The Capital Levy 9780231892407

Citation preview

The Capital Levy SHUN-HSIN

CHOU

Φ King's Crown Press MORNINGSIDE HEIGHTS · NEW YORK 1945

Copyright 1945 by SHUN-HSIN CHOU Printed in the United States of America

KING'S ORO Vi ΡBBSS is a division of Columbia University Press organized for the purpose of making certain scholarly material available at ainimta cost. Toward that end,, the publishers have adopted every reasonable economy except such as would interfere with a legible foraat. The work is presented substantially as subnit ted by the author, without the usual editorial attention of Columbia University Press.

Lithoprinted In U.S.A.

EDWARDS ANN

BROTHERS,

ARBOR.

1945

MICHIGAN

INC.

ACKNOWLEDGMENTS I feel particularly Indebted to Professor Robert M. Halg for his encouragement at the Initial stage of the present undertaking and his discerning guidance In various stages of Its evolution during the past tvo years. My thanks are also due to Professor Carl Shoup and to Professor Harold Hotelllng for reading all or portions of my work and for their valuable suggestione through which many improvements have been made and many errors eliminated. Acknowledgment must also be made «to those authors/ and their publishers, from whan many telling arguments and Illustrations have been drawn for use In this work. If through Inadvertence I have neglected to thank any by personal communication, I beg his par dem and plead relief from my error because of the necessity which called me first to London and thence to China before the proof sheets of this work appeared. S.H.C. Hew York City May, I9U5

PREFACE The fiscal device discussed in this study offers the special appeal of novelty. In a realm in which new discoveries and true inventions are notably infrequent, the suggestion that war he financed (or that war-deht he liquidated) hy a maseive onceand-for-all levy on capital does, it is true, carry the distinctive "charm of rarity"; yet it would he a serious error to regard the capital levy merely as a strange fiscal specimen suitable only for entombment in eame volume like Hubert Hall's Antiquities and Curiosities of the Exchequer. For, vithin the memory of our generation, this device has seen considerable actual service, notably in several of the hard-pressed countries of central Europe; it was seriously proposed for adoption in Great Britain toward the close of World War I, and in our own country at that time it was considered sufficiently interesting to Justify detailed study by the Federal Treasury. The story of the interest of our Federal Treasury in the capital levy is an interesting fragment of unwritten history. The episode occurred about the time of Hindenberg's last great effort on the Western front, when the military outlook was still shrouded in doubt and when the market position of some of the outstanding iseuee of Liberty bonds was the cause of concern in official circles. At this Juncture, a competent and hard-headed assistant to the Secretary of the Treasury circulated a communication in which he contended that, if the war did not end soon, a Federal capital levy might became a desirable or even a neceseary feature of the program of war finance, and he urged that detailed studies of the device be undertaken without delay. Such studies were nade but, with the swift arrival of victory, the resulting memoranda were consigned to the Treasury files. From this resting place they were resurrected only once, so far as the writer is aware; ^t the height of the public controversy they were loaned to the officials of the British Board of Inland Revenue who had heard of their existence and vho requested an opportunity to examine them.

vi i i

THE CAPITAL LEVY

Although in this country the capital levy did not become the subject of widespread pttblic discussion during the first World War, the opposite is true of England, There the proposal was strongly supported in the public press and precipitated a controversy wliich continued during a large part of the post-var period. During this controversy the proposed device vas found to involve a fascinating series of theoretical and practical problems, the analysis of which stimulated the interest of such leading economists as Edgeworth, Pigou, Baiton and Stamp, prompted the publication of elaborate memoranda prepared by the Board of Inland Revenue and engaged the attention of such important public bodies as the Select Committee on Increase of Wealth and the Colwyn Committee, Thus it happens that the British literature dealing with the capital levy constitutes the richest existing field of material dealing with the subject. What rôle the capital levy may be destined to play in the finances of the nations in the years that lie immediately ahead cannot at the moment be clearly foreseen but that the device will present itself for consideration and appraisal in numerous post-war situations seams scarcely to be doubted. In view of this outlook it is fortunate that the able young economist, Dr. Chou, should have conceived the project of exploring the subject afresh and of reporting in this volume the reeuite of hie critical ra-examination of the economic analysis that emerged from the controversy of twenty-five years ago. Αβ will be evident to the reader of his pages, Br. Chou has brought to his task a clear and powerful mind and a mastery of the tools of economic analysis that have been developed in the intervening period, Eis work will, I believe, be recognized as authoritative In the areas he has chosen to cultivate. ROBERT MJKRAY HAI G

T A B L E OF

CONTENTS

I

THE NATURE OF THE CAPITAL LEVY

.

II

THE GENERAL LEVY : THE SCOPE OF TAXATION . Taxation of Corporation Property . . . Taxation of "Brain Capital" . . . . Taxation of Personal Effects . . . . Exemptions and Allowances . . . . .

III

THE GENERAL LEVY : TAX RATES Measurement of Graduation . Structure of the Tax Rate .

. .

.

. .

.

.

. .

1 .

h h 11 13 15 19 19 28

. .

APPENDIX I ON THE GEOMETRY OF THE GRADUATED TAXATION.

.

APPENDIX II ON DIGRESSIVE TAXATION IV

THE INCREMENT LEVY Progression of the Tax Rate Allowances and Exemptions . Taxation of Business Capital

V

THE FORCED LOAN

VI

EFFECTS OF The Case The Case The Case

38 M M

. .

. . .

. . .

. . .

. 50 53 57

A CAPITAL LEVY ON PRODUCTION . of Free Competition . . . . of Monopolistic Competition. . of Monopoly . . . . . .

. .

VTI

EFFECTS OF A LEVY ON INVESTMENT AND CONSOMPTION . Effects on Investment. . . . . . Effects on Consumption . . . . .

VIII

EFFECTS OF A LEVY ON FINANCIAL MARKETS. Effects on the Money Market . . Effects on the Exchange Market . .

. . .

. . .

6l 61 67 70 79 79 83 9^ 9^ 103

THE CAPITAL LEVY

H

THE CAPITAL LEVY AND OTHER TAXES The Levy and Excess Profits Tax. The Levy and the Income Taxes . The Levy and the Gift Tax

.

.

106 106 117 120

.

X

THE ESTIMATE OF THE YIELD OF THE LEVY . . . The Estimate of Gross Yield . . . . Allowances for Losses in Death Duties . . Allowances far the Losses in Income Taxes. . Allowances for Other Gaine and Losses . .

123 123 132 13k135

XI

CONCLUSION The Levy for Debt Redemption . . . . The Levy as a Measure for Financing War .

137 137 138

BIBLIOGRAPHY

.

1^0

CHAPTER

I

THE NATURE OF THE C A P I T A L

LEVY

A capital levy is a variety of tax oil capital, not regularly recurrent, and. destined to meet some extraordinary government expenditure. The main characteristics of the imposition are that the tax is usually, though not necessarily, aseessed according to the capital value of property; and that, because of the magnitude of the tax, at least a part of it will he paid out of the capital stock rather than from income. Altogether there are three main forms of capital levy: (l) the general levy, which uses the total value of property as the hase of assessment; (2) the increment levy, which taxes the increase of wealth resulting from war profit; and (3) the forced loan, which bears an interest lower than the prevailing market rate and is to be distributed among property owners in accordance with either the total wealth or the increment thereof. Oftentimes, the idea of capital levy is closely associated with the problem of debt reduction. The primary purpose of the Czech, the Austrian, and the Hungarian levies of 1919-20 was the reduction of bank-notes and other State debts. This is also the type of levy that was widely discussed in England after the last war. There are, however, inatances where the capital levy has been used to finance directly some extraordinary expenditures. without adopting the intermediate step of borrowing. Examples of this type of levy are the Italian and the Hungarian rearmament levies of 1937-38, and the Finnish levy used after the Russo-Finnish vat- in 1939 to finanoe the payment of the war indemnity and the evacuation of residents from the ceded territorities. The capital levy, when imposed on the basis of the capital value of property, is very similar in its general nature to the ordinary property tax. It differs, however, from the latter tax in the following respects. First, the levy ia usually too large to be paid out of income, as in the case of the ordinary proper-

THE CAPITAL LEVY

2

ty tax. AB an implement for effecting any change In the structure of our economy (such as a change in the distribution of wealth, etc.), the capital levy is therefore much less effective than the property tax.1 Second, whereas the property tax is recurrent and its yield is usually pooled with other government revenues to meet ordinary expenditures, the capital levy is usually specifically dedicated to meet expenses caused by factors not regularly recurrent. This very feature of non-recurrency is sometimes regarded as one of the prerequisites to the success of the levy; for the expectation that It will not be repeated in the near future tends to make people less reluctant to pay the tax, despite the high rate. The undesirable psychological reaction which might result from the levy would thus be mitigated. In the Colwyn discussion, the question of government guarantee against repetition was dwelt upon at length. The Committee finally came to.the conclusion that there are valid reasons against a State attempting to bind itself absolutely, on bringing in a levy, not to impose a second. At the same time the question whether a levy proved to be a "beneficial proceeding" or not might... depend in no email degree on the presence or absence of a guarantee limited in same way...any guarantee ought to be wide in its scope, applying to all capital wealth; on the other hand it ought to be limited in time. It would need to be made clear that the levy was emergency legislation, and that, at least for some yeare. it would not be repeated unless there were some serious and unforeseen crisis. We think· suoh an assurance would be of value and would help to allay apprehensions. It would be too sanguine to expect that it would altogether remove them.2 1

"A· Capital Levy on a scale worth having could not be met out of the current consumption of the wealth. They could only pay it by handing over assets to the Government,...." (J. M. Keynes, Sou to Pay for the War (New York, 1940). p· 49.) "It (capital levy] need not be assessed upon capital thcugh it usually will be; the important thing is that the levy is too large to be paid out of income." (J. R. Hicks, U. K. Hicks and L. Rosta, the Taxation of Ifar Wealth (London, 1941), p. 1B0.) 2 Retort of the Committee on Motional Debt an4 taxation (London, 19E7), p. 260. The report will hereafter be referred to as the Colwyn Report.

THE NATURE O F THE C A P I T A L

LEVY

3

The issue of capital levy may be discussed, from several different angles. From an economic standpoint, it may be considered to have merit as a measure well adapted to extricate a nation from serious financial embarrassment with minimum detriment to the national economic system. It is precisely from, this aspect that the levy on capital is generally considered and discussed by students of economics and finance. The levy, however, may also be considered from a social-political standpoint as a means for the expeditious adjustment of a maldistribution of wealth caused by war or by a previous system of accumulation under a regime of capitalism. Finally, the levy on capital may be regarded from a political standpoint; thus it may be conceived, by a defeated nation, as a means of speedily realizing an indemnity in order to pay the victors and thus achieve emancipation from an irksome economic burden; it may be used as a precautionary measure to placate the dissatisfied and to curry favor with the poor classes; or it may be considered as an insurance premium, on the part of the capitalist classes, againet a more drastic confiscation of wealth. In the subsequent discussion, however, it is the economic aspects of the problem that will receive primary attention.

