Chapter

2 A Simple Model of the Effects of Income Tax Rate Reductions on Economic Growth and Aggregate Supply

Author(s):
Ved Gandhi, Liam Ebrill, Parthasarathi Shome, Luis Manas Anton, Jitendra Modi, Fernando Sanchez-Ugarte, and George Mackenzie
Published Date:
June 1987
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Author(s)
George A. Mackenzie

Both mainstream neoclassical economists and popular supply-side writers have in recent years espoused the view that labor supply, investment, and savings may be a good deal more sensitive to their after-tax rate of remuneration or return than had previously been supposed. If this is the case, then a tax reform that reduces appreciably marginal rates of income taxation may have a substantial impact on the rate of growth of the supply of labor and the capital stock and hence on the rate of growth of potential output.

The principal aim of this chapter is to illustrate the possible range of this impact with the aid of the basic one-sector neoclassical growth model. The version of the model presented here includes a tax on income from both labor and capital, and can be used to simulate the effect of a reduction in marginal income tax rates once values are assumed for its parameters.

The limitations inherent in the use of such a rudimentary model need to be stated at the outset. First, it should be stressed that the neoclassical model of growth presupposes well-functioning markets and flexibility of production techniques. Thus, it cannot be the model of choice for dealing with such problems as the constraints on growth in developing countries that may be created because of a shortage of foreign exchange when production techniques allow little substitution between domestic labor and capital and imported capital. Nor would it be appropriate for the analysis of financial repression, because it assumes in effect that the capital stock is directly owned by savers. A further consequence of this is that the decision to save is also a decision to invest, so that the two cannot be analyzed separately.

Second, the model incorporates only income taxes. However, revenues from personal income taxes in industrial countries are generally much higher than in developing countries both in relation to gross domestic product and as a share of total tax revenue. Presumably, this explains why the great bulk of the literature on the incentive effects of tax regimes and of changes in marginal tax rates on labor, savings, and investment decisions pertains to the developed world. Third, a one-sector model cannot be used to analyze allocational questions such as the effect of different tax regimes on the composition of investment.

Finally, the model cannot be used to analyze the question of how the size of the supply response generated by income tax reductions might compare with the increase in aggregate demand that income tax reductions might generate. This question is examined in the Annex to this chapter.

Despite these limitations, the simple neoclassical model can shed some light on the possible magnitude of the impact on growth of reductions in marginal income tax rates and on the conditions under which marginal tax rate reductions could have an appreciable impact. Unless prices and wages are of no consequence at all in the allocation of resources in developing countries, changes in income tax rates that alter relative prices should have some impact on decisions in the labor and capital markets. Moreover, the personal income tax is, or may become, an important source of revenue in some middle-income developing countries, and the marginal income tax rate faced by the average taxpayer might conceivably create disincentives against working or saving.

The various experiments with the model illustrate the conditions under which reductions in marginal income tax rates are likely to have a substantial impact. One basic conclusion is that when other things, and in particular the elasticities of savings and labor supply are held constant, the response to given proportional reductions in marginal tax rates is greater the higher the marginal rates of income tax. Another important but more surprising conclusion is that when labor and capital are substitutable and the marginal product of labor is high relative to its average, that is, when labor’s share of output is high, the response of output to a reduction in marginal tax rates is more sensitive to changes in the assumed labor supply elasticity than to changes in the savings elasticity. In other words, the elasticity of savings is by no means the only relevant parameter.

The experiments also underscore the limitations of a policy aimed at accelerating the rate of growth of aggregate output in developing countries by reducing marginal income tax rates alone. The conditions under which marginal income tax reductions would spark a significant increase in growth are more likely to be present in industrial countries rather than in developing countries. Marginal rates of income tax are typically high in industrial countries, and these countries probably approximate more closely the neoclassical model in terms of the flexibility of their labor and savings markets. Finally, the scope for revenue-neutral income tax reforms, which reduce marginal rates without reducing tax revenue excessively, is probably greater in industrial countries, given the importance in so many of these countries of allowable deductions from taxable income that erode the tax base.

