THE INCIDENCE AND ALLOCATION EFFECTS OF A TAX ON CORPORATE 

DISTRIBUTIONS 

David F. Bradford 

U.S. Treasury Department 

OTA Paper 30 August 1977 

Revised version printed in the Journal of Public Economics, June 1980 

OTA Papers are circulated so that the preliminary findings of tax research conducted by 

Staff members and others associated with the Office of Tax Analysis may reach a wider 

audience. The views expressed are those of the author, and do not reflect Treasury 

Policy. Comments are invited, but OTA Papers should not be quoted without permission 

from the author. 
Journal of Public Economics 15 (1981) 1-22. $) North-Holland Publishing Company 

THE INCIDENCE AND ALLOCATION EFFECTS OF 

A TAX ON CORPORATE DISTRIBUTIONS 

David F. BRADFORD" 

Princeror7 Lliiiwr,yitj.. Pi%ic,erori, !V'J 08544, C'S.4 

Received July 1979. revised version received June 1980 

To stud!, the effects of 'double taxation' (first at the corporation level. then at the shareholder 

le\el) this paper analyzes a model with a tax on all corporate distributions to equity owners and 

no other taxes. Contrary to the coniinoii view, the tax is s!io\vii to have no substitution effect 

~ind.in particular. no effect on the corporate choice between debt and equity (iki retained 

rarnings) finance. The analysis opens to question certain arguments commonly used to support 

inteyxtion of corporation acd individual income taxes via 'dividend relief'. 

There has recently developed in the United States an increasing interest in 

the 'integration' of individual and corporation income tax systems. As seen in 

the policy discussions of this issue, the central problem with the existing 

'classical' system (whereby a tax is levied on corporation profits after 

paynient of interest, independently of distributions) is the double taxation of 

dividends. Double taxation arises because the income generated by corpoi-nte 

investment financed by equity is taxed once at the level of the corporation, 

currently at a marginal rate of 46 percent for corporations with significant 

amounts of income, and then again, at rates ranging from zero to 70 percent 

on the income tax return of the individual shareholder on the portion of the 

remainder that is distributed in the form of dividends. The resulting penalty 

011 equity finance, it is argued, distorts the financial and real decisions of 

corporations. To correct this the usual remedy, which has been extensively 

"I'rince~c>ii University and National Bureau of Economic Research. ,411 early version of this 

paper was written \vhile I was a visiting felli)\r at the Center for Opei-ations Research and 

Econonietrics (CORE). Uni\,ersite Catholique de Louvain. Belgium iJ:inuary~June 19771, and 

appeared as CORE Discussion Paper 7738, August 1Y77. I \vould like to express iny 

appreciation for the exceptionally stimulating research en~ironnicntat CORE as \{.ell as in). 

tl1anks to UCL and the Commission for Educational Exchange Betwecn the United States of 

America. Belgium. and Luxembourg for financial support. Discussions nit11 William Andrews of 

Harmrd Law School. Llaurice Marchand and Henry Tulkeiis of CORE and Pierre Pcstiau of 

the Universiti de Liege. were of great help. Finally, thanks to Martin Hellwig, then of CORE 

and Princetan University. uho wen1 beqond the call of (jut! in reading di-kift\ and educating me 

011 the fine points of the theory of rational expectations. 
2 D.F. Brdford, ESftcts oj a tux on corporate distriburiolz5 

< 

means to apply a tax adjustment which is a function of dividend 

distributions. Most approaches involve either allowing the corporation to 

deduct dividend distributions from the corporation income tax base (much as 

interest payments are deducted) or allowing the shareholder a tax credit 

which stands in relation to dividends as the corporation income tax stands 

to corporation income net of tax. 

Both of these methods have the effect of eliminating the corporation tax 

on fully distributed earnings, but they are not otherwise equivalent to the 

‘full’ integration of corporation and individual income accounts, which is 

commonly regarded as impracticable administratively, even if desirable in 

principle.’ The difference between full and partial integration is in the 

treatment of retained earnings, which are taxed at a flat rate independently of 

the circumstances of the shareholders under partial integration and at the 

shareholder’s marginal income tax rate under full integration. 

The present analysis suggests that the partial integration approach may 

have gotten the matter backwards. The problem on this view is not the extra 

tax imposed on distributions, but the divergence between shareholder and 

corporation tax rates on retained earnings. If the market rate of interest is Y, 

an individual who pays income tax at the marginal rate m earns a rate of 

return (1 -m)~on his savings in ordinary assets. A corporation, on the other 

hand, is able to accumulate at a rate (1 -C)I on the same investment, where 

c is the rate of corporation income tax. The power of compound interest 

being what it is, we would expect the choice of asset types to be dominated 

by the difference in the rates of return, even if a price in the form of a tax on 

distributions must be paid to obtain the favorable rate. 

In this paper I consider the incidence and allocation effects of a tax on 

distributions, as distinguished from a tax on the income of individuals or 

corporations. To isolate the issue I abstract from the taxation of income, as 

well as from uncertainty, nonlinearity of tax rules, and multiplicity of 

individual tax regimes. This paper analyzes the behavior of a system with a 

flat rate tax on corporate distributions to shareholders and no other taxes. It 

is thus concerned with a kind of polar case of the double taxation of 

dividends. 

In view of the abstraction from uncertainty, it might appear to be an open 

and shut case that imposing a tax on distributions will lead to a flight to the 

corner solution of all-bond finance. Or at least, if this is not optimal, it 

would appear obvious that good financial policy toward equity calls for retained 

earnings only, so that stockholders can take their returns in untaxed capital 

vgains. Furthermore, one might expect that should equity finance continue to 

‘For a discussion of some of the problems and a suggested method to solve them see U.S. 