CHAPTER

THE G E N E R A L

LEVY:

II

THE S C O P E O F T A X A T I O N

In the next four chapters the various forms of capital levy will be examined in some detail. The question concerning the scope of assessment for the general levy and the rate of taxation will be dwelt upon in the first two of these consecutive chapters, while the increment levy and the farced loan will be treated in the third and fourth chapters respectively. The questions relating to the scope of a general levy may be conveniently segregated Into the following sub-divisions: 1. questions concerning the taxation of corporation property; 2. questions concerning the taxation of brain capital} 3. questions concerning the taxation of personal effects; U. questions concerning exemptions and allowances; It is to these questions that attention is now directed. The Taxation

of

Corporation

Property

As in the case of the general property tax, one of the most important issues involved in taxing the assets of businesses organized in the corporate form is that the corporation and personal taxes must be properly coordinated BO that no inequitable multiple taxation will result. This objective of taxing all corporate business assets once, and once only, may be attained, by the following alternatives: (l) confining the levy to personal property; (2) confining it to corporate property; or (3) taxing both properties but at different rates -- the rate for the personal property usually being higher than that for the corporate property. Throughout the British discussion of the capital levy, after the last war, it was taken for granted by nearly everyone that the levy would be confined to personal capital, no corporations being involved in the collection. The plan for imposing an

THE GENERAL L E V Y :

THE SCOPE OF

5

TAXATION

increment levy on companies was rejected by the Inland. Revenue Board.1

"Throughout the Colwyn discussions," as Mrs. Hicks has

pointed out, "it was generally agreed that the levy should be imposed only on personal property."

..."when we turn to the

levies which have actually been imposed in other countries, we find without exception that the levies were laid upon business capital; indeed in many cases the greater part of the levy was collected, not from the private individuals, but from firms."3 In most of the central European levies, after the last war, both corporation capital and personal capital were taxed. The basis for advocating the first of these alternatives is the assumption that the ownership of corporation capital is adequately represented by the ownership of the stocks and bonds of these corporations —

that is to say, it is taken for granted

that security quotations are reliable indices of the value of the capital of concerns organized in this form. The levy, therefore, may be collected entirely from the owners in their private capacities, and, in order to avoid double taxation, the companies themselves should be exempted from the imposition. However, reflection will reveal that the_ above assumption is unjustified. In the first place, the postulate that the "actual" value of business capital and the market value of securities representing that capital are identical is unwarranted, (l) If it is the identification of the value of the entire corporate property with only those outstanding legal interests in the property represented by shares in stocks and bonds, it will necessarily leave unaccounted for all the other proprietary and credit claims that are not reflected in the values of these securities. (2) If, on the other hand, these securities are considered to represent the net worth of the business, (e.g., the total assets minus the total liability), we must face the question of how the surplus reserve, under the direct control of a corporation, should be treated. * Cf. Memorandum lo. 5, submitted by the British Board of Inland Revenue to the Select
0) for all values of x: which proves the relation bed f(x) tween f"(x) and

χ

as shown in the table. Similarly, it can

also be proved that if f"'(x) = 0, we have also

χ

¿ 0. For,

d* 2 a 2 f(x) χ dx 2

= 1 (x 2 f"(x) - 2xf'(x) + 2f(x) ). χ3

(3.6)

This expression is positive, zero, or negative for all values of χ if

>

x?f"(x) J 2xf'(x) - 2f(x), or

2xf"(x) + x 2 f"'(x) è 2f'(x) + 2xf"(x) - 2f'(x),

or

f'"(x) > 0 .


I, or f"(x) > 0. As the marginal rate increases with the Increase of χ at the increasing, the constant, or the decreasing rate, the progression itself may be further segregated into three subdivisions: the increasing progression, the constant progression, and the decreasing progression. In addition to the characteristics of progressive taxation in general, that is to say, each of these subdivisions also has its own particular features reflected primarily by the value of f"'(x), or the excess of k over unity. A schedule is said to be of the increasing progression if f ( x ) > 0, or k > 2; and of constant or decreasing progression according as f'(x) = 0, or k = 2. (Cf. column 5 of the table on page 21.) The case of proportional taxation is comparatively simple. Since k = 1, and f"(x) = 0, we know 1. that the total tax of the base χ increases with the increase of χ at a constant rate; 2. that the marginal and the average rates of taxation are equal and constant. There Is no question of sub-classification. The situation at regressive taxation is Just the reverse of that of progressive taxation. Theoretically, the system of the regressive schedule may aleo be broken into (l) the decreasing

® Cf. R. G. D. Allen, Mathematical Analysis for tcorumists (Lore!on, 1938) pp. 2ΘΟ-Θ1. This concept of elasticity of cost is the saie as Moore 's "coefficient of relative return" or "coefficient of relative cost."

24

THE C A P I T A L

LEVY

regression, (2) the constant regression, and (3) the increasing regression; according as (a) 0 < k < 1, (h) k = 0, or (c) -1 < k < 0. But the condition ("b), as shown elsewhere,7 implies that f'(x) = yk/x = 0, and (c) means that f'(x) < 0. That is to Bay, the total tax should always he equal to a given amount in the case of ("b);8 and less than a given amount for all values of χ in the case of (c). Neither of these two schedules, therefore, is of much practical importance in modern government finance; among the three regressive schedules, only the decreasing regression is meaningful in practice. The next question we must examine is which of these two criteria, f"(x) and k, is a better yardstick for our purpose. For, these two measures need not always lead to the same result. According to the first criterion, f"(x), for instance, a tax is said to he progressive when the total tax on the hase χ increases with the increase of χ at an increasing rate.9 That is to say, under progressive taxation, the ratio of the last increment of the tax to the last increment of its hase is greater than the ratio of the penultimate increment of the tax to the penultimate increment of the hase.10 This definition need not he 7

Cf. equation (3.8). A n example of this sort of imposition is the poll tax. Cf. Pigou, Finance, p. 64. 8

9

E.g.,

f (Xg ) - f(Xq)

>

Public

(a)

f ( X l ) - f(x 0 )

where the _f ' (£)'s and the x_'s represent respectively the total taxes and their bases, and jç Q < x^ < Xg. Or, f"(x.) > 0 , if the tax function T_ = f(x) is assumed to be continuous. I ® Algebraically, the statement may be expressed, in notations previously used, as follows: f(Xp) - f(x.,) ^ f ( x x ) - f j x 0 ) . (b) Xg -

Xt -

X0

This inequality is the same as the one given in note· (9). Por, f(Xp ) - f(x 0 ) _ f(Xg) -

f(Xl)-f(x0) 311,1

χ - χ 22

χ

fl^)

f ( X l ) - f(Xq) - χ

+ ι.

Therefore, by the inequality (a) given in note (9), we. have

TOE GENERAL LEVY:

TAX RATES

25

identical with one (based on k) that compares the ratio of the last increment of tax to the last increment of tax "base, not with the ratio ahove stated, hut with the ratio of the total tax to the total tax hase (i.e., the average ratio).11 On a similar ground, progressive, regressive, or proportional taxation may he defined according to whether the ratio of the total tax to the total hase increases, diminishes, or remains 12

constant with the increase of the tax hase. The same ie true in the case of proportional or regressive taxation, mutatis mutandis. Under certain conditions, the first two definitions may lead to conclusions quite different from those derived from the others. This is especially true in the case where the total tax Τ = f(x) + A; (3.9) χ, as before, heing the tax hase over and ahove the exemption, and A, a constant, representing the value of Τ when χ is zero. Apparently, the existence of A does not affect the value of the criterion f"(x), which is the hasis of the first two definitions mentioned in the preceding passage. But A does affect the value f(x) + A ,v f(x) + A = = and therefore the value of [ f ' (χ) ί — ] > which is the criterion for the second eet of definitions mentioned ahove. But if the constant A is zero, this sort of discrepancy will not arise. A geometrical illustration may put the matter in a clearer

t y - f < v ·,*2 - x i t f(x·^ - f(x 0 ) - Xq ' f

which can be easily, transformed into the inequality (b). 11 If f(x) and χ are used to denote respectively the total tax sind the total tax base, the definition stated in the text may be expressed as xf'(x)/f(xj, which, according to our previous definition, is k. For progressive taxation, we have k_ > 1> or £.'(*) > £ & ) & · 12 That is to say, taxation is progressive, proportional, or regressive according as J f(x)/x > 0. If it is progressive, we must have d[f(x)/x] =

dx •Si'lS.) 5?

> o.


P'P"Q"Q'). So far as continuity 1s concerned, the graduation by mathematical formula is clearly superior to the "ccnmon eense" progression-by-brackete method. However, the former method is open to the following objections. In the first place as has been contended,1 8 the mathematical method Is too complex to be comprehensible to the general public. Secondly, the application of the mathematical formula method would require knowledge of the exact value of the tax base and would thus render the collection at the source difficult. For, under the progression-bybrackets method, it is necessary to know only the broad limits within which the amount of the tax base falls, and that information would be sufficient to establish the amount of the abatement which is to be granted and the rate at which the tax is to be Imposed. Collection at source, therefore, is relatively 16

Great Britain Royal Commission o n the Income Tax, Minutes

(London, 191&-80), paragraph 4017.

of

tvidence

32

THE CAPITAL LEVY

variable under that method. If, on the other hand, graduation 1b worked out In accordance with some mathematical formula under which the rate of tax Taries with, 8ay, each dollar of the tax base, it would be necessary to know the exact value of the base before an assessment could be accurately made. Any subsequent adjustment of the assessment on one part of the base would disturb the rate of tax chargeable on all other parts. Hence, to collect the tax at source would be difficult. Eren If we grant the practicability of the mathematical method, there still remains the question as to the basis of selecting the proper formula for determining the constants in the formula. In his paper on "Graduation of Taxes,1,19 ïdgeworth made the following reccranendatlons : If (exclusive of, or in addition to, the exempted minimum) only one constant is allowed, the form recomnended Is Τ = χ - xb, where Τ 1b the tax, χ is the taxable income or capital, b is a proper fraction. If there are (besides the abatement, as before) two constants, we have a choice between theee two expressions : (1) Τ = rf (2) Τ = xrLog (l + x) 20 M+x c .. .If it is advisable to have as many as, and not more than, three constants (besides the abatement) there Is reccnmended a combination of two prescriptions; namely, (l) Τ » χ - χ1·, o 'the Se le et Cossi t tee ο*ι Increase of Wealth (WarJ, paragraph 9.

THE INCREMENT LEVY

45

wealth would call not only for knowledge of the gross difference between the amounts of the wealth at the two points of time, hut also for necessary deductions therefrom. That Is to say, the Imposition should primarily fall upon those Increases of wealth under (l), (2), and (3); but not upon those under (10, (5), (6), and (7). But, In actuality, the gains of the different classes merge Into each other and the endless variety of conditions in different cases renders impossible detailed differentiation along the lines shown above. The best that can be done is (l) to determine as accurately as possible the aggregate increment accrued during the period of war, and (2) to make such deductions therefrom as may appear necessary and practicable in order to eliminate elements of increase which should not be taxed. Consider first the question of valuation. It is sometimes suggested that excess profits, as a rough approximation, may be used as the basis for the increment levy. This suggestion was actually adopted by the Italian government in its decree of November 2k, 1919, for a capital levy. The same excess profits, however, had already been subjected to the tax on war profits established in 1915· Consequently, the increment assessment amounts to nothing more than a surtax upon the classes of income taxable under the war profits tax. All that was done for the purpose of valuation was to subtract from the original surplus the war profits tax and other necessary deductions provided by the new decree. The remainder was the taxable Increment of the property.2 Obviously, this method was adopted primarily as a matter of expediency rather than of equity.3 Indeed, it is too rough an approximation for a country with a competent financial administration to adopt. A more refined approach to the problem has been suggested by the British Board of Inland Revenue in its memorandum submitted to the Select Committee on Increase of Wealth (War). The chief features of the suggestion are:4 2

L. Einaudi, "Taxes on Property Increments in Italy," Quarterly Journal

of Economics, Vol. 35, p. 113. 3 Ibid., pp. 112-13. 4 Memorandum to. 1, paragraphs 64-83 passin.

