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Tax policy, capital use, and investment incentives
Journal
of Public
Economics
TAX POLICY,
12 (1979) 191-204.
CAPITAL
of British
Received October
Publishing
USE, AND INVESTMENT
William University
0 North-Holland
Company
INCENTIVES
E. SCHWORM*
Columbia,
Vancouwr.
1978, revised version
B.C., Canada
V6T
1 WS
received June 1979
In this paper, we investigate the effect of a corporate income tax on the utihzatlon and maintenance of capital and on the demand for capital stock and services. We find that a tax that allows interest deductions is distortionary unless allowable depreciation depends on the firm’s utilization and maintenance decisions. Also, we show that the usual demand equation for capital stock is misspecitied if capital utilization is not a technological constant.
1. Introduction The use of tax policy to affect the aggregate demand for capital is a common practice in most modern economies. In the United States, changes in the corporate tax rate, accelerated depreciation, and investment tax credits have been specifically designed as inducements to purchase capita! equipment [Fromm (1971)]. Following the paper of Hall and Jorgenson (1967), there has been extensive research attempting to measure the investment incentives provided by tax policy [Coen (1968, 1969), Eisner (1969), Hall and Jorgenson (1969), Fromm (1971), King (1972)]. In these investigations, the possibility that tax policy has altered the utilization and maintenance of capital equipment has been ignored. Capital deterioration and capital operating costs have been treated as technological constants that are unaffected by production decisions. Nadiri and Rosen (1969, 1973) have demonstrated the importance of the interaction between capital utilization and investment decisions. The effect of maintenance decisions on investment has been estimated by Bitros (1976). Since the utilization of capital in the U.S. is quite variable [Foss (1963), Perry (1973)], ignoring capital use can lead to erroneous estimates of tax policy’s influence on investment. In this paper we investigate the investment incentives provided by tax policy when a firm is able to vary the rate of utilization and maintenance of capital equipment. We assume that the utilization and maintenance of machines affects their physical deterioration and the inputs required to operate the machines. Therefore, in our model the cost of owning and *I have benefited from suggestions by Richard Hartman, Jonathan Kesselman, Erwin Diewert, Charles
Blackorby
and an anonymous
referee.
192
W.E. Schworm,
Tax polic)
operating capital depends on production decisions that can be influenced by tax policy. Models of capital use have been analyzed previously in Smith (1969), Taubman and Wilkinson (1970), and Schworm (1977).’ The issue of whether or not taxes affect resource allocation has been extensively discussed in the literature [Samuelson (1964) Stiglitz (1973, 1976), King (1974, 1975) Boadway (1978)]. In section 3 we show that if capital utilization and maintenance are variable, then an income tax that allows the deduction of interest payments and specifies depreciation allowances independently of actual capital use necessarily distorts production decisions. A tax system with interest deductibility is neutral if and only if the firm is allowed to deduct the actual economic depreciation that results from capital use decisions. Finally, we show that a tax system that does not allow interest deductions but does allow the immediate write-off of capital expenditures is nondistortionary. In section 4, we show that changes in the tax rate, depreciation allowances, and investment tax credit have an indeterminate qualitative effect on capital utilization and maintenance. As a consequence, accelerated depreciation or an investment tax credit can either increase or decrease the demand for capital stock. Therefore, predicting the effect of tax policy on capital use and capital purchases requires detailed knowledge of the influence of capital use on operating costs and capital deterioration. In section 5, we investigate the effect of tax incentives on the demand for capital’ stock. We show that the demand for capital stock cannot be expressed as a function of a rental price of capital.’ As a consequence, the influence of tax parameters on the capital stock cannot be captured by an implicit rental price of capital. This implies that the models used by Hall and Jorgenson (1967, 1969, 1971), Bischoff (1971), and Coen (1968, 1969, 1971) are misspecilied if capital utilization and maintenance are variable. 2. The model In this section we describe a model of firm behavior that incorporates the firm’s choice of utilization and maintenance of capital equipment. Tax parameters are included in the model to represent (1) the deductibility of interest payments, (2) the deductibility of capital depreciation allowances, and (3) the investment tax credit. Our treatment of the tax system closely follows the analysis of Hall and Jorgenson (1967). Output is determined by the vector of variable inputs, x, and the capital services, k, obtained from the stock of capital. The production function, ‘For models with a more general specification of the effect of utilization on capital deterioration, see Diewert (1977) and Epstein (1977). Models that assume variable capital utilization is an adjustment to rhythmical movements in factor prices have been analyzed by Winston (1974) and Winston and McCoy (1974). ‘This point has been made by Taubman and Wilkinson (1970).
W:E.Schworm, Tax polic!
19.3
F(x, k), is smooth and strictly concave. The gross profit function for the firm specifies the optimal profit the firm can achieve by the choice of variable inputs for a given quantity of capital services [Gorman (1968)]. The gross profit function is defined as (I) where p is the price of output and w is a vector of factor prices associated with x. The rate of capital utilization, U, is defined as the capital services obtained from a machine in a single time period. If a firm owns capital stock, K, that yields the capital services, k, then utilization is given by u= k/K. The maintenance per unit of capital is denoted by m. Capital utilization and maintenance affect the cost of capital services by influencing the physical deterioration of capital and the input requirements for operating capital. We discuss each of these effects in turn. As capital ages, its efficiency in production deteriorates. The rate of capital deterioration is specified as a smooth, strictly convex function of utilization and maintenance, 6(u, m), with 6,>0 and 6, ~0.~ The deterioration of capital increases with increases in utilization and decreases with increases in maintenance. For many types of machines certain inputs are required in fixed proportions to operate the machines. We suppose that capital services are produced by combining machines with fuel. The fuel required to operate a machine is specified as a smooth, strictly convex function of utilization and maintenance, u(u,m), with a,>0 and a,
of funds but debt is being
the tax saving
associated
with buying
a unit of capital
is rqz where
~(t)=jexp[-r(l-r)(s-r)]d(t,s)ds.
(2)
In addition, a firm can deduct a proportion 6, of current capital expenditures from the current tax payment. The acquisition cost of a unit of capital, denoted q(l - sz -O), is the market price of capital less the present value of the depreciation allowances and the tax credit. The cost of capital services consists of a charge for operating machines and a charge for owning machines. Assuming that the acquisition cost of capital is constant over time, the cost of owning a machine consists of an interest charge plus a capital deterioration charge: (3)
%?=(r(l-T)+d(U,Wl))q(l-TZ-0).