I. Incorporating Marginal Income Tax Rates in the One-Sector Neoclassical Model

The basic assumptions incorporated in the model are as follows. First, the supply of labor grows at a constant rate, other things being equal, but is also made a function of the marginal real wage after tax. Second, saving in one period adds to the stock of capital in the following period, and is also a function of the after-tax rate of return to capital at the margin. Third, the neoclassical production function chosen is the Cobb-Douglas. This choice implies a substantial degree of substitutability between capital and labor, and has an important bearing on the simulation results. Fourth, the before-tax wage rate equals the marginal product of labor, and the before-tax return to capital equals the marginal product of capital. Both the wage rate and the return to capital are expressed in units of final product. Finally, technical progress is assumed to be labor-augmenting and exogenous: that is, it is independent of the rate of investment. The assumption of labor-augmenting technical progress permits the measurement of labor in terms of efficiency units. Endogenous technical progress is subsequently introduced into the model by making the rate of technical progress partly a function of the share of output saved.

With these assumptions, the variables of the model are determined by the following relationships:

Where

Y(t) = output at time t;

K(t) = capital stock at time t;

L(t) = labor supply at time t;

w(t) = before-tax wage rate at time t;

r(t) = before-tax rate of return to capital at time t;

els = elasticity of labor supply with respect to after-tax wage;

ess = elasticity of savings with respect to after-tax rate of return;

g = rate of increase in “efficiency units” of labor supply;

tw = tax on labor income;

tw = tax on capital income; and

A = constant term.

Equation (1) represents the production function; equation (2) is the supply curve of labor; equation (3) is an inverted demand for labor curve; equation (4) is the savings function; and equation (5) determines the rate of return to capital.

One very important characteristic of the one-sector neoclassical growth model when technical progress is exogenous is the constancy of the steady-state rate of growth, which is given by g, the rate of growth of labor measured in efficiency units. This characteristic does not depend on the specific parameters of the production function. It has the well-known implication that increases in the savings rate cannot permanently raise the rate of growth, although they can raise it above its steady-state rate for a substantial period of time.

Once initial values for the variables Y,L, and K and for the parameters a, g, and tw, and tr are chosen, it is possible to simulate the impact of changes in the two income tax rates.1 The value of a, the share of capital income, is set initially at 0.2, and the value of g, the steady-state rate of growth of output, at 3 percent. The estimates are not derived from an empirical study of any one economy, but they would nonetheless approximate the characteristics of a number of industrial economies. It is not necessary to worry over the choice of the steady-state capital output and savings ratios, because, as may be shown, the choice does not affect the simulation.

The scale parameters in equations (2) and (4), LA and S, are made functions of els and ess in such a way that the economy remains on its steady-state growth path when the two taxes are held at their initial values regardless of the assumed values for the two elasticities. This assumption permits a comparison of the effect of changing the income tax rates under a variety of assumptions regarding the elasticity of savings and labor.

II. Assumed Elasticities and Simulation Results

The elasticities of labor and savings were each allowed to range from 0 to 1.0. The upper bound of 1.0 substantially exceeds most estimates for the elasticity of aggregate savings and labor supply made for the United States, where most of the empirical work has been done. Nonetheless, it needs to be emphasized that there is no firm consensus as to the most likely value for either parameter, and in particular for the elasticity of savings.2

Rosen (1980) summarizes some earlier research on labor supply elasticity in two “stylized facts”: (1) for prime-age males, the substitution effect of changes in the net wage on hours worked is small and often statistically insignificant and the hours of work are unresponsive to changes in net wages; and (2) the hours of work and the decisions of married women as to labor force participation are quite sensitive to changes in the net wage, with some elasticity estimates exceeding 1.0. Fullerton (1982) calculated a measure of aggregate labor supply elasticity of 0.15 based on the estimates of elasticities for male and female workers in various econometric studies. The study by Hausman (1981) estimated uncompensated supply elasticities for secondary female earners of close to 1.