46

THE CAPITAL LEVY

1. that the taxpayer should, be under ob liga ti cm to make a report, not merely of the sources of his wealth, but also of its pre-war and post-war values — e.g., the onus of valuation Is placed primarily upon the taxpayer rather than on the financial administration; 2. that the taxpayer should be under obligation to make payment on the basis of his return and to submit to a further assessment at a later date if his return after examination is found inadequate, or in the converse case to receive a refund; 3. that a heavy rate of interest should be charged on additional assessment, if the original return is found to be inexcusably Inadequate. In one sense, it may be contended, the question of accurate valuation is more serious for the increment levy than fear the general levy. This is because in the former case the amount of duty chargeable would depend, not on a single valuation, but upon a compariβon of two valuations; one before and one after the war. So, in many cases, an overvaluation at the first date combined with an undervaluation at the second may suffice to eliminate much taxable increase. On the other hand, the double valuation may also mitigarte the errors if the bias involved in the two valuations is in the same direction. The Progression

of Taxation

The question of graduation will be examined next. Unlike others of the simpler taxes, the graduation for the increment levy has a twofold function. It alms at taxation discriminating against not only large property but also war wealth. In order to attain this dual purpose, the use of a double progression system is sometimes advocated, e.g., one in which the rate scale progresses with respect to both the amount of the increment and the total resources of the taxpayer. Moreover, in a case where both the increment levy and the general levy are imposed, it is also necessary to see to it that the progression of the total rate for both levies with respect to the aggregate property has been properly effected. The question of progression on the basis of increment ÍB very similar to the same issue concerning the excess profits

THE INCREMENT LEVY

47

tax. The amount of the increase Òf capital, as in the case of excess profits, can be reckoned either in its absolute magnitude or in the relative tern of the total amount of the wealth as it stands at either the pre-war or the post-war date. That is to say, in dealing with double progression it ia necessary to take into account all the possible combinations that might emerge from these four factors: (l) the absolute amount of the increment, (2) the relative magnitude of the increment in terms of total wealth, (3) the total resources at the pre-war date, and (¡0 the same resources at their post-war level. The most obvious difficulty of the method based upon the relative amount of the increase of capital and the total pre-war resources is that it is unfair to small property owners. That is to say, if a man possessed only a nominal amount of capital before the war, an increase which might not be large might still be a sum many times exceeding the pre-war capital, and would thus be chargeable with the highest duty imposed. Assume, for instance, that as the result of war profit, the value of A 1 s property increased from χ to χ', while that of B's rose from J to . It is also known that χ < j, and χ' - χ = -jr. Therefore, the percentage of increase based on the pre-war values of the properties is greater in the first case than in the second. If the increment tax is to be graduated with respect to the relative increase, A will be more heavily taxed than Β although the absolute changes in both cases are the same. Thus, it is obviouB that, unless accompanied by the system of double progression, the relative method has a tendency to overtax small property. This, of course, is an anomaly which runs counter to our basic principle of progressive taxation. To avoid such an anomaly, two proposals have been made. The British Board of Inland Revenue, in its memorandum to the Select Committee on the Increase of Wealth (War), suggested that the "pre-war capital for purposes of the graduation should be presumed to be not less than same defined amount, which might be fixed as an absolute sum, or possibly as a percentage ... of the taxpayer's total post-war resources."5 In Italy's decree of 1919 > where the increment levy was graduated with reference to 5

Board o f Inland Revenue, Memoranda*

¡0. 2, paragraph 3 4 .

TOE CAPITAL LEVY

48

the ratio of the increase to the pre-war total, two different rate scales were used: one for manufacturers and business men, who usually have large amounts of capital; another for brokers and others who normally need little or no capital to carry on their buaineas. However satisfactory these remedies may be, the fact that the percentage method per se Is open to serious objections is obvious. As a whole, the absolute method (e.g., to reckon the tax on the basis of the absolute magnitude of the Increase) appears to be preferable. If both the general levy and the increment levy are imposed, and if both rates are graduated, there still remains the question regarding the Joint effect of the two levies upon the graduation of the scale of the imposition as a whole. For, by superimposing one progressive scale on another, there may result the anomaly of taxing the small property at a rate higher than that levied on the large property. This can be shown diagrammatlcally as follows: γ

O

Μ

Ν

Χ

BASE FIGURE 4-1 In the preceding diagram, the curve a shows the amount of the general levy for different values of the taxable property

THE INCREMENT LEVY

49

shown on the x-axia, b the amount of the increment levy, and o the total of two taxes obtained by super Imposing a upon b. In order to find the average tax rate for the Increment levy when the tax base le ON, we may erect a line from Ν perpendicular to the x-axie and cutting the curve a at A. Thus the required average rate may be measured either by the slope of the line OA, Joining the origin and the point A, or the size of ¿k and c given, it is necessary to have = e.g.,

£=δο ρ 6f

- c = 0.

(6.1) (6>la)

or ρδο = côf. (6.1h) (6.1a) gives the familiar equilibrium condition that, at a point of equilibrium, the marginal productivity should he equal to the ratio of cost to price; whereas (6.1b) denotes the same condition except that the equilibrium is expressed in the terms of equality between marginal revenue (= ρδο) and marginal cost (= o§f). Moreover, in order to make the critical point a maximum rather than a minimum, it is neceesary to have δ2π = ρ o. (6.2) < ôf2 ôf2 (6.2) implies that 5 2 o ^ f 2 must be negative, as the price £ in the equation is usually positive. That is to say, at the point of equilibrium, if the price of the product is positive, the marginal productivity of the factor must be diminishing, as more of the factor is employed in production. This means that the productivity curve, with jr and χ axes denoting respectively the amounts of output and factor employed, must be convex upwards, the marginal productivity diminishing, and the marginal cost increasing at the point of equilibrium. It is also known that, under the conditions of atamietic competition, profit = po - cf = 0; or ρ = 21 (6.3) * o

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

63

where cf/o is the average cost. Since under such conditions the price is usually equal to the marginal cost, the marginal and average costs by (6.3) will also he equal at the point of equilibrium. Since the average and marginal costs are equal only when the average cost is at its minimum and when the marginal cost is increasing as output expands, the average cost curve must "be falling to the left, rising to the right of the equilibrium point, and tangent at the equilibrium to the demand curve which, in case of atomistic competition, is a horizontal line. Graphically, the situation under equilibrium as depicted in the previous discussion may be shown as follows :

Here the curves me, ate, ave, and d denote respectively marginal cost, average total cost, average variable cost, and demand schedules. Since the demand schedule under atomistic

64

TOE CAPITAL LEVY

competition is a horizontal line, it coincides with the marginal revenue schedule. OM is the optimum scale of output, for it ia the point where the marginal revenue schedule and the marginal cost schedule intercept each other. So any output that falls short of the scale would have a marginal cost lower than its corresponding marginal revenue; and thus, by extending output to OM, the total profit may he increased. On the other hand, if the output exceeds the scale OM, the marginal cost will exceed the marginal revenue. The total profit of the firm will therefore also he reduced if its output is extended beyond 0M. Now how will the above situation he affected hy a capital levy that increases overhead charges of the producer and thus shifts the average total cost curves, ate, to a new position, say, ate'? The shift, as will he observed, will not he symmetrical, because the greater the output the less will he the increase of the average cost per unit of output. Therefore, the spread between the curves ate and ate' tends to dwindle as the output expands. Reflection will reveal that under this new circumstance, the optimum output, at which the loss will be minimum, is still OM, because this is the point where the marginal cost is equal to the marginal revenue, and thus any output that falls short of or exceeds OM will bring about a greater loss to the firm than would have incurred at output OM. It is obvious, then, from the previous diagram that when the average cost is measured along the schedule ate' and the price along the line d, the loss incurred by the firm at output OM may be measured by the area of the rectangular ACIB. Despite the loss there are, however, good reasons to believe that the firm may prefer to remain in business rather than to suspend production entirely, for by keeping the plant in operation, the loss in overhead charges may at least be reduced. This can be shown as follows. Under the conditions where the tax-including average-cost curve lies above the demand schedule d, the optimum scale of output, as shown in a previous discussion, will remain OM, where the marginal cost is equal to the marginal revenue. Therefore, although a loas represented by the

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

65

area ACIB will be Incurred as the result of the upward shift of the average cost curve from ate to ato', the firm will still he ahle to avoid a loss on the fixed charges (= CEFD) which would he left uncovered if production were suspended entirely. CEFD is the product of DF (= CE) the fixed charge per unit of output, and EF (= CD), the output. Long-Run Effects Long-run average cost is defined as the lowest possible average cost of producing any product when the entrepreneur has adequate time to make all desired adjustments. Tinder certain special conditions the long-run curve touches the minima of the short-run average cost curves, and is the envelope of the fami ly of short-run average cost curves. A long-run marginal cost curve may he derived from the long-run average cost curve. It represents the cost of an additional unit of output when all productive service varies. Long-run marginal costs may he greater or less than short-term marginal costs. The short- and long-run marginal costs are equal only at the point where the short- and long-run average cost curves touch. In the long run, average cost must equal price. If price exceeds average cost, new firms will enter the industry, and their additions to output will eventually force the price down to minimum long-run average cost. On the other hand, if the price were less than the minimum long-run average cost, firms would leave the industry. Therefore, long-run marginal cost, long-run average cost, short-run average cost, short-run marginal cost, and price should he equal in long-run competitive equilibrium. Graphically, the situation may he shown as in Figure 6-2 on the following page. In the diagram: saCjj « short-run average cost for firm η (η = 1, 2...) hefore tax Ime = long-run marginal cost emc = short-run marginal cost lac = long-run average cost before tax lac1 = long-run average cost after tax

66

THE CAPITAL LEVY

d = demand schedule before tax d1 = demand schedule after tax It may "be seen from, the diagram that the tax may raise the long-run average cost from lac to lac'. The shift, however,

FIGURE 6-2

will not he symmetrical; the further the output extends, the smaller will he the amount of increase. Meanwhile, the shortrun average cost curves, which lie along the long-run curve, will he raised accordingly. As a result of this rise, price (= CB) will fall short of the long-run average cost, and thus may force many firms out of operation. A new equilibrium will not he attained until the exodus of marginal firms brings the demand schedule from d to d' and thereby raises the price from OB to OA, e.g., until the price is equal to the long-run average cost (measured by lac') at the output OH. That is to say, the long-run effects of the capital levy on a firm operating· under competitive conditions is to raise both output and price. In the present case AB, the price increase, is determined by the difference between CN and EM, i.e., the difference between the heights of the two minima of the long-run average cost

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

67

curves after and before the tax. The price, however, will not be raised by the full amount of the tax, because the difference between two long-run average cost curves tends to dwindle as output expands. The changes in price and output will depend upon the slope of the long-run marginal cost; the steeper the slope, the greater will be these changes. 2. The Case

of Monopolistic

Competition

Short-Run Effects Falling between the two extremes -- monopoly and free competition -- is monopolistic competition. As in the case of monopoly, the demand schedule for the individual firm under monopolistic competition has also a downward slope. But unlike the case·of monopoly, the equilibrium price does not give the individual producer any rent. At equilibrium, (l) marginal cost is equal to marginal revenue, and (2) the demand curve is tangent to the average total cost curve so that the price la equal tc average cost. These equilibrium conditions may be shown diagr'-mmatically as in Figure 6-3.1 In the following diagram the curves me, ate, ave, d, and mr denote, as before, the marginal cost, average total cost, average variable cost, demand, and marginal revenue schedules respectively. OM is the optimum output, where the marginal cost and marginal revenue are equal. Since free entry is assumed, the curve ate must be tangent to the demand schedule at D. Otherwise, new firma will continue to be attracted to the industry if the actual demand schedule lies above d, and old firms tend to be driven out of production by business losses if that schedule lies below 3I. The tangency of ate to d Implies also equality between the average total cost and price, the latter being represented by the height of the demand schedule measured from the horizontal axis. The conditions (1) and (2) are true only in the case of free entry; i.e., in the case where additional firms will be tempted in so long as the firms in business make profits and where actual losses would drive firms out of the industry. If the entry is closed, it is conceivable that the price may exceed total unit cost to give the finn a net profit.

