CAN TAX REVENUES GO UP WHEN TAX RATES 

GO DOWN? 

Don Fullerton 

Princeton University 

OTA Paper 41 September 1980 

OTA Papers are circulated so that the preliminary 

findings of tax research conducted by staff members and 

others associated with the Office of Tax Analysis may

reach a wider audience. The views expressed are those 

of the author, and do not reflect Treasury policy. 

Comments are invited, but OTA Papers should not be 

quoted without permission from the authors. Managing

editors are Michael Kaufman and Gary Robbins. 

Office of Tax Analysis 

U.S. Treasury Department, Room 1116 

Washington, D.C. 20220 

Issued: September 1980 
Table of Contents 

Abstract 
 

1. In troduc t i.on 
 

2. A Brief Literature Review 
 

3. Another Simple Curve 
 

4. The General. Equilibrium Model 
 

5. Estimation 
 

6. 	 What is the True Labor Supply 
 Elasticity 
 

7. Conclusion 
 

i 

1 
 

4 

9 

11 

15 

23 
 

26 
ABSTRACT 
 

When Arthur Laffer and other "supply side advocates" 
 

plot the "Laffer Curve," a relationship between tax revenue 
 

and a particular tax rate, they draw an upward-sloping 
 

segment of the curve called the normal range, followed by a 
 

downward-sloping segment called the prohibitive range. The 
 

prohibitive range is said to exist because high tax rates 
 

stifle economic activity and encourage leisure pursuits. 
 

Since a given revenue can be obtained with either of two tax 
 

rates, government would act rationally by choosing the lower 
 

rate of the normal range. 
 

This paper introduces a new curve which summarizes the 

combinations of tax rates and the responsiveness of the 

amount of labor supplied to tax rates that result in maximum 

revenues, thus separating the "normal area" from the 

"prohibitive area." Looking at labor tax rates and total 

revenue, for example, the tax rate that maximizes revenue 

will depend on the assumed labor supply response to taxes. 

A general-purpose empirical model of the U.S. economy is 

used to plot the Laffer curve for several response rates, 

and to plot the newly introduced curve using the labor tax 

example. Results indicate that the United States could 

conceivably be operating in the prohibitive area, but that 

the tax rate on U.S. labor income and/or labor supply 

response would have to be much higher than most economists 

have estimated. 
CAN TAX REVENUES GO UP WHEN TAX RATES GO DOWN?* 
 

Don Fullerton** 
 

1. INTRODUCTION 
 

Ever since Arthur B. Laffer first drew his famous curve on a 

napkin in a Washington restaurant si.x years ago, there has been 

considerable public debate about the possibility of an inverse 

relationship between tax rates and government revenue. As drawn 

in Fi.gure 1, the curve plots total revenue against the tax rate 

and indicates that there are two rates at which a given revenue 

can be collected. The upward sloping portion of the curve is 

called the "normal" range and the downward sl.oping segment is the 

"prohibitive" range. The prohibitive range is said to exist 

because the high tax rates stifle economic activity, force consumers and businesses to barter, and encourage leisure pursuits. &/ 

No rational government would knowingly operate on this range in 

the long run. 

* 	 Some results in this paper also appeared in National Bureau 

of Economic Research (N.B.E.R;) working paper no. 467 in 

April 1980 entitled "On the Possibility of an Inverse 

Relationship Between Tax Rates and Government Revenues." 
 

** I am indebted to my colleagues A. Thomas King, John B. 

Shoven, and John Whalley with whom I developed the general 
 

equilibrium model used in this study. I am also grateful. to 
 the Treasury Department's Office of Tax Analysis for finan­
 cial assistance. This revised version of the N.B.E.R. paper 
 

incorporates changes suggestsd by David Bradford, Shantayanan 
 Devarajan, Ronald E. Grieson, Michael Kaufman, James E. 
 

Rauch, Harvey Rosen, and Nicholas Stern. I wish to thank 
 

Carole Garland of the Office of Tax Policy for coordinating 
 the clerical efforts and assisting with production. I retain 
 

full responsibi1,ity for errors and for the views expressed. 
 
-2-

Figure 1 

Debate about the validity of the Laffer curve has been conducted mostly in the spheres of politics and journalism, and has 

included a wide variety of unsupported claims and opinions. 

These range all the way from the assertion that the prohibitive 

range does not exist to Laffer's claim that "we are well within 

this range at present." 2/ Simple theoretical models can show 

that the prohibitive range does indeed exist, but the U.S. position on the curve is clearly an empirical matter. Despite the 

obvious importance of this issue for fiscal policy, there has 

been no serious estimation of the curve using an economic 

model. 3J This paper attempts to correct this deficiency by 

using a general equilibrium A/ taxation model to address two 
-3-
 

questions. First, what is the posi.tion of the United States on 

the curve today? Second, what is the relationship between the 

location of the curve itself and critical numbers such as the 

appropriate factor (production input) supply elasticity? %/ g/ 

The next section offers a brief review of some salient points 
 

from the debate. A common aspect of previous studies is that a 
 

prohibitive range for some local or non-U.S. economy is always 
 

associated with particularly high tax rates, high factor supply 
 

elasticities, or both. The third section sets out the conditions 
 

under which, in the long run, a lower tax rate could resu1.t in 
 

higher revenues. These conditions are summarized in a new curve, 
 

plotting the appropriate factor supply elasticity against the tax 
 

rate. The fourth section describes the general equilibrium model 
 

used to simulate the effects of various tax rates. The estima­
 

tions of these effects are in section five, and both the Laffer 
 

curve and the new curve are plotted for an example with a labor 
 

tax and labor supply elasticity. Section six provides some evi­
 

dence on the value of the critical labor supply elasticity, and 
 

the last section concludes that to operate in the prohibitive 
 

range, the tax rate on labor income and/or the factor supply 
 

elasticity must be very high. 
 
-4-
 

2. -A BRIEF LITERATURE REVIEW 

The idea of an inverse relationship between tax rates and 
 

revenue is not entirely new. Adam Smith, in =Wealth of 
 

Nations (1776)could hardly be more explicit: 
 

High taxes, sometimes by diminishing the consumption Of 
 the taxed commoditi.es, and sometimes by encouraging smug­
 gling, frequently afford a smaller revenue to government than 
 what might be drawn from more moderate taxes. (Book VI 
 Chapter 11) 
 

The international trade literature, as exemplified by Caves and 
 

Jones (1973), has reflected an understanding of the existence of 
 

a revenue-maximizing tariff. This pre-Laffer edition contains a 
 

hump-shaped tariff revenue curve which looks just like Figure l. 
 