An often-cited study by Boskin (1978) estimated the elasticity of savings with respect to the expected after-tax interest rate at between 0.2 and 0.4. While this is not the highest estimate ever reported, it is higher than most previous studies.3 Boskin’s estimate may even understate the elasticity of financial savings with respect to changes in after-tax rates of interest, because even if an increased rate of return has little effect on total saving, it may increase the desired rate of accumulation of financial assets at the expense of real assets (i.e., consumer durables and housing).

The first set of simulations of the model were performed with tw set at 40 percent and tr set at 50 percent. The elasticities of labor supply and savings ranged from 0 to 1. A 30 percent reduction in both tax rates—that is, a reduction of tw to 28 percent and tr to 35 percent—can generate substantial increases in growth in the initial years following the reduction, if the labor supply elasticity is sufficiently high, even if the savings elasticity is zero. For example, with a labor supply elasticity of 0.4, the model generates an increase in the average annual rate of growth in the first ten years following the tax reductions from its steady-state value of 3 percent to 3.59 percent.

However, the initial increase in growth is not greatly affected by the increase in the elasticity of saving: for example, when this is 0.4 instead of zero, the average annual rate of growth in the first ten years following the tax reductions is raised to 3.69.

The initial spurt in growth is not much influenced by the assumed savings elasticity because even if savings—and thus investment—is boosted substantially by the income tax reductions, the impact on the total stock of capital cannot be very great. This point can be illustrated by a simple numerical example. With a savings rate of 9 percent and a capital output ratio of 3, savings and investment are 3 percent of the capital stock. An increase in savings of as much as 33 percent adds only 1 percent to the growth of the capital stock, and given the assumption that capital’s share is 0.2, this increase in the stock of capital adds just 0.2 percent to output. However, with a labor supply elasticity of 0.4, an increase in the after-tax real wage at the margin of 10 percent generates an increase in labor supply of 4 percent—and the increase in labor supply produces an increase in output of 3.2 percent.

The initial spurt in growth quickly tapers off, because the response of labor to its after-tax real wage is immediate and not lagged. Thus, with both the elasticity of savings and the elasticity of labor equal to 0.4, the average annual rate of growth in years 11-20 is 3.09 percent, which is not much different from its steady-state value (Table 1).

After the initial spurt in growth is over, growth is fostered by two processes. First, the initial increase in the supply of labor raises the ratio of labor to capital, and hence output to capital. With a given savings rate, the rate of accumulation of capital is raised and remains above its steady-state rate for some time. Second, if savings are responsive to their after-tax rate of remuneration, the savings rate increases, and this in turn increases the rate at which capital accumulates.

Although in the initial impact on growth, the labor supply elasticity is the more important parameter, in later years the savings elasticity’s effect becomes relatively more important as a result of the processes described above. For example, with a labor supply elasticity of 0.4 and a zero elasticity of savings, the average annual rate of growth tapers off to 3.03 percent by years 11-20. With a savings elasticity also equal to 0.4, growth is 3.09 percent (Table 1).

Table 1.Average Annual Growth Rate of Output for Indicated Periods When Tax Rates Are Reduced by 30 Percent in Period 1 from Initial Values of 40 Percent for Labor Income Tax and 50 Percent for Capital Income Tax, for Various Combinations of Elasticities(In percent)
Labor Supply Elasticity
Savings

Elasticity
Period00.20.40.81.0
0-103.003.313.594.124.37
011-203.003.013.033.073.10
21-303.003.013.033.063.08
0-103.033.343.644.194.44
0.211-203.023.043.063.123.15
21-303.023.033.053.093.11
0-103.063.383.694.254.52
0.411-203.043.063.093.163.20
21-303.033.053.073.123.14
0-103.113.453.784.394.67
0.811-203.073.103.143.223.27
21-303.043.063.093.143.18
0-103.143.493.824.454.75
1.011-203.083.123.163.253.30
21-303.053.073.093.153.18

What the simulations do make clear is that, given the assumptions of capital-labor substitutability, the impact on the growth of aggregate output is greatly affected by the elasticity of labor supply. Growth is not simply a function of the volume of savings and the elasticity of savings.