Government (1977). 
D.F. Bradford, Efects of LI tax 011 corporate distributions 3 

exist, the investmei1.f ci'iterion of the firm would be affected. The conclusion 

of the analysis is that-none of these results obtains. While the issue of new 

equity may become unattractive (unless this form of negative, distribution is 

subsidized at the same rate that positive distributions are taxed), all those 

financial plans involving non-negative distributions, over which indifference 

prevails in the absence of the tax, continue to be indifferent. The all-debt 

policy acquires no special place, nor are dividends discouraged in favor of 

retained earnings, As for real investment, the criterion used by the firm 

remains the equating of marginal returns to the rate of interest, regardless of 

the chosen level of debt finance. 

These points emerge from a careful treatment of the determination of the 

value of equity claims. For if, as is often assumed, a dollar of retained 

earnings leads to a one dollar increase in the market value of equity, 

shareholders could obtain their returns free of the tax on distributions. The 

conclusion of the present analysis, based on a rational expectations model of 

asset pricing, is that an extra dollar of retained earnings (with a 

corresponding reduction in borrowing) increases the value of equity by one 

minus the rate of tax on distributions. This is why shareholders are 

indifferent between dividends and retained earnings, and why real investment 

continues to be determined by an implicit trade-off between it and 

retiring debt. 

As for incidence, an implication of the equity valuation result is that an 

unanticipated change in the rate of taxation of distributions affects the 

market value of existing equity claims and, hence, the wealth of their holders. 

For a given rate of interest and for given corporate indebtedness and capital 

stock, the value of equity is simply proportional to one minus the rate of tax 

on distributions. The wealth shifts resulting from a change in tax rate may 

constitute the major, even the only, incidence effects. We take up below a 

particularly striking case in which an increase in tax rate is accompanied by 

a one-time government expenditure financed by an increase in government 

debt. The incidence of this combination turns out to be confined wholly to 

the wealth loss of holders of equity at the time. There is no deadweight 

efficiency loss, and no burden to be the subject of subsequent concern. 

This explains my earlier remark to the effect that the partial approach to 

integration may be correcting the wrong problem. While the present analysis 

is far too simple to support policy conclusion, it does suggest that in so far 

as partial integration amounts to eliminating a tax on distributions, it may 

result primarily in windfall wealth redistributions, reversing the, by now, 

irrelevant wealth changes that occurred when the tax was introduced, while 

leaving the features of the tax system giving rise to inefficiency. 

The modeling of equity valuation in general equilibrium has some 

interesting implications beyond those concerning the neutrality and incidence 

of the tax on distributions. One is that along an equilibrium path the total 
4 D.F. Bradford, Effects of a tax on carporntr distributions 

,I! .,I l;f;{ ;113d cq:j;ty 

depend on the financial policy of the firm. In the present model this policy is 

indeterminate, even though the firm’s real capital stock is determinate. The 

larger the fraction of equity finance, the lower is the market value of the firm 

(which is less than or equal to its replacement cost if the firm is not a net 

creditor). This contrasts with the well-known Modigliani-Miller (19%) 

proposition that the value of the firm is independent of its financial structure. 

a property holding here only when the distribution tax rate is zero. 

A second interesting feature of the model is the apparently ‘Ricardian’ 

behavior of government debt.2 The inclusion of government debt in the 

model is not fortuitous. Since corporate financial policy is indeterminate. so 

also is the flow of government receipts from the distribution tax. It seemed 

compelling from the point of view of both empirical relevance and modeling 

simplicity to make government expenditure independent of tax receipts, with 

variation in government debt issue and retirement taking up the slack. The 

equilibrium conditions of the model include a term reflecting the present 

value of potential receipts from the distribution tax, comparable and 

opposite in sign to the quantity of government debt. A cash flow deficit, 

requiring an increase in government debt, is exactly offset by an increase in 

the potential tax receipts term. In effect the economy does not treat 

endogenously occurring changes in government debt as wealth changes. This 

result is not immediately obvious from the assumptions made. In the model, 

no one has explicit expectations about taxes. Furthermore, each generation is 

concerned only with its own consumption and thus the response to debt 

changes does not derive from the combination of extraordinary foresight 

about the distant future and a long chain of bequests, a much challenged liiili 

in the theoretical argument for the fiscal neutrality of government deficits 

[see Barro (1974)l. While the model has been developed primarily to make a 

particular point in tax analysis, the lessons here for the analysis or 

cgovernment debt (it may matter whether it changes endogenously or 

exogenously) and for the limitations of cash-flow budgeting (it tells us 

nothing in this model) seem well worth noting.3 

1.I. Iiztiritirr r.uplaizLitiott oj the results 

It may assist an understanding of the results to consider the analogy of the 

tax on distributions with a tax on all withdrawals from satings accounts 

‘This is the label attached by B~icha~iaii(1976) to the notion that private demands are 

independent of the extent of deficits as a method of financing public expenditure (presumably 

because taxpayers anticipate the correspondingly higher future taxes). Both the label and the 

idea have provoked controversy. For recent reviews and some evidence see Buiter and Tobin 

(1979) and Feldstein (1980). 

3Feldstein (1980) seeks to incorporate the relationship between expectations about future taxes 

and current deficit-influencing events in his empirical study. 
D.F. Bruiljord, EfSects of a tax 011 corporate disributiniis 5 

opened bef'ore some specified date in the past. Were they bough; 

are bonds, the market value of such accounts would presumably fall, upon 

imposition of the tax, to one minus the tax rate times their face value 

'replacement cost'. Once the tax is in place, there is no particular incentive 

for existing account owners to accelerate the pace of withdrawals; a growing 

value of balances in such accounts (due to accumulating interest) and, 

therefore, a growing absolute divergence between market and replacement 

I Lilues, is fully consistent with optimizing behavior. 