With respect to internal taxes, Jules Dupuit in 1844 states: 
 

By thus gradually increasing the tax it will reach a 

level at which the yield is at a maximum . . . Beyond, the 

yield of tax diminishes . . . Lastly a tax [which is 

prohibitive] will yield nothing. 

After the introduction of the Laffer curve (or perhaps the 
 

reintroduction of the Smith-Dupuit curve) in 1974, the quality of 
 

debate deteriorates significantly. Jude Wanniski (1978) chron­
 

icles various fiscal catastrophes from the fall of the Roman 
 

Empire to the Great Depression and attributes each of them to 
 

some tax hike occurring within a few years in either direction. 
 
-5-
 

At various points in his analysis Wanniski suggests that the peak 

of the curve is at a 25 percent tax rake (page 260), and that the 

peak of the curve “is the point at which the electorate desires 

to be taxed” (page 98). I/ He states that the welfare maximizing 

government would operate somewhere on the normal range with the 

size of its budget determined by standard cost-benefit analysis. 

For the opposition, Kiefer (1978) asserts that there is no 
 

tax rate for the overall economy which can be measured on the 
 

horizontal axis, and that “the Laffer Curve represents a gross 
 

simplification of a major portion of macro-economics into a 
 

single curved line” (page 15). These arguments are not com­
 

pelling either in view of the large number of economic models 
 

which oversimplify in order to comprehend and convey economic 
 

phenomena. Kiefer also reminds us that i.ncome and substitution 
 

effects tend to be offsetting. For example, though a reduction 
 

in his personal income tax rate gives the individual an incentive 
 

to work more and consume less leisure, this tax reduction also 
 

allows him to work less and consume more leisure while main­
 

taining the same after-tax income. The tendency to work more is 
 

the substitution effect and the tendency to work less is the 
 

income effect. 
 

Kiefer argues agai.nst overemphasis on the supply side, 
 

claiming that “by concentrating primarily on incentive and 
 

supply-side effects, the Laffer Curve largely ignores the actual 
 
-6-
 

mechanism by which fiscal policy exerts its biggest and most 

immediate impact--demand side effects." These antagonists appear 

to be using different models that are riot comparable. E/ 

Canto, Joines, and Laffer (1978) build a simple equilibrium 

model with one output, two factors of production, and a 

labor/leisure choice on the part of consumers. The utility function ?/ of individuals in their model includes the discounted 

values of consumption and leisure of each future period, g/a 

formulation which is very similar to the larger empirical general 

equilibrium model used later in this paper. Another similarity 

is that the capital stock is fixed in any one period, but can 

grow over time. Labor taxes in these models decrease the net-of-, 

tax wage received by workers. Each individual reacts to this decrease with an income effect and a substitution effect. In their 

model, however, government revenues are returned to workers 

through transfers or used to buy goods which are perfect substitutes for private goods. This modelling cancels out the income 

effect and therefore leaves the economy with a labor supply that 

unambiguously decreases as the labor tax rate increases. 

There are three objections raised by this modelling. The 

first objection, recognized by these authors, is that if transfers are given to individuals other than those who pay taxes, and 

if individuals have different preferences for income versus 
-1-
 

leisure, then income effects do not necessarily cancel. The 

second objection is that if a government does nothing other than 

tax labor and rebate the revenue to the laborers, then overall 

economic welfare will decrease. Clearly government will. make 

people worse off if it taxes them into working less and then 

spends the tax revenue on something they could have provided just 

as well themselves. Thus these authors' model does not account 

for the inherent efficiency gain that OCCUKS when government corrects market failure by providing a "public good." The benefits 

of consuming such goods spill over to other individuals who have 

not paid for them, so that private persons will not buy as much 

of them as their social benefits would justify. Police protection and street lighting are good examples. Since the private 

market for such goods does not allocate resources efficiently, 

government can increase consumer welfare by providing them. 

Thirdly, it is clear that some public goods like police protection may actually act to encourage private production. The labor 

taxes that reduce workers' desire to supply labor at a given wage 

may be spent by the government on public goods that cause producers to willingly increase wages in their attempt to hire more 

labor and increase output. Therefore, the "balanced budget" 

labor supply does not have to decrease with labcr tax rate 

increases as these authors insist. Econometric estimates of how 

it responds will be surveyed in a later section. g/ 
-8-
 

In empirical work, Grieson (1977) find the possibility 

of an inverse relationship between tax rates and revenue for 

local government in New York. "The inclusion of state taxes lost 

when economic actitity leaves both the city and state would . . . 

raise the possibility of a net revenue loss as a result of an increase in business income taxes." They find that the nonmanufactUring Sector has fewer alternatives to the New York City location and should be taxed mare heavily relative to the manufacturing sector whose response to tax is more elastic. Grieson 

(1979) finds the two sectors reversed for Philadelphia, where 

nonmanufacturing is under greater competitive pressure. Still, 

"Philadelphia may have been at or very close to the revenue maximizing point . . . before the recent income tax increase, which 

raises the possibility of it having been in excess of the 

socially optimal one. 

Finally, Charles Stuart (1979) uses a fairly simple twosector model to find that the current 80 percent marginal tax 

wedge in Sweden exceeds their revenue-maximizing rate by 10 

percent. According to Stuart's analysis, Sweden's high tax rates 

encourage barter and non-market activity, placing its economy on 

the prohibitive range. 
-9-
 

3. ANOTHER SIMPLE CURVE 

A common feature o� arguments from both sides of the debate 

is an implicit or explicit reference to factor supply elasticities. The offsetting income and substitution effects pointed out 

by Kiefer merely imply that the relevant supply elasticity might 

be low or negative, i.e., that the relevant factor supply may 

increase very little or even decrease in response to an increase 

in the net-of-tax wage. The emphasis on large incentives in the 

supply-side argument implies a large elasticity. The "open" 

nature of a local economy, i.e., the fact that labor and capital 

can move in and out of it more easily than they can move in and 

out of a national economy, implies a more elastic response to a 

local tax. Indeed, the entire debate reduces to the empirical 

matter of the size of the relevant factor supply elasticities. 