68

THE CAPITAL LEVY

Now what will happen if, as the result of a capital levy, the average total cost curve Is shifted from ate to ate', while the demand schedule remains unaffected? Reflection will reveal that OM will still remain the optimum output. For, as shown in Figure 6-3, the marginal cost will he lower than the corresponding marginal revenue so long as the output falls short of OM, and will exceed the same cost if the output is extended beyond OM; in either case, the net yield to the firm will he less than in

FIGURE 6-3

It is true that when the average-total-cost schedule is shifted to the position of ate', the selling price will fall short of the average cost and then the firm has to operate at a loss. By a similar line of reasoning, which has just teen demonstrated with reference to the maximization of a firm's

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

69

profit, it may be shown that the loas will he minimum when the output is maintained at the scale of OM, where the marginal revenue and marginal cost schedules intercept each other. Under such circumstances, the loss incurred may he represented, "by the area rectangular ACDB. Despite the loss, there are, however, reasons to believe that the firm will remain in production, for, by doing so, it may save at least a part of its losses on fixed charges, which would be incurred if the production were suspended entirely. In our diagram (6-2), the loss thus averted may be denoted by the rectangular CEFD where EF (= CE) is the fixed charge per unit of output and EF (= OM) the output.

FIGURE 6-4

70

THE CAPITAL LEVY Long-Run Effects

Aa in the previous cases, the capital levy will shift the long-run average cost curve from lac to lac' (Figure 6-U) along the marginal cost curve lmc which will remain unaffected by the tax. If the demand, scheme remains at ar, cost reckoned according to the new average schedule will exceed price, and the firm will produce at a loss. This, however, is not a atable condition. Long-run adjustments will soon result in suspension of the ertra-marginal firm and thus raise the demand schedule to the position ar', to which lac' is tangent at the point P. The equilibrium output will accordingly be shifted from QM to 0M', and the equilibrium price from OB to OA. Thus the long-run effect on a firm operating under monopolistic conditions is to increase both price and scale of output. 3. The Case of Monopoly

Short-Run Effects Unlike the case of free or monopolistic competition, equilibrium under monopoly does not necessarily imply that average coet muet be equal to price or that the average cost curve must be tangent to the demand curve. On the contrary, a monopolist normally maximizes his profit by merely fixing his output at the point where marginal cost is equal to marginal revenue. For any output falling short of this scale will have a marginal cost lower than the corresponding marginal revenue; and any output exceeding this point will have a marginal cost higher than the corresponding revenue. In either of these two cases, the total profit of the firm will be smaller than that which it might reap by maintaining its output at Just the equilibrium point. Meanwhile, at the point of equilibrium, the average cost of a monopolist usually falls short of price and thus there exiets a surplus rent represented by the product of (l) the difference between the price and the average cost and of (2 ) the volume of output at the equilibrium. Diagrammatically, the foregoing discussion may be demonstrated as follows:

EFFECTS OF A CAPITAL L E W ON PRODUCTION

71

Y

M

Ο FIGURE

6-5

In the above diagram, d dénotée demand schedule, mc marginal cost, mr marginal revenue, ate average total cost, ave average cost, and the area of the rectangular CGHD the surplus rent to 2 the producer at the output OM, before a capital levy is imposed. After the levy is imposed, the average cost curve, for reasons explained elsewhere, will then be shifted from ate to ate' as shown in diagram (6.5). Since the marginal revenue and merginal cost schedules remain unaffected, the output (= OM) of ^ The curves ate ' and ate" in the diagram may be ignored for the time being.

72

THE CAPITAL LEVY

the firm, which is determined by the point of intersection of these schedules, will also remain unaffected. So long as the tax-including average cost falls short of the price at the equilibrium output, there will he a rent for the producer. In our diagram, the rent, after allowing for the tax, is denoted by the area CEFD. This area will of course he much smaller than the area CGHD, representing the pre-levy rent. Thus far, it has been assumed that the tax-including average cost falls short of the price at the equilibrium output. Suppose now, as a result of the imposition of a levy, the whole average cost schedule is shifted to a position over and above the demand line, say, ate". Under such circumstances, whatever the output may he, average cost will always exceed the corresponding unit price and the firm will thus have to produce at a loss. The total loss for output, say, CM, may he represented by the area of the rectangular ACIB with its width CD (= OM) representing the output and the height BD (= AC) the loss per unit of output. If the firm is to continue to produce, the question that it has to face is one of adjusting its output to a scale that will minimize its loss. Reflection will reveal that, under such conditions, the optimum output will still he one where marginal cost and marginal revenue are equal. In diagram 6-5> the scale OM represents this output. An extension of the output beyond this scale will make marginal cost higher than marginal revenue and will thus increase the amount of loss. Meanwhile, any output falling short of this scale will yield a marginal revenue higher than the corresponding marginal cost; the total loss may, however, be reduced by extending the output to OM.3 ® This point may also be demonstrated mathematically as follows: Suppose x_ is the output, the function p(x), the unit price of the product when its output is χ, and the function C(x) the total cost incurred for producing the output. The total loss L for the output χ will then be C(x)X [p(x ) - χ J or x.p(x) - C(x); where x.p(x) and C(x)/x are respectively the total revenue and average unit cost. Minimizing the loss L, we have dL _ d(x. f(x ) ) _ d (Cjx)) = dx dx dx

0>

or

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

73

It ia less likely In a case of monopoly than in that of free or monopolistic competition, that the demand schedule of the firm vili be expanded at the expense of other producers. However, there are good reasons to believe -- even more in the case of monopoly than in the other two cases -- that the firm will continue to operate, for by doing so, it can at least avoid a part of the loss on fixed charges represented by the area GIJH (cf., Fig. 6-5). Here HJ (= Gl) is the fixed coat per unit of output and IJ (= OM) the scale of output. The saving would be particularly great for monopolists whose fixed costs are usually high in comparison with those of the producers operating under free or monopolistic competition. Long-Run Effects In analyzing the long-run effects of the levy upon the monopolist, it will be convenient to break the analysis down into three parts, dealing respectively with the conditions of constant, increasing, and decreasing cost. Constant cost: Under the conditions of constant coat, the marginal and average cost schedules will be coincident and may be represented by a horizontal line parallel to x-axis. The equilibrium is determined by the intersection of the marginal revenue and cost schedulee (= marginal cost schedule). In Figure 6-6, mc is the cost (average and marginal) schedule, ar the average revenue curve, and mr the marginal revenue curve, the equilibrium before the tax ia determined by the point N, the intersection of mc and mr. The equilibrium price and output thus determined will then be OB and OM respectively. After the levy of the tax, the average coat achedule will be ahifted from ac (= mc) to ac'. Unlike ac, the new average coat schedule is no longer a parallel line to the x-axis; it tends to decline with increase of output. This is true because the tax ia a fixed sum and the amount of tax to be allotted to each d(x.f(x)) _ d(C(x) ) _ dx dx This last e quation implies equality between marginal revenue and marginal cost. Thus the loss is at its minimum when the marginal cost and marginal revenue schedules intercept each other.

THE CAPITAL LEVY

74

unit of product déclinée ae output expands. The marginal coet schedule after the tax leyy, however, will take the course of ASH instead of IH; the initial coet on the first unit of output is increased by the amount of the tax (= AW), while the rest of the schedule remains unaffected.4 f

Since equilibrium is determined by the intersection of the marginal revenue and marginal cost schedules (e.g., mr and mc) and the positions of these two schedules are not affected by the tax, the equilibrium price and output will remain unchanged after imposition of the tax. 4 Of course, a new segment (AD) has been added to the marginal cost schedule. 5 The situation here is very similar to the illustration »Aich its. Robinson gave on pp. 3β-39 of "Economics of Imperfect Competition" (Loolon, 1906). "In this case," as she pointed out, "marginal cost is constant and average coet falls as output increases. The average curve is a rectangular hyperbola subtending an area equal to the fixed cost.. .and the marginal cost curve is a horizontal line to which the average curve is asymptotic."

(Ibid.,

p. 3 9 . )

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

75

The tax, however, does shift the average coat schedule frcan ac to ac'. As a result, the profit of the monopolist is reduced from BQUD to BQPC. The hurden of the tax will therefore be torne "by the monopolist. The faster ac, or the slower ar declines, (e.g., the faster the cost decreases or the slower the price declines as output expands), the less will he the "burden, and vice versa. Unlike the case of free or monopolistic competition, neither the equilibrium output nor the equilibrium price is altered by the tax. These results are due chiefly to the fact that under monopoly there are no extra-marginal firme to be expelled from the market and thus force the surviving firms to shoulder the tax "burden.

FIGURE 6-7

Decreasing cost: The case of decreasing cost is very similar to that of constant cost except (l) that the tax-including cost schedules, marginal as well as average, decline much more rapidly than constant cost schedules; and (2) that no great part of the marginal cost schedule will "be parallel to the horizontal axis. Consequently, as in the case of constant cost, "both the

76

THE CAPITAL LEVY

equilibrium output and. the price vili remain unaffected. The •burden of the tax, which falle exclusively on the monopolist, will he reflected In the reduction of the monopolist's profit fren ACRP to ABQP. Since the tax does not change the scale of output, elasticity of the demand schedule has no direct hearing upon the tax burden: this is true of both the constant and the decreasing cost conditions. Increasing cost: In the case of Increasing cost, however, the situation Is somewhat different. Before the tax was imposed, the equilibrium output Ib OM and the equilibrium price QB; the equilibrium is determined by the intersection of the curves mr and mc, representing the marginal revenue and marginal cost respectively. The monopolist'β profit is represented by the area BE6Q. After the tax levy, the average-cost curve, for the reasons given In previous discussions, will be shifted from ac to ac'. Unlike the caee of constant or decreasing cost, the marginal cost schedule under Increasing cost conditions usually rises faster than that of average cost. So the average schedule lies above the former curve for all output values. A shift of the average curve, therefore, will raise the marginal curve from mr to mr1. It is obvious from the annexed diagram (6-8) that theee changes will raise the equilibrium price to OA and reduce output to OA and COT. Profit will be reduced from BDSQ to ABRP. It may also be shown by the diagram, when the amount of the tax is given, (l) that the steeper the cost curves, the higher will be the price increase and the smaller the reduction In output; (2) that the faster the revenue curves decline, the greater will be the price Increase and the smaller the reduction In output, and vice versa. Whether the monopolist's profit will be increased or decreased by the tax will depend upon the relative slopes of these revenue and cost curves. Thus, under the increasing cost condition, the capital levy may reduce the output of the monopolist and raise the unit"price of his output. The distribution of the tax burden between the monopolist and the consumere of his products, through the change of price, will be determined by the relative slopes of the cost and revenue curves; it is

EFFECTS OF A CAPITAL LEVY ON PRODUCTION

77

conceivable that in some cases the tax may, as a consequence of high prices, result in a net gain to the producer. While elasticity of demand, may be ignored under a condition of constant or decreasing cost, it becomes one of the main determinants in apportioning the tax burden.

FIGURE 6-8 Conclusion

To sum up, then, the effects of the capital levy on firms under free competition are the same as those under monopolistic competition. This holds for the short-run as well as for the long-run analysis. In "both cases of competition, the Immediate effect of the levy will not alter the equilibrium output and price of those firms that hear the burden of the tax and may even have to produce at a loss. But when enough time is allowed for producers to make necessary adjustments, the equilibrium price and the equilibrium output of the producing firm, in both cases of competition, will be raised; and the burden of the tax will fall ultimately upon those extra-marginal firms that have been forced to suspend because of the tax.