In the analysis presented here, the corporate 'vessel' is the analogue of the 

si\,ings account, and the tax on distributions the analogue of the tax on 

\\.ithdrawals, The tax is the price that must be paid to get cash out of the 

coi-poration. Like the hypothetical tax on bank accounts, it would be 

necessary for a tax on corporate distributions to be imposed ex post, or at 

least as something of a surprise, for it to find any base to subject to tax. The 

usual analysis of the corporation income tax, in effect, assumes it is being 

imposed before the system 'starts up'. The discussion below illustrates how 

profound a difference it may make to examine instead a tax on dividends 

imimed on a systeni already in existence. 

The approach taken here bears some similarity to that taken in papers by 

Stiglitz (1973) and King (1974) which slmw that the relationship between 

income tax rules and optimal corporation financial and investment policies is 

1110re complex than had been previously understood." By an:ilyzing the 

corporation's choices as part of a multiperiod optimization problem, these 

authors are able to treat consistently the interactions between individual and 

corporation incoine tax systems. Both papers conclude that the optimal 

financial structure may be indeterminate, given certain relationships among 

the relative rates of taxation of corporate income, corporate distributions, 

interest payments and capital gains. the history of the corporation (in 

Stiglitz's analysis), and expected future values of the tax parameters (in 

King's analysis). For these cases and for a wide further class as well, the 

corporation's real investment decisions are unaffected by the taxes. 

The present paper differs from these predecessors in its explicit attention to 

general equilibrium, including equilibrium in the asset inarket in an infiniteimizoii world with rational expectations. Stiglitz devotes little attention to 

lhe question of asset valuation. As far as the question of financial structure is 

concerned?his analysis is best described as a theory of the small. closely held 

corporation. His results turn on the tax-technical matter of whether a 

'See also the follow-on papers by Stiglitz (1976). King (1975) and Asimakopulos and Burbidge 

(1975).as well as King (1977). 
6 D.F. Bradford, Effects of ci tux on corporcite disrributiom 

LlLiJIl ib Jn,siIicd a3 CL c 

individual income tax ‘- the tax on distributions). The corporations 

accounting for the vast bulk of corporate assets in the United States rarely 

approach the condition of having distributions which qualify as return of 

capital. As a consequence, the necessary conditions for optimality of financial 

policy [Stiglitz (1973, p. 13)] are not fulfilled empirically by the large public 

corporations, essentially permanent, horizonless institutions, constituting the 

major share of the corporate sector. A different theory is needed to explain 

their behavior, and it can probably neglect the special treatment of return of 

capital, as is done here (and in King).’ 

Whereas Stiglitz looks at the corporation as the vehicle of an individual 

investor, King views the problem of corporate decision-making as that of 

maximizing the present market value of equity. King’s paper can be regarded 

as a theory of the market value of a firm setting financial and investment 

policies optimally with respect to present and expected tax parameters. 

Presumably because his analysis is in a partial equilibrium setting, King does 

not concern himself with the wealth changes implied by changing tax 

parameters which are given special attention here. However, the neutrality 

results described here can be derived as a special case of King’s model, and it 

might be interesting to impose his richer structure of tax institutions on the 

general equilibrium model examined here.6 For present purposes, however, 

the single tax on distributions is sufficient. 

1.3. Outliize oj’ the paper. 

Section 2 contains the formal description of the model economy. including 

the equilibrium concept employed. Section 3 derives a solution of the model. 

Section 4 contains a discussion of the results summarized above. while section 

5 contains concluding remarks. 

2. Formal model of rational expectations equilibrium with a tax on 

distributions 

The model underlying the analysis is in the Samuelson (1958) consumption 

loan traditi~n.~Individuals live for two periods in an infinite horizon world. 

’There is a further difficulty with Stiglitz’s representation of the provisions in U.S. tax law 

distinguishing return of capital from other distributions. Whereas Stiglitz (1973, p. 9) makes this 

distinction a matter of the cumulative amount the owner has received from the corporation, it in 

fact depends upon the relationship between cumulative earnings and cumulative distributions. 

Under the Stiglitz version, in effect, the first distributions represent return of capital while the 

US. law may be described as making the last distributions return of capital. 

6Using King’s notation, the special case is that of 171, =0,z,=0, t,.=0, 0 =1-c, where c is the 

rate of tax on distributions. 

’Diamond (1965) presents a model which includes government debt. Unlike the Diamond and 

Samuelson models, this model does not assume constant population growth, nor is the analysis 

confined to steady states. 
, 

D F. Bitidford, Effecis of a tax 011 corporate distributions 7 

i:; it,1.1 I, 

value is X,let Xi,X, +, et 

its value in .the preceding period. We shall also require a ilotation for 

expectations. Let X> denote the value of X expected to obtain in the next 

period, (X:)e+ the value expected for next period‘s expectation, and so on.) 

In the first life-period each individual works (offering one unit of labor 

inelastically), consumes, and saves for retirement. ‘Retirement’ describes the 

second life-period, when each individual consumes his savings, leaving 

nothing to his heirs. 

All production takes place in a single corporation, which may be thought 

of as a consolidation of the corporate sector in an actual economy. (It would 

be a simple extension to allow noncorporate production.) Production 

conditions are described by a constant-returns-to-scale production function, 

F (K.LD),of capital, K, and labor employed, LD.The capital available to the 

corporation in any period is inherited from the previous period, and is thus 

fixed in amount before the time of actual production. The output of a period 

may either be consumed or frozen into an increment of the infinitely durable 

capital stock. To avoid having to deal with corner solutions, investment is 

assumed to be reversible, i.e. the capital stock can be consumed. 

