1954) owing to the absence of a well-developed market system in these economies. The literature on incomplete markets and imperfect information can be view­ ed as formalizing some of these ideas: in particular by demonstrating the 'failure’ of decentralized Walrasian mechanisms in these contexts to achieve Pareto-satisfactory outcomes (to borrow Hurwicz’s term). Nevertheless, advocates of the 'big push’ appeared to believe that governments initiating large-scale industrialization programmes would not be similarly constrained by any of the factors (such as information or transaction costs) that may have been responsible for the failures of decentralized market solutions in these economies. In effect, the recommendation for large-scale government intervention was based on comparison between a second-best market system and the myth of an ideal, benevolent social planner with unlimited communicational, co­ ordination, and enforcement ability. In other words, the theoretical demonstration of the failure of (a certain depiction of) market outcomes to achieve first-best Pareto-satisfactory outcomes was grossly misinterpreted. All the problems of communication, coordination, in­ centives, and enforcement that one would equivalently expect of cen­ tralized systems were ignored The theory that I have attempted to review in this essay has been concerned with unravelling underlying, fundamental factors (such as informational and transaction costs) that explain the absence or imper­ fections of many kinds of markets, and the presence of various non­ price mechanisms in free enterprise systems. These informational and transaction costs are sought to be placed on par with the more tradi­ tional 'primitives’ of the Walrasian theory, such as preferences, tech­ nology, and endowments. In my view, the main contribution o f the theory is to depict the ‘economic environment* in these terms as “XA distinct from the mode o f economic organization. In so doing, it ^For instance, the imperfection of capital markets may not necessarily manifest an imperfection of the market system (that can be ameliorated by governmental intervention, such as monopoly aspects); rather they may be a symptom of a deeper informational asymmetry that would afflict both market and governmental mechanisms.

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creates the awareness that informational, transactional, and enforcement costs are present in both market and non-market systems. It then proceeds to attempt comparisons between the two systems when both are subject to similiar 'environmental' constraints. While its success in the latter respect is undoubtedly questionable, the lack of any simple, general answers should cause 'believers’ in either pro-market or pro-government camps to reflect on the appropriateness of their respective views. Another related contribution of the theory is to enlarge the range of organizational mechanisms beyond the traditional market/government dichotomy. One is led to consider alternative mechanisms that mix elements of the two polar systems. For instance, observers of the Japanese economy have frequently commented on the special relation­ ship between their private and public sectors: the latter plays an important, non-traditional role in coordinating private sector activity via informal means of communication and persuasion (rather than explicit, direct involvement). The role of informal mechanisms such as reputations, and social norms of trust, reciprocity, and third-party sanctions, with or without the conjunction of some centralized initia­ tives, have been discussed in connection with common resource and environmental problems. In contexts of health, education, and rural welfare programmes, firms that are in the nonprofit-cum-nongovemmental sector often play an important role.35 The lack of a profit motive ensures that these firms do not have the same temptations to exploit informational asymmetries as profit-oriented firms. On the other hand, they avoid the bureaucratic costs and corruptibility of governmental organizations, most often by relying upon the services of dedicated volunteers. To provide yet another example, the public sector may be responsible for the provision of public goods, but not necessarily their actual production. Mixed private-public solutions may involve financing of public-good provision by the government, while franchises or procure­ ment contracts are awarded to private firms that are more cost-effective.36 wSee Wdsbrod (1988) for an overview of the literature on non-profit firms. *See Borcherding, Pommerehne, and Schneider (1982) for a summary of fifty empirical studies comparing costs between public and private supply in a number of different countries. The majority of these cases (forty out of fifty) revealed private supply to be more cost-effective. For a general discussion of empirical results, see Chapter 7 in Wolf (1988).

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Game-theoretic models of such alternatives have been emerging in recent years as a natural offshoot of the maiket failure literature.37 To provide an illustration of the foregoing viewpoint, consider the context of rural credit markets in underdeveloped economies. It has been ob­ served by many scholars that these markets are fragmented; are interlocked with markets for labour; land, and services; involve rationing and usurious interest rates, as well as steep collateral requirements. It is tempting to draw the conclusion that substantive government intervention is warranted. Such a conclusion may be defended on redistributional grounds, or from the need to reduce the monopoly power of local moneylenders. But it may be more difficult to defend on the basis of efficiency considerations, such as the need to encourage technological improvements and higher productivity. A careful approach to the efficiency issue would require analysis of some of the underlying informational and transactional constraints that may have contributed to some of the observed features of these markets. For instance, interlocking of different markets could conceivably arise as an efficient response to moral hazard problems (see Braverman and Stiglitz, 1982), and the thinness of credit markets may derive from adverse selection and moral hazard problems. Further; recommendation of governmental intervention should follow detailed analysis of some of the informational, incentive, and enforcement problems one may anticipate with such programmes. In order to be successful such programmes might also be forced to rely to some degree on features observed in unregulated markets such as close monitor­ ing of financed projects, credit rationing, and collateral requirements. One might also consider 'mixed* alternatives such as rural credit co-operatives that receive some form of governmental support. Models with an explicit specification of informational and other transaction costs may then aid in the understanding of some of the advantages and disadvantages of such organizational forms (for instance, the advantage of mutual monitoring and enforcement, against the disadvantage of attendant free-rider problems).39 Some authors such as Stiglitz (1988, 1989) have stressed that the 37On the coordination of R&D efforts of different firms, see Picard and Rey (1990) and Gandal and Scotchmen (1988). On social norms, see Axelrod (1984,1986), Milgrom, North, and Weingast (1989), and Bendor and Mookherjee (1987, 1990). On contract design, see McAfee and McMillan (1987), and Laffont and Tiiole (1991). MFor an elaboration of this view, see Eswaran and Kotwal (1989). 39See Varian (1969) for a theoretical analysis of the practice followed by Bangladesh's Grameen Bank of inducing monitoring of borrowers by each other.