78

THE CAPITAL LEVY

The situation under monopoly, hcwerer, le eamevhat different. In the short run, the tax burden vili he either absorbed by the monopolist's profit, or added to his loss; neither price nor output vili be changed. In the long run, the result varies according to the cost conditions under which the firm Is operated. Under constant or decreasing cost conditions, price and output vili not be affected; the full amount of the tax vili be absorbed by the monopolist's profit. In the case of increasing cost, on the other hand, output vili be reduced and price increased as a result of the tax. The tax burden is to be apportioned between the producer and consumers through the adjustment of price in accordance vlth the relative slopes of the cost and revenue curves.

CHAPTER

VII

EFFECTS OF A LEVY ON INVESTMENT AND CONSUMPTION 1.

Effects

on

Investment

In order to estimate the effects of the tax on investment, we need first to understand how, under given condition», the amount of Investment by a single entrepreneur and by the economy as a whole Is determined; and also how these Investments are distributed among various branches of production. The subsequent discussion will therefore fall Into two main divisions: (l) the effects of the capital levy on the amount of investment, and (2) the effects of the levy on the distribution of investment. As to the effects on production let us take the equation I =

+ TïTiT Tl+i)n; ^ where , j 2 , .... represent respectively the expected incomes of the periods 1, 2, .... n, and I its present worth; then 1 is the rate of the expected yield of the investment. The reason why the expected yield Is so defined may be explained as follows. Take as investment I which has a two-period income stream y9 . . (6 2) il α α ί T W · where 1, as before, denotes the rate of the expected yield. It Is also assumed that the individual has given resources which can produce various incomes of for period 1 and various incomes of for period 2, subject always to a given transformation relation

T(7V7Z)

= 0.

(6.3)

The primary interest of an investor is to adjust the j's in such a way as to maximize the present value I. To attain this result, it is necessary to have = 1 • ï-A-il* = 0 « ij1 1 + i dyt

(6.IM0

80

THE CAPITAL LEVY i

. ι

=

=

frp. -

fri,

(6.1Λ)

dy1 and

di 1 d2y„ „ — = < 0. dy 1 + i dy1¿

E. (6.5)

(6,5) is a necessary condition for the maximum present value. It is satisfied in the normal case where the transformation curve plane y^y^ concaves to the origin. ( 6 A a ) and (6.Vb) imply that when the present value is at its maximum, the distribution of the income of these two periods must he such that the marginal rate of return over cost is equal to the rate of expected yield, in Fisher's terminology, 1

or the marginal effi-

ciency of capital in the Keynesian sense. 2 If r is used to denote the market rate of interest, it follows that Profit = l(i - r )

(6.6)

will h e at its maximum if f j = i - r = 0; or i = r.

(6.7)

^ "...by cost," as Fisher explains, "is meant the comparative loss from one's income stream at first, caused by substituting one use of capital for another, and by return is meant the comparative gain Vilich accrues usually later, by reason of this same substitution. The cost is literally the difference it makes today and the return is the difference it makes in the future — the first negative, the second positive." (Irving Fisher, The Theory of Interest, New York, 1930, p. 157.) 2 "Although he does not call it 'the marginal efficiency of capital,' Professor Irving Fisher has given in his Theory of Interest...a definition of what he calls 'the rate of return over cost' which is identical with my definition [of the marginal efficiency of capital]. "The rate of return over cost,' he writes, 'is that rate which, employed in computing the present worth of all the costs and the present worth of all the returns, will make these two equal.' Professor Fisher explains that the extent of investment in any direction will depend on a comparison between the rate of return over cost and the rate of interest. To induce new investment 'the rate of return over cost must exceed the rate of interest.' 'This new magnitude (or factor) in our study plays the central role on the investment opportunity side of interest theory.' Thus Professor Fisher uses his 'rate of return over cost' in the same sense for precisely the same purpose as I employ 'the marginal efficiency of capital.'" (J. M. Keynes, The General Theöry of Employment Interest and Money, New York, 1936, pp. 140-41.) For a detailed discussion of the meaning of the marginal'efficiency of capital, see Chapter 11 of Keynes's book cited.

81

EFFECTS OF A LEVY ON INVESTMENT AND CONSUMPTION

This provee the famillar proposition that entrepreneurs always like to push their investment up to the point where the expected rate of yield is equal to the market rate of interest. Now observe what happens if a tax Τ is imposed upon the investors. First, take an instance where the value of Τ is independent of the value of I -- as in the case of specific duty. The value of

as given in (6.7) will then remain unaffected' αϊ since Τ in this case is a constant. The equilibrium will remain at the point where i. = r. If, on the other hand, Τ is a function of I, thén we shall have π = I (i - r - T), < and

+

η

(6

·8)

£j=i-r-t=0.

Therefore, i = r + Τ (6.9) instead of i = r as shown ahove. It may therefore he observed that a tax whose amount is fixed once for all usually has a less depressing effect on private investment than a tax that varies with the value of the yield of the investment taxed. Thus a capital levy is usually less detrimental than an income tax, so far as the effect on incentive to invest is concerned. The above line of reasoning, however, does not imply that the capital levy would have no effect whatsoever on new investment; there still remains one channel through which the tax may exert its influence -- e.g., the rate of interest.3 With the marginal efficiency or the expected yield of the capital given, investment may increase with a fall in.the rate of Interest, and vice versa. So long as the levy is comprehensive and affects all properties on an equal basis, no shift of capital from one use to o Moreover, the fact that this has happened once tends to induce a fear among taxpayers that it will happen again, and the fear of anticipated taxes (whether or not they materialize) may also discourage investment. The question of government guarantee against repetition, which has been dwelt upon at -length in the Colwyn discussion (cf. p. 2 above), is particularly significant in connection with the present discussion.

82

THE CAPITAL LEVY

another will enable taxpayers to evade the tax. Such situations, however, exist only on rare occasions, if at all. As has "been pointed elsewhere, even a well-planned general levy may involve some discrimination against equity capital, and may thus encourage the use of borrowed funds. Moreover, the exemption of consumption goods (particularly the durable consumption goods), which may be made on practical grounds, may offer another loophole through which capital may with impunity escape taxation. Last, but not least, capital flight through the foreign exchange market, unless properly controlled, may work havoc with any fruit that the capital levy might bear. The discrimination against equity capital, however, exists only from the standpoint of the borrower; it is rather immaterial so far as the lenders are concerned. The existence of the anomaly may render possible the evasion of the tax by means of mutual borrowings among taxpayers, and thus reduce the government revenue therefrom. An algebraic illustration may .put the matter in a clearer light. Suppose two firms, say 1 and 2, have at the outset the 'same balance-sheet equation as follows: α α α a' = the value of asset, = the value of liability, = the value of surplus reserve, = the value of capital stock, (= 1, 2, ... Ν) is the notation denoting a particular firm. If there are altogether Ν corporations with a similar financial structure, then the aggregate tax base for those Ν firms will be where A L S C α

Σ" (Αα - L a ) or Σ Ν (S + C ). a a a a a=l a=l Let us further assume that the assets of both firms are expanded by $d: firm 1 financed the expansion by invested capital, whereas firm 2 used borrowed loans. Consequently, the new balance-sheet equations will appear as follows: firm 1: (A1 + d) - L 1 = S 1 + (C^+d), and firm 2: (A + d) - (L + d) = S + C . 2 2 2 2 Therefore, the taxable surplus for firm 1, in comparison vith

E F F E C T S O F A LEVY ON INVESTMENT AND CONSUMPTION

83

its earlier equation, is increased by d; whereas that of firm 2 remains S 2 + Cg. Suppose that, of the N firms, m followed the example of firm 1 and expanded by issuing new stock; while η adopted the policy of firm 2 by haying recourse to borrowings. Then the aggregate base for Ν firms will be or at onoe, and for once only, sacrificed $2,000.8 A similar view is expressed by De Viti de Marco. From the point of view of objective value [he says] it is a matter of indifference whether one sells (property) or contracts a loan. That is, it is all the same whether one sells a piece of property in order to realize $5,000 once and loses forever the annual income of $250, or contracte a loan of $5 »000 and pays an annual interest charge of $250 in perpetuity. 9 In other words, as J. S. Mill puts it: If property bore the whole interest of the debt, property might, with great advantage to itself, pay it off; since this would be merely surrendering»to a creditor the principal sum, the whole annual proceeds which were already his by law; and would be equivalent to what a landowner does when he sells part of his estate to free the remainder from a mortgage. 10 Since a direct tax on capital would impose no greater burden on 8

Cf. Economic Journal (1Θ18), p. 253. Antonio de Viti de terco, Principles of Public Finance (translated byEdith P. Marget, New York, 1936), p. 382. De Viti, however, does admit that from "the point of view of subjective value,...the landowner will prefer to contract a loan, in order to preserve his land as a field of future investment for himself and for his heir;... Similarly, the capitalists who have chosen far their savings short-term investments — that is, loan — for the sake of preserving the greatest possible freedom in the disposition of their property,..." [Loc. cit.) 9

J. S. Mill, Principles

of Political

Economy

(Ashley Edition), p. 877-

TOE CAPITAL LEVY

118

the taxpayer than would subsequent installment Impositions on income, the argument continues, elimination of government debt is preferable, because it will at least save the expense of administering the debt aerrice -- not to mention the injustice which might result frcm the interest payment. Reflection will reveal that these contentions are open to serious objections. In the first place, it will be observed, they are based primarily on the narrow view that the capital levy is to be used only for debt repayment; the service of the tax in other connections is neglected. A still more serious objection, however, is the gross simplication of the actual conditions. It is assumed that the capital value of property can be determined simply by capitalizing the current income at the current rate of interest. That is to say, c

= Ύ

(1 +

TîTT)

+

7TT)2+

···•

e t 0

-)U

(9,8)

In other words, the capital value may be estimated on the basis of the sum of the present value of future yields. This formula does not alwaye hold true, for the income of future periods and the interest rate at which these incomes tire capitalized are not necessarily constant. In order to determine the value of C, we need to know, at least, (l) the magnitude and the temporal distribution of future income streams; (2) the rate of interest to be used for discounting these incomes; and (3) the life of the assets. Lack of knowledge regarding any of these variables makes it impossible to apply thle income-capitalization method of valuation satisfactorily. A brief consideration of each of these variables will show that, by their very nature, direct information on them is not likely to be available for any but minor groups of wealth items, In view of the dynamic nature of our economy, the current year's lnccme can scarcely, if at all, be a reliable basis for estimating future yields. Even with the assistance of experts, the estimating of such incomes is usually conjectural. Similar difficulty will also be encountered in predicting the future course of the interest rate. Probably it is more difficult still to determine the temporal distribution of the variables, 11

C = capital, Y = yield and i = rate of discount.

THE CAPITAL LEVY AND OTHER TAXES

119

the Income and the Interest rate, so that the lncooe for each year may he properly discounted hy ite corresponding Interest rate. This distribution usually has a very significant effect upon the final result, for the earlier a large share of expected income matures, or the more rapidly the rate of interest falls with the lapse of time, the greater vili he the current value of the capital, and vice versa.12 Moreover, in the actual market, there is no "rate of interest" as such. To find the value of goods that are different in their nature and functions, the interest rates at which Incomes are to he capitalized should he varied from one category of property to «mother in order to reflect such discrepancies.13 The above discussion shove clearly the inadequacy of the usual procedure of income-capitalization valuation based either on the income and interest rate of the current period, or on some other arbitrarily determined value. Since the relation betveen income and capital is so indefinite, any observation predicated upon a supposed relation betveen these tvo variables is at best precarious. It follows, then, that none of the arguments advanced by Β i cardo and his follovere, mentioned above as the basis for supporting the capital levy, is tenable. Moreover, it is agreed among students of public finance that income taxes can reach only Income-yielding properties, material or Inmaterial, and property taxes only material properties, with or vithout income. In other vorda, the existence óf immaterial capital renders impossible a comparison of the Income tax and the capital levy simply by capitalization of the former at a selected rate of interest. It is obvious, therefore, that the position taken by Ricardo and his followers In regarding ^ Suppose the present value of a stream of future income is equal to l+y^/i + + y n /i, where i represents the rate of interest and the y's denote the incomes of different periods. Apparently, the earlier the income is realized, the smaller will be the amount to be discounted. ^ Suppose the rates of discount for various periods are i.^. ••¿η· Then we have the present value

ρ= 1 +

1

1

•

+

i

1+11 (1+4) (1+12) (l+i1)...(l+in) Therefore, the smaller the value of the i.'s in the later periods, the greater will be the value of P.

