STATE CORPORATE INCOME TAX: 

LAMBS IN WOLVES' CLOTHING? 

Charles E. McLure, Jr. 

Rice University 

OTA Paper 25 March, 1977 

Off ice of Tax Analysis 

U.S. Treasury Department, Room 1104 

Washington, D. C. 20220 

Issued: April 1977 
TABLE OF CONTENTS 

Page 

I. Introduction........................ 1 

TI. Tax on Economic Profits .................. 3 

111. Tax on Accounting Profits ................. 10 

IV. Tentative Thoughts on Incidence .............. 13 

V. Further Analysis of Results ................ 16 

VI, Concluding Remarks: Implications for Policy ........ 19 

A. State Tax Policy .................... 19 

B. The National Perspective ................ 20 
-- 

I. INTRODUCTION* 

In an earlier paper I asserted without proof that state corporation income taxes levied on multistate firms have essentially the same 

effects as discriminatory state taxes on corporate payrolls, property, 

or sales (at origin or destination), if the profits of the firm are 

allocated among the states for tax purposes on the basis of formulas 

including payrolls, property, and sales.L' This Paper Provides a 

rigorous justification for this surprising assertion and describes 

the circumstances under which (or the extent to which) it is accurate. 

It also reiterates another point made earlier, that state corporation 

"income" taxes are needlessly complicated and non-neutral devices for 

collecting such mundane non-income taxes. Finally, implications of 

this analysis for federal policy toward state corporation income taxes 

especially the need to replace the taxes with federal revenues -- are 

discussed. 

It is assumed initially that the state corporation income tax 

applies only to economic profits. Later this rather unrealistic 

assumption is modified to recognize that the tax may apply as well to 

the normal return to equity capital. No account is taken of the 

deductibility of state taxes in calculating federal income tax liabilities. 

But in general this should not affect the qualitative analysis, as the 

"federal offset" should roughly halve any effect that would otherwise 

occur. 

*The author wishes to thank Wayne Thirsk and Gary Hufbauer for 

comments on an earlier draft, but not to implicate them in any errors. 
-2-

Finally, it must be noted at the outset that the analysis 

presented here takes the point of view of the taxing state, in which 

taxes in all other states are taken to be no more relevant than the 

weather, rather than asking the effects of the "system" of corporation 

income taxes levied in the United States.L/ In this regard it resembles 

Mieszkowski's analysis of the excise effects of the property tax.-3/ 

Mieszkowski correctly notes that any local change in property taxes 

will be borne primarily by locally specific factors and consumers, and 

will have little effect upon'the return to capital, even though a 

nationally uniform property tax will be borne by owners of capital and 

have few other important effects.5' By the same token, any one state 

corporation income tax can be expected to have the effects postulated 

here, even though in the aggregate, state corporation income taxes are, 

indeed, income taxes.-51 
-3-

11. Tax on Economic Profits 

Suppose that a given multistate corporation has total economic 

and taxable profits that can be described by the following definition: 

a = S - R - W, (1) 

where is corporate profits, S is total sales, R is payments to owners of 

property (including the normal return to equity invested in the firm), 

and W is the firm's total wage bill. It is assumed for convenience 

that payments for the services of property and labor are the firm's 

only expenses.-6/ 

Under a three factor allocation formula that includes sales, 

payrolls, and property, such as the so-called Massachusetts formula, 

state i would levy a tax on the following tax base: 

where Si, Ri, and Wi are the amounts of the firm's sales, use of 

property, and wage payments occuring in state i.z' Letting t and T 

denote the tax rate and revenue yield, respectively, of state i, we 

could also write: 

By rearranging terms fn equation (3) we could, if we wfshed, also 

characterize the state "profits" tax as being comprised of three 

separate smaller taxes, each levied at one-third the statutory rate, on 

rSi/S, TRi/R, and hWi/W. It will be convenient to do so, but in order 

to avoid unnecessary complications and duplication in the analysis that 

follows, we shall focus upon the first of these smaller taxes Tis, which 
we shall call the "sales related portion" of the profits tax. It has 

the following yield in state i: 

Tis = tin fl Si/S = atin # (4 1 

0

where ti is one-third the statutory corporate tax rate in state i and 

a is state i's share in the total sales of the firm. The object will 

be to compare explicitly the effects of the sales-related portion of the 

state corporate profits tax with the effects of a true income tax and 

a simple gross receipts tax on corporate output, and, by analogy, the 

payroll and property-related portions of the "profits" tax to a true 

income tax and to taxes levied directly on corporate payrolls and 

property. 

The following simple exercise demonstrates clearly that state 

income taxes based on formula allocation are not truly taxes on income 

arising in the state. Make two extreme assumptions: (a) that the 

firm's profits change due entirely to exogenous events that can be 

identified as changing profits truly attributable to the taxing state-;8/ 

and (b) that the change in the profitability of operations does not 

affect sales in the stat-' Differentiating equation (4) with respect 

to profits truly attributable to the taxing state reveals: 

or: 

/

dTis= ti a dlii (5a) 

That is, tax receipts from the sales-related portion of the "profits" 

tax change not by the product of the tax rate and the change in the 
-5-

profits truly attributable to the taxing state, as under a true income 

tax, but by only the fraction Si/S times that much. Due to formula 

allocation, the change in profits truly attributable to a given state 

is effectively divided among the states in proportion to sales, rather 

than entering solely and entirely the tax base of the state in which 

it occurs. 