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traditional presumption of economists in the neoclassical tradition of the efficiency of competitive markets needs to be seriously questioned in contexts of incomplete markets and imperfect information. Market outcomes rarely achieve first-best outcomes, and may be characterized by some fundamental pecuniary externalities. To the extent that the transaction costs of private ‘internalization’ of such externalities are high, there exists a potential for efficacious governmental interpreta­ tion. Lacking a satisfactory theory of such transaction costs, it is difficult to say anything general about the kinds of contexts where governments may have an important role. Until such time that some such theory ^merges, we may have to be satisfied with a pragmatic, case-by-case judgment of the relative efficacy of private and public responses to these coordination problems. On the other hand, of course, there is no general presumption either for the desirability of governmental interventions in contexts of incom­ plete markets or informational imperfections. Instead, they may be justified on a case-by-case basis, depending on appraisal of the speci­ fic features of a given sector of the economy. Of course, interventions can be defended on the grounds of redistributing real incomes, alleviat­ ing poverty, and ensuring satisfaction of basic needs, though the specific form of such policies and their implementation need to be thought through carefully. On efficiency grounds, there is a stronger presumption for the need for governmental interventions in contexts of classical non-pecuniary externalities, and the provision of public goods, particularly when these involve very large numbers of people. Such contexts include the areas of environmental protection, education, health, transport, as well as various forms of activities associated with the production and dissemination of knowledge (e.g. development and diffusion of new technologies and organizational practices, testing and certification of products and occupational workplaces for their safety, generation of information about external market conditions to private exporters). In addition, the government has a role in regulating natural monopolies, as well as preventing the emergence of ‘unnatural’ ones. On the whole, this represents a radically different perspective on the role of the government from that represented by advocates of the ‘big push’.

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Efficient Resource Allocation Under Increasing Returns R a jiv V o h r a *

1. INTRODUCTION Consider a private-ownership economy in which all the ideal condi­ tions of perfect competition are satisfied except for one—there exists a technology characterized by increasing returns. For concreteness, think of this technology as one which can be used to produce a commodity with a fixed cost (in terms of one input) and constant marginal cost. Gearly, a firm using this technology is a natural monopoly—it is not efficient to have more than one firm use this technology. The presence of such a firm is often described as a reason for ‘market failure’. More precisely, competitive behaviour may not lead to an efficient allocation of resources. In any case, in this context, competitive behaviour may not even be an appropriate descriptive assumption. On the other hand, non-competitive, profit-maximizing behaviour may not be consistent with an efficient allocation of resources. Efficiency will generally require that the firm operating under increasing returns be regulated. And this provides a rationale (certainly not the only one) for introduc­ ing a public sector in such an economy. This paper will be concerned with a theoretical analysis of the static resource allocation problem in a mixed economy of a particularly simple kind—one in which govern­ ment intervention is restricted to operating an increasing-retums tech­ nology in the interests of economic efficiency. It will be possible to view government intervention either as the operation of a public sector or as the regulation of a firm. In particular, we shall be concerned with *1 would like to acknowledge the helpful comments of participants of a seminar at the University of Rochester, the 1991NBER-NSF Conference on Decentralization at Cornell and the 1991 SITE Summer Workshop at Stanford.

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the theoretical justification for regulation and an attempt to charac­ terize the nature of regulation which is consistent with an efficient allocation of resources.1 In terms of efficiency, the ‘market failure’ associated with increasing returns may be described as follows. Suppose all agents in the economy behave competitively in the sense that they take the vector of market prices as given and maximize their individual objectives—consumers maximize utility and firms maximize profits. A competitive equilibrium is described as a vector of market prices and a collection of competitive demands and supplies such that all markets clear simultaneously. Accord­ ing to the first welfare theorem an allocation corresponding to such an equilibrium is Pareto optimal. Thus competitive behaviour leads, in equilibrium, to an efficient allocation of resources. It is noteworthy that this result requires no assumptions on the preferences of the technologies. However, the welfare prescription of this result presupposes the existence of a competitive equilibrium; the fact that a competitive equilibrium has a desirable property is of no significance if such an equilibrium does not exist. The classical results of Arrow and Debreu (1954) and McKenzie (1954) provided sufficient conditions for the existence of a competitive equilibrium. Apart from some technical conditions, the principal assump­ tions of this result are that all utility functions are quasi-concave (pre­ ferences are convex) and all firms face constant or decreasing returns to scale (production sets are convex). Thus, in the absence of increasing returns, competitive behaviour leads to an efficient allocation of resour­ ces. However, if there exists a firm operating under increasing returns, then competitive behaviour may not be consistent with an efficient allocation of resources simply because there may not exist any such equilibrium. The failure of existence can be seen even in the simple case of a single consumer, two-commodity economy in which there is a single firm with a U-shaped average-cost curve; there may be no intersection of the supply and demand cuives. Another property of the competitive solution is that it is incentive compatible in an economy with a large number of agents.2 And this *Of course, these are by no means the only issues in optimal regulation, and the reader is referred to BOs (1985) for a more comprehensive survey. 2In a precise sense, the competitive assumption is not an assumption at all if every agent is truly negligible; see Aumann (1964).