The cost of operating
a machine
is the expenditure
for fuel and maintenance:
0=ca(u,m)+sm,
(4)
where c is the price of fuel and s is the price of maintenance. cost of capital services, $‘(ti,m) is the after tax operating ownership costs per unit of capital services:
If all tax parameters
are zero, then the cost of capital
services
The after tax costs plus the
is denoted
by
$(n, m). The expression (5) for the cost of capital services differs from the usual one [Jorgenson (1963), Hall and Jorgenson (1967)] in that the cost of capital services depends on the firm’s capital use decisions. Changes in utilization and maintenance affect capital deterioration and operating costs and, thereby, affect the cost of capital services. Also, we have included machine operating costs in the cost of capital services. The distinction between operating and ownership costs is important since operating costs are fully deductible while capital expenditures are depreciated over time. The after tax profit is the after tax gross profit less the after tax cost of the obtained capital services:
The firm chooses capital services, utilization, and maintenance to maximize after tax profit. If tax parameters, r, z, and 0, are zero, then profit is denoted
W.E. Schworm, Tax policy
195
by Il. An examination of the profit function in (6) reveals that capital utilization and maintenance affect profit only by affecting the cost of capital services. Therefore, the firm chooses utilization and maintenance to minimize the cost of capital services. The quantity of capital services is chosen to maximize profit conditional on the optimal choices of utilization and maintenance. This recursive structure of the optimization problem is a consequence of the firm’s ability to obtain additional capital services either by purchasing additional machines or by increasing the utilization of the existing machines. The choice between increased utilization and increased capital stock is made to minimize the cost of capital services. In our model, tax policy has several different effects on capital expenditures. First, changes in the tax parameters directly affect the cost of capital services by affecting the acquisition cost of capital and the cost of funds. Secondly, the different tax treatment of operating costs and capital expenditures induces changes in capital utilization and maintenance and, therefore, depreciation. The tax induced changes in capital use and depreciation cause changes in the capital stock required to produce a given level of capital services and cause changes in capital replacement requirements. In the following sections we investigate the incentives provided by tax policy for capital expenditures.
3. Tax neutrality In this section we examine the conditions under which tax policy does not affect production decisions if the firm can choose the utilization and maintenance of capital. The neutrality conditions depend critically on the information available to the tax authorities when the tax parameters are chosen. First, we assume that the depreciation allowances, the tax credit, and the tax rate are specified by the tax authorities prior to the firm’s capital use decisions. In addition, we assume that the tax parameters are chosen independently of market prices. We want to determine if the tax authorities can choose values of 5, z, and 0 that do not distort the capital use decisions or the factor demand decisions.’ The firm chooses utilization and maintenance to minimize the cost of capital services. The after tax cost of capital services can be written as
-T6(U,
m)) .
(7)
5We do not consider the movement of firms among industries in response to tax parameter changes. Therefore, our results apply to a short run in which the base of a pure profit tax is not eroded.
Capital use decisions are unaffected prices if and only if the term
Z((r(l-7)+6(
by tax parameters
for any set of market
U,m))(TZ+6)-Td(U,m)j
is unaffected by variations in capital utilization and maintenance. Therefore, necessary and sufficient conditions for the neutrality of tax parameters with respect to capital use are that (72+0-~))6,u=
((r(l-r)+6(~,m))(~z+fI-76(u,m)J
(9)
and (TZ+B-T)S,=O
(10)
for all values of (u,m). The neutrality conditions (9) and (10) can be satisfied for all prices and all choices of capital use if and only if tax parameters satisfy the following conditions:
(11)
TZ+H=T
and
rz+e=--
Td(U,
WZ)
41 -T)+d(U,Wl
1’
(12)
The first condition states that the present value of tax depreciation plus the tax credit 7~ +8 must equal the tax saving from an immediate write-off of capital expenditures. The second condition states that tz+H must equal the present value of a deduction of the current rate of economic depreciation in each future time period. Notice that this is not equal in general to the present value of future economic depreciation since depreciation can change over time in response to price changes. An alternative interpretation of (12) is that the current rental value of tax allowances, (TZ+e)(r(l -T)+~(u, m)), must be equal to the current tax saving from allowing economic depreciation, 744 m). Conditions (11) and (12) indicate that capital use neutrality requires both immediate expensing and economic depreciation of capital expenditures. Combining (11) and (12) reveals that this is possible if and only if 7r( l-7) =O, i.e. if and only if 7 = 1 or 7 =O. If 0 < 7 < 1 and tax parameters are set independently of market prices and capital use, then any tax policy with interest deductibility distorts capital use decisions.
197
W.E. Schworm, Tax policy
Next, suppose that in determining tax parameters the tax authorities have and use information on market prices and the cost of capital services function, tiT(n,rn). In this case the tax authorities know the actual capital use decisions and depreciation that would result from any set of tax parameters. We continue to assume, however, that tax parameters must be specified prior to capital use decisions. Capital use neutrality requires in this case that (8) be unaffected by variations in utilization and maintenance in the neighborhood of the neutral capital use values. Therefore, conditions (9) and (10) must be satisfied for the values of utilization and maintenance that minimize the neutral cost of capital services, $(u,m). The neutrality condition for maintenance (10) implies immediate expensing is required. This and the neutrality condition for utilization imply that economic depreciation is required. Therefore, the additional information is of no help in achieving neutrality. These results are summarized in the following proposition. Proposition 1. If interest payments are tax deductible, 0
7
and O-CT < 1, then a are chosen to satisfy
198
W.E. Schworm.
ikr
policy
This condition for neutrality is similar to the neutrality condition in models without endogenous capital depreciation [Samuelson (1964), Hall and Jorgenson (1971), King (1975), Stiglitz (1976)]. Our condition, however, must hold for whatever rate of capital depreciation results from a firm’s capital use decisions. Therefore, in our model neutrality requires that capital depreciation allowances be endogenous to the firm. When making capital use decisions, the firm must recognize that allowable depreciation will be set ex post to equal economic depreciation. The practical difficulties of implementing a nondistortionary corporate income tax when capital use is not variable have been widely recognized [e.g. Smith (1963)]. These difficulties are greatly compounded when economic depreciation is endogenous. For an income tax with interest deductibility to be neutral, the tax authorities must be able to observe the actual rate of depreciation of capital equipment. This task is complicated by the fact that capital depreciation varies in response to changes in market prices and tax parameters. If capital depreciation is exogenous, then it is well known that a tax scheme without interest deductibility and with immediate expensing of capital expenditures is nondistortionary [Smith (1963). King (1975), Stiglitz (1976)]. We show that this result is true even if utilization and maintenance and, therefore, capital depreciation are endogenous. If interest is not deductible, then the cost of funds is r. In this case the cost of capital services can be written as
(13)
Capital use is unaltered by the tax parameters if and only if sz+Q=t. That is to say, the depreciation allowance plus the tax credit must provide the same tax saving as the immediate expensing of capital expenditures. Proposition write-off tax credit)
3.