The converse is, of course, also true. Assume that a change in 

profits occurs, none of which is attributable to the taxing state. 

Differentiating equation (4) with respect to T, the firm's total 

(national) profits yields: 

#

-dTi,s=tiSi/S, 

dr 

and 

Thus the state takes its share of changes in the total national tax 

base, independently of whether profits truly attributable to the state 

change. 

We can also demonstrate that the sales-related portion of the 

profits tax affects corporate decisions in much the same way as a tax 

on corporate gross receipts in (from) the taxing state. As a preliminary 

step, let us review the traditional result that a national tax on 

corporate profits has no effect on price and output decisions of a 

profit maximizing fir$' TO do this, we differentiate both equation (1) 

and the following expression for net profits (7) with respect to Q, the 

output of the corporation, and set the two results equal to zero: 
-6-

'IT, = (1-t)s = (1-t) (S-R-W) (7) 

(7a) 

dQ 

The traditional result is readily apparent from a comparison of 

equations (la) and (7a); so long as the tax rate t is a constant, 

a profit maximizing firm sets marginal cost equal to marginal revenue, 

whether it is gross or net profits that is the maximand. Thus the 

general corporate profits tax, being a tax on economic rent, does not 

affect output or price, and is not shifted in the short run. This 

result does not hold for a state tax on corporate profits, as usually 

imposed. 

To see this, we focus upon the sales-related portion of the state 

corporation income tax. We begin by differentiating equation (1) with 

respect to Qi, the quantity of sales in state i, and setting the result 

equal to zero: 

Profits are maximized by setting marginal revenues resulting from sales 

in a given state equal to the marginal capital and labor costs 

associated with those sales. Let us now consider whether this result 

holds when state i imposes a sales-related corporate profits tax. 

An expression for net corporate profits, taking account of only 

the sales-related element of the corporate income tax in state i, 
-- 

-7-

is derived by subtracting equation (4) from equation (1):-111 

= (s-R-w)(I-~ ti). I 

This expression differs from equation (7) in that t is replaced by 

at:, which is not generally constant ab Qi changes, even if tlis. 

Differentiating equation (8)' with respect to Qi, the quantity of 

the firm's output sold in state i, and setting the result equal to 

zero yields the following equation:- 121 

' dS = 0. (8a) -

drn = (dS - dR - dW ) (1-a - (1-a) t E - (dQi dQi dQi 

I ti) 

dQi dQi 

Algebraic manipulation of this expression produces the following 

equation : 

dS. 

dS - dR -

d

dW = (1-a) t'L 1*.

dQi dQi Q i m iS dQi 

Thuswe see that in the case of the sales-related portion of the state 

corporate income tax, for the profit-maximizing firm, marginal revenue 

resulting from sales in the taxing state does not generally equal 

marginal cost due to those sales, as it does in the cases of no tax 

or a general (national) tax on the firm's profits?' Rather, marginal 

revenue exceeds marginal cost attributable to these sales by the amount 

141 

on the right-hand side of the equal sign in equation Qk 

If the firm sells only a small fraction of its output in the taxing 

state, a(=si/S) is near zero, and the divergence between marginal cost 

8 dSi 

% and marginal revenue is near ti\ . The product of the first two

terms is readily interpreted as a sales tax rate. That is, the ratio 
-- 

-8-

of profits to sales, ~/s,tellsus how much of the firm's nationwide 

profits are attributed to each dollar of sales. Multiplying t(by this 

ratio generates an effective sales tax rate. This can also betshownin 

another way. We can use the identity given in equation (4) above to 

substitute for t./ in t/IT dSi . This yields the following expression

1 i S dQi 

for the divergence of marginal revenue from marginal cost, assuming Si/s 

is arbitrarily close to zero and can be ignored: 

Ti/Si is the fraction that revenues from the sales-related portion of the 

"profits" tax represent of the firm's sales in the state; that is, a firmspecific effective tax rate on gross receipts. Thus the divergence between 

marginal revenue and marginal cost can be interpreted as the sales-tax 

equivalent of the sales-related portion of the corporation income tax.-

15/ 

That this is a reasonable interpretation can also be seen by writing 

out the expression for the net profits of a firm selling in state i if a 

gross-receipts tax levied at rate ts were used instead of a sales-related 

profits tax:-161 

yields: 
-9-

Comparison of the divergence between marginal costs and revenues in the 

two cases (equations 8c and 9b) for a given revenue yield from the taxed 

firm shows them to be almost identical if a small fraction of a firm's 

sales are made in the taxing state. Thus, for a state constituting a 

small fraction of the national market for a firm's products, the salesrelated portion of the state corporation income tax under a formula 

allocation rule is essentially equivalent to a simple gross receipts tax 

levied on the corporation's sales in that state, though at rates that 

differ between firms. Thus it is likely to have roughly the distributional 

effects of a tax levied on the firm's sales in the state, and not simply 

to reduce profits by the amount of the tax, as a general income tax does. 

Similar procedures would establish analogous results for the payroll and 

property-related portions of the state corporation income tax. 