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provides another source of scepticism with respect to competitive behaviour in the presence of increasing returns. It is simply not an appropriate descriptive assumption for a firm which produces under increasing returns. Indeed an example of such a firm, which is of considerable economic interest, is precisely one where the firm is a natural monopoly. On both normative and descriptive grounds, therefore, one must adandon the purely competitive model in studying economies with increasing returns. In general, non-competitive firm behaviour leads to an inefficient allocation of resources or to an outcome which forces competition through entry (or the threat of entry). It is easy to see that it is not conducive to efficiency in the presence of a natural monopoly. Thus if we consider the normative problem of efficient resource allocation, and this is the main concern of this paper, we shall have to abandon not only competitive behaviour but also profit-maximizing behaviour (at least on the part of the firm producing under increasing returns). In other words, any equilibrium notion which leads to Pareto efficiency in an economy with increasing returns will, a priori, have undesirable incentive properties. This is the inescapable cost of insist­ ing on efficiency in the presence of increasing returns.3 In the interests of efficiency, we shall need to consider an equilibrium notion which involves regulating the firm producing under increasing returns. While the question of incentive compatibility is undoubtedly an important one, we shall, nevertheless, ignore it and concentrate only on the issue of optimal regulation. Clearly, a characterization of optimal regulation is necessary before one can analyse the possibilities of implementing it. And, as we shall see, the theory has yet to provide a general solution to the optimal-regulation problem. What is well known, at least since Hotelling (1939), is that a necessary condition for Pareto optimality is that the market price of the commodity being produced under increasing returns be equated to its marginal cost. This can be seen as a necessary first-order condition of 3The competitive mechanism also has the attractive property of being a decentralized resource-allocation mechanism. This too may be a desirable property that may need to be sacrificed in insisting on efficiency under increasing returns. As has been shown by Calsamiglia (1977), there exists a class of economies with increasing returns in which there does not exist any decentralized resource-allocation mechanism such that every equilibrium is Pareto optimal.

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an appropriately defined constrained-maximization problem. All that is involved is the observation that the classical Pareto-optimality condi­ tions, in terms of all marginal rates of substitution in consumption being identical to all marginal rates of transformation in production, are necessary conditions irrespective of any convexity assumptions. Under appropriate convexity assumptions, these conditions are not only necessary but also sufficient for Pareto optimality. In the next section we shall present a generalized second welfare theorem which shows, in a very general context, the necessity of marginal-cost pricing for Pareto optimality. Marginal-cost pricing has at least two important implications. First, a natural monopoly may not have an incentive to follow this pricing rule; it may be inconsistent with profit maximization even if the firm is a price-taker. Secondly, the firm may actually incur a loss by charging marginal-cost prices. Thus the natural interpretation of a firm following this pricing rule is one of a regulated firm which has its resulting losses covered through a subsidy from the government. Clearly, to maintain efficiency, this subsidy should be covered through lump-sum taxes on the consumers. Indeed, this was the argument made by the proponents of marginal-cost pricing; see Ruggles (1949, 1950) for a survey of the early literature on this subject. What does a generalized second welfare theorem tell us about the form of efficient regulation? It says that marginal-cost pricing along with lump-sum taxation is necessary. Unfortunately it does not, in general, imply that efficiency can in fact be achieved through such a policy. At one level, the reason for this is quite obvious. Marginal-cost pricing is only a necessary and a local condition for efficiency. In the presence of increasing returns, it may not be sufficient for global efficiency; there may be many allocations where prices are equal to the marginal cost and some of these may be inefficient. This is easy to see even in a single consumer, two-commodity economy in which one of these commodities is produced under increasing returns. The indif­ ference curve may be tangent to the production possibility curve at many places and only one of these may correspond to the optimum. Thus the first welfare theorem does not hold for marginal-cost pricing; an equilibrium with marginal-cost pricing may not necessarily be Pareto optimal.

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Unfortunately, there may be a more fundamental failure of efficien­ cy. It may be impossible to find any maiginal-cost pricing equilibrium which yields efficiency. This phenomenon is somewhat more subtle. It cannot arise in a single consumer economy. There, under standard compactness conditions, a Pareto-optimal allocation exists, and by the generalized second welfare theorem this can be sustained as an equi­ librium with marginal-cost pricing. In an economy with many con­ sumers we can again ensure that Pareto-optimal allocations exist under standard conditions. And, by the generalized second welfare theorem, any such allocation can be sustained as a marginal-cost pricing equi­ librium provided income is redistributed in an appropriate manner. However, the recent literature on increasing returns has shown that if there is some restriction on the ability of the government to carry out a redistribution of income, then none of the marginal-cost pricing equi­ libria may be efficient. This, of course, is in sharp contrast to the first welfare theorem: for any given income distribution, every competitive allocation is Pareto optimal. In a pioneering paper, Guesnerie (1975) was the first to show that if the rules for income distribution are exogenously fixed then there exist economies in which no marginal-cost pricing equilibrium is Pareto optimal. The hypothesis that the rules for income distribution are exogenously fixed requires some comment and we will elaborate on this shortly. For now, consider a private-ownership economy in which consumers hold equal endowments of two commodities. Suppose one of these commodities can be used to produce the second commodity through an increasing-retums technology. An example of fixed rules for income distribution is the case in which all profits (or losses) of the firm are distributed, in a lump-sum manner, equally among the con­ sumers. Guesnerie (1975) provides an example of such an economy in which every marginal-cost pricing equilibrium (with these rules for income distribution) is inefficient. One may question the rationale for the exogenously-given rules for distributing the losses of the firm. Moreover* there is the possibility that changing the distribution of the tax liability among the consumers may restore the efficiency of at least some marginal-cost pricing equilibrium. This expectation is based on the observation that changing the tax liability is tantamount to some change in the income distribution, and from the second welfare theo­

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rem we know that arbitrary changes in the income distribution will allow us to sustain any Pareto-optimal allocation as an equilibrium. Alas, even this flexibility in choosing the distribution of the tax liability among the consumers may not be enough. As we shall see, there exist economies in which for all possible rules for distributing the losses of the firm, all the marginal-cost pricing equilibria are inefficient.4 The paper is organized as follows. In Section 2 we shall present the general equilibrium model and the generalized second welfare theorem which applies to economies with non-convex technologies. In Section 3 we consider the issue of optimal regulation and draw out some implications of the second welfare theorem. In Section 4 we provide a simple example of a two-consumer, two-commodity economy with a technology characterized by fixed costs and constant marginal costs. In this economy, the initial distribution of the endowments are specified exogenously (it is in this sense a private-ownership economy) and for every possible way of distributing the losses of the firm in a lump-sum manner among the two consumers, every marginal-cost pricing equi­ librium is inefficient. Efficiency requires not only marginal-cost pric­ ing but also an explicit redistribution of income. In Section 5 we present a special case in which it is possible through some choice of the tax liabilities to ensure the existence of at least one Pareto-optimal marginal-cost pricing equilibrium. 2. A GENERALIZED SECOND WELFARE THEOREM In this section we shall present a general result which shows that marginal-cost pricing is necessary for efficiency. It is possible to derive this conclusion by making differentiability assumptions and using the mathematical-programming approach. Consider the constrai­ ned-maximization problem of maximizing the utility of one consumer subject to the given utilities of the others, and the given technological and resource-availability constraints. The first-order conditions of this 4It is important to note that this phenomenon cannot arise if we allowed some consumers to get a subsidy while others are taxed, for in that case, by the generalized second welfare theorem, any Pareto-optimal allocation could be sustained as a marginal-cost pricing equilibrium with some taxes and subsidies.