If
interest
of all capital is necessar!,
payments
expenditures
are
not
deductible,
(or equicalent
und sgjjicient
then
depreciation
the
immediate
ullowances
plus
,ftir neutrality.
This result indicates that neutrality can be achieved with a simple and practical tax system. The tax parameters can be set independently of capital use decisions and market prices. Also, the tax authorities do not need any information about the actual depreciation of capital.
4. The effect of tax policy on capital use In this section
we investigate
the effect of tax parameters
on capital
use
WE. Schworm, Tax policy
199
decisions. The firm chooses utilization and maintenance to minimize the cost of capital services as given in (5). Since the tax rate is exogenous, capital use decisions minimize the following:
~=C(ca(u,m)+sni+(rT+6(u.m))qT},
(14)
where rT=r(l-r) and qT=q(l -tz-O)/(l -r). The first order conditions for this problem are ca”+qrS,=$r/(l-r)
(15)
s+ca,+qT6,=0.
(16)
and
The first equation states that utilization and maintenance are chosen so that the marginal cost of utilization equals the cost of capital services. Since the firm can increase capital services either by increasing utilization or by purchasing new machines, the marginal costs of obtaining capital services by each method are equated. An increase in maintenance increases maintenance expenditures, reduces fuel requirements, and reduces capital deterioration. The second equation states that these marginal effects must sum to zero. The necessary conditions (15) and (16) can be solved for the capital utilization and maintenance equations
u* = ‘(i (c, s, rT, 4’)
(17)
m* = ./H (c, s, rT, qT).
(18)
and
Since the capital use decisions are separable from the factor demand decisions, utilization and maintenance depend only on a subset of the prices in the model. Also, these equations indicate that tax policy influences capital use by altering the cost of funds, rT, and the acquisition cost of capital, qT. To determine the influence of tax parameters on capital use decisions, we compute the partial derivatives of (17) and (18). Performing ordinary comparative static calculations with (15) and (16) yields the following results:
(19)
(20)
200
WE. Schwarm, Tax policy
(21)
(22) where H is the Hessian matrix for {ca(u, m)+qTG(u, m)} and Hij is the (i,j) term of this matrix. In general, little can be said about the qualitative effects of tax parameters on capital utilization and maintenance. A change in either r, z or 8 affects the marginal cost of utilization, the marginal benefit of maintenance, and the cost of capital services. The effect of a tax parameter change depends on the relative magnitude of these changes. For example, an increase in the acquisition cost of capital, caused by a decrease in either z or 8, increases the cost of capital services, GT/(l -r), but also increases the marginal cost of benefit of maintenance, ca, +qT6,. utilization, ca, + qT6,, and the marginal The net effect depends on the interaction between utilization and maintenof 6, relative to (rT+h)/u. In addition, ance, ca,, + qTdUm, and the magnitude and capital the qualitative effects of tax policy on fuel consumption deterioration are indeterminate. There are several special cases of our model that are of some interest. First, suppose there are no inputs required to operate machines so that a(u, m)-0. Then, by using (15) and (16) in (19) and (21), one can derive
The effects are still ambiguous owing to the interaction of utilization and maintenance. Secondly, suppose a(u, m) 2 0 but a, = 6, =0 so that maintenance does not enter the model. Then, by substituting from (15) and (16) into (19) and (21), we derive (24)
If no fuel is required for machines that generate no services, then (a,-U/U) >O. In this case an increase in the acquisition cost of capital increases the utilization of capital. Finally, if there is no input requirement and no maintenance, then (15) and (19) imply that variations in qT have no effect on utilization. To determine the effect of tax policy in the general model on capital use, fuel requirement, and depreciation, one needs detailed information on the fuel requirement function and the deterioration function.
W.E.Schworm, Tux polic)
201
5. The demand for capital services and capital stock The firm chooses capital services to maximize profit given that capital decisions have been made to minimize the cost of capital services: maxn*/(l-t)=g(p,w,k)-Il/*k,
use
(25)
where $* = min IclT(u,m)/( 1 -r). u.m The capital
service demand
function
can be expressed
k*=k(p,w,II/*).
as follows: (26)
The demand for capital services is a function of the output price, the variable factor prices, and the minimal cost of capital services. The cost imputed to capital services is conditional upon the cost minimizing choices of utilization and maintenance. This optimal cost of capital services acts as a summary statistic by capturing the effect of (c,s, rT,qT) on the demand for capital services. Tax policy affects the demand for capital services only by influencing the cost of capital services. The effect of tax parameters on the cost of capital services can be determined from the effects of qT and rT:
w* l?qT -
rT+6*
----00; U*
(7**
T
-2>o.
2rT
U*
(27)
An increase in the present value of allowable depreciation or an increase in the investment tax credit reduces qT and, therefore, reduces the cost of capital services. An increase in the tax rate has an indeterminate effect on the cost of capital services since it has an ambiguous effect on qT and also affects rT. The demand for capital services increases if the cost of capital services declines. Therefore, accelerated depreciation and an investment tax credit cause an increased demand for capital services. These results relating tax policy to the demand for capital services are similar to results others have derived for the demand for capital stock [Hall and Jorgenson (1971). Coen (1968), Sumner (1973)]. The differences between our model and models that ignore capital use are revealed when the demand for capital stock is investigated. The demand for capital stock is determined by the demand for capital services and the optimal rate of capital utilization:
QJ~wIC/*)=rc(p,w,c,s,rT,qT).
K*=
(28)
42 (c, s, rT, qT)
The optimal maximization
capital problem:
stock
K*
is the
solution
to
the
following
profit
LIT
----=g(p,w,u*K)-u*$*K. “,““(I -5)
(29)
An important implication of our model is that the demand for capital stock cannot be expressed as a function of p,~, and a rental price of capital. The prices, c, s, rT, and qT enter the demand function separately. Variations in these prices have different effects on the demand for capital stock since they have different effects on capital utilization. Therefore, the specification of the desired capital stock employed in Hall and Jorgenson (1967, 1969, 1971), Coen (1968, 1969, 1971) and Bischoff (1971) is inconsistent with the variability of capital use. The effect of the tax parameters on the capital stock can be decomposed into their effect on the demand for capital services and their effect on capital utilization : ?K” ?qT -u*
1 ?k* ;$* (?$* ‘;qT
K*iu* o u* c?~T’ ’
(30)
An increase in z or 0 causes a reduction in the acquisition cost of capital. This induces an increase in the demand for capital services but can either increase or decrease capital utilization. Therefore, the demand for capital stock can either increase or decrease in response to accelerated depreciation or increased investment tax credits. An increase in the tax rate causes rT to fall but has an ambiguous effect on qT. Therefore, an increase in the tax rate can either increase or decrease the demand for capital stock. The effect of ignoring variations in capital utilization is apparent in eqs. (30) and (31). If capital utilization is independent of prices, then the second terms on the right-hand side of (30) and (31) are zero. Changes in the capital stock induced by price variations are scalar multiples of the changes in capital service demand. If capital utilization adjusts to price changes but the variations in utilization are ignored, then estimates of tax incentives are biased. The direction of the bias depends on the properties of the fuel requirement function and the deterioration function.