The importance of the magnitude of the elasticity of labor supply is further illustrated by reducing only the tax on capital income and not the tax on labor income, because the impact on growth that results is much diminished (Table 2). For example, even with a savings elasticity of 0.4, the average annual rate of growth over the first ten periods increases to just 3.06 percent when a zero elasticity of labor supply is assumed. Nonetheless, even though only the tax on capital income and not the tax on labor income has been lowered, the impact on growth does depend on the assumed labor supply elasticity. With a labor supply elasticity of 0.8, the average annual rate of growth increases to 3.09 percent (Table 2).

Table 2.Average Annual Growth Rate of Output for Indicated Periods When the Tax Rate on Capital Is Reduced by 30 Percent in Period 1, with Initial Values of 40 Percent for Labor Income Tax and 50 Percent for Capital Income Tax, for Various Combinations of Elasticities(In percent)
Labor Supply Elasticity
Savings

Elasticity
Period00.20.40.81.0
0-103.033.033.043.043.05
0.211-203.023.023.033.033.04
21-303.023.023.023.033.03
0-103.063.073.073.093.10
0.411-203.043.053.053.073.07
21-303.033.033.043.053.05
0-103.113.133.153.183.19
0.811-203.073.083.093.123.13
21-303.043.053.063.083.09
0-103.143.163.183.223.24
1.011-203.083.093.113.143.15
21-303.053.063.073.093.10

The impact on growth of the tax rate reductions simulated above is substantially increased if it is assumed that technical progress is partly a function of the share of output saved. This assumption of endogenous technical progress also increases the significance of the elasticity of savings.

To illustrate this, the model was resimulated with the assumption that the rate of labor-augmenting technical progress increased by 0.4 percent for every 1 percentage point increase in the savings rate above its initial value. With savings and labor supply elasticities each set equal to 0.4, this results in an increase in the average annual rate of growth to 4.06 percent during the first ten years after the reductions (Table 3). Moreover, the steady-state rate of growth can be higher than 3 percent, so that the growth rate does not fall sharply in latter years as it does with the original version of the model.

It is interesting to note that when both taxes are reduced in this second version of the model, the growth rate is still considerably influenced by the assumed elasticity of labor supply. For example, with a zero elasticity of labor supply and an elasticity of savings of 0.4, the average growth rate in the first ten years is 3.39 percent.

Table 3.Average Annual Growth Rate of Output for Indicated Periods When Tax Rates Are Reduced by 30 Percent in Period 1 from Initial Values of 40 Percent for Labor Income Tax and 50 Percent for Capital Income Tax, for Various Combinations of Elasticities: Case of Endogenous Technical Progress(In percent)
Labor Supply Elasticity
Savings

Elasticity
Period00.20.40.81.0
0-103.003.313.594.124.37
011-203.003.013.033.073.10
21-303.003.013.033.063.08
0-103.193.343.824.384.64
0.211-203.193.043.253.313.34
21-303.203.033.233.283.30
0-103.393.744.064.664.93
0.411-203.413.443.483.563.61
21-303.423.443.463.513.54
0-103.854.234.605.285.60
0.811-203.933.974.024.134.19
21-304.024.003.994.024.04
0-104.104.524.915.645.98
1.011-204.264.304.344.454.51
21-304.514.394.324.274.27

The increases in growth generated by both versions of the model in response to reductions in the marginal income tax rates when both elasticities are greater than zero depend to a considerable degree on the initial marginal income tax rates and not just the proportional size of the reduction. When the marginal rates of tax assumed above of 40 percent for labor income and 50 percent for capital income are reduced by 30 percent to 28 percent and 35 percent, respectively, after-tax labor income increases at the margin by 20 percent and after-tax capital income by 30 percent.4 Thus, it is perhaps not surprising that a substantial response of output can take place when the elasticity of savings and labor supply are positive.