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problem yield marginal-cost pricing. Differentiability, however, turns out to be a redundant assumption for this result if one makes use of some recent results in non-smooth analysis. This is the approach we shall follow. In particular, we shall use Clarke’s normal cone as a formalization of marginal rates of substitution. The reader who is familiar with the result based on the programming approach may, if so indined, skip the proof of Theorem 1 without any loss of continuity. In the rest of this paper we shall not be using any crucial properties of Garke’s normal cone. Under suitable differentiability assumptions, the Kuhn-Tucker con­ ditions of the constrained-maximization problem imply that at every 'interior* Pareto-optimal allocation, all marginal rates of substitution must be identical. This goes back at least to Allais (1943), Hicks (1939), and Lange (1942). This version of the second welfare theorem was generalized by Arrow (1951) and Debreu (1951). Their proofs were based on an application of the separating hyperlane theorem and showed that differentiability assumptions are redundant—the crucial assumptions are convexity assumptions (convexity of preferences and of production sets). Moreover, by stating the results in terms of prices, boundary solutions are easily incorporated Their result states that corresponding to any Pareto-optimal allocation, there exists a vector of prices such that (evaluated at these prices) every consumer’s consump­ tion plan minimizes expenditure over the 'at least as good as’ set and every firm’s production plan maximizes profits over the production set. The proof, however, does not allow for increasing returns. It is clearly desirable to have a general version of the second welfare theorem which applies both to the non-smooth and the non-convex case. It is clear that any such generalization will have to provide a suitable generalization of the notion of marginal rates of substitution. Consider the simple case where one input is used to produce one output through a production function /. If / is smooth, then the marginal rate of substitution can be identified with the derivative of /. If it is not smooth then it can be identified with the entire set of points between the left and right derivatives of /. Now consider the case where the technology is described by a production set Y which is a subset of R 7, the /-dimensional Euclidean space. If the set is convex, the maigjnal rate of substitution at a production plan y E Y may also

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be identified with the set of prices which make y a profit-maximizing plan over the set Y. For a general theory we require a generalization of the notion of a derivative which gives us the usual characterization of the marginal rates of substitution in each of the above cases. One such generalization which has proved very fruitful in this context is Clarke's normal cone. We shall now formally define the normal cone and state some properties which are of special interest to the problem at hand; for further mathematical details the reader is referred to Clarke (1983).

FIG. l

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Before defining Clarke’s normal cone it will be useful to view the profit-maximizing prices in the convex case as follows. Consider a ‘tangential approximation’ of Y at y E Y and translate this set to the origin; see Fig. 1. The set of normals or marginal rates of substitution is simply the polar of this set. For a set A C R 7, the polar is defined as A* - \p E R 7 I p - x s O f o r all x EA},

FIG. 2

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where pjc denotes the inner product of p and x. Notice that the polar of any set contains 0 and is, therefore, non-empty. Clarke provided a tangent approximation, called Clarke’s tangent cone, which is always a closed convex cone (even if the set is not convex). For a non-empty set Y C JR.1and y E Y , the tangent cone of Y at y is T(Yf ^ - { z G R 1 | for every sequenceyq E Y ,y q y and every sequence ft E (0, oo), f -*• 0, there exists a sequence z9 EIR*, z* -* z, such that yq + tq& G Y for all q}. The normal cone to Y at y E Y is defined as

For an illustration of the tangent and the normal cones see Figs. 1 and 2, where the dashed lines are the boundaries of the tangent cones translated to y. For a more detailed discussion see Khan and Vohra (1987). It will be useful to state a few basic properties of T(Y,y) andW(y,y). We shall use dY to denote the boundary of the set Y. 1 Suppose y C R i and y E Y , T(Y, y) is a non-emptyy closed convex cone and if y E dY, then W y ) * R'. I f p . y * p - y' for ally' ^ Y, thenpeN (Y ,y). I f Y is convex andp EN(Y, y \ thenp . y ^ p y' for ally1E Y. I f Y is a C1 manifold and y E dY> then N(Y, y) coincides with the usual space o f normals at y.

Lem m a

(1) (2) (3) (4)

Proof. See Clarke (1983). Based on this result (in particular on Lemma 1 (2), (3), and (4) we shall define the set of marginal-cost prices for a production set Y at a production plan y simply as N(Y, y). We shall follow Debreu (1959) in defining an economy. There are m consumers, indexed i E { 1 , . . . , m}, each consumer i having a con­ sumption set Xi and a utility function 14. There are n firms indexed j E { 1 , . . . , n}> with production sets Yj. The aggregate endowment is denoted by co. A consumption plan is x - (jcx, . . . , xm) E X - n,- Xf and a production plan is y - (yj,. . . , yn) E y - fly Yj. There are I commo­

Efficient Resource A llocation Under Increasing Returns

111

dities indexed h E { 1 , . . . , /} and all consumption and production sets are subsets of R*, the /-dimensional Euclidean space. The economy may now be defined as £ - {(A',-, m,), «,'(*,")}• Let G - R d x f ) + 2 R, does not belong to this set. However, the tangent cones (suitably translated) can be larger than the sets them­ selves, and we need to prove that (1 )

a) £ G.