WE.Schworm,
Tux policy
203
6. Concluding remarks There are several issues pertinent to tax policy and investment incentives that have not been dealt with in this paper. First, we have ignored factors that cause lagged capital adjustments such as costs of adjustment or irreversibilities. If the capital stock only gradually adjusts to parameter changes, then our model pertains only to the desired or long-run capital stock. Hartman (1978) and Boadway (1979) have analyzed the investment incentives provided by tax policy when there are capital adjustment costs. Capital use decisions could be included in such a model. Secondly, we have not considered the complex issues involved in determining the optimal financial structure of the firm. Capital use and financial structure do not appear to be complementary issues and probably should be investigated separately. This has led us, however, to give an exceedingly simplistic treatment to the cost of funds [King (1974)]. Thirdly, we have employed the usual assumptions of no subjective uncertainty and static expectations with respect to the cost of capital. The assumption of static expectations is easily relaxed but this does not add any interesting results. The consideration of uncertainty only adds to the analysis if either firms are risk averse or there are lagged capital adjustments. Either of these modifications would greatly complicate the analysis. Finally, we have ignored the general equilibrium aspects of the problem. Our most serious assumptions in this regard are that the before tax interest rate and the price of new capital goods are independent of tax parameters. Also, we have ignored the long-run allocation of firms among industries. Asimakopulos and Burbidge (1975) have discussed the interindustry movements of firms in response to tax policy. Christensen (1970) and Klein and Taubman (1971) have attempted to analyze tax policy in general equilibrium models. References Asimakopulos, A. and J.B. Burbidge, 1975, Corporate taxation and the optimal investment decisions of firms, Journal of Public Economics 4, 281-287. Bischoff, Charles W., 1971, The effect of alternative lag distributions, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 61-130. Bitros, G.C., 1976, A statistical theory of expenditures in capital maintenance and repair, Journal of Political Economy 84, 917-936. Boadway, Robin, 1978, Investment incentives, corporate taxation, and efticiency in the allocation of capital, The Economic Journal 88, 47tS481. Boadway, Robin, 1979, Corporate taxation and investment: A synthesis of the neo classical theory, Discussion Paper No. 324, Queen’s University, Kingston, Ontario. Christensen, Laurits R., 1970, Tax policy and investment expenditures in a model of general equilibrium, American Economic Review 2, 18-22. Coen, Robert M., 1968, Effects of tax policy on investment in manufacturing, American Economic Review 2, 20&211. Coen, Robert M., 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 370-379.
Coen, Robert M., 1971. The effect of cash flow on the speed of adjustment, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution. Washington, D.C.) 131-196. Diewert, W.E., 1977, Walras’ theory of capital formation and the existence of a temporary equilibrium, in: G. Schwodiauer, ed.. Equilibrium and disequilibrium in economic theory (D. Reidel, Dordrecht, Holland) 733126. Epstein, Larry G., 1977, Essays in the economics of uncertainty, Ph.D. Dissertation, University of British Columbia. Eisner, Robert, 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 3799388. Foss, M.F., 1963. The utilization of capital equipment: Postwar compared with prewar, Survey of Current Business, 8816. Fromm, Gary, ed., 1971, Tax incentives and capital spending (The Brookmgs Institution, Washington, D.C.). Gorman, William M., 1968, Measuring the quantity of fixed factors, in: J.N. Wolfe, ed., Value, capital, and growth (Edinburgh U. Press, Edinburgh) 141~~172. Hall, Robert E. and Dale W. Jorgenson, 1967, Tax policy and investment behavior, American Economic Review 3, 391-414. Hall, Robert E. and Dale W. Jorgenson, 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 3888401. Hall, Robert E. and Dale W. Jorgenson, 1971, Application of the theory of optimum capital accumulation, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 9960. Hartman, Richard, 1978, Investment neutrality of business income taxes, Quarterly Journal of Economics, 2455260. Jorgenson, Dale W., 1963, Capital theory and investment behavior, American Economic Review 2, 2477259. King, Mervyn A., 1972. Taxation and investment incentives in a vintage investment model, Journal of Public Economics I, 121-147. King, Mervyn A., 1974, Taxation and the cost of capital, Review of Economic Studies 41, 21-35. King, Mervyn A., 1975, Taxation, corporate financial policy, and the cost of capital, Journal of Public Economics 4, 271-279. Klein, L.R. and Paul Taubman, 1971, Estimating effects within a complete econometric model, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 197-242. Nadiri, M.J. and S. Rosen, 1969, Interrelated factor demand functions, American Economic Review 4, 457-571. Nadiri, M.J. and S. Rosen, 1973, A disequilibrium model of demand for factors of production (National Bureau of Economic Research, New York). Perry, George L., 1973, Capacity in manufacturing, Brookmgs Papers on Economic Activity 3, 701-742. Samuelson, Paul A., 1964, Tax deductibility of economic depreciation to insure invariant valuations, Journal of Political Economy 6, 604-606. Schworm, W.E., 1977, User cost and the demand for capital, Discussion Paper 77-22, University of British Columbia. Smith, K.R., 1969, The effect of uncertainty on monopoly price, capital stock, and utilization of capital, Journal of Economic Theory 1, 48859. Smith, Vernon L., 1963, Tax depreciation policy and investment theory, International Economic Review 1, 8&91. Stiglitz, Joseph E., 1973, Taxation, corporate financial policy, and the cost of capital, Journal of Public Economics 2, l-34. Stiglitz, Joseph E., 1976, The corporation tax, Journal of Public Economics 5, 3033311. Sumner, M.T., 1973, Investment and corporate taxation, Journal of Political Economy 4, 982m 993. Taubman, Paul and Maurice Wilkinson, 1970, User cost, capital utilization, and investment theory, International Economic Review 2, 209215. Winston, Gordon C., 1974, The theory of capital utilization and idleness, Journal of Economic Literature 4, 1301-1320. Winston, Gordon C. and Thomas 0. McCoy, 1974, Investment and the optimal idleness of capital, Review of Economic Studies 4, 419-428.
of Public
Economics
TAX POLICY,
12 (1979) 191-204.