The corporation is assumed to behave as a price taker in output, factor 

and financial markets. Here output is taken as numeraire, measured in 

d.ollars. The wage rate is denoted by M\. Because .the firm is the only user of 

physical capital, and owns the stock, there is no actual market for capital 

services. Thefe are, however, markets for the bonds and equity of the 

corporation. Bonds are issued on a one-period discount basis. The total 

corporate indebtedness, B, inherited from the previous period, must be repaid 

during the current period. The current rate of interest is denoted by I’, so 

that the corporation raises B+/(l t- I-) dollars by a new issue of B, bonds. 

The ‘ex dividend’ value of a 100 percent equity interest in the firm is 

denoted by I.: This is the value at the end of a period, when the equity 

interest is exchanged, after production is complete, and distribution and 

investment decisions have been made. V will be a function, V(K+,B+), 

determined in the market, of the capital stock and indebtedness that will be 

carried forward as a result of those decisions. It is this function that the 

firm’s owners take as given. It will simplify matters to assume that both sales 

and purchases of stock by the corporation itself are prohibited, so that 

distributions may be equated with ordinary dividends. Alternatively, 

purchases and sales of equity by the firm may be allowed (and treated as 

negative and positive distributions) provided they are subject to the 

distribution tax (a subsidy in the case of sales). Note that by definition, 

distributions, new bond issue proceeds? and real investment must sum to a 

constant in any period. 

The model also includes a government which ordinarily acts simply as a 
i ::L>Lr . :t IlrLll^ IjIdCL.ijjlL& i C3;lOU c, LriJj? L 

. redeem an outstanding stock, LI~, of one-period bonds. It finances this 

redemption with the receipts, tD, from the tax at flat rate, t, on corporate 

distributions, plus the proceeds, B:/(l+ r), of the sale of new bonds. 

Individual savings may thus be held in three forms: bonds issued by the 

corporation, shares of its common stock, or bonds issued by the government. 

A given generation of individuals acquires these financial assets at the end of 

its first life-period, after production for that period has been completed. and 

after the financial and investment decisions of the corporation have been 

fixed. The typical ‘young’ individual is conceived of as allocating his labor 

earnings among first-life-period consumption, cl, corporate bond holding, h + , 

government bond holding, 175, and a fraction, s, of the ownership in the 

corporation, to maximize a utility function, u (c’, c2). 

The holders of its common stock ‘own’ the corporation. The L- ‘old’ 

individuals will thus be owners at the beginning of a period. By choosing L” 

they control that period’s production, and by choosing K, they determine 

the amount of capital which will be available for use at the beginning of the 

next period. They also specify the financial policy for the current period, 

which means they set the amount of funds to be distributed to themselves as 

dividends, D, and the amount of corporate borrowing, B+. The objective of 

the individual stockholders is to maxim&e c’. which calls for the 

maximization of the sum of distributions net of tax and the residual balue of 

the equity claims. (1 -t)D + V(KI-r B, ). 

Eq II i I i h18 iu IH c’o11 d iI ioI is 

As we have seen. certain conditions of the model economy are inherited 

from the past, in-”particular the capital stock, the corporate debt obligation. 

and the government debt obligation. The labour supply is exogenously 

determined. I refer to the vector of predetermined and exogenous variables 

(K,B, B”L) as the ‘state of the economy’. 

The endogenous quantities to be determined by the equilibrium conditions 

include the labor employed by the corporation, and its capital stock and 

debt obligation carried forward into the next period. There are also two 

prices of a conventional sort, namely the wage rate, \\’. and the interest rate. 

I., and a third price-like element, the ‘valuation function’, V(K,, BT ). Finally. 

expectations about future prices and equity valuation are determined 

endogenously. All individuals are assumed to have identical point 

expectations, represented by the vector (w:, I-‘+, Vi3,). 

Determination of these endogenous variables involves clearing fi1.e 

markets. for labor, corporate bonds, government bonds. equity. and goods. 

In each period the prices of labor and bonds (government and corporate 

bonds are assumed perfect substitutes), and the evaluation function relating 
D.F. Br~dfoiI.d,6flect.s Uf'a tm on coiporute distrihutioiis 9 

uqui;y indue to corporate financial and investment decisions,' adjust to clear 

rhese markets. Naturally, demands and supplies depend upon expectations. A 

~CHI~OYO~J' equilibrium, conditional upon both the state of the economy and 

expectations, is a balancing combination of prices and a valuation function, 

together with a specification of L", K,, B+ and B$, such that all markets 

c I cit 1'. 

The temporary equilibrium quantities in any period depend on the capital 

stock. outstanding debt obligations, and the size of the new generation, in 

hlioi-t. on the state of the economy. The evolution of the economy is the 

result of the exogenous development of the population and the determination 

h!, market clearing of the values of capital stock and bond obligations 

carried into the next period. Population growth is assumed describable by a 

first-order difference equation.* Because of this assumption, it will be taken 

for granted below that knowing the relationship between a current 

cndogenous variable and L - is equivalent to knowing that between it and L. 

Ah has been mentioned, the expectations on which temporary equilibrium 

depcnds are endogenous to the model. It will be assumed that expectations 

arc 'rational' in the sense introduced to the economics literature by Mutli 

(19611. In the present. nonstochastic model. the notion of rationality of 

cspqJations is taken to encompass two properties. The first is that rational 

cspc'chtions are c~oi~i'cc-rin that in an economy eijolving acccrding to a 

ic~{ucnczof temporary equilibria, each dependent upon that period's 

expectations, each period's expectations will be fulfilled in the following 

~wiod.The second property embodies the idea that if two economies are 

identical in structure and have reached the same state (where the calendar 

diitc is not considered part of the state description), their agents should have 

the sm;e expectations. Expectations satisfying the second property can be 

described as stationary functions of state variables.' Note that there is no 

parantee that rational expectations exist for an economic system, nor that if 

tile exist they are unique. 