Marginal rates this high may be representative of rates facing the average taxpayer in many industrial countries, but they are clearly well above the rates that would characterize even most middle-income developing countries.

When the initial value of the marginal rate of tax on labor income is 20 percent instead of 40 percent and the initial value of the tax on capital income is 25 percent instead of 50 percent, a proportional reduction of 30 percent in each tax has far less impact on output. When labor supply is completely inelastic, the response is practically negligible (Table 4). Nonetheless, even with these lower tax rates the average rate of growth in the first ten-year period does increase to 3.27 percent when elasticities of 0.4 are assumed for both savings and labor supply.

Table 4.Average Annual Growth Rate of Output for Indicated Periods When Tax Rates Are Reduced by 30 Percent in Period 1 from Initial Values of 20 Percent for Labor Income Tax and 25 Percent for Capital Income Tax, for Various Combinations of Elasticities(In percent)
Labor Supply Elasticity
Savings

Elasticity
Period00.20.40.81.0
0-103.003.123.233.443.54
011-203.003.013.013.033.04
21-303.003.003.013.023.03
0-103.013.133.253.473.56
0.211-203.013.023.023.053.06
21-303.013.013.023.043.04
0-103.023.153.273.493.59
0.411-203.013.023.033.063.07
21-303.013.023.033.043.05
0-103.043.173.303.533.64
0.811-203.023.043.053.083.10
21-303.023.023.033.063.07
0-103.053.183.313.553.66
1.011-203.033.043.063.093.11
21-303.023.033.043.063.07

III. Conclusions

These few experiments give some idea of the variety of characteristics of an economy that would have to be taken into account to determine the conditions under which reductions in marginal income tax rates would have an impact on the rate of growth. In particular, they illustrate the basic importance of the nature of the process of growth itself. The assumption of endogenous technical progress makes a good deal of difference to the results.

The experiments show that the impact of marginal income tax rate reductions depends on the values of many parameters and that the elasticity of savings, somewhat surprisingly, may be relatively unimportant. The experiments also show the importance of the level of marginal income tax rates. If these are low to begin with, and the elasticities of savings and labor supply only moderate, then the impact of income tax rate reductions on growth is very limited. Finally, they illustrate indirectly how little impact marginal income tax rate reductions would have in an economy where marginal rates were low to begin with and capital labor substitutability was limited.

ANNEX
A Simple Model of the Impact of Income Tax Reductions on the Aggregate Demand-Supply Balance

The effect of an income tax reduction on aggregate supply and demand is examined in this Annex with the aid of a version of the elementary Keynesian model, where aggregate supply, instead of being fixed, is a function of a fixed capital stock and a supply of labor that varies directly with the after-tax real wage. Prices are fixed in this model, so that financial effects cannot be examined.

The model is specified as follows:

where

YD = aggregate demand;

YD = aggregate supply;

E = autonomous expenditure;

C = aggregate consumption;

K = capital stock;

LS = labor supply;

LD = labor demand;

L = actual employment;

Y = actual aggregate output;

atw = average tax on labor income;

tw = marginal tax on labor income;

atr = average tax on capital income;

tr = marginal tax on capital income;

w = real wage rate (in units of output);

r = real rate of return to capital (assumed equal to before-tax return to saving); and

A, F, c, g = constant terms.

Average tax rates must be incorporated in the model if it is to be used to analyze the effects of a tax reduction on aggregate demand. Marginal rates are related to average rates by equations (13) and (14). For simplicity, the tax on capital income is assumed to be proportional to the tax on labor income (equation (12)).

Because it is desired to investigate the conditions under which the increase in aggregate demand caused by an income tax reduction would be offset by an increase in aggregate supply, an equilibrium condition for the product market has not been included. In the specification of the model, it has been assumed that the labor market always clears (the real wage playing the equilibrating role). Equations (9), (10), and (11) determine labor market equilibrium. Labor supply (equation (9)) is a function of the after-tax real wage. The demand for labor (equation (10)) is a function of the fixed capital stock and the real wage.

