Office of Tax Analysis 

U.S. Treasury Department 

Washington, D. C. 20220 

Issued : November, 1976 

Tax Neutrality Between Capital Services 

Provided by Long-Lived and Short-Lived Assets 

Emil M. Sunley, Jr. 

Brookings Institution 

OTA Paper 10 February 1976 
TABLE OF CONTENTS 

I. Introduction ..................... 

11. Rental Cost of Capital ................ 111. Rate of Return .................... IV. Comparison of the Two Criteria ............ V. Neutral Investment Tax Credit ............ 

page 

1 

3 

8 

11 

13 
I. INTRODUCTION 

A major theme of economics is the need to use capital and labor 

efficiently. Neutrality, particularly tax neutrality, between longand short-lived assets is an important aspect of this theme. Only if 

the tax system is neutral between capital services provided by long- and 

short-lived assets can capital and labor be efficiently combined. 

Congress has provided a number of tax incentives, including tax 

depreciation more rapid than economic depreciation and the investment 

tax credit, aimed at stimulating additional investment. Attempts to 

stimulate investment should be done in a way which is evenhanded or 

neutral between capital services embodied in long- and short-lived 

assets. This paper focuses on the criterion for a neutral tax incentive 

(or disincentive) L’ for investment. The paper is not concerned with 

neutrality between capital and labor. Rather it is assumed that, while 

we may want to tilt economic decisions towards capital or labor, we do 

not want to bias the source of capital services supplied by long- and 

short-lived assets. 

Confusion concerning tax neutrality between long- and short-lived 

assets arises in part because there are two somewhat conflicting neutrality 

criteria--one based on the rental cost of capital and one based on the 

rate of return. The rental cost of capital criterion implies that a 

tax incentive should proportionately decrease the rental cost of all 

investments, The rate of return criterion requires that a tax incentive 
-2-

should proportionately increase the rate of return of all investments. 

These two criteria are not consistent with each other, and it is the 

intention of this paper to demonstrate that the rate of return criterion 

must be used in order to achieve tax neutrality as to the source of 

capital services, whether provided by long- or short-lived capital 

assets. 
-3-

11. RENTAL COST OF CAPITAL 

The rental cost of capital is essentially the factor cost or 

social cost of using a unit of physical capital for one period. It is 

the price for the use of physical capital just as the wage rate is the 

price for the use of labor services. It includes an amount for capital 

recovery, a net after-tax return on the amount invested, and the tax on 

this income. Hall and Jorgenson [3] have defined the rental cost to be: -

21 

1-uz c = q(r +S) -

1-u 

where c = rental cost 

q = price of new capital asset 

r = after-tax "normal" rate of return 

6 = economic decline rate 

u = nominal tax rate 

z = present value of tax depreciation per dollar of original cost. 

Various commentators have suggested that neutrality between longand short-lived assets requires a tax incentive that proportionately reduces 

the rental cost of capital for all investments [4]. For example, I asserted 

that an investment tax credit of k percent with a basis adjustment (for 

purposes of calculating depreciation allowances) is a neutral incentive 

[4]. Such a tax credit reduces the rental cost of capital by k percent. 

Its effect on the rental price is exactly the same as a k percent reduction in the price of all new capital goods. Economists are accustomed 
-4-

to thinking that tax neutrality is achieved within any group of goods 

if their relative prices are not disturbed by the tax change. In this 

sense, an equal percentage reduction in the price of all capital goods 

appears to be neutral. 

One way to see that an investment credit with a basis adjustment 

ensures a proportionate reduction in rental cost is to suppose that, 

on August 15, 1971, the President, instead of proposing restoration 

of the 7 percent tax credit (without a basis adjustment), had ordered 

an across-the-board 7 percent reduction in the prices of machinery and 

equipment (while freezing all other prices). Under this course of 

action, businesses would have found that the initial outlays required 

for capital investments in machinery and equipment were reduced by 

7 percent. In addition, the basis for depreciation, and, thus, all 

future depreciation deductions would also have been reduced by 7 percent. 

Similarly, a 7 percent tax credit with a basis adjustment also reduces 

the initial outlays by 7 percent and the basis for all future depreciation deductions by 7 percent. 