3. .-4 solution to the model 

TO describe the behavior of the model economy in an equilibrium with 

rational expectations we must write down expressions for the endogenous 

'If population evolution \\.ere describable o11ly by a higher order difference equation. 

additiorial state i,ariables, in the form of a sufficient number of observations of past pOpLilation 

h-1~10 determine the solution of the difference equation. would be required. The basic 

;l~i?llment\I ould. ho\vever. be unaffected. 

"To express this notiori precisely, let K,([i)denote the set of possible successors to ii as a result 

tcmpoi.ary eqtiilibii~iin.gi\,eIi e..rpectatioris vector e. Formally. expectations will be described 

a> nirimw/ if there exists a mapping, E, from the set of state ~ectorsinto the set of' expectations 

\CCtOrS. such tliat for all possible state vectors. (1, and all possible s~iccessorstates. 11, in TE,or(~~ 1. 

t1w c.xpcctations are correct. i.c. ~iii)=(\I,-. I._. 1'- 1. 
variables, including expectations, IIi ~eims of the state variables, with the 

property that, given expectations, markets clear and expectations are 

correct.1° 

The natural way to proceed would be to solve for the temporary 

equilibrium as a function of the agents' expectations and then to seek a form 

of expectations that is self-fulfilling. Given the large set of possible 

expectations (recall that the valuation of equity is represented by a Jirnctiorz) 

this is rather complicated. Instead, I shall take the approach of first 

developing a reasonable conjecture about the temporary equilibrium under 

rational expectations, then describing the associated scheme of expectations, 

and finally showing that the optimizing behavior of agents holding those 

expectations will produce the originally conjectured temporary equilibrium. 

I therefore follow a somewhat artificial sequence in which the first step is 

to write down equations which are asserted to determine the endogenous 

variables other than expectations. I then write down the equations asserted 

to determine the expectations from the state variables, and show that when 

the system evolves as described in the previous section these expectations are 

correct. Only then do I go through the steps to show that if the agents have 

these expectations, their optimizing behavior will indeed lead to a temporary 

equilibrium with the originally asserted relationship between state variables 

and current prices and quactities. 

iu 

3.1 . End ogerzoiis CII I' ici hles in tempo rci "1' eqir ili bi' iii in 

The strict logic of the argumc-nt does not call for any discussion of 

equilibrium until step three. However, the asserted relationships between 

current prices and quantities and state variables in temporary equilibrium 

with rational expectations will be recognizably conditions of competitive 

market clearing, and will be more readily understood if discussed in these 

terms. 

Eqs. (1) and (2) below, with their associated definitions, eqs. (3) and (4). 

describe wage and interest rate determination by labor and goods market 

clearing. The function K" defined in (3) and evaluated at (Y,L,) gives the 

capital stock which equates the rate of interest to the marginal product of 

capital at full employment in the next period. This is the amount of capital 

which will be carried forward into the next temporary equilibrium. Problem 

(4)is a lifetime utility maximization problem of a representative individual 

with lifetime consumption preferences described by ti, when the rate of return 

on savings is i' and with wealth equal to ~ 3 ,the wage reward for one unit of 

"Throughout the following discussion of equilibrium it is assumed that the tax parameter. t. is 

constant. One-time policy changes are assumed to be unexpected. Furthermore, non-negativity 

constraints are ignored. King's (1974) analysis incorporates expectations concerning tax 

parameters and makes considerable use of various non-negativity constraints. 
D.F. Bradford, Effects of a tcix on corporate distributions 11 

iaoor. Eq. (1) is ihe conail! jn of equaiity of wage and,marginal product of 

labor at full employment. Expression (2) specifies that total savings of the 

young generation equals the cripital stock carried forward plus the 

government debt less a term equal to the tax receipts that would result from 

liquidation of the firm. The latter term can be loosely interpreted as the 

present value of all future distribution tax proceeds, and thus has the effect in 

the model world of offsetting government debt. 

\.1.’ =F2 (K,L), 

(w -c1 (r., \v))L=K*(r,L, )+Bg -t (F (K,L)-\vL -B +K). (2) 

Here F, denotes the derivative of F with respect to its ith argument; 

K*(IS, L, ) is defined by 

and c1(I.,lv) solves the problem 

subject to 

The next relationship is based on the market valuation of the equity 

interest in the firm, Since there is no uncertainty in production, that value 

shcuid simply be the discounted sum of next period’s distribution, net of 

distribution tax, and next period’s valuation of the firm after its real 

investment has been determined. However, this describes a relationship 

among endogenous variables over time, whereas our objective is to describe 

endogenous variables as functions of current state variables. It is natural to 

conjecture that the equilibrium valuation of equity will be related to 

the poreiztial net-of-tax withdrawals from the firm. Since all withdrawals are 

taxed, the expected net withdrawal obtained if no debt is issued in the next 

period (in effect ‘closing the account’) would be the obvious basis for 

eyaluation. This is given by 

Since there is no uncertainty, this sum will be discounted at the rate of interest, 
RecaIl that our objective is to specify the endogenous variables as functions 

of state variables. Noting that I' has been described as a function of state 

variables by (1)-(4). we must only anticipate the rational expectations of 

wages to write V in the required form. The expected wage level will 

presumably clear the labor market when the endogenously determined 

capital stock is available. Hence. we conjecture, by analogy with (1): 

so that the equity valuation function is itself expressed as a function of statc 

variables by 

1 - t

V(K+.B-)=__ (F(K-,L+) 1-I. 

-F, (K""(V> L, ), L+)L+-B+ +K+), (7) 

which says that the value of equity is equal to the discounted value of the 

after-tax proceeds of distributing in the next period all of the anticipated 

resources of the corporation. after paying off the debt. As we shall see beloif.. 

this temporary equilibrium relationship among endogenous and state 

variables implies the desired intertemporal relationship between one period's 

equity value agd next period's distribution and equity value. 