Employment and, hence, aggregate supply are a function of tw, the marginal tax on labor income, as may be seen by solving equation (10) for w, substituting this expression for w in equation (9), making use of the labor market equilibrium condition, and solving for L as a function of tw. The standard production relationship of equation (7) makes aggregate supply a simple function of employment, as the capital stock is assumed to be fixed. The production relationship of equation (7) implies that the shares of labor (LS) and capital (KS) in national income are fixed and are equal to(1—a) and a, respectively. The consumption function (equation (8)) makes consumption a function of labor income, profits, and the after-tax rate of interest. Given the assumptions of this model, the only strictly supply-side effect of a tax reduction is its effect on the supply of labor. However, the model allows for the possibility that changes in the tax rate on capital income may affect the savings propensity.

It is assumed that aggregate demand (YD) and aggregate supply (YS) are initially equal. To determine the effect of a change in income tax rates, the responsiveness of both YD and YS to such a change must be calculated.

By appropriate substitutions, aggregate supply can be expressed as a function of (1—tw), as follows:

with D being a constant term.

This in turn implies the following expression for the elasticity of aggregate supply with respect to atw, the average tax rate on labor income:

The elasticity of aggregate demand with respect to atw can be expressed as follows (superscripts denoting partial derivatives):

C1 and C2 are, respectively, the marginal propensities to consume from labor and capital income and are both positive in sign. C3 is the partial derivative of consumption with respect to the after-tax rate of return on capital, whose sign is uncertain.

Because the elasticity of savings is related to C3 by the formula

ess = -C3r (1 - tr)/SAVING,

equation (17) can be re-expressed as follows, with S representing the savings rate:

Thus, given initial values for the marginal propensities to consume from capital and labor income, the share of capital and labor, the marginal and average tax rates, the savings rate and the elasticity of savings, equations (16) and (17a) can be solved for that value of b, the elasticity of labor supply with respect to the after-tax marginal wage, for which the responses of supply and demand to a change in the two tax rates will equal one another. It should be noted that the supply response is determined uniquely by b, given a and tw.

The savings rate was set initially at 9 percent, the average tax rate of labor income at 20 percent, and the average tax rate on capital income at 25 percent. In the first set of simulations, the parameter g in equations (13) and (14) was set at 1, so that average and marginal rates of tax are equal.

When the marginal propensity to consume from labor income is set at 0.8, the marginal propensity to consume from capital income at 0.5, and when savings are completely unresponsive to changes in their rate of remuneration, a labor supply elasticity of 2.9 is required to maintain the equilibrium of aggregate demand and aggregate supply (Table 5). Even when the savings elasticity is set at higher levels, the required labor supply elasticity remains at a value well above reported empirical estimates of aggregate labor supply elasticity (Table 5). Similarly, when the labor supply elasticity is less than 1.5, the required savings elasticity must exceed 2.

Table 5.Labor Supply Elasticity Required for Maintenance of Aggregate Supply-Demand Equilibrium Following an Income Tax Reduction: Marginal Tax Rates Equal Average Tax Rates
Elasticity of Savings

with Respect to

After-Tax Rate of Return
00.20.40.60.81.01.52.0
2.92.82.62.42.32.11.81.5

However, it should be noted that any positive response of either savings or labor supply to an increase in the real after-tax rate of return and in the real wage rate, respectively, means that the conventional multiplier analysis overstates the extent to which an income tax cut creates an inflationary gap or reduces a deflationary one. Table 6 presents illustrative calculations of the relative magnitude of the supply and demand effects in the simple Keynesian model resulting from a reduction in tw under a range of assumed values for the elasticities of savings and labor supply. The ratio displayed in the main body of the table represents the ratio of the elasticities with respect to tw of aggregate supply and aggregate demand, given, respectively, by equations (16) and (17a) and expressed in percentage form. The relative size of the supply effect is not insignificant in all cases, even in cases of modest values for labor supply and savings elasticities.