Since the tangent cones are non-empty and convex, by the same o argument as in Debreu (1959) it follows that G is a convex set. A proof of ( 1 ) is the only additional complication that our set-up in­ volves. To establish (1), let us suppose it does not hold, i.e. there exist x/> E Ri’(*/'), X; E R fa ) for all i + i' and E T\Yj, yj) for all j such that a ) - Z x ; - Z ( Z ; + >-;). * J

Since co - 2 f-xt - Zyyy, thisimplies that xj). i

(2)

•

From assumptions (a), (b.l), and (b.2) it follows that for any real number t E (0,1), x? + t(x{> - xj) E Ry (xj>) and x, + 1(x{ - x,) E R fa ) for all i * i\ From (2), therefore, we have 2 x,- + t Z z j E R?(*,') + 2 R,{xi)for all t E (0 , 1 ). *

j

(3)

i »• i'

Since z} E T(Yj, yj) for all j, from the definition of the tangent cone, we

114

RAJIV VOHRA

know that for any sequence of positive real numbers f such that fi 0, there exists, for each j, iff such that -* z} and y} + E Yj. For q large enough, z? becomes arbitrarily close to Z;-zy By the continuity of tiy (assumption (b.l)) and (3) it follows that there exists a q large enough such that IX ' + f l Z z J e R ^ x r f + YR.U;). i

Since

2,-xt -

j

- .

Moreover,

Zy {yj + fitf) E Z; YJ. But this, along with (4), contradicts the Pareto optimality of ((*,), (yj))t and completes the proof of (1 ). We can now appeal to the separating hyperplane theorem to assert that there exists p 6 R ; such that p * 0 andp* a * p - (0 for all a EG. Let G - 2j(T(Yj,yj) + {y,}). By the same argument jas in Debreu (1959), we can claim that G belongs to the closure of G and, therefore, p . a * p . co for all a E G.

(5)

Since a) - Z,*,- - Zjyj and jc,E/?,i - (15,0),

0)2-(3,12)

«

, ( 1*11 * !+ 15 > otherwise I * ' 2* ' 5 u2(x2) - min (x2i, *22)The technology for producing commodity 2 involves a fixed cost of 5 *The example in Vfohra (1990) which illustrates a similar phenomenon relates to an economy with three commodities and two firms.

122

RAJIV VOHRA

units of commodity 1 and a constant marginal cost of half a unit in terms of commodity 1. The production set of this firm (firm 1) is defined as follows: { y i € R 2 | y n s 0 ; y 12s0> ify»*-5 {yi € R 2 | y n * 0; 2yu +y n + 10 s 0} otherwise The indifference curves of the consumers and the production pos­ sibility set are illustrated in Figs. 3, 4 and 5, respectively. It will be useful to begin by looking at some obvious implications for Pareto optimality. Notice that the technology allows substituting 10 units of commodity 1 into 10 units of commodity 2 and allows such a substitution at an even more favourable rate if more than 10 units of commodity 1 are given up. In other words, if we normalize p\ - 1, the average cost of production is 1 if the output is 10 and is less (greater) than 1 if the output is greater (less) than 10. Given consumer l ’s preferences, it follows that if we have an allocation where x u + x12 - 15 and x \2 < 5, then the technology should be used; if it is not used, then a Pareto improvement can be made by using the technology, producing more than 10 units of output and changing consumer l ’s consumption away from commodity 1 and in favour of commodity 2. On the other hand, if consumer 1 is consuming 15 units of commodity 2 and the output of the firm is positive but less than 10 units, then a Pareto improvement can be made by shutting down the firm and having consumer 1 substitute away from commodity 2 and in favour of commodity 1 . This observation may be summarized as follows: An allocation ((xj), f aXyi ) is not Pareto optimal if either *11 + *12 - 15, x12 < 5 and y x - (0,0), (*> X\2 ■ 15 and 0 < y\2 < 10. Given the preferences of consumer 1, it is clear that corresponding to any regulated market equilibrium the prices of commodity 1 must be positive. This allows us to use the normalization p\ - 1, which will be more convenient than the normalization p E S . In searching for equilibria that involve marginal-cost pricing, it is clear that if produc­ tion is positive iy\2 > 0) then P2 - 0.5. If the firm is not used (yj - 0)

Efficient Resource A llocation Under Increasing Returns

123

then any p 2 * 0 will satisfy the first-order conditions for profit maxi­ mization10 and will serve as a marginal-cost price. In searching for efficient equilibria, given the preferences, we need not consider produc­ tion plans where the input is used and no output is produced Thus, there are two possibilities to consider: (a) the technology is not used and (b) the technology is used and p - ( 1 , 0.5). We shall now consider equilibria of both kinds and show that in case (a), x n + x12 - 15 and x\2 < 5 and in case (b), jc12 - 15 and y 12 < 10. By (*), this will imply that in neither case can the equilibria be Pareto optimal. (a) yi - 0. In this case, the public sector has zero profits and there are no taxes or subsidies. The equilibrium simply corresponds to the competitive equilibrium of the exchange economy. It is easily verified that there is a unique equilibrium. xi “ (10.5, 4.5), *2 - (7.5, 7.5), p - ( l , l ) , 10More precisely, W(ylt 0) - R j .

*-0.