These equations determine the two prices and the equity ixluation 

function. The capital stock carried into the next period will be given by 

K*(r.,L+). It remains to determine B, and BS,.The stock of debt the young 

will want to hold. with present value (B- + Ej, (1 +r). will depend on their 

evaluation of equity. The aggregate portfolio value of the young is 

determ i ned by thei r consu mpti on d ecisi on . Therefore, \v 2 h ;Lv e 

It turns out that any combination of B, and BY satisfying (S) is compatible 

with equilibrium. Associated with a larger value of B, Pvill be lower values of 

V and Bc. Note that condition (8). together with (7), implies 

tB- +B; =constant. (9i 

where the constant depends upon I., \v, and L, 
D.F. Bradford, Efects qf u tax otz corpowte distributions 13 

j.-, Aiiii~i~i L:x~LII/ /Lil ioris

Expression (6) relates the expected wage to the labor force in the next 

period and the capital stock that would be optimally employed with the 

labor if capital services were directly marketed and had a price equal to I^, 

the rate of interest. The value of 14 is determined from state variables by (1)-

(3) The remaining expectations of interest rate and equity valuation function 

are. like (6), obtained by adding the expectation superscript to the 

appi'opridte temporary equilibrium condition and making use of the 

functional relationship between state variables and current prices and 

quantities, as already described. 

The ialue of 14; is obtained by combining (1)-(4). (6), (9) and (10): 

Si111ila1.1y . t hwexpected valuatioii function is given by 

, 

The ori-ecmcss of' exyectut ioiis 

GiIen our approach to developing the expectations formulae. it will be no 

surprise that they will be correct if the next period's equilibrium is described 

b) relationships (1)-(4), (7) and (8), suitably updated. For example, since K, 

=k'" (i., L A). conditio11 (6) implies that w-=\C. 

that vT =I^: 

Similar reasoning implies 

and 11, ve+. 

3.3. The tempoi.ar\. eqzrilihriuiii is the righi OW 

It remains to show that if the agents form their expectations in the way 

described, then eqs. (1)-(4).(7) and (8) indeed characterize a temporary 

equilibrium. For this we need to derive the demands and supplies of the 

agents on the various markets and test for market clearing. 

The budget constraints of the young and old generations together with the 

behavioral rule ascribed to the government imply that the excess demands on 

I?.-
-- 

7 , ti : 1 'I (I \'dl r'&.)l&iIlI bnbirriI 

four markets implies clearing of the fifth. This may be most easily seen if ne 

for a moment regard the old generation as two sets of agents: stockholders 

and corporation managers. The budget balance requirement for the young 

implies that the sum of the values of their excess demands for the fibe 

'commodities' (labor, corporate bonds, government bonds, equity and goods I 

must be zero. The sum of the values of excess demands of stockholders will 

be B+Bg+ (1 -t)D as the old generation cashes in its old bonds (which are 

not commodities marketed in the current period) and collects the after-tax 

proceeds from the corporate distribution. The sum of values of the excess 

demands of the corporation will be -B-D, as it pays off the inherited debt 

obligation and makes its distribution. For the government, which supplies 

new debt to cover the difference between old debt and tax receipts. the sum 

of excess demands is -Bs+tD. It may be verified that the four classes of 

excess demands aggregate to zero. Hence, if market excess demands of four 

of the five commodities are zero the fifth market excess demand must be zero 

as well. 

3.3.1. Excess ilenziiiicls of the j'oung 

Consider first the young generation. They anticipate solving the problem 

of optimally managing the corporation as Owners of its equity. with capital 

stock and debt repayment obligation given by (K-. B -). That is. the! 

anticipate so1vi n g 

where D - is the distribution they make to themselves from the corporation: 

D, =F(K,. Lf ) -\\: LL-' -R, tK, -K - t + -

B - -

-. i 1-41 1 +r: 

Substitute (ll), (12) and (14) into the maximand. thereby eliminating the 

decision variables B, + and D,, and calculate first-order conditions for a 

solution with respect to the remaining two. The anticipated labor demand 

satisfies 

Using (6) and the assertion (3) that K, =K*(i.,L,) (used in implicitlq 

determining according to rational expectations). we conclude that 

LD, =L-. 116) 
D.F. Brndfo~d,Ef{ects of a tas 011 corporate distributioris 15 

*I IIL' fii-st-order cgiidntion for optimality with respect to K+ + in (13, is 

tlulrr'b theorem applied to the constant-returns-to-scale production function 

implies that, given the asserted relationships between state variables and 

current endogenous variables, the solution of (13) can be expressed as 

In 118) the determination of L, and 11,; as a function of current state 

\ ariLiblcs is iinplicitly taken for granted. 

30\4, imagine that a Walrasian auctioneer has called off wages. interest 

i.;itc itnd \.aluatioii function and the existing owners of the corporation have 

ici h . and 8,. The representative young person now solves the lifetime 

i'c ii ?; ti 111p t io n maxiinizat i on problem : 

Thc trio constraints in (19) can be combined to imply 

Problem (19) is unbounded, and the resulting demands incompatible with 

~quilibriumunless the term in parentheses is zero: 

(21j 

\+'e mal xerify from (5) that this conditio11 is satisfied if the wage. interest 

rdtc and valuation function are in the suggested temporary equilibrium 

re1at I o11ship. 

\Wien condition (21) is satisfied, the young are indifferent about their 

W~tfoliocomposition alllong the t\vo tj pes of bonds and corporate equity. 
16 D.F. Bradford. Effects of (1 tn.x on corporate disrrihtitinris 

!L'> sui 

financial instruments by the young is (w -c1 (I.,~J))L. The aggregate value of 

their goods demand is c1(1', w)L.Their labor is supplied inelastically. 