Because no state accounts for a zero fraction of the sales of a firm 

actually selling in the state, the corporate profits tax is not fully 

equivalent to a gross receipts tax. However, we can use equation (8b) to 

calculate the fraction of the sales-tax equivalent of the sales-related 

part of the profits tax that results in divergence between marginal costs 

and marginal revenues. Such calculations are presented for a range of 

sales-related corporate tax rates and values of Si/S in Table 1.-17/ 
- 10 -

Table 1 

I Representative values of (l-Si/S)/(l-tisi/S) 

for selected values of ti/

and Si/S 

Values : Values of ti' 

of 

SiIS : .01 .05 .10 .15 .20 

.05 .950 .952 .955 .957 .960 

.10 

.20 

.go1 

.802 

,905 

.808 

.go9 

.816 

.914 

,825 

.918 

.833 

.50 .SO3 ,513 .526 ,541 ,555 

.80 .202 .208 .217 .227 .238 

We 4see that except for very large values of ti, the value of (1-a)/ 

(l-at{) is very near the value of (1-a). Thus, these calculations suggest 

that even if the firm makes as much as 20 percent of its sales in the 

taxing state, more than 80 percent of the sales-related portion of the 

"profits tax" finds its way into divergence between marginal costs and 

revenues, and that over half of it does so even if the firm sells as much 

as half of its output there. Thus while the equivalences are not total 

and absolute, they are quite strong for many multistate corporations. 

Finally, to the extent that payrolls and property are more concentrated 

in a few states than are sales, the payroll and property-related portions 

of the state profits tax are more nearly true profits taxes than is the 

sales-related portion--but only for the states in which production is 

concentrated. 

111. Tax on Accounting Profits 

Strictly speaking, the results presented in the previous section are 

applicable only to monopolistic firms and firms operating in oligopolistic 
- 11 -

industries, since in competitive industries there are no economic profits, 

except as a transitory phenomenon. Moreover, it might be objected that 

the results presented thus far depend upon the unrealistic assumption that 

state corporation in%ome taxes are levied only on economic profits. That 

the results presented above are generally valid and that this objection 

is misplaced are bo$h easily demonstrated. To do so, let us define taxable 

corporate profits to include the normal return to equity capital, N, as 

follows: 

Thus net profits are the following, for a nationwide tax on profits defined 

in this way: 

rn= (S-R-W)(1-t) - tN. (10) 

Differentiating equation (10) with respect to Q, we derive the usual 

result that a tax on corporate profits defined in this way drives a wedge 

between marginal costs and marginal revenues: 

or 

dS -E- dW f- t -_ dN .18/

dQ dQ dQ 1-t dQ 

If we differentiate equation (lO)with respect to Qi, rather than 

with respect to Q, we see that there is no qualitative difference in the 

results: 
- 12 -

The result is quite different if we consider a state tax on taxable 

profits defined to include the normal return to capital, but apportioned 

among the states according to formula. Net profits, taking account of only 

the sales-related portion of the profits tax in state i, are then: 

Differentiating with respect to the quantity of sales in the taxing state 

and setting the result equal to zero yields the following: 

c 

-

dW IT dS 

dQi (1-ti a) - t i S dQi -(1-a)

As before, this can be rewritten, this time, as follows: 

Comparing equation (12a) with equation (lob), we see that in the 

former there is an extra component in the divergence between marginal cost 

and marginal revenue due to the formula allocation of taxable profits, and 

that this extra term is exactly analogous to the right side of equation (8b). 

Moreover, the component corresponding to the divergence in equation (lob) 

is now Et:/ (1-at:y (dN/dQi), rather than simply fi/(l-t)J (dN/dQi) . This 

component vanishes for small values of 5, the taxing state's share of the 

firm's total sales. Finally, comparison of equations (12a) with (8b) reveals 

that, as before, for small values of a (if Si/S is small) the difference 
- 13 -

'7t between marginal cost and marginal revenue is simply ti--, dS and 

S dQi 

the sales-related portion of the profits tax is merely a disguised gross 

receipts tax. Similar comments apply to the property and payroll-related 

portions of the tax on profits defined to include the normal return. 

IV. Tentative Thoughts on Incidence 

While we have shown that the profits tax in any one state is equivalent 

to taxes levied at differential rates on each firm's gross receipts, property, 

and payroll, we have not analyzed the incidence of these differential taxes. 

While we cannot go into the latter question in detail, we can give some tentative suggestions about results. 

Yet another way to see the 

similarity between the sales-related 

portion of the state corporation 

income tax and an ordinary sales 

tax in the case of values of2 

near zero is to rewrite equations 

(8c) and (9a) in yet another way, 

as follows: 

IT/ MRi (1 - 2 ti) MCi (ad) 

and 

MRi (1 - ts) = MCi (9c) 

P 

Pd 

Pi 

Qi 

Figure 1 

Thus we can expect reactions to the sales-related part of the profits tax 

that are similar to reactions to gross-receipts taxes. This is most clearly 

seen in the monopoly case. 
- 14 -

Using the terminology of Figure 1, we can see that in the case of a 

monopolist, the sales-related part of the corporate income tax affects 

the corporate decision on prices and output in just the same way as an 

equal-yield sales tax.-''/ It reduces the marginal revenue curve as seen

by the firm form MRi to q<where MR[= MRi(l-ts) or MRi (l-t(TF/S), and 

results in a fall in the profit-maximizing output from Qi to Qi/and a rise 

in price from Pi to pi

< Because the analysis of the incidence of sales 

taxation on a monopoly is generally understood, there is no need to repeat 

it here. Of course the results are somewhat different once non-zero values 

of a are taken into account, but the analysis of Table 1 suggest that they 

are similar. 