124

RAJIV VOHRA

FIG. 4 Consumer 2

This is illustrated in the Edgeworth box in Fig. 6; see also Figs. 3 and 4. However, it follows from (*) that this allocation is not Pareto optimal. In particular, consumer 1 is willing to give up 10.25 units of com­ modity 1 for the same amount of commodity 2 in return, while the technology allows for converting 10.25 units of commodity 1 into 10.5 units of commodity 2. Thus it is inefficient not to use the technology. Another way of seeing this is to construct the Scitovsky indifference curve going through (18, 12 ) corresponding to the allocation x\ (10.5, 4.5) and x2 - (7.5,7.5). This curve is simply the boundary of the sum of the corresponding *better than sets’ and is labelled S1 in Fig. 5. The fact that this curve cuts below the production possibility set simply means that this allocation is not Pareto optimal. (b) y i2 >®- In this case marginal-cost pricing implies that p -

Efficient Resource Allocation Under Increasing Returns *12 + *22

125

FIG. 5

(1,0.5). The firm will make a loss of 5 units, which will have to be distributed among the two consumers. Consumer l ’s after-tax income will lie between 15 and 10. Since p2 - 0.5, consumer 1 will consume exactly 15 units of commodity 2, whatever the tax (see Fig. 3). For consumer 2, the before-tax income is 9 units and the tax may again vary from 0 to 5 units. If the tax on consumer 2 is 0, then the demand of this consumer will be (6, 6). For positive taxes the demand for both commodities will be even lower (see Fig. 4). Thus for any tax struc­ ture, the aggregate demand for commodity 2 will never exceed 21 and the output of the firm will never exceed 9. Since consumer 1 consumes 15 units of commodity 2, we can now appeal to (*) and claim that the allocation is not Pareto optimal. It is important to note that this is the

126

R a jiv v o h r a

case for any tax structure. For example, if the entire tax is borne by consumer 1 , the marginal-cost pricing equilibrium is X\ - (2.5,15), *2 - ( 6, 6), * - ( - 9 .5 ,9 ) , p - (1,0.5) and the Scitovsky indifference curve (labelled S2 in Fig. 5) through (8.5, 21) cuts below the production possibility curve. A positive tax on consumer 2 will also lead to a similar outcome.

We have shown in this example that there exists no regulated market equilibrium with marginal-cost pricing which is Pareto optimal. It should also be clear that this phenomenon is robust to small changes in the data of the economy. However, we cannot appeal to Proposition 2 to claim that there does not exist any regulated market equilibrium which is Pareto optimal. This is simply because the preferences are not smooth. In fact, there does exist a regulated market equilibrium which is Pareto optimal. Consider the equilibrium where p - ( 1 , 1 ) and the t 2 firm makes a profit by producing y - ( - 10 j, 10 j). Suppose the profits are distributed to consumer 2. It is easy to see that x\ - (0,15) and *2 - (7§> 7|) are demands. Thus the markets clear and this is a regu­ lated market equilibrium. By tracing out the Scitovsky indifference curve it can also be verified that the allocation is Pareto optimal.

Efficient Resource Allocation Under Increasing Returns

127

It is possible, however, to modify this example so that there exists no regulated market equilibrium which is Paieto optimal. For example, if we replace consumer 2 ’s utility function with the following, 3 log (*21 - 4J ) + *22 3 (*2i - 5.5) + *22

*21 * otherwise,

consumer 2’s demand will be (7.5,7.5) if the firm is not used and p - ( l , 1). If the technology is used and p - (1 ,0.5), consumer 2 ’s demand is (6, 6) provided no tax is levied on this consumer (for positive taxes, the demand of both commodities is even lower). We therefore have the same conclusion as before regarding the inefficien­ cy of all marginal-cost pricing equilibrium for all tax structures. Next, we claim that in any Pareto-optimal, regulated maiket equilibrium X2 ** 0. The only case to consider is one in which production is positive. If *22 - 0, as before, aggregate demand for commodity 2 will be too low. If JC21 - 0, then this cannot be Pareto optimal with positive production. (This follows simply from the observation that the mar­ ginal rate of substitution for consumer 2 is then 3 while the maiginal rate of transformation is 2, and a Pareto improvement can, therefore, be made by producing less and having this consumer substitute away from commodity 2). Since jc2 x» 0 corresponding to any Pareto-optimal equilibrium and consumer 2 ’s indifference curves are smooth, we can now appeal to Proposition 2 to claim that a search for Pareto-optimal, regulated market equilibrium can be restricted, without loss of gen­ erality, to a search for Pareto-optimal marginal-cost pricing. And as we have seen, there exist no such equilibria in this economy. Gearly, if there exists no Pareto-optimal regulated market equi­ librium, it would be natural to study the question of second-best regulation (the second-best problem here is one which arises due to the inability of the government to make arbitrary redistribution). This issue is considered in Vohra (1988) but only in the context of a given tax structure. A characterization of the second-best problem in an economy where the tax structure is endogenous remains an important open problem. An essential feature of the above example is that the relevant Scitovsky indifference curves cross each other, i.e. preferences cannot be aggregated. This is also the essential ingredient in the examples of

128

RAJIV VOHRA

Guesnerie (1975), and Brown and Heal (1979); see, in particular, the discussion in Guesnerie (1989) and Brown (1990). But the inefficiency problem illustrated in the present example is somewhat more dramatic in that it pertains not just to one given tax structure but to all possible tax structures. We will now consider an explanation of this phenomenon which will also allow us to make a comparison with the material in the following section. If the technology is not used (case (a)) we have an allocation such that, starting from this allocation, consumer 1 can gain if the firm is used, marginal-cost prices are charged, and the entire loss is im­ posed on consumer 1. This is what makes the original allocation Pareto inefficient. But if the firm is actually used, and follows marginal-cost pricing, the new prices will reduce consumer 2 ’s income (consumer 2 owns the entire endowment of commodity 2 and is a net supplier of commodity 2). Consumer 2 will be worse off even if no tax is imposed.11 What is more important here is the fact that at the lower price for commodity 2, consumer 2 has a higher net supply of this commodity, enough to make the total production of commodity 2 too low to justify using the increasing-retums technology; the average cost turns out to be greater than 1 and consumer 1 can be made better off by shutting down the firm. The only way to justify positive production (from the point of view of efficiency) is to ensure that production is ‘high enough’. From Theorem 1 we know that this can be achieved through a suitable redistribution of income. The point here is that any such redistribution requires that consumer 2 be given a subsidy while consumer 1 is taxed an amount which is more than the loss incurred by the firm. 5. A SPECIAL CASE Consider again the special case of a two-good, one-firm economy in which a commodity can be produced with a fixed cost and constant marginal cost. Should the technology be used? An obvious way to nOfcourse, what has been said so far can happen even if the firm has a convex technology. However, in that case even if one consumer gains while the other loses when the firm is used, it is guaranteed that the new equilibrium will be Pareto optimal. That a change in die price of a commodity can have an income effect which is important for determining the welfare impact od a group of consumers is also well known; see Gale (1974).