120

THE CAPITAL LEVY

the capital levy merely as a capitalization of future income ie really a gross βimplication of the actual conditions and cannot l>e accepted vithout question. The Levy

and

the Gift

Tax

Another difficult and important problem to he faced in assessing the capital levy is presented hy perfectly legal and straightforward gifts inter vivos. Such transfers may lighten the tax burden, if the net reduction in the amount of the capital levy paid hy the donor and the donee exceeds the amount of the gift tax resulting frcm the transfer; or to state it in a different way, if the decrement of the levy on the donor's capital exceeds the increment to the levy on the donee's capital plus the gift tax. This may he shown algebraically as follows. SupposeZ (EC) and Σ (re) represent respectively the a=l — a «=1 — a amounts of the capital levy to he paid hy the donor and hy the donee in the absence of the gift; E and r being the rates, and C emd c the tax bases for the property bracket α. Σ (pG)a i β - ß-l — Ρ the gift tax, where £ and G are used to denote respectively the tax rates and bases and indicates the tax bracket, δ_ Is the decrement in the levy on the donor's capital, -- the increment to the tax burden of the donee — both results of the gift transfer. It follows then that It would be worth while to effect such transfers as long as

δ

δ >δ + (9 10) 1 *δ2 1 2 PP&V · This type of evasion is usually attained by giving away a part of the taxable property to, say, a prospective heir possessing little or no property bo that the properties, vhich would otherwise fall into the top brackets, would not be taxed at a low rate. The more progressive the rate, the greater will be the temptation to avoid the tax. Loopholes of this sort, however, may easily be plugged simply by both raising and steepening, at least temporarily, the progressive tax rates on gifts Inter vivos, in accordance vith the

TOE CAPITAL LEVY AND OTOER TAXES

121

rate schedules of the capital levy. A cumulative provision 14 must "be Included, for otherwise the effect of the progressive rate may he nullified by dividing a taxable gift into installments of email amounts. The practical difficulties involved in revising temporarily the gift tax rate, however, may render this measure less satisfactory than the other two remedies to he discussed in subsequent paragraphs. Another possible solution of the difficulty is to include in the tax base for the capital levy all the gifts made with an eye to evasion of the tax —

euch as gifts made after the an-

nouncement of the government's intention to impose the levy. Gifts of this type can probably be determined with less difficulty and arbitrariness than can gifts in contemplation of death, in connection with estate taxes. In dealing with the latter gifts, the chief difficulty lies in drafting and applying a definition of "contemplation of death." One approach is to set an arbitrary period of a certain length, and then to include gifts made during this period in the estate left at ^ The meaning of the cumulative provision may be shown by the following illustration: "The donor's first reportable gifts after the enactment of the Revenue Act of 1932 were in the calendar year 1934 when he made a gift of $75,OCX) to A and a gift of $55,000 to B. The total amount of gifts during 1934, for the purposes of the tax, was $120,000, after excluding $10,000 for the donees in accordance with the provisions of article 10. The amount of the net gifts far that ye air was $70,000 after deducting the $50,000 specific exemption in accordance with the provisions of article 12. The tax on the net gifts of $TO,000, . . .amount to $42,125. "During the calendar year 1935, the donor made a gift of $20,000 to A and a gift of $25,000 to B. After excluding $10,000 for the two donees, the total amount of gifts during that year was $35,000. Since the amount of the specific exemption authorized was exhausted, the amount of the net gifts for 1935 was $35,000. The taut for the calendar year 1935 is canputed as follows : 1. Amount of net gifts for 1935 $35,000 2. Net gifts for preceding calendar year (1934) 70,000 3. Total amount of net gifts 105,000 4. Tax computed on item 3 4,650 5. Tax computed on item 2 2,175 Tax for year 1935 (items 4 minus item 5) 2,475" (Regulations 79 (1936 edition), Relating to Gift Tax, Washington, D. C., 1936, p..13).

THE CAPITAL LEVY

122 death, to determine rangements ble. 1 5 B u t

the total h a s i s for the estate tax.

of this sort are necessarily in t h e c a s e o f t h e c a p i t a l

the government's

intention to

tive and definite meaning

arbitrary and

Ar-

inéquita-

levy, the announcement

impose the tax has a more

than has the term

of

objec-

"contemplation

of

death." A third measure, w h i c h undoubtedly w o u l d also contribute discouraging

evasion through gift transfers,

levy b y using the family as a unit tax returns for husband and These three remedies plementary rather

than

la t o i m p o s e

-- s u c h a s t h e u s e o f

to the

Joint

wife.

should

of c o u r s e b e c o n s i d e r e d a s

com-

competitive.

^ "It is...inequitable," as Wedgewood has pointed out, "in the sense that the liability of gifts to Estate Duty will be largely a matter of luck. The more long-lived persons — and these are on the whole the richer — will be able to hand on a larger proportion of their property during life than those whom death catches at an earlier age. Thus those whose parents die young will receive a smaller proportion of the latter's property than those whose equally rich parents live to ripe age. Yet, if anything, the needs of the former are likely to be greater than the needs of the latter. Moreover the parents who die young are likely on the whole to leave less property than those who have their full span of life in which to work and save. Hence to fix an arbitrary period before death during which gifts are liable to duty results to some extent in a fortuitous reduction of the intended rate of progression of the tax." (Josiah Wedgewood, The Sconouics of Inheritance, London, 1939, pp. 23θ-40·)

CHAPTER Χ

THE ESTIMATE OF THE YIELD OF THE LEY! The Estimate

of the Groes

Yield

The problem of estimating the yield of the levy is mainly one of ascertaining the amount and distribution of private property. There are two available methods of computing the national wealth, which are commonly used, namely, the Giffen or income method, and the multiplier or estate method. The Giffen or income method consists of estimating national wealth on the hasis of income tax returns. The method is to discriminate as far as possible in these returns between the different sources of income, to capitalize them at a suitable number of years' purchase, and then to make allowance or conjecture for the capital of the income not liable to income tax and for the capital that does not yield any income.1 The second method of estimate consists of applying a properly computed multiplier or multipliers to estate-tax'returns to obtain the aggregate wealth of the economy. In view of the close relation between the capital levy and taxes, it appears that the multiplier method would probably be a more appropriate approach in estimating the yield of the levy. It is on this method, therefore, that the discussion in thie chapter will mainly be based. Under the multiplier method, there are two possible approaches: (1) the general-multiplier method, and (2) the specific-multiplier method. According to (l), the total wealth liable to the levy is determined simply by multiplying by a common multiplier, the total value of the estates passing at 1 For detailed discussions of this method, see Robert Giffen, "Recent Accumulations of Capital in the United Kingdom," Journal of the Statistical Society (March, 1878), ard The Growth of Capital (London, 1889); Sir Josiah Stamp, British Incomes and Property (London, 19S0), and "The National Capital," Journal of the Boyal Statistical Society (1931); H. Campion, Public and Private Properties in Oreat Britain (London, 1939), Chapter III.

THE CAPITAL LEVY

124

death within a giren year. Thus the possible receipt from the levy aay he computed by applying the appropriate tax rate to each group of the estates in order to obtain the tax yield free each class; the yields are then summed up and the aggregate is multiplied hy a properly determined multiplier. The result thus obtained may he considered to be the gross yield from the levy. Algebraically, the procedure of estimating the total wealth nay he summarized hy the formula M^ ΣΕ, and that of estimating the tax yield hy the formula M v ΣγΕ; where tj^ is the value multiplier, E the value of the representative estate of each estate group, and r the representative tax rate applicable to each group ? There still remain to he examined the meaning of the "multiplier" and the procedure under which its value is determined. A brief excursion into the literature on the subject of the "multiplier" reveals that there are at least two possible forms of multiplier: the number multiplier and the value multiplier. In the first approximation, these multipliers may be defined algebraically as follows:3 7alue or estate multiplier >ί, = and Number multiplier M n =

Σ Er(ir/dr)

r—

Σ

Σ Dr(ir/dr) r

Er

;4

(10.1) (10.2)

2

See Hugh telton, The Capital Levy txplained (New York, 1923), pp. 75-77. Cf. the arithmetical computation of the multipliers given by Messrs. Mallet and Strutt in their article of 1915 (»Tourna 1 of Boyal Statistical Society (1015), Tables V-VI, on pp. 563-Θ5. ) 4 In comparing the estate and number multipliers, Messrs. Daniels and Campion made the following observation: "Since the amount of capital held increases with age, and the appropriate multipliers for higher age groups are less than for lorer age groups, the general estate multiplier will aluays be less than the general multiplier." (G. W. Daniels and H. Campion, The Distribution of lational Capital (Manchester, 193Θ, p. 5).) It is obvious free the above formulas that this is not always the case, for H ^ < ^ according as Σ Ej. (* r /d r ) > Σ E r 3

Σ D r ; since the denominator δ - δ = δ - δ = 0 . This means that the gifts inter vivos —m —η — — -— will definitely raise the value of the multiplier. In case (2), the term on the right-hand side of (10. 5b) will he reduced to (/ /d ). The whole inequality may thus "be rewritten as Σ E

< (á) .

(10.6)

σ ε

Therefore, if η is an old-age group, it is very likely that the new multiplier will he greater than the one "before the gifts were transferred} "because the term on the left side of (10.6) is the weighted average of all the (i/d)' s. Similarly, in case (3) where and a&n with a < 1, the formula (l0.5b) may "be rewritten as ^ i l i < a - Φ (10.7) > ΣΕ (a - 1) in order to see how the gifts inter vivos change the value of the multiplier. These are only the effects of such gifts on the general estate multiplier; they are not applicable to the case of the general number multiplier, which is not likely to "be much affected except in so far as people deliberately reduce their holdings of capital below the exemption limit of the estate duties and those receiving the gifts inter vivos had up till then no more than that limit. The effects of gifts inter vivos on the general estate multiplier have "been discussed at length, but there still remain to be examined the repercussions of such transfers upon the total value of estates computed by the general estate multiplier method.6 It is sametimeö contended that although gifts inter vivos from the older to younger generations may raise the value of the general estate multiplier, the "bolstering effect may be compensated by a corresponding shrinkage in the value of estates, upon which the multiplier is to operate. Beflection will 0 Their effects under "the specific-multiplier method will be examined presently.

128

THE CAPITAL LEVY

reveal that this contention can be accepted only with reservations. For, according to the formula (10.5a), the changes in the value of the estates can offset only the changes in the value of the estate multiplier arising from changes in the denominator of the multiplier, but not those due to the change in the numerator.7 After the values of the multipliers are determined, the remaining step in ascertaining the total value or -the distribution of the estate will be simply to apply these multipliers to the corresponding values or numbers of the estates passing at death. As a method of approximation, the multipliers used in the present method need not be those computed from the same set of estate data upon which they are to operate. That is to say, once the general multipliers are determined from same properly selected data, they may be used to approximate the total values or distributions of estates for other years, with a reasonable degree of accuracy.8 Of course, the results thus obtained will have to be approximations; but the method is a convenient shortcut and will in general serve our purpose. Down to this point, our discussion has covered only the cases where general multipliers are used -- the value of estates is determined by applying the general estate multiplier to the value of the estates passing at death, while the number of prop7

For the total value of the estates after the gift transfers will be

[

Σ Ε ( Λ +• (^ϋ-)δ d *m m ¿n Σ E 4-δ π - δ η

n

1

lE

+

6

m - V ·

® "Since death rates and the age and sex distribution of the population are likely to change only gradually, corresponding changes in the general number multiplier may be expected also to take place only gradually." The general estate multiplier, however, will "vary more widely from year to year since in addition to the factors making for changes in the general number multiplier, it is also affected by possible disparity of movements in the values of different forms of capital and the practice of gifts inter vivos. If, for example, the values of land and of stocks and shares — held mainly by older people with large estates — rise to a greater extent than the value of house property held mainly by younger people with small estates — the general estate multiplier will fall and vice versa." (Daniels and Campiori, The Distribution of national Capital, pp. 4 and 5.)