CAPITAL
of British
Received October
Publishing
USE, AND INVESTMENT
William University
0 North-Holland
Company
INCENTIVES
E. SCHWORM*
Columbia,
Vancouwr.
1978, revised version
B.C., Canada
V6T
1 WS
received June 1979
In this paper, we investigate the effect of a corporate income tax on the utihzatlon and maintenance of capital and on the demand for capital stock and services. We find that a tax that allows interest deductions is distortionary unless allowable depreciation depends on the firm’s utilization and maintenance decisions. Also, we show that the usual demand equation for capital stock is misspecitied if capital utilization is not a technological constant.
1. Introduction The use of tax policy to affect the aggregate demand for capital is a common practice in most modern economies. In the United States, changes in the corporate tax rate, accelerated depreciation, and investment tax credits have been specifically designed as inducements to purchase capita! equipment [Fromm (1971)]. Following the paper of Hall and Jorgenson (1967), there has been extensive research attempting to measure the investment incentives provided by tax policy [Coen (1968, 1969), Eisner (1969), Hall and Jorgenson (1969), Fromm (1971), King (1972)]. In these investigations, the possibility that tax policy has altered the utilization and maintenance of capital equipment has been ignored. Capital deterioration and capital operating costs have been treated as technological constants that are unaffected by production decisions. Nadiri and Rosen (1969, 1973) have demonstrated the importance of the interaction between capital utilization and investment decisions. The effect of maintenance decisions on investment has been estimated by Bitros (1976). Since the utilization of capital in the U.S. is quite variable [Foss (1963), Perry (1973)], ignoring capital use can lead to erroneous estimates of tax policy’s influence on investment. In this paper we investigate the investment incentives provided by tax policy when a firm is able to vary the rate of utilization and maintenance of capital equipment. We assume that the utilization and maintenance of machines affects their physical deterioration and the inputs required to operate the machines. Therefore, in our model the cost of owning and *I have benefited from suggestions by Richard Hartman, Jonathan Kesselman, Erwin Diewert, Charles
Blackorby
and an anonymous
referee.
192
W.E. Schworm,
Tax polic)
operating capital depends on production decisions that can be influenced by tax policy. Models of capital use have been analyzed previously in Smith (1969), Taubman and Wilkinson (1970), and Schworm (1977).’ The issue of whether or not taxes affect resource allocation has been extensively discussed in the literature [Samuelson (1964) Stiglitz (1973, 1976), King (1974, 1975) Boadway (1978)]. In section 3 we show that if capital utilization and maintenance are variable, then an income tax that allows the deduction of interest payments and specifies depreciation allowances independently of actual capital use necessarily distorts production decisions. A tax system with interest deductibility is neutral if and only if the firm is allowed to deduct the actual economic depreciation that results from capital use decisions. Finally, we show that a tax system that does not allow interest deductions but does allow the immediate write-off of capital expenditures is nondistortionary. In section 4, we show that changes in the tax rate, depreciation allowances, and investment tax credit have an indeterminate qualitative effect on capital utilization and maintenance. As a consequence, accelerated depreciation or an investment tax credit can either increase or decrease the demand for capital stock. Therefore, predicting the effect of tax policy on capital use and capital purchases requires detailed knowledge of the influence of capital use on operating costs and capital deterioration. In section 5, we investigate the effect of tax incentives on the demand for capital’ stock. We show that the demand for capital stock cannot be expressed as a function of a rental price of capital.’ As a consequence, the influence of tax parameters on the capital stock cannot be captured by an implicit rental price of capital. This implies that the models used by Hall and Jorgenson (1967, 1969, 1971), Bischoff (1971), and Coen (1968, 1969, 1971) are misspecilied if capital utilization and maintenance are variable. 2. The model In this section we describe a model of firm behavior that incorporates the firm’s choice of utilization and maintenance of capital equipment. Tax parameters are included in the model to represent (1) the deductibility of interest payments, (2) the deductibility of capital depreciation allowances, and (3) the investment tax credit. Our treatment of the tax system closely follows the analysis of Hall and Jorgenson (1967). Output is determined by the vector of variable inputs, x, and the capital services, k, obtained from the stock of capital. The production function, ‘For models with a more general specification of the effect of utilization on capital deterioration, see Diewert (1977) and Epstein (1977). Models that assume variable capital utilization is an adjustment to rhythmical movements in factor prices have been analyzed by Winston (1974) and Winston and McCoy (1974). ‘This point has been made by Taubman and Wilkinson (1970).
W:E.Schworm, Tax polic!
19.3
F(x, k), is smooth and strictly concave. The gross profit function for the firm specifies the optimal profit the firm can achieve by the choice of variable inputs for a given quantity of capital services [Gorman (1968)]. The gross profit function is defined as (I) where p is the price of output and w is a vector of factor prices associated with x. The rate of capital utilization, U, is defined as the capital services obtained from a machine in a single time period. If a firm owns capital stock, K, that yields the capital services, k, then utilization is given by u= k/K. The maintenance per unit of capital is denoted by m. Capital utilization and maintenance affect the cost of capital services by influencing the physical deterioration of capital and the input requirements for operating capital. We discuss each of these effects in turn. As capital ages, its efficiency in production deteriorates. The rate of capital deterioration is specified as a smooth, strictly convex function of utilization and maintenance, 6(u, m), with 6,>0 and 6, ~0.~ The deterioration of capital increases with increases in utilization and decreases with increases in maintenance. For many types of machines certain inputs are required in fixed proportions to operate the machines. We suppose that capital services are produced by combining machines with fuel. The fuel required to operate a machine is specified as a smooth, strictly convex function of utilization and maintenance, u(u,m), with a,>0 and a,
of funds but debt is being
the tax saving
associated
with buying
a unit of capital
is rqz where
~(t)=jexp[-r(l-r)(s-r)]d(t,s)ds.
(2)
In addition, a firm can deduct a proportion 6, of current capital expenditures from the current tax payment. The acquisition cost of a unit of capital, denoted q(l - sz -O), is the market price of capital less the present value of the depreciation allowances and the tax credit. The cost of capital services consists of a charge for operating machines and a charge for owning machines. Assuming that the acquisition cost of capital is constant over time, the cost of owning a machine consists of an interest charge plus a capital deterioration charge: (3)
%?=(r(l-T)+d(U,Wl))q(l-TZ-0).