It seems likely that results for oligopolistic industries will also 

be similar to those for a true gross receipts tax, though the analysis 

required to demonstrate it is not so clear-cut. The problem is not that 

the tax does not resemble a sales tax for the interstate firm with relatively small amounts of sales in the taxing state. Rather, the problem 

is (a) that for a given firm the tax falls somewhere in the spectrum 

between a true profits tax and a sales tax, depending upon the firm's 

value of&, as noted above, and (b) that for the interstate firm the 

effective sales tax rate depends upon the firm's profitability in the 

nation as a whole. Because various firms have different values of5 

and different profit margins, and therefore different effective sales 

tax rates, the degree of shifting for a given industry is not clear, 

even if we ignore usual complexities of market interaction that plague 

the analysis of incidence of taxes in oligopolistic industries. It 
- 15 -

seems reasonable to believe, however, that in industries dominated by 

interstate firms, the high-profit firms selling relatively small fractions 

of their output in a given state are likely to hold a price umbrella over 

the less profitable firms and/or intrastate firms for whom the tax is more 

truly a profits tax. Thus it seems quite likely, especially for the smaller 

states, that the sales-related portion of the state profits tax is shifted 

in roughly the way we would expect a true state sales tax to be.- 201 

Oligopolistic interaction merely strengthens this supposition. 

The arguments of the previous two paragraphs applies, strictly speaking, 

only to a state tax levied on economic profits. But there is little reason 

to believe that the result would be much different for a tax on accounting 

profits. 

Finally, we can consider briefly the case of pure competition, for 

the tax on accounting profits. (In long-run equilibrium there would be no 

profits in the competitive case, and therefore no tax, if economic profits 

were the tax base.) Though the analysis would again be tricky, it seems 

likely that the tax would be reflected in higher prices. By how much the 

price would rise, however, is unclear, since firms would pay different 

tax rates, and there is less presumption of price umbrella affects, etc. 

As with any tax on the use of a factor, rather than on sales, the 

property and payroll-related portions of the corporate income tax are not 

easily portrayed using the partial equilibrium diagram of Figure 1 except 

in the case of complete impossibility of factor substitution.- 211 But in 

the cases of both monopoly and pure competition, the property and payroll 

portions of the tax on economic or accounting profits are almost certainly 
- 16 -

borne, at least in part, by owners of immobile factors, land and labor, 

located in the taxing state.Z/ The real analytical problems involve the 

oligopolistic sector. Here it is quite possible that the factor-related 

portions of state profits tax are shifted to consumers of taxed products 

throughout the nation via price-umbrella effects, rather than reflected 

in lower factor returns, especially if production is dominated by a few 

firms and geographically centered in the taxing state.-23/ 

V. Further Analysis of Results 

In order to understand better why the surprising results of the previous 

three sections oceur, we need only examine equation (4) and its counterpart 

in the case in which the tax applies to the normal return to equity, as 

well as to economic profits. To facilitate the examination we can rewrite 

these expressions as follows: 

Tis = (ti/ IT/S)Si (44

and 

Concentrating upon equation (4a), we see immediately why the sales-related 

portion of the profits tax is roughly equivalent to a tax on the sales of 

the corporation in the taxing state, which could be written as follows: 

T,= ts Si . 

Revenue from the sales-related portion of the profits tax is simply 

the product of three things: the statutory tax rate ti,/ the corporation's 

ratio of profits to sales for the nation as a whole, and the corporation's 
- 17 -

sales in the taxing state, Thus, by analogy, we can characterize the 

product of the first two of these factors as an effective sales tax rate 

applied to sales in the taxing state, and rewrite equation (4a) in the 

same functional form as (4c): 

T =tS. is ei 

Of course, this effective sales tax rate is not a statutory constant, 

as is ts, the statutory sales tax rate. In particular, it depends inter 

-9alia upon sales in the taxing state and on profits from those sales. If 

however, the taxing state constitutes a small part of the firm's market, 

r/S, and therefore the effective sales tax rate, will be little affected 

by activities in the taxing state and revenues from the "profits tax" will 

simply be roughly proportionate to sales in the state. In other words, the 

sales-related portion of the state profits tax is essentially a disguised 

tax on the corporation's sales, especially in states in which the firm does 

a small fraction of its business. 

That the profits tax is roughly equivalent to a composite tax on 

corporate sales, payroll, and property does not, of course, imply that it 

is equivalent to a general tax on those economic variables. First, the 

tax applies only to sales, payrolls, and property in the corporate sector 

of a state's economy, and distorts choices on sales and production in that 

state away from the corporate form of organization. This may or may not 

make good sense on non-economic grounds, but it is certainly questionable 

on economic grounds, unless there is some reason to believe that corporate 

activity should be taxed at differentially heavy rates. That question is 
-- --- 

- 18 -

beyond the scope of the present paper. 

Second, as equation (4a) shows, the effective sales tax rate applied 

to a given firm's sales in a state depends on the firm's overall ratio of 

profits to sales (and on the statutory tax rate). Similar comments apply 

to the effective payroll and property tax rates. In other words, firms 

with unusually high (low) ratios of profits to sales, payrolls, and property 

are subjected to higher (lower) than average effective rates of sales, 

payroll, or property taxation. Thus there is discrimination both between 

firms in the same industry, and due to the different profit margins in 

various industries, between industries.=' Again, there seems to be no 

economic rationale to justify this kind of discriminatory tax treatment. 

Of course, it can be argued that the tax is really a profits tax after 

all, in that the effective tax rates depend crucially upon the profitability 

of the firm. This argument, however, is invalid, for at least two reasons. 