If they are hi.gh enough, people would reduce their work effort or 

investment so much in response to increased taxes that the 

economy could be on the prohibitive range. 

The very location of Laffer's curve in Figure 1 depends on 

the supply elasticity of the factor bei,ng taxed. g/If that 

elasticity were fairly low, the total revenue maximizing point 

would be at a higher tax rate for that factor, and conversely. 

One can imagine a third dimension on that diagram giving different elasticity values. If one made the total revenue axis perpendicular to the page, the diagram's hill would be converted 
-10-
 

into a mountain range, with the total revenue peaks occurring at 

points running from a low tax rate and high elasticity combination to a high rate and low elasticity pair. This series of 

peaks is plotted in Figure 2. Everything to the southwest Of 

that curve signifies the "normal area", where raising rates gain 

revenue, and northeast of the curve is the "prohibitive area," 

where no rational government would knowingly operate. Each point 

on the curve shows the tax rate that maximizes total revenue for 

a given elasticity. u/ 

At an infinite supply elasticity, the owners of a factor such 

as labor or capital will respond to a tax by refusing to supply 

it at all. The government cannot acquire additional revenue by 

taxing that factor, and the maximum total revenue would be obtained elsewhere (a zero tax rate for that factor is best). For 

a large finite elasticity, the tax rate would have to be very low 

to remain in the normal range. As this elasticity decreases, 

higher tax rates will maximize revenues. Finally, at a zero 

elasticity, factor supply is unaffected, and the only bound on 

revenue is given by total product of the factor. 

From this description, we can place all the advocates on a 

single spectrum those who say we are in the prohibitive area 

believe that the relevant elasticity and/or tax rate are higher, 
-11-
 

Figure 2 
 

Factor 

supply Prohibitive 

elasticity area 

I I--+ Tax rate 

those who say we are in the normal area believe they are lower, 

and those who deny the existence of the inverse relationship must 

believe that the supply elasticity is zero or negative. 

4. THE GENERAL EQUILIBRIUM MODEL 

To simulate the effects of different tax rates for a variety 

of factor supply elasticities, a previously developed general 

equilibrium taxation model is used. This model is still evolving 

after several years of work, and it has already been used for 

other purposes including the evaluation of various tax reform 
-1.2-
 

proposals. However, it was built as a general purpose model, and 

its features are surprisingly well suited for this application. 

No adjustments were required to obtain the following estimates. 

Since more thorough descriptions of the model are available elsewhere, only an outline of its features is presented here. %/ 

The model's economy is divided into 19 profit maximizing producing sectors, 15 consumption commodities and 12 consumers 

differentiated by income class. Each industry has a Cobb-Douglas 

or Constant Elasticity of Substitution (CES) production function, 

where the elasticity of substitution between capital and labor =/ 

is chosen as a "best-guess" value from evidence in the literature. 

Each output can be used as a intermediate input. Outputs can be 

purchased by the government, used for investment, or converted 

into consumer goods. There is also a simple foreign trade 

sector, though factors of production cannot move across national 

boundaries . 

Each consumer has initial endowments of labor and capital 

services which can be sold for use in production. Because of the 

assumptions of perfect factor mobility and competition, the 

net-of-tax return to each factor is equal across industries. E/ 

A consumer can also choose to withhold some of his labor endowment, consuming leisure instead of working. The capital stock is 

fixed in any one period, but the dynamic version of the model 
-13-
 

allows savings to augment the stock in later periods. The elasticity of substitution between present and future consumption is 

based on an estimate of the savings elasticity with respect to 

the net-of-tax of return on savings. This elasticity is used 

because the after-tax rate of return on savings tells the 

individual how much extra future consumption he can get by 

sacrificing present consumption. For this value the 0.4 percent 

change in savings per 1 percent change in the rate of return as 

found by Boskin (1978) is used. The elasticity of substitution 

between consumption and leisure is based on an estimate of the 

labor supply elasticity with respect to the net-of-tax wage. For 

this value a 0.15 percent change in labor supply per 1 percent 

change in the wage is typically used, but relationships for 

different labor elasticity values will be derived below when the 

curve in Figure 2 is plotted. 

The various Federal, state, and local taxes are typically 

modelled as tax rates on the value of purchases of appropriate 

products OK factolcs. Corporate income taxes and property taxes 

are modelled as taxes on the use of capital that differ by industry because, for example, different proportions of industries 

are incorporated. Social security, workmen’s compensation and 

unemplqment insurance appear as taxes on use of labor. These 

rates differ by industry partly because different proportions of 

Workers are subject to the social security maximum, but in 1973 
-- 

-14-
 

they averaged 9.1 percent of gross payments to labor. Personal 

income taxes operate as different schedules for each consumer 

group, with tax rates on the last dollar of income earned 

(so-called marginal tax rates) increasing from an average of 1 

Percent for the lowest income group to an average of 40 percent 

for the highest income group. 

The numerical coefficients of the model have been estimated 

for 1973 using data from the National Income and Product 

Accounts, the Bureau of Labor Statistics' Consumer Expenditure 

Survey, and the Treasury Department's Merged Tax File. These 

data are adjusted for known inaccuracies in government data 

collection procedures, e.g., the fact that depreciation of plant 

and equipment for tax purposes is different from their economic 

depreciation, and for general equilibrium consistency 

requirements. 