3.3.2. Excess demands of the old 

As owners of the corporation, the old generation must choose labor 

demand, real investment, and new bond obligations to maximize the sum of 

after-tax distributions and proceeds from the resale of the equity interest. In 

other words, their problem is: 

max (1 -t)D+ V(K+,B-), (22) 

LD.6 + ,B -. D 

where 

D =F (K,LD ) -n>LD-B +K -K + +-, 

B+ (23) 1+I' 

Substitute (7) and (23) into (22) and derive first-order conditions: 

F (K,LD) =tt', (941 

F,(K+,L+)=y, (25) 

from which 

K, =K"(I",L-). 

Euler's theorem applied again gives us the value of the objective function at 

an optimum of W(K,B;L,N~), as defined by (18). This is the maximum the 

owners of the firm can realize, given \t' and the inherited capital stock and 

debt obligation (and given the equity valuation function (7)). 

In the solution to the maximization problem the financial policy is 

indeterminate. Given the other variables, a unit increase in B,, resulting in a 

net distribution larger by 1-t, leads to a reduction of 1 -t in the market 

value of equity. The supply of corporate bonds may thus be arbitrarily set by 

the owners of the corporation. On the remaining markets they (the old) 

supply inelastically 100 percent of the ownership interest. They demand 

consumption goods amounting to the sum of W B and Bg.In addition they 

demand K - in the goods market for the corporation to carry into the next 

period. 

3.3.3. Ex cess de mand s of goL' eI' iz ment 

Because I have chosen to consider the markets for labor. corporate bonds, 
D.F. Bradford. Effects of a fox ON corporate distributions 17 

equity. and goods, we do not need to give more consideration to the 

demands and supplies of the agent 'government' than was involved in 

establishing the appropriate version of Walras' law for this model. 

Ordinarily, the government does not appear on either side of any market 

except that for government bonds, the commodity dropped from the 

dependent system of market-clearing relationships. 

3.3.4. Market cleariug 

Having established the excess demands of each of the agents, we can 

proceed to the analysis of market clearing, The indifference of the young 

:.%enerationabout portfolio composition and that of the corporation's owners 

about financial policy assures clearing of the equity and bond markets. The 

!'ou~igpurchase all of the equity in the corporation (at the price described by 

(7))and all debt offered for sale by the corporation. 

This leaves the labor and goods markets. Clearing of the labor market 

requires L~=L or, from (24): 

F,(K,L )=it'. 

Equaling demand and.supply in :he goods market implies: 

Using (18). we can rewrite (28) as: 

Eqs. (27) and (29) are the same as eqs. (1) and (2), from which we conclude 

that the latter do, indeed, describe the determination of wage and interest 

rate in temporary equilibrium, given expectations formed as described in the 

previous subsection. This completes the argument. 

3.3.j. Uniqueness oj equilibriunz 

AS noted above, the definition of equilibrium with rational expectations 

does not imply its uniqueness. We shall not attempt here to prove the 

uniqueness of the equilibrium of the model specified above. However, we can 

show that what might loosely be described as the 'conventional view' of 

\,ahation of the firm, in which each extra dollar of retained earnings is 

reflected in a dollar increase in equity value, will not be consistent with 

rational expectations in this model. For if this valuation rule prevailed, 

agents would be led to demands incompatible with equilibrium. To express 
1iIL cdLvGll!;cil I < 'uy(l--!; L i 

-t)-' I/;, cancelling the effect oi tlic tax on equilibrium valuation as seen in 

(5) and (11). Now the anticipated valuation problem (13), after the 

substitution of D into the maximand, continues to have B, + as an argument, 

with constant coefficient -t (1 +I.?) - '. The solution value B - = -x 

implies an infinite valuation of the firm by equity demanders. and an infinite 

supply of bonds by the young (individual borrowing to purchase stock). By 

the same reasoning with respect to problem (22), the owners of the 

corporation are led to an infinite supply of bonds, ruling out market clearing. 

The same sort of conclusion follows if I/ and V?+are multiplied by any other 

constant different from unity. 

4. Commentary 

4.1. CIinmcteristics oj'eqitilibritrm patlzs 

The analysis of section 3 demonstrates the assertion made in the 

introduction that the indifference between debt and equity characterizing 

financial policy in the absence of taxes in this no-uncertainty world continues 

to hold in the presence of the tax on distributions. The key to this 

conclusion is found in the equity valuation fkmction (5). from which it follows 

that an extra dollar. of retained earnings induces an increase of only 1 -t 

dollars in the value of equity. 

The conclusion that the investment criterion of the firm (KL=K'$ (i'. L, )) 

is unaffected by the tax on distributions is in itself not surprising. since 

without rli ncer t ai nt y a11 financi ng ~ and in part icu 1a r margin a1 financi n g- ca n 

take the form of debt. Note, however, that this result holds even if the firm's 

owners do not c'3nsider financing the marginal investment through bonds. It 

is only required that the firm's potential shareholders compare the return on 

a dollar retained by the corporation and invested in capital with that on a 

dollar invested in bonds. 

The implication that financial policy is indeterminate follows immediately 

from (5). It can also be shown, using (1) and (2), that the path of the 

economy through time is independent of the choice between debt and equity 

finance. From (2) it follows that the determinants of temporary equilibrium 

values of NS and I' include B. the inherited corporate bond obligations, when t 

is positive. However, equilibrium depends also on Bg, the inherited 

cgovernment bond obligation. In the evolution of the economy these tlvo 

types of debt are interrelated: a larger issue of corporate bonds in a period 

implies a larger corporate distribution, larger tax receipts. and smaller issue 

of government debt. Using the government behavioral equation, Bg =�3: ( 1 

+I')-'+tD, and the definition (23) of D, we conclude that the time path of 

Bg+tB is independent of corporate financial policy (as represented by B, ), 
D.F. Brudford. Effects of a rux on corporutr distrihutioi~~ 19 

-l.\'L+K-K*(I.,L,))], (30) 

and it is this sum which enters the goods market clearing condition (2). 