Most obviously, the effective tax rate depends on the firm's profitability in the nation as a whole. As argued above, this may be largely 

independent of its profitability in the taxing state. Second, even though 

effective tax rates are directly proportionate to profit rates, the firm's 

total profits are not likely to be seriously curtailed by the state profits 

tax, except in those cases in which the firm is earning some sort of monopoly 

rents in the state. Since it is in effect sales, property, and payrolls 

which are being taxed under the profits tax--albeit at rates that depend 

upon profit rates--corporations will adjust the geographic location of 

their sales, property, and payrolls in response to the tax, until the 

conditions described in equations (812) or (12a) are met.25' This being the 
- 19 -

case, it seems safe to believe that it is consumers (for the portion of the 

tax levied effectively on sales at destination) or immobile factors owners 

(for the portion related to sales at origin, payrolls, or property) who 

bear the bulk of the tax, and not that the tax simply lowers after-tax 

profits, as a true profits tax would. 

VI. Concluding Remarks: Implications for Policy 

The analysis presented here has important implications for tax policy. 

But, as in the case of Mieszkowski’s analysis of the incidence of the 

property tax, the implications are somewhat different, depending upon 

whether one takes the point of view of one state, or that of all states 

or the nation as a whole. Nonetheless, the most important implication 

of both points of view is that the carporatlon income’tax is an unsatisfactory 

source of revenue for state governments and should be replaced by other forms 

of state or federal taxation. 

A. State Tax Policy 

The upshot of this analysis for state tax policy is clear. Economists 

have long recognized that state and local governments have little business 

engaging in redistributional taxation implemented through corporate income 

taxes and progressive personal income taxes, because geographic mobility 

is likely to doom such efforts.-26’ The analysis of this paper suggests that 

the prospects are even worse than usually supposed. Rather than being the 

potentially progressive tax that it appears to be, the state corporation 

income tax is actually levied on two bases that would usually be agreed to 

lead directly to regressive taxation, sales and payrolls. Moreover, recent 
- 20 -

analysis of the incidence of the property tax suggests that the propertyrelated portion is likely to be regressive, as well.-27/ Thus the state 

corporate income tax does not do what many would seem to intend it to do, and 

it works only very clumsily, and possibly at considerable cost. Therefore, 

any single state would seem to be well-advised at least to replace the 

corporation income tax with a tax levied directly on corporate sales, 

payrolls, and property (or whatever else happen8 to be in its present 

allocation formula) .-28/ The only real changes would be (a) the use of a 

standard rate of tax, instead of one that depends upon the firmrs national 

profit performance, and (b) a considerable simplification of tax administration and compliance. Moreover, unless there is a clear reason for preferring to discriminate against the corporate form of organization, it 

would seem even better to levy the sales, payroll, and property tax on 

all activity in the state economy, instead of only in the corporate sector. 

Finally, the portions of the adjusted tax based on payrolls, property, 

and Bales at orlg%n could probably be peplaced by a state personal income 

tax (or increase in the state income tax), and the portion on rates at 

destination could be absorbed Into the (perhaps newly enacted) state retail 

sales tax.21 I submit that this kind of replacement of the corporation 

income tax would make economic and administrative sense for any state. 

B. The National Perspective 

There are at least three good reasons why state governments should 

not employ corporation income taxes, aside from the two already made (that 

states have no business levying taxes such as this that are supposedly 

progressive, and that the tax, as seen by any one state, is not really an 
- 21 -

income tax anyway): 

(1) even as a federal levy, the corporation income tax makes no 

sense, except as a withholding device; 

(2) ft is generally logically impossible to tax the corporate profits 

of a multfstate firm orighating in any particular state accurately; 

(3) the locational allocation of resources is distorted by differentials in the corporate profits taxes levied in various states, 

The first of these is beyond the scope of this paper, and has been 

discussed elsewhere, in any event.%/ But the analysis of this paper 

is directly germane to the second and third. 

Like joint costs such as overhead, corporate profits cannot be 

accurately allocated to any one state. This is true whether we are 

talking about economic profits or accounting profits. This is, of 

course, the fundamental reason why it is necessary to employ such an 

arbitrary and unsatisfactory approach as formula apportionment to 

allocate national profits of a firm among states. Nor is the use of 

separate accounting (the practice under which a firm’s activities in 

each state are treated as constituting a separate business), much better. 

As experience with Section 482 of the U.S. Internal Revenue Code has 

demonstrated in the international sphere, joint costs and problems of 

transfer pricing render separate accounting as arbitrary as formula 

apportionment.-31’ Since accurate state taxation of corporate income is’ 

often a logical impossibility, it seems best to abandon this tax as a 

source of state revenue.- 32/ One way to encourage this abandonment would 
- 22 -

be to disallow the deduction of state corporate income taxes in the 

calculation of income for federal tax purposes. 