The cost of operating
a machine
is the expenditure
for fuel and maintenance:
0=ca(u,m)+sm,
(4)
where c is the price of fuel and s is the price of maintenance. cost of capital services, $‘(ti,m) is the after tax operating ownership costs per unit of capital services:
If all tax parameters
are zero, then the cost of capital
services
The after tax costs plus the
is denoted
by
$(n, m). The expression (5) for the cost of capital services differs from the usual one [Jorgenson (1963), Hall and Jorgenson (1967)] in that the cost of capital services depends on the firm’s capital use decisions. Changes in utilization and maintenance affect capital deterioration and operating costs and, thereby, affect the cost of capital services. Also, we have included machine operating costs in the cost of capital services. The distinction between operating and ownership costs is important since operating costs are fully deductible while capital expenditures are depreciated over time. The after tax profit is the after tax gross profit less the after tax cost of the obtained capital services:
The firm chooses capital services, utilization, and maintenance to maximize after tax profit. If tax parameters, r, z, and 0, are zero, then profit is denoted
W.E. Schworm, Tax policy
195
by Il. An examination of the profit function in (6) reveals that capital utilization and maintenance affect profit only by affecting the cost of capital services. Therefore, the firm chooses utilization and maintenance to minimize the cost of capital services. The quantity of capital services is chosen to maximize profit conditional on the optimal choices of utilization and maintenance. This recursive structure of the optimization problem is a consequence of the firm’s ability to obtain additional capital services either by purchasing additional machines or by increasing the utilization of the existing machines. The choice between increased utilization and increased capital stock is made to minimize the cost of capital services. In our model, tax policy has several different effects on capital expenditures. First, changes in the tax parameters directly affect the cost of capital services by affecting the acquisition cost of capital and the cost of funds. Secondly, the different tax treatment of operating costs and capital expenditures induces changes in capital utilization and maintenance and, therefore, depreciation. The tax induced changes in capital use and depreciation cause changes in the capital stock required to produce a given level of capital services and cause changes in capital replacement requirements. In the following sections we investigate the incentives provided by tax policy for capital expenditures.
3. Tax neutrality In this section we examine the conditions under which tax policy does not affect production decisions if the firm can choose the utilization and maintenance of capital. The neutrality conditions depend critically on the information available to the tax authorities when the tax parameters are chosen. First, we assume that the depreciation allowances, the tax credit, and the tax rate are specified by the tax authorities prior to the firm’s capital use decisions. In addition, we assume that the tax parameters are chosen independently of market prices. We want to determine if the tax authorities can choose values of 5, z, and 0 that do not distort the capital use decisions or the factor demand decisions.’ The firm chooses utilization and maintenance to minimize the cost of capital services. The after tax cost of capital services can be written as
-T6(U,
m)) .
(7)
5We do not consider the movement of firms among industries in response to tax parameter changes. Therefore, our results apply to a short run in which the base of a pure profit tax is not eroded.
Capital use decisions are unaffected prices if and only if the term
Z((r(l-7)+6(
by tax parameters
for any set of market
U,m))(TZ+6)-Td(U,m)j
is unaffected by variations in capital utilization and maintenance. Therefore, necessary and sufficient conditions for the neutrality of tax parameters with respect to capital use are that (72+0-~))6,u=
((r(l-r)+6(~,m))(~z+fI-76(u,m)J
(9)
and (TZ+B-T)S,=O
(10)
for all values of (u,m). The neutrality conditions (9) and (10) can be satisfied for all prices and all choices of capital use if and only if tax parameters satisfy the following conditions:
(11)
TZ+H=T
and
rz+e=--
Td(U,
WZ)
41 -T)+d(U,Wl
1’
(12)
The first condition states that the present value of tax depreciation plus the tax credit 7~ +8 must equal the tax saving from an immediate write-off of capital expenditures. The second condition states that tz+H must equal the present value of a deduction of the current rate of economic depreciation in each future time period. Notice that this is not equal in general to the present value of future economic depreciation since depreciation can change over time in response to price changes. An alternative interpretation of (12) is that the current rental value of tax allowances, (TZ+e)(r(l -T)+~(u, m)), must be equal to the current tax saving from allowing economic depreciation, 744 m). Conditions (11) and (12) indicate that capital use neutrality requires both immediate expensing and economic depreciation of capital expenditures. Combining (11) and (12) reveals that this is possible if and only if 7r( l-7) =O, i.e. if and only if 7 = 1 or 7 =O. If 0 < 7 < 1 and tax parameters are set independently of market prices and capital use, then any tax policy with interest deductibility distorts capital use decisions.
197
W.E. Schworm, Tax policy
Next, suppose that in determining tax parameters the tax authorities have and use information on market prices and the cost of capital services function, tiT(n,rn). In this case the tax authorities know the actual capital use decisions and depreciation that would result from any set of tax parameters. We continue to assume, however, that tax parameters must be specified prior to capital use decisions. Capital use neutrality requires in this case that (8) be unaffected by variations in utilization and maintenance in the neighborhood of the neutral capital use values. Therefore, conditions (9) and (10) must be satisfied for the values of utilization and maintenance that minimize the neutral cost of capital services, $(u,m). The neutrality condition for maintenance (10) implies immediate expensing is required. This and the neutrality condition for utilization imply that economic depreciation is required. Therefore, the additional information is of no help in achieving neutrality. These results are summarized in the following proposition. Proposition 1. If interest payments are tax deductible, 0
7
and O-CT < 1, then a are chosen to satisfy
198
W.E. Schworm.
ikr
policy
This condition for neutrality is similar to the neutrality condition in models without endogenous capital depreciation [Samuelson (1964), Hall and Jorgenson (1971), King (1975), Stiglitz (1976)]. Our condition, however, must hold for whatever rate of capital depreciation results from a firm’s capital use decisions. Therefore, in our model neutrality requires that capital depreciation allowances be endogenous to the firm. When making capital use decisions, the firm must recognize that allowable depreciation will be set ex post to equal economic depreciation. The practical difficulties of implementing a nondistortionary corporate income tax when capital use is not variable have been widely recognized [e.g. Smith (1963)]. These difficulties are greatly compounded when economic depreciation is endogenous. For an income tax with interest deductibility to be neutral, the tax authorities must be able to observe the actual rate of depreciation of capital equipment. This task is complicated by the fact that capital depreciation varies in response to changes in market prices and tax parameters. If capital depreciation is exogenous, then it is well known that a tax scheme without interest deductibility and with immediate expensing of capital expenditures is nondistortionary [Smith (1963). King (1975), Stiglitz (1976)]. We show that this result is true even if utilization and maintenance and, therefore, capital depreciation are endogenous. If interest is not deductible, then the cost of funds is r. In this case the cost of capital services can be written as
(13)
Capital use is unaltered by the tax parameters if and only if sz+Q=t. That is to say, the depreciation allowance plus the tax credit must provide the same tax saving as the immediate expensing of capital expenditures. Proposition write-off tax credit)
3.