White and White [6, p. 1101 concluded that a neutral tax incentive 

should reduce proportionately the rental cost of capital of all investments: 

To produce a stimulus to expand the capital stock in a manner 

that would be neutral as among assets depreciating at varying rates, 

the appropriate policy would be one that reduced the rental cost 

of capital proportionately for all types of assets covered. A 

tax resulting in such proportionate reductions would have no substitution effect among capital assets. That is, at a given size 

capital stock, there would be no cost advantage to substituting 

one type of capital service for another--which would be a form of 

neutrality. A uniform investment tax credit would provide such a 

neutral stimulus to investment, so long as the credit is deducted 

from the original cost of the asset for depreciation computation ... Such a credit would not, of course, offset an unneutral depreciation policy, but it would not aggravate nonneutrality. 
-5-

The proportionate reduction in the rental cost of capital does 

have considerable intuitive appeal as a neutrality criterion. Neutrality, 

as we generally think of it, requires that the tax system does not distort 

relative prices and the rental cost of capital is the price which a 

business firm must pay (or impute to itself) for the use of capital 

assets. However, in the short run, a proportionate reduction in the 

rental cost of all capital assets will tend to favor short-lived assets 

because a short-lived asset experiences more depreciation per unit of 

rental cost than a long-lived asset. If the price of beef, lamb and 

pork were all reduced by the same proportionate amount, there would be 

no tendency for consumers to substitute one type of meat for the other. 

But if the price of a one-year asset, a five-year asset and a fifty-year 

asset are all reduced by the same proportionate amount, producers will 

purchase relatively more of the one-year asset and relatively less of the 

fifty-year asset. The reason for the difference between types of 

meat and types of assets is that, while all types of meat are entirely 

Ilused up" during the period of purchase, only a portion--and, more 

importantly, a varying portion--of capital assets are "used up" each 

period. 

The example in Table 1 illustrates the effect of a uniform proportionate 

reduction in the rental cost of assets. Each asset is combined with 

the same amount of labor and raw material to produce output. The assets 

differ only with respect to service life. In the short-run, when value 

added by machines is fixed, economic profit is what remains after the 

"normal" rate of return (here, an interest rate of 10 percent) and depreciation have been paid. With a uniform proportionate reduction in the 
-6-

TABLE 1 

Service Lives (in years) 

Item of Expense : 1 5 50 : 

Cost of machine 109 400 1000 

Interest or "normal" return (10%)

Economic profit (assumed zero in 

11 40 100 

initial equilibrium) O O O 

Depreciation 109 80 20 

Value added by machine (rental 

cost of machine) 120 120 120 

REDUCE COST OF MACHINE BY 50 PERCENT - SHORT RUN RESULT 

Cost of machine 54. 5 200 500 

Interest or "normal" return (10%)

Economic profit,before commodity 

5.5 20 50 

prices change 60 60 60 

Depreciation

Value added by machine, before 

54.5 40 10 

commodity prices change (rental 

cost plus economic profit on 

machine) 120 120 120 

Economic profit as percent of 

cost of machine, before commodity 

prices change 110% 30% 12% 

REDUCE COST OF MACHINE BY 50 PERCENT - LONG RUN RESULT 

Cost of machine 54.5 200 500 

Interest or "normal" return (10%) 5.5 20 50 

new equilibrium) O O O 

Depreciation 54.5 40 10 

Value added by machine, after 

commodity prices change (rental 

cost of machine) 60 60 60 

Percent decrease in value added by 

machine, after commodity prices 

Economic profit (assumed zero in 

change 50% 50% 50% 
-7-

price of all assets, and hence in their rental costs, in the short-run 

the economic profit as a percentage of the cost of the machine rises 

much more for the one-year asset than for the fifty-year asset. Thus, 

in the short-run, a proportionate reduction in the rental cost of 

all assets is not equivalent to a proportionate increase in the market 

return on all assets (defining market return as the "normal" return 

plus economic profit). Hence, as producers add to their capital stock 

in response to positive economic profits, short-lived assets will be 

favored and long-lived assets will be disfavored. Ultimately, in 

the long-run, commodity prices will adjust downward so that economic 

profits on all assets are zero. But in the process of reaching this 

new equilibrium, producers' choices will have been biased towards 

short-lived assets. 
-8-

111. RATE OF RETURN 

Economic theory suggests that investment occurs at the margin 

until the after-tax rates of return of alternative investments are 

equalized .A’ Theref ore, any incentive which increases the after-tax 

rate of return more for some investments will induce a shift towards 

those investments with the higher after-tax rates of return. Such a 

shift will occur until the rates of return on the favored investments 

and unfavored investments are again equalized. 

If r is the equilibrium after-tax rate of return on an investment 

before the tax incentive, and rs is the equilibrium after-tax rate 

of return after the incentive, the effective subsidy rate, s, can be 

defined as the proportionate increase in the rate of return: 

rs - r r

S 

s= = --1 

r r 

Only if the subsidy rate is the same for all investments will the incentive not induce an artificial shift towards favored investments. 

A subsidy which increases proportionately the after-tax rate of 

return on all assets will increase the demand for capital services. 