These results are very sensitive to the parameters of the tax functions. If the value of g is set at 2 instead of 1, so that marginal tax rates are twice average tax rates, a given proportionate reduction in average tax rates results in a much greater increase in marginal after-tax rates of remuneration to savings and labor. For example, with the average tax rate on labor of 20 percent and on capital of 25 percent and marginal tax rates on labor of 40 percent and on capital of 50 percent, a 10 percent reduction in taxes increases after-tax labor income by 6.7 percent and capital income by 10 percent.

If, instead, the marginal rate of tax on labor is 20 percent and that on capital is 25 percent, a 10 percent reduction increases after-tax labor income by just 2.5 percent and capital income by 3.3 percent.

Table 6.Comparison of Demand and Supply Effects of an Income Tax Reduction
Labor Supply Elasticity
0.20.40.60.81.0
Supply Effect0.0380.0740.1070.1380.167
Savings

Elasticity
Demand

Effect
Supply Effect as Percentage of Demand Effect
00.37010.420.028.937.245.0
0.20.35810.820.830.138.846.8
0.40.34511.321.731.440.448.8
0.60.33211.822.732.842.251.0
0.80.31912.323.734.344.253.4
1.00.30712.924.936.046.356.0
Note: The demand effect is the arithmetic inverse of the elasticity of aggregate demand of the simple Keynesian modet with respect to tw. The supply effect is the arithmetic inverse of the elasticity of aggregate supply with respect to tw.
Note: The demand effect is the arithmetic inverse of the elasticity of aggregate demand of the simple Keynesian modet with respect to tw. The supply effect is the arithmetic inverse of the elasticity of aggregate supply with respect to tw.
Table 7.Labor Supply Elasticity Required for Maintenance of Aggregate Supply-Demand Equilibrium Following an Income Tax Reduction: Marginal Tax Rates Double Average Tax Rates
Elasticity of Savings

with Respect to

After-Tax Rate of Return
00.20.40.60.81.01.52.0
0.80.70.60.50.40.30.1-0.1

With g set at 2, the labor supply elasticity required to maintain the balance of aggregate demand and supply when the savings elasticity is zero is much less: 0.8 instead of 2.9 (Table 7).

References

    BoskinMichael J.“Taxation, Saving, and the Rate of Interest,”Journal of Political Economy (Chicago) Vol. 86No. 2Part 2 (April1978) pp. S3S27.

    EvansOwen J.The Life Cycle Inheritance: Theoretical and Empirical Essays on the Life Cycle Hypothesis of Saving (unpublished doctoral dissertation, Philadelphia: University of Pennsylvania1982).

    FullertonDon “On the Possibility of an Inverse Relationship Between Tax Rates and Government Revenues,”Journal of Public Economics (Amsterdam) Vol. 19 (October1982) pp. 322.

    HausmanJerry A.“Labor Supply,”inHow Taxes Affect Economic Behaviored. by Henry J.Aaron and Joseph A.Pechman(Washington: Brookings Institution1981).

    McLureCharles E. Jr. “Taxes, Saving and Welfare: Theory and Evidence,”National Tax Journal (Columbus, Ohio) Vol. 33 (September1980) pp. 31120.

    RosenHarvey S. “What Is Labor Supply and Do Taxes Affect It? “American Economic Review Papers and Proceedings of the Ninety-Second Annual Meeting of the American Economic Association (Nashville, Tennessee) Vol. 70 (May1980) pp. 17176.

The choice of initial values for Y, K, and L determines the value of A, the scale parameter in equation (1).

A discussion of the problems involved in the econometric estimation of savings elasticities may be found in McLurc (1980).

Evans (1982. pp. 251-52), having surveyed some studies of the interest elasticity of savings, notes that the more Circumspect and careful studies favor a small positive interest elasticity of aggregate saving—in the United States—but that the issue is far from closed.

For a given gross wage rate W, the after-tax wage increases from ((100 - 40)/100)* W to ((100 - 28)/100)* W or from 0.6* W to 0.72* W. The increase for after-tax income from capital at the margin for gross income YK is from 0.5* YK to 0.65* YK.

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