Efficient Resource Allocation Under Increasing Returns

129

answer this is to ask how much each consumer will be willing to pay for the privilege of buying the produced commodity at its marginal cost. If the aggregate willingness to pay exceeds the fixed cost then the technology should be used. Moreover, if no consumer is made to pay more than the corresponding *willingness to pay’ (compensating varia­ tion in income), the new outcome Will not only be Pareto optimal but will actually be a Pareto improvement over the initial one. This simple rule for deciding whether to use the technology or not is certainly well known in the partial equilibrium literature. Indeed, the corresponding equilibrium provides a way of constructing a Pareto-optimal system of two-part tariffs. And there is a presumption in the literature that if different consumers can be charged different fixed parts, then efficien­ cy can be achieved through such a pricing rule; see Oi (1971) and Brown and Sibley (1986). In view of this argument the example of the previous section certainly seems paradoxical. What is the resolution to this apparent contradiction? The answer lies in the fact that in our example consumer 2 has an endowment of commodity 2 to begin with. And when the commodity is produced, its marginal cost is lower than the initial equilibrium price. This makes consumer 2 worse off even if no tax is imposed. At the same time it is true that consumer 1 is willing not only to bear the fixed cost but also compensate consumer 2; using the technology satisfies the Kaldor criterion. However, if this compensation is not actually made, there is the possibility that the new outcome will not be Pareto optimal; given the new allocation, shutting down the firm may also satisfy the Kaldor criterion. If consumer 2 did not have any endowment of commodity 2, the simple rule of collecting from each consumer no more than what they are willing to pay will lead not only to a Pareto improvement but also to a Pareto-optimal allocation.12 What is crucial for this argument is the fact that in this case there are no potential losers when the produced good is made available at marginal cost. This in turn is a result of the fact that there are no income effects due to the change in the price of the produced commodity. We can, therefore, be sure that if there are two commodities, no initial endowment of commodity 2 and the technology involves fixed 12We leave it to the reader to show that if in the example of Section 4, of revenue via indirect taxes, the aim of the government is to keep the utility of the consumer at the highest level possible, where the utility function is denoted by U - U ( X 0, X h . . . , X n)

(2)

The objective of the consumer is to maximize his utility subject to the budget constraint he faces, given by 2 piXi - 0 i -0

(3)

Note that in this model, labour X q is the only factor of production and is measured negatively. Equation 3 implies that the amount of labour earnings is equal to the amount of expenditure on goods. It is easy to show that when the government seeks to maximize U subject to the tax revenues being at least as much as R, the first-order conditions for a maximum are

Optimal Taxation and India 137

where \jl is the Lagrange multiplier associated with the revenue con­ straint. Remembering that the consumer is maximizing his utility subject to the budget constraint, we have the usual first-order neces­ sary condition of equilibrium given by Ui - X p i - 0, i - 1 , . . . , n

(5)

Combining (4) and (5) above and making use of the Slutsky equation

(6) and the symmetry of the substitution terms, it is easy to derive the Ramsey rule (1927)

(7)

The left-hand side of equation (7) denotes the relative drop in demand for commodity j following the tax change, provided that the consumer is compensated to stay on the same indifference curve. The Ramsey rule thus states that the proportionate drop in demand for all commodities along the compensated demand curve ought to be the same. In general, this would imply a rate of tax that is not uniform across all goods, unless certain additional restrictions are made. Also, it should be pointed out that the Ramsey rule is valid only for an arbitrarily small tax revenue, whereas in actual practice the require­ ment of tax revenue is far from being close to zero. In one of the early formulations of the problem, Corlett and Hague (1953) considered a model with two goods and labour and showed that one should tax more heavily the good that is more complementary with leisure. We thus have Eio > £20 f°r hlP\ K tyP2 where e# is the compensated elasticity of good i, at the optimum, with the wage. Extending this model to a world with many goods, Sandmo (1976), Sadka (1977), and Deaton (1981) have shown that if compensated

138 M.N. MURTY AND PUUN NAYAK cross-elasticities with leisure are equal then all goods, other than labour, ought to be taxed at the same rate. It can be checked relatively easily that uniform taxation is desirable when one of the following conditions is satisfied: (1 ) the income elasticities of all taxed goods are equal, and utility is separable be­ tween consumption and labour; (2) labour is completely inelastic in supply, in which case one may either tax labour without incurring any dead weight loss, or one may leave labour alone and tax all the consumer goods at the same rate (see Sandmo, 1976). It is also easy to establish that when all cross derivatives of the demand functions vanish as between the taxed goods, then the tax rate applicable on good k is inversely proportional to its own price elasticity of demand. Finally it can be shown that when the utility function is directly additive, the optimal tax rate depends inversely on the income elas­ ticity of demand (Atkinson and Stiglitz, 1980, p. 379). The above analysis, by assuming a single consumer, has ignored the question of equity altogether. This may be incorporated by considering a world with H households. Denote V h {p, I h) : Indirect utility function of h-ih individual WfV1, .. . y H) : Social welfare function X i: Demand for i-th commodity Xi : Demand of h-th individual for i-th commodity p : n x 1 vector of consumer prices p ° : n x 1 vector of producer prices t - p - p°, n x 1 vector of commodity taxes I h : Income of /i-th individual R : Government revenue. Assuming that producer prices are constant, optimal commodity-tax rates may be obtained by maximizing the following Lagrangean with respect to tax rates (f,). Z ,- W + \i[ L t i X i - R )

i

(8)

The first-order conditions for optimal commodity taxes may be written as follows (see Diamond and Mirrlees, 1971; and Diamond, 1975).