The model does not include involuntary unemployment or inflation per se. It expresses all prices in relative terms there 

is no money in the model. Voluntary unemployment is captured 

through the labor/leisure choice, however, and the interaction of 

inflation with progressive tax rates is simulated by, for 

example, moving individuals into higher tax brackets. =/ The 

model thus concentrates on long-run, microeconomic behavior and 

is therefore consistent with the models of the supply-side 

advocates. 
-15-
 

There is a potential difference, however. The model used in 

this paper assumes government transfers are made to consumer 

groups in proportion to their observed 1973 receipts from social 

security, unemployment compensation, food stamps, and other 

welfare programs. Supply-side advocates may believe that these 

payments reduce the incentives of the people who receive them to 

work. The degree to which the supply-side advocates are correct 

depends on the program's ability to isolate important characteristics such as age, disability, and number of dependents which 

make the recipient unable to work. If the program successfully 

isolates those characteristics, its payments will have little or 

no disincentive effect. Our model does in fact treat them as 

having no disincentive effect. To the extent that larger disincentive effects exist due to transfer payments, higher tax rates 

should be used in describing the current U.S. economy. lg/ 

5. ESTIMATION 

Supply-side advocates refet to several different types of 

taxes when they claim that an inverse relationship exi.sts between 

a particular tax rate and government tax revenue. The curve in 

Figure 2 could be plotted by varying a product tax rate against 

the price elasticity of demand for that product, or by plotting 

capital tax rates against the elasticity of savings with respect 

to the net-of-tax return to capital. The latter example was 
-16-

attempted with the empirical model, but no prohibitive area was 

discovered. -19/ For this reason, the example used here is the 

labor tax against the labor supply elasticity. 

In our model the tax on labor used by industry averages 9.1 

percent of gross payments to laborers. The personal income tax 

\ takes another 1 percent to 40 percent of marginal (or last dollar 

J )

at1 labor income, depending on the consumer's marginal tax 

bracket. The total tax rate thus ranges from about 10 percent to 

over 40 percent of labor income. 2OJ One problem with interpreting a general formulation like the Laffer curve is that the tax 

rate on the horizontal axis in figure 1 may be either average OK 

marginal. The distinction is necessary because marginal rates 

are more important for incentive effects. If the tax is steeply 

progressive so that marginal rates are very high, it will take a 

significantly lower average rate to get onto the prohibitive 

range than if the tax is not at all progressive. A solution is 

to vary the industrial labor tax rate of 9.1 percent since this 

rate is both average and marginal, i.e., it takes 9.1 percent of 

all labor income 9.1 percent of the last dollar earned. 

Variations in this rate alone are reported below, but the reader 

should remember that the additional personal income tax and other 

taxes always remain. The tax rates reported are thus 

understatements of the model's true rate. z/ 
Table 1 

Total Revenue Associated with Each Labor Tax Rate, 

in Billions of 1973 Dollars 

Tax Rate on 

Gross Income : Labor Supply Elasticity with Respect to Net-of-Tax Wage 

.15 : .50 : 1.00 : 1.50 : 1.75 : 2.00 : 2.50 : 3.00 : 4.00 

-.111 

.ooo 

.048 

.091 360.00 

.130 

.167 

.200 

.231 439.48 

.286 

.310 

-333 503.71 

* 375 

.412 555.56 

.474 597.41 

.487 

.500 615.16 

.565 657.84 

-600 678.84 

.630 694.90 

.667 711.16 

.697 719.58 

.706 720.89 

.714 721.53 

.718 721.60 

.722 721.52 

-730 720.92 

.750 715.79 

.778 697.79 

.800 670.19 

.833 593.30 

341.79 

355.82 365.57 

354.00 357.46 360.56 365.93 

360.00 360.00 360.00 360.00 360.00 360.00 360.00 360.00 

364.00 361.98 358.23 349.18 

369.80 365.17 360.85 

370.82 363.62 356.91 

391.82 369.60 350.57 295.40 

396.49 361.52 

396.60 

395.43 

389.75 

474.13 380.36 

481.65 

481.98 

481.78 336.60 

476.01 

Office of the Secretary of the Treasury 

Office of Tax Analysis 

Simulations were made selectively to save computational expense. Not all possible rates are reported. 
Figure 3 

LafferCurve with a .I5 Labor Elasticity 

700 

65C 

60C 

55c 

500 

450 �

400 

350 

I 

"091 "10 "20 .30 .40 "50 .60 .70 

Tax rate on gross labor income 
Figure4 

Laffer Curvewith a 4.0 Labor Elasticity 

400 

375 

35C 

32F 

30f 

27: 

251 

-1.0 0 ,091 .la .20 "30 "40 .50 

Tax rate on gross labor income 
I 

Figure 5 
 

Elasticityand Tax Rate Combinations 
 

4.c 

3.5 

3°C 

2.E Prohibitive 

Area 

1.E 
 

1 .c 

Normal 

Area 

.6 

II I -".-I 

,091 .IO "20 .30 "40 "50 .60 .70 

Tax rate on gross labor income 
-21-

The consistent 1973 data set, with adjustments described in 

section 4, shows a total tax revenue of $360 billion compared to 

a national income of $1,252 billion. =/ These valees are replicated in Table 1 for anv possible labor supply elasticity, 

holding tax rates constant. Estimated revenues resulting from 

labor tax rates other than 9.1 percent will depend on the labor 

Supply elasticity. Revenues in excess of $360 billion are 

rebated to consumers in proportion to their original after-tax 

income. These rebates are necessary because general equilibrium 

conditions require a balanced government budget, and increases in 

government purchases would influence the equilibrium solution. z/ 

The results from over 60 experiments with different elasticities and tax rates are summarized in Table 1. 24J The first 

column shows the total revenue resulting from different labor tax 

rates using the model's base value of .15 for the labor supply 

elasticity with respect to the net-of-tax wage. The "observed" 

total icevenue of $360 billion corresponds to the base tax rate of 

9.1 percent, and total revenues increase with tax rates up to a 

tax which is 71.8 percent of Gross labor income. Beyond that 

rate, revenues start to fall. z/ 

Any column of data from Table 1 can be used to plot an 

example of Figure 1, as is done in Figure 3 for the .l5 elasticity. In any of these Laffer curve diagrams, the modelled U.S. 
-22-

economy is represented by .091 on the labor tax rate axis. If 

the various tax rate, transfer, and elasticity assumptions 

employed in this paper are reasonably accurate, then the U.S. 

economy is well down the normal range of the curve. For those 

who prefer a high elasticity, Figure 4 plots another Laffer 

curve. The 4.0 labor supply elasticity and current tax rates 

place the United States well onto the prohibitive range. %/ 

Underlined in each column of Table 1 is the maximum revenue 

point for that elasticity. These tax rate and elasticity combinations correspond to points on a curve like Figure 2. The curve 

plotted for this example is shown in Figure 5. On this curve, 

with the basic tax rate of 9.1 percent (recall that the personal 

income tax rates of 1 percent to 40 percent have been in effect 

throughout), the labor supply elasticity would have to be at 

least 2.5 to put the U.S. economy over the peak and onto the 

prohibitive range. Alternatively, if the supply elasticity is at 

least 1.0 percent and the tax rate is at least 30 percent then 

the U.S. economy would again be operating on the prohibitive 

range. Figure 5 allows the reader to select a plausible tax rate 

and elasticity combination to determine whether the united States 

is now in the prohibitive area. 
-23-

6. WHAT IS THE TRUE LABOR SUPPLY ELASTICITY? 

The basic tax rates, including the .091 labor tax rate, were 

carefully calculated when the model was developed. Bowever, 

estimates of the aggregate labor supply elasticity are harder to 

establish. The econometric literature gives many estimates for 

population subgroups, since different individuals will typically 

have different rates of response to a new net-of-tax wage. 