As the quantity of capital increases, the marginal product of capital 

falls. When the marginal product of capital falls, the rental price of 

long-lived assets falls more than that of short-lived assets. This is 

so because interest is a greater proportion of the rental cost for longlived assets than it is for short-lived ones. Thus, a tax incentive 
-9-

which increases proportionately the after-tax rate of return of longand short-lived assets has exactly the same impact on investment as a 

decrease in the interest rate. (At lower interest rates, long-lived 

assets will be favored relative to short-lived assets, as the investor/ 

borrower becomes more willing to undertake long-term projects.) 

As Table 2 illustrates, in the short-run with fixed commodity 

prices, the economic profit as a percentage of the cost of the machine 

remains constant for assets of all service lives, given a proportionate 

decrease in the interest rate. In this respect, investors would be 

temporarily indifferent between one-year and fifty-year assets. But 

in the long run, commodity prices will adjust downward so that the 

economic profit on all machines is zero. Since the value added by 

machines can decrease by a larger percentage, consistent with zero 

economic profit, for a fifty-year asset than for a one-year asset, 

the adjustment process clearly creates a competitive advantage for 

long-lived assets. Thus when we stimulate investment by proportionately 

increasing the after-tax rate of return on all assets, we also 

stimulate the use of long-lived assets which embody a larger capital 

services component. 
- 10 -

TABLE 2 

Service Lives (in years) 

Item of Expense 1 5 50 

Cost of machine 109 400 1000 

Interest or "normal" return (10%)

Economic profit (assumed zero in 

11 40 100 

initial equilibrium) 0 0 0 

Depreciation

Value added by machine (rental 

109 80 20 

cost of machine) 120 120 120 

REDUCE INTEREST RATE OR "NORMAL" RETURN BY 50 PERCENT - SHORT RUN RESULT 

Cost of machine 109 400 1000 

Interest or "normal" return (5%) 5.5 20 50 

Economic profit, before commodity 

prices change 5.5 20 50 

Depreciation 109 80 20 

Value added by machine, before 

commodity prices change (rental 

cost plus economic profit on 

machine) 120 120 120 

of machine 5% 5% 5% 

Economic profit as percent of cost 

REDUCE INTEREST RATE OR 1 1 ~ ~ RETURN ~ ~ 1 BY1 50 PERCENT - LONG RUN RESULT 

Cost of machine 109 400 1000 

Interest or "normal" return (5%)

Economic profit (assumed zero in 

5.5 20 50 

new equilibrium) 

Depreciation

Value added by machine, after 

0 

109 

0 

80 

0 

20 

commodity prices change (rental 

cost of machine)

Percent decrease in value added 

114.5 100 70 

by machine, after commodity 

prices change 4.6% 16.7% 41.7% 
- 11 -

IV. COMPARISON OF THE TWO CRITERIA 

White and White 16, p. 1101 contend that a proportionate 

reduction in the rental cost of capital "would have no 

substitution effect among capital assets". In fact, a proportionate 

reduction in the rental cost of all assets would bias the source 

of capital services towards assets with shorter lives and thus 

a small capital service component in their annual cost (as 

illustrated in Table 1). A neutral tax incentive designed to 

encourage the use of capital services should instead encourage the 

substitution of long-lived assets for short-lived assets. As 

Gaffney [2, p. 341 has indicated, long-lived assets are more 

capital-intensive than short-lived ones, and thus "the market 

solves the glut of capital by letting it be sequestered in long 

maturities". Bailey [l, pp. 140-441 has pointed out that the mix 

of investment naturally shifts towards long-lived assets during 

recessions when the interest rate falls. In conclusion, I 

believe that a neutral tax incentive designed to increase 

uniformly the use of capital services should not provide a 

proportionate reduction in the rental cost, but should instead 

provide a proportionate reduction in the "normal" rate of 

return. 
- 12 -

One final way to see that the rate of return is the 

appropriate neutrality criterion is to examine what happens 

when an investment incentive is provided in a world where savings 

are completely inelastic and aggregate demand is maintained. 

In such a world an investment incentive increases investment 

demand, but there is no increase in total investment. Rather 

the interest rate is bid up until the demand for investment again 

equals the fixed amount of savings. Only if the investment 

incentive increases proportionately the rate of return on all 

investment will the bidding up of the interest rate just offset 

(or neutralize) the increase in the rate of return, thus insuring 

no change in the durability of investment. Clearly if total 

investment does not change, we do not want the durability of 

investment to change. 
- 13 -

V. NEUTRAL INVESTMENT TAX CREDIT 

If a proportionate decline in the rental cost were the appropriate 

criterion for a neutral tax incentive, then an investment tax credit with 

a basis adjustment would be neutra1.i' However, if a uniform increase in 

the rate of return is the right criterion, then the tax credit, with or 

without a basis adjustment, should be lower for short-lived assets 

than for long-lived assets. 