In discussions of state taxation of multistate corporations, relatively little has been said about the extent to which differential rates 

of profit taxation distort investment and other decisions, except in the 

context of discussions of the effects of taxes and tax incentives on 

industrial location. This is in marked contrast to the situation in the 

international sphere, where considerable attention has been focused upon 

the consistency of various systems of taxation with worldwide efficiency, 

i.e., the neutral allocation of resources (primarily capital), among nations.-331 

It is usually thought to be necessary for the achievement of locational 

efficiency that the tax levied on a given amount of profit be invariant 

with regard to the geographic source of that profit.-34’ In the present 

context--and inevitably, where we are concerned with taxes levied in an 

open economy--we cannot generally identify the geographic source of profits, 

as noted above. But it seems reasonable to argue more generally that locational efficiency requires that the tax levied on a given amount of profit 

should be invariant with respect to where property is located.-35 I 

Naturally enough, the property-related portion of the total corporate 

tax of the firm is invariant to the location of property only if the tax 

rate in all jurisdictions is the same or if the firm earns no profits.-361 

(But under those circumstances locational efficiency is relatively easy to 

achieve using many systems of taxation.) If profits are positive, formula 

apportionment is generally non-neutral, since it tends to discourage 

investment in high-tax states. 
- 23 -

Concern with locational efficiency of resource allocation thus suggests 

that states should not use formula-apportioned corporation income taxes, 

or at least that rates should be uniform across states.-37/ Supposing 

that the tax continues to be used, despite what has been said here, this 

last conclusion has important ramifications for intergovernmental fiscal 

relations. First, it suggests that the Multistate Tax Commission (MTC), 

or something like it, should concern itself with rate differentials, as 

well as with the definition of income and apportionment formulas.-38/ This 

may, of course, be a large order indeed, since membership in 

MTC is voluntary.=/ Elimination of differentials would require 

as a first step the imposition of corporation income taxes in 

the states now abstaining from using this source of revenue. 

But we have argued above that this is an fnferior form of state 

tax, regardless of whether it is appraised from the state or 

the national point of view, Thus, any federal requirement 

that all states levy state corporate income taxes so that rates 

could be equalized is hardly a clear step forward. A more 

sensible approach would be to prohibit state use of this tax 

and make up the lost revenues through federal taxation and 

grants to the states.*/ A surcharge on the federal corporation 

income tax might be the obvious choice, since it is more or 

less equivalent to a uniform state tax. But given the faults 

that an unintegrated corporation income tax has, even at the 

federal level, one might hope that a better source of revenue 

could be found.G/ Though this is not the place to go into that 

question, logical candidates might be a value-added tax, the 

the personal income tax, or a progressive tax on personal expenditures. 
- 24 -

FOOTNOTES 

-1/ Charles E. McLure, Jr., "Revenue Sharing: Alternative to Rational 

Fiscal Federalism?" Public Policy, Vol. 19 (Summer 1971), p. 472. For 

a description of state practices in the field of corporation income 

taxation and recent efforts to gain uniformity, see Charles E. McLure, Jr., 

"State Income Taxation of Multi-State Corporations in the United States of 

America," The Impact of Multinational Corporations on Development and on 

International Relations, Technical Papers: Taxation (New York: United 

Nations, 19741, pp. 58-111. Whether all states use the same allocation 

formula-and definition of income for tax purposes is largely immaterial 

for the argument made here, but it is convenient to assume uniformity. 

Finally, references to "sales" are to gross receipts, rather than to retail 

sales. 

-2/ For a further discussion of this approach, see Charles E. McLure, Jr., 

"The Interstate Exporting of State and Local Taxes: Estimates for 1962," 

National Tax Journal, Vol. 20 (March 1967), pp. 49-77. State corporation

income taxes do, of course, constitute even less of a "system1'than do the 

local property taxes. 

-3/ Peter Mieszkowski, "The Property Tax: An Excise or a Profits Tax," 

Journal of Public Economics, Vol. 1 (April 19721, pp. 73-96. 

-4/ For an elementary exposition of how the.se apparently conflicting 

results can be reconciled, see Charles E. McLure, Jr. "A Caveat to 

Incautious Users of the 'New View' of the Property Tax," National Tax 

Journal, Vol. 30 (March 1977). 

-5/ Again following Mieszkowski, we can use the analysis presented here 

for deviations from the average rate of state income taxation, the 

average being borne like a nation-wide income tax. 

-6/ If there are any rents resulting from patents, mineral deposits, etc. 

they can be thought of as being included inr if owned by the firm. 

-7/ No distinction is made between sales at origin and sales at destination, 

since the mathematics does not require it. If the profits tax is based on 

a formula that includes sales at destination, the sales portion of the tax 

resembles a conventional destination principle sales tax. If the formula 

includes sales at origin, the resemblance is to a tax on sales at origin, 

or production.

Moreover, to be strictly correct we should note that the Massachusetts 

formula employs the capital stock, rather than payments to capital, in the 

property component. But little is lost, and some simplification is gained, 

by using the return to capital as the measure of property. 
- 25 -

-8/ Such information is, of course, generally unavailable. If it were 

not, there would be no reason to resort to arbitrary formula allocation 

of profits. 

9/ Perhaps the most convenient way to visualize this is to imagine the 

discovery of mineral deposits on land in state i owned by the firm. Profits 

might well increase while sales in state i remained unchanged. 

-lo/ The analysis presented here is essentially short-run, abstracting from 

the intersector repercussions described in Arnold C. Harberger, "The 

Incidence of the Corporation Income Tax,'' Journal of Political Economy,vol. 70 

(June 1962) PP. 215-40, The point: is that the state corporation income tax 

will have effects more like those of a state tax on corporate sales, property, 

or payrolls than like those of a tax on corporate profits in the short run, 

and hence even if long run general equilibrium interactions are taken into 

account. 

-11/ This equation and the conditions for profit maximization are based on 

the assumption that there are no corporate taxes in other states, and would 

be different if indeed other states levied corporate income taxes. But if 

we impound other taxes in ceteris paribus, the differences in conditions for 

profit'maximization with and without a corporate tax in state i are as 

indicated here. Alternatively, if we were examining a national system of 

state corporate income taxes, this analysis would be appropriate for 

differentials from the national average tax rate. 