Optimal Taxation and India 139 "

H ,

-

2 t,, 2 4

- - ^

i - l A-1

B*„»

+ ^

M-

+

"

2 r,

(

h\ 2 4

i-1 ^ h

d/i

, * - 1 , 2 , ......../l(9)

H

where Xk - 2 A{///, and A- 1 pA-

dW dV*

, social marginal utility of income to the fc-th indivi­

dual. We can alternatively write (9) as & «'■*

*_\ H
o)

(23)

where p 1 and p° are, respectively, the post and pre-reform prices, and L i Yq is the observed income of the h-th individual. Atkinson’s inequality index is defined as: / - l-p where Y : Equally-distributed equivalent level of income, and Y : Mean of observed incomes. Y is defined as o ( y , . . . , f ) - ^ i , . . ->YH)

(24)

(25)

where O is a welfare function defined over incomes. The proportional social gain as defined in (22) is equivalent to the increase in mean equivalent income adjusted for changes in inequality. The alternative

Optimal Taxation and India 153 welfare measure that we have also used here is the weighted sum of equivalent gains (EG?*) as a result of tax reform. It is defined as H 2 bl'EGh - D h- 1

(26)

Since ECr* is defined as the difference between equivalent income (y £) and observed (Yq) or pre-reform income, this measure may give us an idea about incremental welfare as a result of the reform. We have also calculated Atkinson's inequality index of equivalent expenditures under alternative reforms. Using a model for computing the optimal commodity taxes described in Section 3.1, the data on observed tax rates, consumer demand levels for the year 1983-4, (National Sample Survey, 38th Round), and the estimates of demand derivatives based on LES parameter estimates (Ray, 1986), we have calculated the measures of proportional welfare gain (S), Equivalent gains (D), and Atkinson's inequality index (I) for equivalent incomes under two revenue-neutral tax regimes: (a) optimal taxes, and (b) uniform tax for India. These estimates are reported in Table 3. As expected, there are significant welfare gains from moving TABLE 3 ESTIMATES OF 5, D AND / UNDER TWO TAX REGIMES (a) Optimal Ibxes

(b) Uniform Tbx

s D

1.066

0.981

0.292

0.063

/

0.576

0.616

Note. D represents per-capita incremental welfare gain with govern­ ment’s revenue as numeraire.

to optimal taxes from the initially observed taxes. There is a 6.6 per cent increase in the mean equivalent income adjusted for inequality and the incremental per capita welfare is 0.292. However, in the case of changing to uniform commodity taxation, there is a 2 per cent fall in mean equivalent income even though there are small incremental per-capita welfare gains. The Atkinson's inequality index of equivalent incomes (I) is higher with uniform taxation in comparison with op­ timal taxes. With a linear expenditure system without leisure and no

154 M.N. MURTY AND PUUN NAYAK lump-sum subsidies, as expected, uniform taxation is not optimal for India. However, if the assumptions underlying the tax model we used are valid for the Indian economy, the welfare losses associated with uniform taxation may be justifiable if one takes into account the savings in the cost of tax administration. 4. OPTIMAL INCOME TAXES AND TAX REFORMS: AN APPLICATION TO INDIA Empirical work on the structure of optimal income tax in the Indian context is very scarce, essentially because of formidable problems of data. The deficiency of data is considerably more acute in the case of income tax in comparison to commodity taxes. In order to obtain certain bounds on the optimal income-tax rates one needs to have information on the responsiveness of labour supply to the marginal income-tax rate. Reliable information on this is simply not available in the Indian context and, at best, only tentative information on this question is available in the context of advanced countries such as the USA and UK (see Heckman and Macurdy, 1981). A more important question pertains to the notion of optimality when alternative income-tax schedules are being considered. One needs to ask whether the most crucial response to marginal changes in incometax rates is to be confined to alterations in labour supply, or also in terms of other relevant behavioural responses such as the attitude towards risk-taking, siphoning off income into illegal activities, or an increase in tax evasion. The last issue has been theoretically modelled by Allingham and Sandmo (1972), Srinivasan (1973), and Nayak (1978), among others. Ahmad and Stem’s (1983) evaluation of the structure of personal income taxes in India is confined to examining the desirability of marginal reforms. They caution at the outset that they cannot analyse quantitatively any incentive or disincentive effects of the income tax associated with factor supplies. Personal income taxes in India comprised 21.37 per cent of total tax revenue in 1950-1. The share of this tax in total tax revenue has steadily declined and it formed around 5 per cent of total tax revenue in 1987-8. The total number of assessees in the books of the Depart­

Optimal Taxation and India 155 ment of Income Tax was 62.61 lakhs as on 31 March 1987 (CAG Report, 1988). It is worth remembering that agricultural income is not subject to income tax. Ahmad and Stem examine the desirability of three sets of reforms, namely (i) a marginal change in the exemption limit; (ii) a 1 per cent increase in the marginal income-tax rates with existing exemption limits, and (iii) increase in the top two marginal rates from 55 per cent and 60 per cent to 60 per cent and 65 per cent, respectively. The welfare loss from each reform is calculated and compared with the welfare losses associated with the existing set of indirect taxes. The major policy recommendation that emerges from the study is that if one is concerned about inequality then one ought to increase income taxes relative to commodity taxation. Secondly, it is seen that it would be preferable to raise additional revenue by an increase in the top marginal rates rather than by a flat 1 % increase in all marginal rates. The authors caution that administrative costs, incentive effects, and the possibility of tax evasion may reduce the attractiveness of stepping up tax revenues at very high income-levels. The welfare losses computed for the above three marginal tax-reform measures are presented in Table 4. The welfare losses are computed for alternative values of the inequality aversion parameter e. TABLE 4 WELFARE LOSSES ASSOCIATED WITH INCOME-TAX REFORMS i o

H i