Finegan's (1962) occupational study found managers, craftsmen, 

and clerical workers varying from a -.29 to a +.42 percent change 

in labor supply per 1 percent increase in the net-of-tax wage, 

while Boskin's (1973) division by sex, race, and age found estimates from -.07 (for prime-age white males) to a +1.60 (for 

elderly black women). Since taxes generally do not vary with 

these characteristics, the relevant labor supply elasticity is an 

aggregate one. Table 2 summarizes a number of econometric 

studies and is based mostly on discussi,on in Killingsworth (1976). 

There is a certain injustice to these authors in reporting 

their results in such a summary fashion. Each study has its own 

measure of the wage, its own data-year or time-period, and its 

own methods of estimation. The studies differ as to how they 

account for labor participation rates and as to whether they 

account for the "balanced budget" effects of government spending 
-24-

as discussed on page 7. The numbers in Table 2 are only presented to provide the reader with a basis for choosing a plausible aggregate labor supply elasticity. Since few aggregate 

studies are available, male and female estimates can be roughly 

combined. 

Elasticity estimates for males are mostly small and negative, 

ranging from -.40 to zero. Borjas and Heckman (1978) review the 

econometrics of these studies and reduce the bounds to -.19 and 

-.07. The estimates for females are more often positive, and can 

be large in absolute value. Rillingsworth finds that females' 

elasticity estimates are mostly between .20 and .90 in crosssection studies. One can obtain the model's .15 aggregate labor: 

supply elasticity by performing a rough numerical calculation. 

The Statistical Abstract of the United States shows that the 

median money income of male employed civilians has consistently 

been twice that of the females. It also shows about a 1.7 ratio 

of males to females in the labor force, a ratio which is 

decreasing with time. In any case, the ratio of male to female 

income should be at least 3.0. Taking a relatively high male 

elasticity of -.lo and a relatively high female elasticity of 

+.go, the three-to-one weighted average is a .15 aggregate 

elasticity (.75 x -.lo t .25 x .90 = .15). 
-25-
 

Table 2 
 

EstiwteS of the Labor Supply Elasticity 
 

Fineqan (1962) Male family heads 
 Inter-occupational 

RDsen (19691 Male family heads 
 Interindustrial 

Kal.achek-mines ( 1970) Male family heads 
 U.S. cross-section 

Gwen ( 1971) Male family heads 
 U.S. tiE series 

Greenburg-Kosters ( 1973) Poor de family heads 
 11.53. cross-section 

Boskin (1973) Different wle subsroups 
 US. cross-section 

F&l.l(173) br de family heads 
 U.S. cross-section 

Ashenfelter-Heck" (1973) Male family heads 
 US. cross-section 

FleisherParsons-Porter (1973 Males ages 45-59 
 US. cross-section 

Ashenfelter-Heck" (1974) Married wles I1.S. cross-section 

Fineqan (1962) 
 Femles 
 Inter-occupational 

LeuthoLd (1968) 
 Fewles 
 U.S. cross-section 

Kalachek-Raines (1970) 
 Femles 
 U.S. cross-section 

Boskin (1973) 
 Different fenale subgroups 
 US. cross-section 

AshenfeI.ter-Hec!" ( 1974) 
 Married fewles 
 US. cross-section 

Winston (1966) 
 Aggregate Internati,ona* crosssection 

Lucas-Tapping ( 1970) Short run aggregate Tim-series 

Lucas-lapping (1970) Ionq run aggregate Tinrrseries 

Office of the Secretary of the Treasury 

office of Tax Analysis 

-.35 to -.25 

-.30 to -.07 

+.OS to +.30 

-.24 to -.11 

-.16 to -.OS 

-.07 to 1.1.8 

-.32 to -.07 

-.E 

-.25 to -.lo 

Zero 

-.095 

-.067 

+.20 to +.go 

-.04 to +1.60 

.a7 

-.I1 to -.05 

1.35 to 1.58 

zero to 1.12 
-26-

7. CONCLUSION 

This paper investigates a number of analytical and empirical 
 

arguments about the relationship between tax rates and government 
 

revenues. A general equilibrium tax model was used to examine 
 

this relationship. Another curve was developed that shows the 
 

combinations of tax rates and factor supply elasticities at which 
 

tax revenue is maximized. This new curve indicates that the U.S. 
 

economy could conceivably be operating in the "prohibitive range" 
 

of tax on labor income, but that labor supply elasticities would 
 

have to be very high for this possibility to be realized, or 
 

labor taxes would have to be much higher than those calculated in 
 

this paper. Available evidence about the value of the labor 
 

supply elasticity does not support the view that our government 
 

is currently behaving irrationally with respect to that tax. 
 

The model could be applied to find circumstances where the 

tax rates, for example, on capital income of secondary earners, 

and the income of welfare recipients are in the prohibitive 

range. This should be the agenda of future research. 

The model may also be used to determine when state and local 

taxes are in the prohibitive range. McGuire and Rapping (1968, 

1970) find labor supply elasticities of 20 to 100 for particular 
-27-
 

states or industries. These elasticities imply that one juris­
 

diction cannot charge higher tax rates than its neighbors, and 
 

they are perhaps becoming more and more applicable to nations 
 

because factor mobility across national boundaries is itself 
 

increasing. These latter considerations do not confirm the 
 

existence of a tax on the prohibitive range, but they make one 
 

much more plausible. 
 