-12/ The analysis reported here considers an increase insales to the taxing 

state which also represents an increase in total sales, rather than a re­

-13/ Of course if the firm either has no profits (.rr=O) or has sales only in 

the taxing state (Si's and a=l), marginal cost equals marginal revenue. But 

in the case that interests us, the case of a profitable multistate corporation, 

marginal revenue exceeds marginal cost for the profit-maximizing firm. 

-141 One is tempted to go on to say that the tax reduces sales in the taxing 

state, increases the prices of goods sold there, and is passed on in part to 

consumers. However, that is more than we need to say, and more than we can 

say orit,hout a more detailed examination of conditions in the industry, 

including the market interaction of corporate firms of various degrees of 

profitability, unincorporated firms, and consumer demand. The point we want 

to make is that the sales-related portion of the profits tax should effect 

corporate behavior in roughly the same way as a corporate sales tax levied at 

differential rates would. The further repercussions of such a sales tax are 

discussed further below. 
-- 

- 26 -

-15/ Since profits tax represents a different fraction of sales for various 

firms, the tax is not a uniform flat-rate sales tax. This point is considered 

further below. 

-16/ This sales tax rate is defined as a percentage of the tax-inclusive price 

rather than of the tax-exclusive price, which is more common in the United 

States. 

-17/ Recall that ti'is only one-third the statutory rate. Thus, the first 

two columns are all that are really relevant in the U.S., especially once 

the federal offset is considered. Other columns may, however, be relevant 

in an international context. 

-l8/ The part of the tax levied on economic profits does not distort economic 

decisions, but the part levied on normal profits does. Suppose the tax 

were levied only on normal profits. Thus, n,=(S-R-W)-tN. Differentiating, 

we have: 

dS dR - -dW -dN . -dN can also be written as dN dS

dQ ?Q dQ dQ dQ dS dQ 

the product of the normal profit margin on marginal sales and marginal revenue. 

Employing m=dN/dS, we can rewrite equation (loa) as follows: 

The divergence between marginal cost and marginal revenue thus depends upon 

the profit margin and the tax rate. 

-19/ In order to be able to draw this diagram we treat the operations attributable to sales in state i as separable from those in other states, though 

they will generally not be separable. 

-20/ If the apportionment formula employs sales at destination, the shifting

would be to consumers. If it includes sales at origin, backward shifting 

to immobile factors, land and perhaps labor, is more likely. 

-21/ For a further discussion of this problem, see Charles E. McLure, Jr., 

"General Equilibrium Incidence Analysis: The Harberger Model after Ten Years," 

Journal of Public Economics, Vol. 4 (February 1975), pp. 125-61. 

-22/ To the extent that locational monopoly rents exist, the tax may be borne 

ip part by owners of the firm (or other owners of the economic interest in 

the assets generating rents). 

-

23/ For a discussion of this issue in a slightly different context, see

Charles E. McLure, Jr., "The Relevance of the New View of the Incidence of 

the Property Tax," in Taxation of Urban Property in Developing Countries, 

Roy Bahl, editor, University of Wisconsin Press, forthcoming. 
- 27 -

-24/ If the tax is levied on a base that includes the nom1 return to 

equity capital, the sales-related portion discriminates against capitalintensive activities. 

-25/ It is ironic that precisely the most profitable firms are likely to be 

discouraged from undertaking activity in the state--a result at variance 

with announced intentions in most states to attract industry. 

-26/ See, for example, Richard A. Musgrave, The Theory of Public Finance 

(New York: McGraw-Hill, 1959), pp. 181-82 and Wallace E. Oates, "Theory of 

Public Finance in a Federal System,'' Canadian Journal of Economics, Vol. 1 

(February 1968) pp. 37-54. 

-27/ Recall that we are dealing with the tax as seen from the vantage point 

of individual states. 

-28/ It may be worth repeating, as we near the end of this paper, that the 

analysis presented here is predicated upon the proposition that decisions 

on state taxes are made by individual states, and not at the national level. 

As noted earlier, what is true for each state is not true for all acting 

together. That'is, if all states levied the same corporation income tax, 

corporate profits would be burdened (if we continue to ignore Harbergertype shifting to owners of non-corporate capital). But this is largely 

irrelevant to decisions made in any statehouse, since any deviations from 

that uniform tax would have the effects described here. 

-29/ One real problem with state personal income taxes is the difficulty of 

inclusion of corporate-source income, and especially retained earhings. This 

is one possible justification for not taking the final step to replacing 

the state tax on property and payrolls with a state personal income tax. On 

the other hand, allowance can be made for family circumstances under the 

personal income tax, but this is impossible under the present corporate 

profits taxes and flat-rate payroll and property taxes. Similarly, retail 

sales taxes allow exemption of key items, which does not occur under state 

corporation income taxes. If the corporate and personal income taxes were 

integrated at the federal level, it should be substantially easier to obtain 

the information necessary to tax personal income at residence. 

-30/ For a detailed discussion of the lack of rationale inherent in a separate 

tax on corporation income, see Charles E. McLure, Jr,, "Integration of the 

Personal and Corporate Income Taxes: The Missing Element in Recent Tax Reform 

Proposals," Harvard Law Review, Vol. 88 (January 1975), pp. 532-82. 
- 28 -

-31/ For discussions of problems of Section 482, see, for examp1GM.L. Hamlin, 

"Correct Allocations under Section 482 Are Still Difficult Despite New Regs." 