If
interest
of all capital is necessar!,
payments
expenditures
are
not
deductible,
(or equicalent
und sgjjicient
then
depreciation
the
immediate
ullowances
plus
,ftir neutrality.
This result indicates that neutrality can be achieved with a simple and practical tax system. The tax parameters can be set independently of capital use decisions and market prices. Also, the tax authorities do not need any information about the actual depreciation of capital.
4. The effect of tax policy on capital use In this section
we investigate
the effect of tax parameters
on capital
use
WE. Schworm, Tax policy
199
decisions. The firm chooses utilization and maintenance to minimize the cost of capital services as given in (5). Since the tax rate is exogenous, capital use decisions minimize the following:
~=C(ca(u,m)+sni+(rT+6(u.m))qT},
(14)
where rT=r(l-r) and qT=q(l -tz-O)/(l -r). The first order conditions for this problem are ca”+qrS,=$r/(l-r)
(15)
s+ca,+qT6,=0.
(16)
and
The first equation states that utilization and maintenance are chosen so that the marginal cost of utilization equals the cost of capital services. Since the firm can increase capital services either by increasing utilization or by purchasing new machines, the marginal costs of obtaining capital services by each method are equated. An increase in maintenance increases maintenance expenditures, reduces fuel requirements, and reduces capital deterioration. The second equation states that these marginal effects must sum to zero. The necessary conditions (15) and (16) can be solved for the capital utilization and maintenance equations
u* = ‘(i (c, s, rT, 4’)
(17)
m* = ./H (c, s, rT, qT).
(18)
and
Since the capital use decisions are separable from the factor demand decisions, utilization and maintenance depend only on a subset of the prices in the model. Also, these equations indicate that tax policy influences capital use by altering the cost of funds, rT, and the acquisition cost of capital, qT. To determine the influence of tax parameters on capital use decisions, we compute the partial derivatives of (17) and (18). Performing ordinary comparative static calculations with (15) and (16) yields the following results:
(19)
(20)
200
WE. Schwarm, Tax policy
(21)
(22) where H is the Hessian matrix for {ca(u, m)+qTG(u, m)} and Hij is the (i,j) term of this matrix. In general, little can be said about the qualitative effects of tax parameters on capital utilization and maintenance. A change in either r, z or 8 affects the marginal cost of utilization, the marginal benefit of maintenance, and the cost of capital services. The effect of a tax parameter change depends on the relative magnitude of these changes. For example, an increase in the acquisition cost of capital, caused by a decrease in either z or 8, increases the cost of capital services, GT/(l -r), but also increases the marginal cost of benefit of maintenance, ca, +qT6,. utilization, ca, + qT6,, and the marginal The net effect depends on the interaction between utilization and maintenof 6, relative to (rT+h)/u. In addition, ance, ca,, + qTdUm, and the magnitude and capital the qualitative effects of tax policy on fuel consumption deterioration are indeterminate. There are several special cases of our model that are of some interest. First, suppose there are no inputs required to operate machines so that a(u, m)-0. Then, by using (15) and (16) in (19) and (21), one can derive
The effects are still ambiguous owing to the interaction of utilization and maintenance. Secondly, suppose a(u, m) 2 0 but a, = 6, =0 so that maintenance does not enter the model. Then, by substituting from (15) and (16) into (19) and (21), we derive (24)
If no fuel is required for machines that generate no services, then (a,-U/U) >O. In this case an increase in the acquisition cost of capital increases the utilization of capital. Finally, if there is no input requirement and no maintenance, then (15) and (19) imply that variations in qT have no effect on utilization. To determine the effect of tax policy in the general model on capital use, fuel requirement, and depreciation, one needs detailed information on the fuel requirement function and the deterioration function.
W.E.Schworm, Tux polic)
201
5. The demand for capital services and capital stock The firm chooses capital services to maximize profit given that capital decisions have been made to minimize the cost of capital services: maxn*/(l-t)=g(p,w,k)-Il/*k,
use
(25)
where $* = min IclT(u,m)/( 1 -r). u.m The capital
service demand
function
can be expressed
k*=k(p,w,II/*).
as follows: (26)
The demand for capital services is a function of the output price, the variable factor prices, and the minimal cost of capital services. The cost imputed to capital services is conditional upon the cost minimizing choices of utilization and maintenance. This optimal cost of capital services acts as a summary statistic by capturing the effect of (c,s, rT,qT) on the demand for capital services. Tax policy affects the demand for capital services only by influencing the cost of capital services. The effect of tax parameters on the cost of capital services can be determined from the effects of qT and rT:
w* l?qT -
rT+6*
----00; U*
(7**
T
-2>o.
2rT
U*
(27)
An increase in the present value of allowable depreciation or an increase in the investment tax credit reduces qT and, therefore, reduces the cost of capital services. An increase in the tax rate has an indeterminate effect on the cost of capital services since it has an ambiguous effect on qT and also affects rT. The demand for capital services increases if the cost of capital services declines. Therefore, accelerated depreciation and an investment tax credit cause an increased demand for capital services. These results relating tax policy to the demand for capital services are similar to results others have derived for the demand for capital stock [Hall and Jorgenson (1971). Coen (1968), Sumner (1973)]. The differences between our model and models that ignore capital use are revealed when the demand for capital stock is investigated. The demand for capital stock is determined by the demand for capital services and the optimal rate of capital utilization:
QJ~wIC/*)=rc(p,w,c,s,rT,qT).
K*=
(28)
42 (c, s, rT, qT)
The optimal maximization
capital problem:
stock
K*
is the
solution
to
the
following
profit
LIT
----=g(p,w,u*K)-u*$*K. “,““(I -5)
(29)
An important implication of our model is that the demand for capital stock cannot be expressed as a function of p,~, and a rental price of capital. The prices, c, s, rT, and qT enter the demand function separately. Variations in these prices have different effects on the demand for capital stock since they have different effects on capital utilization. Therefore, the specification of the desired capital stock employed in Hall and Jorgenson (1967, 1969, 1971), Coen (1968, 1969, 1971) and Bischoff (1971) is inconsistent with the variability of capital use. The effect of the tax parameters on the capital stock can be decomposed into their effect on the demand for capital services and their effect on capital utilization : ?K” ?qT -u*
1 ?k* ;$* (?$* ‘;qT
K*iu* o u* c?~T’ ’
(30)
An increase in z or 0 causes a reduction in the acquisition cost of capital. This induces an increase in the demand for capital services but can either increase or decrease capital utilization. Therefore, the demand for capital stock can either increase or decrease in response to accelerated depreciation or increased investment tax credits. An increase in the tax rate causes rT to fall but has an ambiguous effect on qT. Therefore, an increase in the tax rate can either increase or decrease the demand for capital stock. The effect of ignoring variations in capital utilization is apparent in eqs. (30) and (31). If capital utilization is independent of prices, then the second terms on the right-hand side of (30) and (31) are zero. Changes in the capital stock induced by price variations are scalar multiples of the changes in capital service demand. If capital utilization adjusts to price changes but the variations in utilization are ignored, then estimates of tax incentives are biased. The direction of the bias depends on the properties of the fuel requirement function and the deterioration function.