Finally, though the results of this paper tend to reject the 
 

notion of an inverse relationship between major U.S. taxes and 
 

government revenues, they do not necessarily invalidate the claim 
 

that these taxes should be lowered. Even on the normal range, 
 

taxes may be higher than desired by voters. Preferences can 
 

change over time, voters may now demand fewer public goods, and 
 

they can legitimately request a tax decrease. Though incentive 
 

effects can be important even if they do not have perverse 
 

effects on revenue, the point is that the "economics of the tax 
 

revolt" are less the economics of incentive effects and more the 
 

economics of public choice. 
 
-28-

FOOTNOTES 

1. The tax rate of Figure 1 generally refers to any particular
 tax instrument, while revenues generally refer to total tax 
 receipts. Thus we must account for the effect of one tax or1
 all other tax bases. An increase in the payroll tax rate,
 for example, could affect not only its own revenue, but work 
 effort and therefore income tax revenues. 
 

2. 	 Michael Kinsley (1978) correctly claims that there is no 
 logical necessity for revenues to be zero at 100 percent tax 
 rates, due to nonmonetary incentives for work effort, but he 
 incorrectly infers that "there's no logical reason to assume 
 without proof that the Laffer curve ever reverses direction 
 at all." Laffer (1978) points out that there must be some 
 higher rate where economic activity goes to zero. "If every
 time a person goes to the office he receives a bill from the 
 government instead of receiving a a check from his employer, 
 sooner or later even the wealthiest and most highly motivated 
 will stop going to the office. There won't be any earnings,
 and total government revenue will equal zero. For the sake 
 of argument, imagine the government collects zero revenue at 
 100 percent tax rates." The quotation in the text is from 
 Laffer's "Statement Prepared for the Joint Economic Committee 
 Hearings on the Macroeconomic Impact of the Administration's 
 National Energy Plan," May 20, 1977, reprinted in Laffer and 
 Seymour (1979). 
 

3. 	 Several papers have described models in which there exists 

the possibility of a prohibitive range. See Canto, Laffer 

and Odogwu (1977) and Canto, Joines and Laffer (1978). Other 
 empirical papers have found examples of local governments
 operating in this range. See Grieson et a1 (1977) and Ronald 
 E. Grieson (1979). Estimates from DRIXrton, and Chase 
 Econometric models are also provided in Kiefer (1978). None 
 of these papers plot out the Laffer curve however, or esti­
 mate its relationship to various elasticities. As shown be-
 

low (page g), an "open" economy like a local government is 
 more likely to be burdened with a ceiling on revenues. 
 

4. 	 An equilibrium model is one in which there is no excess 
 demand for or excess supply of any consumption good or pro­
 duction input (such as labor) at prevailing prices. For 
 example, involuntary unemployment cannot exist in an equili­
 brium model because it implies an excess supply of labor 
 (though an equilibrium model could include a minimum wage in 

which case those people who would be willing to work for a 

lower wage would be involuntarily unemployed). An equilibrium model is general when it contains -all markets, none of 
 which can have excess demand or supply. 
 
-29-

5. 	 In general, the location of the curve depends on consumption
 behavior, production technology, and other circumstances in 
 the economy. In wartime, for example, individuals might be 
 willing to work harder at higher tax rates to generate larger 
 tax revenues. Later sections estimate the curve with a model 
 of the 1973 U.S. economy. 
 

6. 	 The elasticity of factor supply is the percentage change in 
 the quantity of the factor supplied in response to a percent-
 age change in the price of that factor. For example, the 
 elasticity of labor supply is the percentage change in the 
 quantity of labor supplied in response to a one percent
 change in the net-of-tax wage. 
 

7. 	 Other interesting claims of Wanniski include "if the tax rate 

is zero . . . production is maximized," (page 97) and 

"revenues plus production are maximized at [the peak of the 

curve]" (page 98). Walter Heller (1978) has his own complaints about Wanniski's evidence: "At a time when only a 

few million Americans paid income taxes and Federal spending 

was less than 5 percent of GNP (it was 3 percent in 1929), we 

are asked to believe that federal income tax cuts alone 

powered the growth of GNP from $70 billion in 1921 to $103 

billion in 1929." Arthur Laffer, on the other hand, calls 

Wanniski's book "the best book on economics ever written." 

8. Kiefer would seem to have in mind the Keynesian model of an 
 economy suffering from insufficient aggregate demand, re­
 

sulting in substantial involuntary unemployment of labor and 
 other resources. The Keynesian model is not comparable to 
 the model Laffer and his supporters are using because the 
 former assumes the existence of substantial price inflexi­
 bility, while the latter uses an equilibrium model in which 
 prices move to eliminate all excess demands and supplies.
 

Nowadays economists resolve the conflicts between the two 
 types of models by saying that price inflexibility can occur 
 only in the "short run" and must disappear in the "long run," 
 so that Keynesian models are more relevant in the former case 
 and equilibrium models are more relevant in the latter case. 
 For the rest of this paper we implicitiy take the long-run

point of view. 
 

9. 	 The utility function contains information relevant for 
 determining the satisfaction an individual derives from 
 consumption and leisure. 
 

10. If one receives income P in the present period, one can 

invest it at the prevailing interest rate r, and n periods

later one will have PAl+r) . Income received in the present

period is worth (l+r) times the same dollar amount received 

n perjlods later, so the future income mmst be discounted by

(l+r) . 
-30-
 

11. These three shortcomings of the Canto, Joines, and Laffer 
 

(1978) theoretical model are not explicitly corrected in the 
 empirical model used below, but they are implicitly corrected 
 through the possibility of positive or negative labor supply
 elasticities. 
 

12. 	 Product taxes such as tariffs are equally relevant. One can 

convert general product taxes to equivalent taxes on the 

factors that produce them. One can also consider specific

product taxes by plotting them against demand elasticities, 

thus defining the boundary of the prohibitive area where 

buying is reduced so much in response to the tax that total 

tax revenue decreases. 

13. This analysis over-simplified by using a given elasticity for 
 all tax rates to find the revenue-maximizing point. As the 
 tax rate varies, so would equilibrium prices, incomes, and 
 preference numbers like the factor supply elasticity. Also 
 

the curves in both Figure 1 and Figure 2 are intentionally 
 vague about the particular tax rate and elasticity involved 
 because they have a general significance which requires
 specific application. Both curves will be estimated for a 
 particular factor tax and factor supply elasticity. 
 