Journal of Taxation, Vol. 43(December 30, 1975), pp. 358-63 and C. Phillips, 

"The Current Status of the Application of Section 482 to Foreign ~ Related

Corporations," Taxes, Vol. 48- (1972) , pp. 472-78. 

In recent years there has been some interest in the use of formula 

apportionment to replace the separate accounting approach found in the tax 

treatment of multinational firms by national governments. As evidence of 

this, see The Impact of Multinational Corporations on Development and on 

International Relations, Technical Papers: Taxation, 2.cit. For expression

of preference for formula apportionment in the international field, see 

Peggy B. Musgrave, "International Tax Base Division and the Multinational 

Corporation," Public Finance, Vol. 27 (1972), pp. 394-413. The present

criticism of formula apportioned income taxation should not be interpreted 

as a preference for separate accounting. Which of these approaches is a 

superior way allocating the unallocable is beyond the scope of this paper. 

-32/ The basic problem is jointness or indivisibility of the firm's operations, 

and the same principles that apply to public goods in the literature on fiscal 

federalism seem to apply here also. The allocation of responsibility for the 

provision of various public goods among levels of government should depend 

upon the area over which benefits extend. Similarly, taxation of the multistate firm should be imposed by the jurisdiction most nearly congruent

with the area the firm's activities cover. If the decision units are smaller 

than optimal, problems arise. Among the problems are the locational effects 

discussed below. 

_.33/ This difference in emphasis almost certainly reflects the different 

principles upon which state and national income taxes are based. State 

corporation income taxes are based essentially upon a territorial principle. 

That is, states ostensibly attempt to tax only profits whose source lies 

within their borders, independently of the legal site of residence of the 

corporation or its owners. On the other hand, many nations (but not all of 

even the important industrial nations), apply a worldwide principle, under 

which all profits of resident firms are subject to profits tax, wherever 

earned. 

Under the territorial principle the net return to investment (assuming 

the corporation income tax actually to be levied on profits produced in a 

given area, instead of through formula apportionment), depends upon where 

capital is invested, unless effective tax rates are the same in all jurisdictions. Thus, the territorial principle inherently interferes with nationwide (or worldwide efficiency). By comparison, the achievement of worldwide 

efficiency is at least generally consistent with the worldwide principle. 

However, nations applying this approach almost always also tax all profits

originating within their borders. For an excellent background discussion of 

various methods of relieving the double taxation that results from overlapping 
dT 

- 29 -

-33/ Footnote continued. 

taxes being levied on the same income, and other issues relevant to the 

material covered in this section, see. K. Sato and R.M. Bird, "International 

Aspects of the Taxation of Corporations and Shareholders," IMF Staff Papers, 

Vol. 22 (July 1975), pp. 384-455. We take as given continued reliance on the 

territorial principle, since corporate taxation at residence does not have 

the appeal in the interstate context that it has in the international sphere. 

-34/ See, for example, Peggy B. Husgrave, United States Taxation of Foreign 

Investment Income: Issues and Arguments (Cambridge, Mass.: Harvard Law 

School, International Tax Program, 1970). 

-35/ Concern with locational effects on investment is most analogous to 

concern about equal taxation of profits, which is essentially a matter of 

the locational allocation of capital. 

-36/ In order to show that formula apportionment does not generally result 

in locational efficiency, we write the following expression for the propertyrelated portion of the profits tax on a firm collected in state i and in all 

other states (lumped together as j # i): 

T = pi 4- (l-b)t 31T 

or 

where tj is the weighted average of tax rates in all states other than i. 

Differentiating with respect to b, the fraction of total property of the 

firm located in state (nation) i, we obtain: 

-db = (ti-tj)lT . 

-37/ It is ironic, but natural, that the property-related portion of the

state tax is both the culprit most responsible for adverse locational effects 

and perhaps the most natural choice as the best single apportionment factor 

in the Massachusetts formula. Similarly, locational distortions can be 

avoided only if all states levy the same corporation income tax. Fortunately 

that uniform tax can have a zero rate! 

-38/ For descriptions of the Multistate Tax Commission and its activities, 

see McLure, "State Income Taxation of Multistate Corporations ...,I1 3.&., 

and "Taxation of Multi-Jurisdictional Corporate Income: Lessons of the U.S. 

Experience," in Wallace Oates, editor, The Political Economy of Fiscal 

Federalism, (Lexington, Massachusetts: Lexington Books, forthcoming), and 

especially Eugene F. Corrigan, "Interstate Corporate Income Taxation - Recent 

Revolutions and a Modern Response," Vanderbilt Law Review, Vol. 29 (March 1976), 

pp. 423-42. 
- 30 -

-39/ Moreover, several of the member states of the NTC do not even levy 

corporate income taxes. 

-40/ This suggestion might seem to be inconsistent with the author's 

questioning of the role of unconditional grants in "Revenue Sharing: An 

Alternative to Rational Fiscal Federalism," 9.c.But he argued there 

that state corporation income taxes have no place in a rational system 

of fiscal federalism, whereas unconditional grants may be more or less 

equivalent to broadbased general taxes such as sales and personal income 

taxes, and therefore acceptable. 

-41/ Moreover, if this tax were used, there might be a natural tendency to 

assume that grants to states should be based upon corporate income originating in the states. But such an assumption would resurrect the insurmountable problems of income measurement that lead us to suggest that the 

states should not use the corporate income tax.