THE ESTIMATE OF THE YIELD OF THE LEVY

129

erty owners is computed by applying the general number multiplier to the number of deaths in the year concerned. Since mortality rates vary widely, not only with age but also with sex, a more satisfactory approach would he to apply the multipliers (e.g., the reciprocals of the appropriate mortality rates) to each age group for males and females, rather than to operate a general multiplier upon the aggregate value of the estates. Under the general-multiplier method, one may use the simple formula M^ Σ E for the total value of estates, and Σ D for the number of property owners -- M v "being the general estate multiplier, M n the general number multiplier, Σ E the value of estates passing at death, and Σ D the total number of deaths occurring during the year. Under the specific-multiplier method, the estimates of the value and the number will he respectively Σ (//d)l or Σ (i/d)D. It is therefore clear that in cases where the data from which the general multipliers are determined and the estate statistics upon which they are to operate belong to the same year, the general and specific-multiplier methods will give identical results. The procedure for estimating private properties from estatetax returns by means of the specific-multiplier method may be outlined as follows: 1. For a given period of years find a proper sample of estate passing at death. 2. Classify the estates according to a double entry table; with the vertical argument representing the grouped values of estates and the horizontal argument the age-groups for both sexes. 3. Multiply the value of estates falling in each compartment of the table by the corresponding ratio of the number of living persons to those who have died during the period; e.g., multiply all E's in the first age-group in the second column of the annexed table by ü-j/dj or ν , all E's in the second agegroup by I J d g or y_r¿, etc. U. Sum up these products for each row; these sums are the estimated wealth of various estate classes. After values of property are known, the estimate of. the gross yield of a capital levy at a given rate schedule will then be only a matter of simple arithmetic. In addition to the four

TBE CAPITAL LEVY

130

β top β enumerated, aborre, It le necessary to add only tvo to complete the procedure: 5. Apply the appropriate rates of taxation to the sums obtained In (Ό to compute the amount of the taxes for each estate class. 6. Add these taxes for all classes to obtain the total yield of the levy. The whole procedure of computation Is shown algebraically in the following table.

Estate Claeeee 3

Total Wealth for Each

Male age-group· renale age-groupa Eatate Tax a t ... . a b Clase Bate Τ = Bfïv) Li w ? E αϊ 1 απ η ·' ®an n '»(inll'inni ·· r ar"r «1 »1 ^rEarvr E ßl"l *32V2 ·· •· EßnWn 'ßlnn )V|nn ) "·· Mßr"r «2 B2

total wealth)

(= total yield)

Similarly, it may also be shown that the formula for the estimate of the number of property owners is ^s^r5rsiîr· But for estimating the yield of the capital value, it is the estate value that is of primary concern. Examine next the effects of gifts inter vivoa on the results obtained by the specific estate-multiplier method. It is obvious from the formulas (10.5a) that the total estimated value of gifts inter vivos will be greater or lees than the eame estimate in the absence of such transfers according as Ζ = [Σ E(|) + (¿)6 m - (j»)6n] - [Σϊ(|)] < 0, «

δ.
(Vil δη ΧζΤϋ

I f none of these g i f t s reappear in the e s t a t e - t a x returns of the donees, δ^ = 0, then the d i f f e r e n c e Ζ w i l l be negative. That I s t o say, the g i f t s Inter vivos w i l l lower the estimate. I f , on the other hand, a l l these g i f t s enter the e s t a t e returns so that δ^ = δ n , Ζ w i l l be p o s i t i v e ; since C ^ , / ^ ) , the r a t i o of l i v i n g s to deaths In the younger age group, I s greater than /d^), the corresponding r a t i o f o r the older age group. This means that the g i f t t r a n s f e r s w i l l r a l e e the estimate. I f we assume, as Messrs. Mallet and S t r u t t did i n t h e i r paper of 1915» t h a t , while the g i f t s had reduced by δ_η, the value f o r the donors' group of e s t a t e s passing a t death, the e s t a t e value as shown by the e s t a t e tax returns of the g i f t - r e c e i v i n g c l a e s

the g i f t s transferred, as estimated f r e n the decrement of the value of t h 10 donors' age group. Under euch

equal t o zero ( c f .

(IO.8)). Thus the estimated value of the e s t a t e e w i l l remain constant, despite the g i f t s i n t e r v i v o s . I t I s therefore c l e a r that the position taken by Messrs. Mallet and S t r u t t holds true only under c e r t a i n assumed circumstances and cannot lay claim to general v a l i d i t y ; f o r the v a l i d i t y of t h e i r assumption i s predicated upon a complete homogeneity within the age-group of the donees, including equal d i s t r i b u t i o n of g i f t s , the same health conditions among these i n d i v i d u a l s , e t c . Otherwise, i f the donees happen to be persons with p a r t i c u l a r l y good health who f a i l t o die during the period under consideration, the g i f t e i n t e r vivos may disappear e n t i r e l y frcm the t o t a l value of the e s t a t e s passing a t death, and v i c e v e r s a .

1 0

P u b l i s h e d i n Journal

t i c u l a r l y pp. 570-72.

of toyal

Statistical

Society

( 1 9 1 5 ) . Read p a r -

THE CAPITAL LEVY

132

Allowances

for Losses

in Death

Duties

Stamp suggests that a crude estimate of the loss of death duties as a result of the levy may he made on the following lines : A sum of £3,000,000,000 will disappear frcm individual fortunes liable to estate; this represents, say, an effect of one thirtieth each year, so that the diminution In annual capital under charge will he £100,000,000. The average rate of estate duty payable on estates over £5,000, measured by the total duty on their capital value, is 12-l/2 percent, so that £12,500,000 will he lost annually. To this Is added the loss in legacy and succession duties.11 This method of approximation, however, is unsatisfactory because of the following reasons: 1. It ignores the effects of progressive rates on the loss of estate duty. If the rates are progressive, the loss of one hundred million dollars annually In capital values, In the first place, will not he spread over the whole range in proportion to the amount of wealth in each group. In order to he precise it is necessary to work out the loss due to the levy in each group, and then compute the estate duty on that loss in each group at the appropriate tax rate. Moreover, an estate that was liable to duty at, say, 50 percent, may after imposition of the levy become taxable at only 25 percent because of shrinkage in the size of the estate. A similar loss, due to the lower scale of rate chargeable, occurs throughout the whole tax scale. For a better approximation, allowance mtist be made for these two types of loss kinds. 2. Since not all losses in the estate duty occur immediately or at the βame time, and since the present value of a loss, say, of $1,000,000 in five years' time is not the same as that of the loss which is to be realized in ten years, allowance must must be made for time. That means that one must take into account age of the taxpayer for each range of fortune. A more satisfactory procedure for the estimation of the loss would be as follows: ^ J. Stamp, Studies in Current Problens in finance and Government (London, 1985), p. 256-

THE ESTIMATE OF THE YIELD OF THE LEVY

133

1. The loss of fortune due to the levy 1b firet determined.; this loss conalets of (a) a lose of estate duty upon that amount, and ("b) a Iobb of estate duty on the remainder of the

fortune owing to Ite coming Into a lover class of duty. The aggregate of (a) and (h) represents the loss for each age group.13 2. The expectation of life13 of each age group Is obtained. 3 · The present amount of each loss Is then computed on the has1b of em Assumed r&to of Interest &nd "the expectation of life. it-. The sum of these group losses represents the aggregate present value of all future loeaee. If necessary, the aggregate may be reduced to the terms of, say, 1,000 million of the l e v y — I.e., by measuring the loss In terms of per 1,000 million of the tax. 5. To this aggregate loes In estate duties may also be added the losses In legacy and succession duties. The estimate thus obtained gives the loss upon one devolution or "occasion for duty." upon the next devolution, say, seme 12

Cf. Ibid., pp. 255-63The expectation of life at any age may defined roughly as the average number of years to be lived by persons of that age. The expectation of life based on the assumption of uniform distribution of deaths throughout the year (expectation of life based on these assumptions is known as the "complete expectation of life" ) may be expressed by the formula 13

.1

W A , * « - .

where.,/χ is the number of persons who will years during the following y e a r t h e next year, and so an. But if we assume that all the deaths in any year take place at the very beginning of the year, the expectation of life at age Jt will be _ + / x+3 + etc. x+1 + £x+2 (2)

^

If, on the other hand, we assume that all the deaths in any year take place at the very end of the year, the expectation of life will be ¿ X

4

4*1

+ etc

(3)

It will be noticed that formula (1) is simply the arithmetic average of (2) and (3). (See C. H. Forsyth, Mathematical Theory of Life Insurance (New York, 1984), pp. 16-17.)

THE CAPITAL

134

LEVY

thirty years later, there will he a similar kind of loss. In Stamp's estimate, this loss on the second, devolution was also taken into account. He, however, did not think it necessary to peer further into the future as the two devolutions would practically cover the nominal term of the War Loans with which his discussion of the levy had been closely associated. Moreover, the estimates based on estate tax statistics give only approximations of the values of estates subject to death duties; those falling below the lower exemption limit are not included. Thus, if the exemption allowed by the levy is lower than the corresponding exemption for estates taxes, an addition should be made to the original estimate. Conversely, when the levy exemption is higher than that for the estates tax, proper deductions must be made. In actual caees, the latter situation will be more likely, as the levy exemption, because of administrative difficulties and other reasons, is more likely to be higher than that of the estates tax. Similar reasoning may be applied to the relation between the levy exemption and that of other taxes.

Allowances

for Losses

in Income

Taxes

The effects on income taxes and surtaxes will next be examined. The estimation of the loss of the flat-rate income tax due to a- debt-redemption levy is relatively simple, and its procedure has been very well summarized by Mrs. Hicks as follows: The loss of receipts from income tax could be easily calculated. The total loss of taxable income as a result of the levy would be equal to the gross saving in interest payments. Although the lose of income would be distributed among the taxpayers in a very special manner, due to the sales of property which would be needed in order for the levy to be paid, this would not matter so far as income tax was concerned. Income tax is charged at a flat standard rate (apart from allowances, which are unlikely to be important in this connexion); consequently the loss on income tax can be calculated by applying the standard rate of income tax to the gross savings.14 14

Hicks and others, Taxation

of Mar Health,

p. 279· In the United States where

THE ESTIMATE OF THE YIELD OF THE LEVY

135

In case of the levy used for purposes other than debt redemption, the loss may be determined simply "by applying the standard or normal rate to the property distribution of the pre- and post-levy positions of each class, obtained in connection with estates-tax returns. This method, as Mrs. Hicks has correctly pointed out,15 involves the following assumptions: 1. The incomes affected by the levy are only unearned incomes; those incomes which do not come out of property are not affected. For only under these conditions is it possible to calculate the income before the levy by applying a normal rate of return on capital to the capital on which the levy is to be imposed. 2. The same rate of yield is applied to the estimates of both pre- and post-levy yields on capital. This, of course, is a doubtful assumption; for while the assumption of a uniform rate of yield for all properties is artificial enough, the use of a common rate for estimating both the pre- and post-levy incomes makes the result even more doubtful. The estimation of the loss of receipts from surtaxes is more involved; in such a case, the rate will be progressive and it is therefore necessary to consider the rate of tax payable on each income, before and after the levy. A similar procedure would be to assume an average rate of yield on capital values and then compute the tax loss, also with the help of the property distribution table Just mentioned.16 This procedure is of course open to objections similar to those pointed out in the previous paragraph. Allowances

for Other Gains and Losses

In the case of debt-redemption levies, the losses in death duties, income taxes and surtaxes may be compensated, at least capital gains are subject to income tax, the situation is somewhat different, for in that case, the total loss of taxable income will consist of not only the interest payments on the bonds redeemed but also the taxable capital gains which might ïtrise from these bonds. The author is indebted to Professor R. M. Haig for this point. 15

Ibiâ., p. 279. Both Stamp {Current Probiens in finance and Government, p. 264) and Mrs. Hicks (Taxation of Var Wealth, p. 283) used this method.