14. See Fullerton, Shoven, and Whalley (1978, 1979) and 
 Fullerton, King, Shover1 and Whalley (1980a, 1980b). 
 

15. That is, the percentage change in the ratio of the amount of 
 

capital to the amount of labor employed in production that 
 occurs in response to a percentage change in the ratio of the 
 prices of capital and labor. 
 

16. This is true since if any industry paid factors (e.g., labor 
 and capital) less than the others paid, the factors would 
 migrate to other industries, causing them to be scarce in the 
 low-paying industry and forcing it to bid up before-tax 
 factor payments until after-tax returns in the industry were 
 

equal to those in other industries. If any industry paid
 factors more than the others paid, factors would migrate to 
 that industry, causing them to be abundant in the high-paying
 industry and allowing it to bid down factor payments until 
 after-tax returns in the industry were equal to those in 
 other industries. 
 

17. Effective capital tax rates are calculated by measuring each 
 industry's real use of capital witt replacement cost depreci­
 ation. The simulated effects of inflation on capital gains 
 account for the largely nominal gains that are subject to 
 tax. 
 
-31-
 

18. The difference between paying people who don't work and 
 paying people not to work is the difference between a lump-
 sum payment and a marginal payment with incentive effects. 
 Legally, an employee must be laid off to be eligible for 
 unemployment compensation. A worker can ask to be laid off, 
 but employers may be reluctant to circumvent the intent of 
 the law. These transfers are not automatically and fully
 available to non-workers. Similarly, Aid to Families with 
 Dependent Children (AFDC) payments are designed to select 
 recipients by particular characteristics that minimize 
 disincentive effects. Social security payments are higher
 for the blind or disabled. Finally, note that these trans­
 fers, to the extent that they are disincentives, do not apply 
 to most labor supply decisions. ~f a person has been working
 40 hours per week and decides to work 39 hours instead, he 
 usually does not become eligible for transfers at all. 
 Laffer (1978) states correctly, however, that "if transfer 
 payments included 'means', 'needs', or 'income' tests they
 too should be included [as disincentives]." Another more 
 

thorough study could undertake to measure incentive effects 
 of transfers. 
 

19. Over 40 simulations were performed in seeking a prohibitive 

area for capital taxes. tlsing the dynamic version of the 

model, rates were increased to 83 percent of gross capital 

income, savings elasticities were increased to 4.0, and 

equilibria were calculated out to fifty years in the future. 

There was not a single case discovered where total revenues 

were less than the revenues associated with a lower tax rate 

for the same period. Inverse relationships between tax rates 
 and revenues may exist for high effective rates of tax on 
 

certain types of real capital income for certain individuals. 
 No overall inverse relationship was discovered in this model,
 however, because the tax applies to the savings decision, 
 while savings are only an increment to the capital base. 
 More than fifty years would be required for the tax base 
 reduction to offset a tax rate increase and result in lower 
 revenues. 
 

20. The model measures labor income after the industries' factor 
 

tax but before the individual's personal income tax. Since 
 the factor tax is 9.1 percent of labor income, and personal 
 tax is another 1 percent to 40 percent of marginal labor 

income, the tax rate can be expressed as 10 percent to 45.5 

percent of labor income gross of all taxes. 
 

21. For those who wanted a higher tax rate to account for the 
 disincentive effect of welfare programs, the personal income 
 tax could roughly compensate for the ignored potential
 disincentive of the transfer payments. 
 
-32-

22. 	 An expanded notion of welfare that includes leisure valued at 

the net-of-tax wage equals $1,690 billion. 

23. A decrease in revenue is corrected by a similar lump-sum 
 

charge on consumers in proportion to their original after-tax 
 income, so that government purchases still remain constant. 
 In this sense, the model is much like Laffer's since a change
 in the tax rate is accompanied by a positive or negative
 lump-sum redistribution. 
 

24. 	 These simulations are static in the sense that total amounts 

of labor and capital are fixed. Labor can be sold to industry or retained for leisure in the simulation, while both 

factors can be reallocated among industries. 

25. The computer model provides much other information about the 

simulated equilibrium. With the .15 elasticity and 71.8 percent tax rate, labor supply falls off by almost half. The 

gross-of-tax wage rises, but the net-of-tax wage falls by 40 
 percent in the new equilibrium. Because labor is made more 
 expensive and leisure cheaper than their social costs,
 national income falls by more than the increase in the value 
 

of leisure. Our expanded notion of welfare thus shows a net 
 loss of $269 billion in real terms. 
 

26. In the 4.0 elasticity case, even the small jump from a 9.1 
 percent to 13 percent tax rate causes a 9 percent fall in 
 labor supply and a net welfare loss of $26 billion in real 
 terms. 
 
-33-
 

References 
 

Ashenfelter, Orley, and Heckman, James (1973), Estimating Labor 
 Supply Functions," in Cain, Glen G. and Harold W. Watts 
 (eds.) ), Rand McNalley,

Chicago. 

, (1974), "The Estimation of Income and Substitution 

Effects in a Model of Family Labor Supply," Econometrica,

Vol. 42, No. 1, January pp. 73-85. 

Borjas, George J., and James J. Heckman (1978), "Labor Supply

Estimates for Public Policy Evaluation,' Proceedings of the 

Industrial Relations Research Association. 

Boskin, Michael J. (1973), "The Economics of the Labor Supply,"

in Cain, Glen G. and Harold W. Watts (eds.) Income 

Maintenance and Labor Supply, Rand McNalley, Chicago. 

, (1978), "Taxation, Savings and the Rate of Interest,"

Journal of Political Economy, Vol. 86, No. 2, April, Part 2, 

pp. 53-527. 

Canto, Victor A., Douglas H. Joines and Arthur B. Laffer (1978),
 "An Income Expenditure Version of the Wedge Model," mimeor 
 University of Southern California. 
 

Canto, Victor A., Arthur B. Laffer, and Onwochei Odogwu (19771,
 "The Output and Employment Effects of Fiscal Policy in a 
 Classical Model," mimeo, University of Southern California. 
 

Caves, Richard E., and Ronald W. Jones (1973), World Trade and 
 Payments, Little-Brown and Co., Boston, Toronto. 
 