WE.Schworm,
Tux policy
203
6. Concluding remarks There are several issues pertinent to tax policy and investment incentives that have not been dealt with in this paper. First, we have ignored factors that cause lagged capital adjustments such as costs of adjustment or irreversibilities. If the capital stock only gradually adjusts to parameter changes, then our model pertains only to the desired or long-run capital stock. Hartman (1978) and Boadway (1979) have analyzed the investment incentives provided by tax policy when there are capital adjustment costs. Capital use decisions could be included in such a model. Secondly, we have not considered the complex issues involved in determining the optimal financial structure of the firm. Capital use and financial structure do not appear to be complementary issues and probably should be investigated separately. This has led us, however, to give an exceedingly simplistic treatment to the cost of funds [King (1974)]. Thirdly, we have employed the usual assumptions of no subjective uncertainty and static expectations with respect to the cost of capital. The assumption of static expectations is easily relaxed but this does not add any interesting results. The consideration of uncertainty only adds to the analysis if either firms are risk averse or there are lagged capital adjustments. Either of these modifications would greatly complicate the analysis. Finally, we have ignored the general equilibrium aspects of the problem. Our most serious assumptions in this regard are that the before tax interest rate and the price of new capital goods are independent of tax parameters. Also, we have ignored the long-run allocation of firms among industries. Asimakopulos and Burbidge (1975) have discussed the interindustry movements of firms in response to tax policy. Christensen (1970) and Klein and Taubman (1971) have attempted to analyze tax policy in general equilibrium models. References Asimakopulos, A. and J.B. Burbidge, 1975, Corporate taxation and the optimal investment decisions of firms, Journal of Public Economics 4, 281-287. Bischoff, Charles W., 1971, The effect of alternative lag distributions, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 61-130. Bitros, G.C., 1976, A statistical theory of expenditures in capital maintenance and repair, Journal of Political Economy 84, 917-936. Boadway, Robin, 1978, Investment incentives, corporate taxation, and efticiency in the allocation of capital, The Economic Journal 88, 47tS481. Boadway, Robin, 1979, Corporate taxation and investment: A synthesis of the neo classical theory, Discussion Paper No. 324, Queen’s University, Kingston, Ontario. Christensen, Laurits R., 1970, Tax policy and investment expenditures in a model of general equilibrium, American Economic Review 2, 18-22. Coen, Robert M., 1968, Effects of tax policy on investment in manufacturing, American Economic Review 2, 20&211. Coen, Robert M., 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 370-379.
Coen, Robert M., 1971. The effect of cash flow on the speed of adjustment, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution. Washington, D.C.) 131-196. Diewert, W.E., 1977, Walras’ theory of capital formation and the existence of a temporary equilibrium, in: G. Schwodiauer, ed.. Equilibrium and disequilibrium in economic theory (D. Reidel, Dordrecht, Holland) 733126. Epstein, Larry G., 1977, Essays in the economics of uncertainty, Ph.D. Dissertation, University of British Columbia. Eisner, Robert, 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 3799388. Foss, M.F., 1963. The utilization of capital equipment: Postwar compared with prewar, Survey of Current Business, 8816. Fromm, Gary, ed., 1971, Tax incentives and capital spending (The Brookmgs Institution, Washington, D.C.). Gorman, William M., 1968, Measuring the quantity of fixed factors, in: J.N. Wolfe, ed., Value, capital, and growth (Edinburgh U. Press, Edinburgh) 141~~172. Hall, Robert E. and Dale W. Jorgenson, 1967, Tax policy and investment behavior, American Economic Review 3, 391-414. Hall, Robert E. and Dale W. Jorgenson, 1969, Tax policy and investment behavior: Comment, American Economic Review 3, 3888401. Hall, Robert E. and Dale W. Jorgenson, 1971, Application of the theory of optimum capital accumulation, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 9960. Hartman, Richard, 1978, Investment neutrality of business income taxes, Quarterly Journal of Economics, 2455260. Jorgenson, Dale W., 1963, Capital theory and investment behavior, American Economic Review 2, 2477259. King, Mervyn A., 1972. Taxation and investment incentives in a vintage investment model, Journal of Public Economics I, 121-147. King, Mervyn A., 1974, Taxation and the cost of capital, Review of Economic Studies 41, 21-35. King, Mervyn A., 1975, Taxation, corporate financial policy, and the cost of capital, Journal of Public Economics 4, 271-279. Klein, L.R. and Paul Taubman, 1971, Estimating effects within a complete econometric model, in: Gary Fromm, ed., Tax incentives and capital spending (The Brookings Institution, Washington, D.C.) 197-242. Nadiri, M.J. and S. Rosen, 1969, Interrelated factor demand functions, American Economic Review 4, 457-571. Nadiri, M.J. and S. Rosen, 1973, A disequilibrium model of demand for factors of production (National Bureau of Economic Research, New York). Perry, George L., 1973, Capacity in manufacturing, Brookmgs Papers on Economic Activity 3, 701-742. Samuelson, Paul A., 1964, Tax deductibility of economic depreciation to insure invariant valuations, Journal of Political Economy 6, 604-606. Schworm, W.E., 1977, User cost and the demand for capital, Discussion Paper 77-22, University of British Columbia. Smith, K.R., 1969, The effect of uncertainty on monopoly price, capital stock, and utilization of capital, Journal of Economic Theory 1, 48859. Smith, Vernon L., 1963, Tax depreciation policy and investment theory, International Economic Review 1, 8&91. Stiglitz, Joseph E., 1973, Taxation, corporate financial policy, and the cost of capital, Journal of Public Economics 2, l-34. Stiglitz, Joseph E., 1976, The corporation tax, Journal of Public Economics 5, 3033311. Sumner, M.T., 1973, Investment and corporate taxation, Journal of Political Economy 4, 982m 993. Taubman, Paul and Maurice Wilkinson, 1970, User cost, capital utilization, and investment theory, International Economic Review 2, 209215. Winston, Gordon C., 1974, The theory of capital utilization and idleness, Journal of Economic Literature 4, 1301-1320. Winston, Gordon C. and Thomas 0. McCoy, 1974, Investment and the optimal idleness of capital, Review of Economic Studies 4, 419-428.