136

THE CAPITAL LEVY

in part, by gaina resultine from savings in debt-service charges, Including interest payments and appropriations for a sinking fund. The gross annual earing in Interest as a result of a levy vili of course depend upon the rate or rates of interest on the loans to he repaid. Neither the Stamp estimate nor that made for the Colwyn Committee include any allowance for the sinking fund reduction. But if the amount of the debt redeemed is sizeable, the relief to the b u d g e t from sinkingfund appropriations should he properly accounted far in the computation. In addition to those mentioned, there are etili the following adjustments to he considered. First, there is a deduction to "be made from the gross yield, if a discount is allowed for prompt payment. Second, there Is an addition to he m&de to the yield, in so far as interest is charged on deferred payments. Third, there 1b an addition to he made for interest that may hare accrued on securities received by the government In payment of the levy. Fourth, there is an addition to he made if there is appreciation on securities between their receipt and disposal by the government. Conversely, there is a deduction to be made if they depreciate.17 Thus, the gross yield of the levy may be estimated by the multiplier method on the basis of estates-tax returns. After the gross yield is obtained, various adjustments have to be made for the loeses of death duties and income taxes due to the shrinkage of private property as the result of the levy; for the savings In debt service charges and sinking-fund appropriations, if the levy is used primarily for redeeming public debts; and for other items which may arise as a result of the special conditions under which a levy Is Imposed.

^ The additions or deductions due to interest payments or change in value of securities aure relevant only to those cases where the levy is payable in securities.

CHAPTER

XI

CONCLUSION The Levy

for

Debt

Redemption

The capital levy, aa has "been pointed out, has its own peculiar set of advantages and of shortcomings. Consider first the probable effect on the aggregate propensity to consume. Since the whole procedure of levying taxes and redeeming debts may reduce the concentration of wealth and thereby raise the aggregate propensity to consume,1 it may be helpful in pulling the private enterprise economy out of the stagnation caused by under- consumption. Secondly, non-recurrent levies on capital do not have the marginal effect of discouraging investment, as do annual taxes on income or on profits. Nor will these levies play euch havoc with the accumulation of capital as does a regularly recurrent tax on capital. Against these merits of the capital levy, however, one may, in the first place, set the disturbing effects that it may impose upon the money and exchange markets. But these defects may be remedied, at leaet to a certain extent, by such measures as foreign exchange control, banking operations, and various other devices which may facilitate the payment of the tax. With the recent experiences in coping with the chaos in financial markets, it will probably be agreed that there is considerably more chance for these counteracting measures to succeed than would have been the case twenty years ago. Numerous difficulties will probably be encountered in administering these taxes. But the British Board of Inland Revenue has admitted, in its celebrated memoranda, the feasibility of the increment levy, the administration of which is usually considered one of the most complicated among the various forms of the levy. Becent 1 This is not entirely true when the degree of the progression of the levy is greater than the degree of the concentration of bondholding.

138

THE CAPITAL LEVY

experience with income, death., and excess profits taxes have put tax authorities in a better position to tackle the difficult problems of administration. A further objection may "be raised against the capital levy for its failure to tax "brain capital"; e.g., the earning power of high-income recipients of various professions. Reflection will reveal that this is again not a vital objection. Students of public finance agree that while income taxes can reach only income-yielding properties, material or Immaterial; property taxes can tap only material properties, with or without presently realized income. It is true that the exclusion of "brain capital" is an important shortcoming of the levy, as well as of other property taxes; but this defect alone cannot render the levy less desirable than the impositions of incomes and excess profits, both of which tax only the income-yielding properties but not those without incomes. Here in the United States, there is yet another question to be answered if the capital levy is to be adopted — that is, the question of constitutionality. Concerning this point, a study of the Twentieth Century Fund has this to say:2 The "due process"3 and "direct tax"4 clauses of the Constition cast serious doubts on the constitutionality of a straightforward capital levy, even if it were economically feasible. The nearest approach to a capital levy that seems to be open to us without a constitutional amendment is a system of very heavy inheritance taxes and highly progressive income taxes, including taxes on capital gains and corporations' excess profits. The Levy as a Measure

for F inane ini Var

Since a war may be financed by loans and loans may be redeemed by a capital levy, can war be financed directly by means of a capital levy? The answer to this question is in the negative. For during a time of war, the function of a tax is two2

Twentieth Century Fund, The national Debt and Government Credit (New ïork, 1937), p. 126. ® Article V of the Amendments to the Constitution of the United States. ^ Article I, Section 9, Clause 4 of the Constitution of the United States.

CONCLUSION

139

fold: (l) to obtain for the government a necessary portion of national income and. wealth to meet war expenses; and (2) to divert the nation's resources from civilian consumption to military uses without at the same time disrupting the smooth operation of the economic system. A capital levy, which is to he paid mainly out of past savings, may "be helpful in expanding government revenue, hut it is not likely to he able to curtail civilian consumption to any appreciable extent. On the contrary, the repayments of the levy may make it necessary for people to dissave and thus to holster the aggregate outlay of government and civilian consumption. Such an expansion of outlay is, of course, not a desirable thing to encourage during time of war, if the price level is to be stabilized. It is true that government borrowing is in no way in a better position than a capital levy, so long as it absorbs only savings, rather than the current flow of income; and a capital levy may, too, have a restrictive effect on consumption in so far as it is paid out of income. In curtailing civilian consumption, however, no measures can be so effective as excise taxes or impositions on lower incomes.

BIBLIOGRAPHY1 Allen, R. G. D. Mathematical Analysis for Economists. London: 1938. Black, Duncan. Incidence of Income Tax. London: 19^0. Boribright, J. C. Valuation of Property. New York: 1937. Campion, Ξ. Public and Private Properties in Great Britain. London: 1939. Carson, M. "Réévaluation des Bilans en France," Journal des Economistes (July, 1930).* Cassel, G. "The Theory of Progressive Taxation," Economic Journal (December, 1901). Chamberlain, E. The Theory of Monopolistic Competition. Cambridge, Mass.: 1939· Cournot, Α. Α. Recherches sur les principes mathématiques de la theorie des richessess. Paris: I838. Daniels, G. W., and Campion, H. The Distribution of National Capital. Manchester: 1936. Dalton, H. The Capital Levy Explained. New York: 1923. Dalton, H. Principles of Public Finance. Ninth edition. London: 1936. De Marco, Antonio de Yiti. First Principles of Public Finance. New York: translations, 1935. Due, J. The Theory of Incidence of Sales Taxation. New York: 19^2. Edgeworth, F. Y. A Levy on Capital for the Discharge of Debt. Oxford: 1919. Edgeworth, F. Y. Papers Relating to Political Economy. London: 1925. Einaudi, L. "Taxes on Property Increments in Italy," Quarterly Journal of Economics (November, 1920). Einaudi, L. La guerra e il sistema tributario Italiano. New Haven: 1927. Forsyth, C. H. Mathematical Theory of Life Insurance. New York: 192k. 1

This bibliography includes only books and articles cited.

BIBLIOGRAPHY

141

Fisher, I. The Theory of Interest. New York: 1930. Giffen, E. "Recent Accumulations of Capital in the Kingdom," Journal of the Statistical Society (March, I878). . The Growth of Capital. London: 1889. Graham., B., and Dodd, D. L. Security Analysis, Principles and Technique. New York: 19^0. Great Britain, Royal Commission on the Income Tax. Minutes Evidence. London: 1919-20. Great Britain, Board of Inland Revenue. Memorandum Nos. 1-5, submitted to the Select Committee on Increase of Wealth (War). Great Britain, Treasury. Report of the Committee on National Debt and Taxation. London: 1927Haberler, G. Prosperity and Depression. Geneva: 19^1. Hansen, A. Fiscal Policy and Business Cycles. New York: 19^1. Hicks, J. R., Hicks, U.K., and Rosta, L. The Taxation of War Wealth. London: 19^1. Keynes, J. M. The General Theory of Employment Interest and Money. New York: 1936. . How to Pay for the War. New York: 19^0. Lutz, H. L. Public Finance. Third edition. New York: 1936. Mallet, B., and Strutt, H. C. "The Multiplier and Capital Wealth," Journal of the Royal Statistical Society (July, 1915)· Marschak, J. "Personal and Collective Budget Functions," The Review of Economic Statistics (November, 1939). Marshall, A. Principles of Economics. Eighth edition, London: 1920. Mill, J. S. Principles of Political Economy. Ashley edition. Moore, H. L. "A Moving Equilibrium of Demand and Supply," Quarterly Journal of Economies, May, 1925. Patón, W. A. "Accounting Problems of the Depression," The Accounting Review (December, 1932). Pigou, A. C. "A Special Levy to Discharge War Debt," Economic Journal (June, 1918). . A Capital Levy and Levy on War Wealth. London: 1920. . A Study in Public Finance. London: 1928. Reighard, J. J. "Earning Statements in Periods of Prosperity and Depression," The Accounting Review (June, 1932). Robinson, J. Economics of Imperfect Competition. London: 1936.

142

THE CAPITAL LEVY

Rorem, C. R. "Replacement Cost in Accounting Valuation," The Accounting Review (September, 1929)· Simpson, T. M., Zareh, M. P., and Crenshaw, Β. H. Mathematics of Finance. New York: 1938. Stamp, J. C. British Income and. Property. London: 1920. . Studies in Current Problems in Finance and Government. London: 192k. . "The National Capital," Journal of the Boyal Statistical Society. Part I (1931). . The National Capital and Other Statistical Studies. London: 1937. Stone, R., and W. M. "The Marginal Prosperity to Consume and the Multiplier," Review of Economic Studies (October, 1938). Sweeney, H. W. Stabilized Accounting. New York: 1936. . "Effects of Inflation on German Accounting," The Journal of Accountancy (March, 1927). . "German Inflation Accounting," The Journal of Accountancy (February, 1928). . "How New Dollar Will Affect Your Assets," Forbes (February 15, 193^). . "Approximation of Appraisal Values by Index Numbers," Harvard Business Review (October, 193k)· . "How Inflation Affects Balance Sheets," The Accounting Review (December, 193Ό. . "The Techniques of Stabilized Accounting," The Accounting Review (June, 1935)· "The German Capital Levy Tax: The National Emergency Tax Levy (Reichsnotopfer)," Quarterly Journal of Economics (May, 1920). Twentieth Century Fund. The National Debt and Government Credit. New York: 1937. U.S. Treasury Department, Bureau of Inland Revenue. Regulations 79 (1936) edition: Relating to Gift Tax. Washington, B.C.: 1936. Van Sickle, J. V. Direct Taxation in Austria. Cambridge, Mass.: 1931. Wedgewood, J. The Economics of Inheritance. London: 1929. Weiner, J. L. "Balance-Sheet Valuation in German Law," The Journal of Accountancy (September, 1929).