1.:. The effects of climges ii7 parmeters 

The equations of temporary equilibrium with rational expectations allow 

LIS to analyze the effect of changes in the tax parameter or in government 

behavior, provided these are regarded as one-time changes which are not 

expected to recur. Thus, an unexpected increase in the tax rate will? 

according to (5), result in a loss of wealth (and hence consumption) for the 

old generation. If there is no change in the rate of interest, a five percentage 

point increase in the rate results in a loss equal to 5 percent of what their 

equily claim would have been worth in the absence of the tax. 

In general. we know from (2) that a change in t. given the values of the 

s1:ite \;ariables, will lead to a change in the equilibrium values of w and I', 

Lind consequently, a change in the future course of the economy. In this sense 

the tax on distributions is not neutral. However, the changes in the dynamic 

piitli derive not from substitution away from equity finance, but rather from 

the n.ealth effects of the tax. An increase in the tax rate reduces the perceived 

wealth of the economy by reducing the value of equity. Eq. (2) suggests the 

\iwlth effect may be equivalently viewed as a reduction in the extent to 

\vhich government debt is regarded as wealth. An increase in the tax rate 

results in an increase in the implicitly expected debt retirement (by tax 

receipts) in the future. 

Paradoxically. the implication that an increase in the rate of tax on 

distributions has the opposite effect 011 the path of the economy from an 

increase in government debt means that the latter may be the means not for 

shifting a burden to the future but for confining the consequences of an 

unexpected increase in exhaustive government expenditure to the old 

generation at the time it occurs. Consider an economy moving along a 

rational expectations equilibrium path with tax rate t, arriving at the time of 

[he hypothetical moment of Unexpected government expenditure with 

@utstanding corporate and government debt obligations B and Bg. The 

g@vernment considers an increase in t to meet the expenditure, which we 

shall assume has no effects which interact at any time with ordinary 

c@nsumptionin individual preferences. From (28) we know that an increase 

in r of dt: ceteris paribus, creates a goods demand shortfall of dt (F(K,L 1 

--\t,L-B+K) because it reduces by this much the value of equity with which 

the old generation had planned to finance consumption. This is the extra 

expenditure which can be undertaken by the government, diverting resources 
il t L 43 2 

equilibrium. If this is financed by isbuiiig the requisite amount of extra debt. 

financial market equilibrium will also be maintained. Suppose that in 

subsequent periods the government returns to its normal debt-managing role. 

Then the increased government debt will exactly offset the effects of the 

increased tax rate. In all real respects the path will be unchanged from the 

pre-extraordinary events path. 

To see this note that the original path will continue to be an equilibrium 

one if in every period (from (2)), 

Suppose this relationship holds in some period. Will it hold subsequently 

under the original rules of the economy's evolution? We have from the 

government behavioral equation : 

dB5 dtD +--

1+Y -d Bg. (32) 

We wish to show that this implies 

(331 

iir 

Substituting from (31) into (32) we have 

dB5 dtD+--

1+Y -dt (F (K,L )-\.tlL-B +K). 

from which, using the accounting relationship (33). 

Now check that 

This will hold if 

which we know to be true by Euler's theorem along the original path. 
D.F. Bradford, Efjects of u tax oii corporute distriburioiis 21 

Fiiiall'y. we need to show that the new government debt, created to cover ' 

the extraordinary expenditure, amounts to dBg as defined in (31). Instead of 

the combination of changes dt, dBg, we make the combination dt, dB5, 

v,.liere, because of the tax. the latter depends upon the financial policy of the 

firm such that 

From (32) we see that this produces exactly the same situation in the next 

period as did the originally described pair of changes. The subsequent path 

of the economy thus continues to be an equilibrium. 

5. Concluding remarks 

The principal purpose of this paper has been to demonstrate that the 

double taxation of di\;idends characteristic of the classical corporation 

income tax need distort neither corporation financial nor investment policies. 

U:hile the model embodies drastic simplifications, these have been designed 

to isolate the main point. The usual argument by which it is concluded that 

double. taxation leads to distortion is developed in essentially the same 

setting. What is required is an extra tax on distributions; the presence or 

absence of other taxes has no bearing on the conclusion. This analysis, 

therefore. is sufficient to show where the previous reasoning goes wrong. 

When the connection between the tax on distributions and the valuation 

of equity is taken into account, it is seen that conclusions about the 

distorting effects of the corporation income tax based either on simple 

compounding of statutory corporation and individual income tax rates or on 

measured average tax rates using tax receipts are founded on incorrect 

premises. Both the continued existence of equity finance and the practice of 

making positive dividend payments may be fully consistent with 

rnaxiniization of stockholder wealth, even though dividends are subject to a 

tax and even though (in the model) capital gains are not taxed. 

The picture of the incidence of the double taxation of dividends that 

results from spelling out its effects on asset prices is also somewhat 

surprising. While the precise incidence in this model is a function of 

government debt as well as tax policy. a major, if not the only, burden of a 

tax on distributioiis is borne by equity holders at the time the tax is 

instituted. A significant aspect of such wealth transfers is that they cannot be 

meaningfully reversed at a later date when the equity interests have changed 

hands. Removing the tax on dividends cannot restore the wealth of the 

original losers. but only provide a windfall gain to the new shareholders. 

These effects deserve careful consideration in attempting to understand such 
taxes. 

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