Dupuit, Jules (1844), "On the Measurement of the Utility of 

Public Works," translation in K.J. Arrow and T. Scitovsky

(eds.) Readings in Welfare Economics, published for the 

American Economic Association by Richard D. Irwin, Inc.,

Homewood, Illinois (1969). 

Finegan, T. Aldrich (1962), "Hours of Work in the United States -- A Cross-Sectional Analysis," Journal of Political Economy,

Vol. 70, No. 5, October, pp. 452-470. 

Fleisher, Belton M., Parsons, Donald O., and Porter, Richard D. 

(1973), "Asset Adjustment and Labor Supply of Older Workers,"

in Cain, Glen G. and Harold W. Watts (eds.) Income 

Maintenance and Labor Supply, Rand McNalley, Chicago. 
 
-34-
 

Fullerton, Don, John 8. Shoven, and John Whalley (1978), "General 
 Eauilibrium Analvsis of U.S. Taxation Policv." 1978 
 _I_ Compendium of Tai Research. Office of Tax itialysis, U.S. 
 Treasury Department, Washington, D.C., pp. 23-58. 
 

, (1979), "General Equilibrium Impacts of Replacing the 

U.S. Income Tax with a Progressive Consumption Tax," mimeo,

National Bureau of Economic Research, Cambridge,

Massachusetts. 

Fullerton, Don, A. Thomas King, John B. Shoven, and John Whalley
 (1980a) "Corporate and Personal Tax Integration in the U.S.: 
 Some Preliminarv Findinas from a General Eauilibrium 

Analysis" in R.-Haveman-and K. Hollenbeck (eds.)

Microeconomic Simulation, Institute for Research on Poverty,

Madison, Wisconsin. 
 

, (1980b), "Tax Integration in the U.S.: A General 

Equilibrium Approach" National Bureau of Economic Research 

Working Paper #337R, Cambridge, Massachusetts, forthcoming in 

the American Economic Review 

Greenberg, David H., and Kosters, Marvin (1973), "Income 
 Guarantees and the Working Poor: The Effect of Income 
 Maintenance Programs on the Hours of Work of Male Family
 

Heads," in Cain, Glen G. and Harold W. Watts (eds.) Income 
 Maintenance and Labor Supply, Rand McNalley, Chicago. 
 

Grieson, Ronald E. (1979), "Theoretical Analysis and Empirical
 Measurements of the Effects of the Philadelphia Income Tax,"
 Journal of Urban Economics. 
 

Grieson, Ronald E., William Hamovitch, Albert M. Levenson, and 

Richard D. Morgenstern (1977), "The Effect of Business 

Taxation on the Location of Industry, Journal of Urban 

Economics, Vol. 4, April, pp. 170-285. 

Heller, Walter (1978), "The Kemp-Roth-Laffer Free Lunch," ___ The 

Wall Street Journal, July 12, p. 20. Reprinted in Laffer and 

Seymour (1979). 

Hill, C. Russell (19731, "The Determinants of Labor Supply for 

the Workina- Urban Poor." in Cain. Glen G. and Harold W. Watts 

(eds.) Income Maintenance and Labor Supply, Rand McNalley,

Chicago. 

Kalachek, Edward, and Raines, Fredric Q. (1970), "Labor Supply of 

Lower Income Workers," pp. 159-186 in President's Commission 

on Income Maintenance Programs, Technical Studies, U.S. 

Government Printing Office, Washington, D.C. 
-35-

Kiefer, Donald W. (1978), "An Economic Analysis of the Kemp/Roth

Tax Cut Bill H.R. 8333: A Description, An Examination of Its 

Rationale, and Estimates of Its Economic Effects,"

Congressional Record, August 2, pp. H7777-H7787. Reprinted

in Laffer and Seymour (1979). 

Kilingsworth, Mark R. (1976), "Neoclassical Labor Supply Models: 
 A Survey of Recent Literature on Determinants of the Supply
 of Time to the Labor Market," manuscript, Fisk University. 
 

Kinsley, Michael (1978), "Alms for the Rich," The New Republic,
 Vol. 179, August 19, 1978, pp. 19-26. Reprinted in Laffer 
 and Seymour (1979). 
 

Laffer, Arthur B. (1978), "An Equilibrium Rational Macroeconomic 
 Framework," mimeo, University of Southern California. 
 

Laffer, Arthur B. and Jan P. Seymour (eds.) (1979), The Economics 
 of the Tax Revolt: A Reader, Harcourt Brace Javanovich, New 
 York. 
 

Leuthold, Jane H. (1968), "An Empirical Study of Formula Income 

Transfers and the Work Decision of the Poor," Journal of 

Human Resources, Vol. 3, No. 3, Summer, pp. 312-323. 

Lucas, Robert E., Rapping, Leonard A. (1970), "Real Wages,

Employment and Inflation," pp. 257-305 in Phelps, E.S.,.S __al., Microeconomic Foundations of Employment and Inflation 
 Theory, W. W. Norton Co., New York. 
 

McGuire, Timothy W., and Rapping, Leonard A. (1968), "The Role of 
 Market Variables and Key Bargains in the Manufacturing Wage
 Determination Process," Journal of Political Economy, Vol. 
 76, No. 5, September-October, pp. 1015-1036. 
 

, (1970), "The Supply of Labor and Manufacturing Wage

Determination in the United States: An Empirical
 

Examination," International Economic Review, Vol. 11, No. 2,
 June, pp. 258-268. 
 

Owen, John D. (19711, "The Demand for Leisure," Journal of 
 

Political Economy, Vol. 79, No. 1, January-February, pp. -

Rosen, Sherwin (19691, "On the Interindustry Wage and Hours 

Structure," Journal of Political Economy, Vol. 77, No. 2,

March-April, pp. 249-273. 

Smith, Adam (1776), The Wealth of Nations, J.M. Dent & Sons,

Ltd., London, reprinted 1975. 
-36-

Stuart, Charles (1979), "Swedish Tax Rates, Labor Supply and Tax 
 Revenues," University of Lurid, Sweden, arid University of 
 Western Ontario, Canada, mimeo. 
 

Wanniski, Jude (1978), The Way the World Works: How Economies 

Fail and Succeed, Basic Books, New York. 

Winston. Gordon C. (1966). "An International Comuarison of Income 

and.Hours of Work," Review of Economics and Statistics, Vol. 

48, No. 1, February, pp. 28-39.