Given some assumptions, we can derive values for a neutral investment tax credit (defined with reference to the rate of return criterion) 

for assets of different lives, assuming there is no basis adjustment for 

51 

purposes of calculating depreciation allowances.- We need to solve for 

a tax credit, k, which has the same impact on the rental cost of capital 

as a reduction in the required after-tax rate of return from r to r'. 

Based on equation (l), the neutrality condition may be stated as: 

Equation (3) may be solved for k: 

k= [(r +6)(1 - uz) - (r' +S)(l - UZ')~ (4)

r +6 

Note that if r were reduced to r', z would be increased to z', and the 

value of z' must therefore be used to calculate the appropriate level of k. 

Assume the following values: 

r = .10 

r' = .08 
- 14 -

6 = 2/n 

n = tax life in years 

u = .48 

n . 

z = c dt . 

t=l (l+r) 

n 

d, = depreciation in year t per dollar of original cost, 

assuming the sum-of-years digits method of depreciation. 

If an asset with a life of 5 years received a 4 percent credit, then a 

neutral credit, k, would have the rates shown in Table 3 for assets 

of different durabilities. Given the above assumptions, assets with a 

10-year life (about the average tax life for machinery and equipment) 

would receive a 6.5 percent tax credit which is very close to the permanent 

rate of the investment tax credit, namely, 7 percent. The 2.7 percent 

rate for assets with a 3-year life would be slightly higher than the 

2-1/3 percent rate permitted under present law (which reduces the credit 

for assets with useful lives of less than 7 years). Assets with a 5-

year life would have a rate somewhat below the 4-2/3 percent rate permitted under present law. 
- 15 -

TABLE 3 

Life of asset 

in years 

3 

5 

7 

10 

12 

15 

20 

Neutral Investment 

Tax Credit 

(percent of 

asset cost) 

2.7% 

4.0 

5.1 

6.5 

7.3 

8.4 

9.9 

"Permanent" Invest­ ment Tax Credit 

(percent of 

asset cost) 

2.3% 

4.7 

7.0 

7 .O 

7.0 

7.0 

7 .O 

"Temporary" Invest­ ment Tax Credit 

(percent of 

asset cost) 

3.3% 

6.7 

10.0 

10.0 

10.0 

10.0 

10.0 
- 16 -

FOOTNOTES 

Emil M. Sunley, Jr. is a Senior Fellow at the Brookings Institution. The views expressed are those of the author and are not 

necessarily those of other staff members, officers, or trustees of the 

Brookings Institution. 

This paper was prepared for the Tenth Annual Conference of the 

Committee on Taxation, Resources, and Economic Development at Madison, 

Wisconsin, October 24-26, 1975. Discussions with Nicolaus Tideman 

greatly clarified my own thinking on the issues in this paper. He 

also has discussed the issue of neutrality in a recent paper [5]. 

A’Most of the discussion which follows will be about neutral tax 

incentives for investment. The conclusions are equally applicable to 

neutral tax disincentives. 

Z’This particular formulation of the rental cost is only valid if 

the loss in the value of the asset follows the pattern of geometric 

decay. A more general formulation of the rental cost would not change 

the argument of this paper. 

’This statement and what follows assume that all investments 

are of equal risk and, therefore, the issue of differential riskiness 

is not addressed. 

L’As mentioned before, if one maintains the definition of tax 

neutrality as a tax change that does not disturb relative prices within 

any group of goods, then the rental cost criterion has considerable 

appeal as a neutrality criterion. 

Z’This derivation follows Tideman [5]. 
- 17 -

REFERENCES 

1. Bailey, Martin J., National Income and the Price Level, McGraw-Hill 

Book Company, 1971. 

2. Gaffney, Mason, "Taxation to Make Jobs by Activating Wealth," to be 

published in Arthur Lynn, Jr. (Editor), Property Taxation, Land 

Use and Public Policy. 

3. Hall, Robert E. and Jorgenson, Dale W., "Tax Policy and Investment 

Behavior," The American Economic Review, June 1967, pp. 391-414. 

4. Sunley, Emil M., Jr., "Towards a More Neutral Investment Tax Credit," 

National Tax Journal, June 1973, pp. 209-20. 

5. Tideman, T. Nicholaus, "Refinements in the Formula for the Price of 

Capital Services and Their Application to Tax Neutrality," 

(Unpublished paper, 1975). 

6. White, Melvin and White, Anne, "Tax Neutrality of Instantaneous versus 

fl, Economic Depreciation," in Richard M. Bird and John G. Head,

University of Toronto Press, 1972, pp. 105-116.