A Reexamination of the Use of Ability 

to Pay Taxes by Local Governments* 

Timothy J. Goodspeed

U.S. Treasury Department 

OTA Paper 56 April 1987 

OTA Papers and Briefs are circulated so that the preliminary

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U.S. Treasury Department, Room 4040 

Washington, D.C. 20220 

* This paper is derived from my doctoral dissertation. I would 

like to thank my adviser, Wallace Oates, and the other members 

of my committee, Maureen Cropper, Robert Schwab, and Mahlon 

Straszheim for their many helpful suggestions and criticisms. 

I would also like to thank Len Burman, Radu Filimon, Don 

Fullerton, Daphne Kenyon, and Jim Nunns for many helpful 

comments on an earlier draft. Any remaining errors are my own. 
Table of Contents 

I. Introduction 

11. The Model 

111. Further Assumptions 

IV. Simulation Results for Benchmark Parameters 

V. Sensitivity Analysis 

VI. Summary and Conclusions 

Footnotes 

Bibliography 

Appendix. Derivation of Elasticity Conditions 

List of Figures 

Figure 1. An Illustration of the Role of Westhoff's 

Assumption 

Figure 2. The Level of Public Good and Tax Rate of 

Community j 

Figure 3. The EV(Y) Function for the 6 Community,

Benchmark Case 

List of Tables 

Table 1A. Benchmark Case, 2 Community Model 

Table 1B. Benchmark Case, 6 Community Model 

Table 1C. Benchmark Case, 12 Community Model 

Table 2. Sensitivity Results 

Page 

1 

7 

16 

19 

28 

29 

33 

35 

38 

11 

14 

27 

20 

21 

22 

30 
A Reexamination of the Use of 

Ability to Pay Taxes by Local Governments 

I. Introduction 

The orthodox local public finance literature states that 

local governments should rely on benefit taxes or taxes on 

immobile factors. Ability to pay taxes, such as an income tax, 

should be left to higher levels of government. Although many 

authors (e.g. Break (1980) and Rubinfeld (1983) among others) 

have expounded this view, the seminal treatment is found in Oates 

(1972). He suggests two underlying rationales, one concerned 

with efficiency and the other having to do with equity. The 

first rationale is presented by Oates (197'2)as follows:1 

A local tax of this sort may also result in a second 

and more serious sort of excess burden: it may

distort the selection of a community of residence. 

The tax-price to a consumer of public goods would 

depend, in this case, not only on his level of 

consumption of the good, but also on the individual's 

income. High-income residents would pay a higher

tax-price than would poorer residents. This implies

that the adoption of the tax would immediately

establish some pecuniary incentives for relocation: 

the wealthy would have an incentive to move to 

localities where they could obtain local public goods 

more cheaply. Conversely, poorer persons would tend 

to move into this community because they could consume . public goods for a relatively low tax-price. As a 

result, the local income tax could induce an 

inefficient pattern of location of individual economic 

units, as well as possibly introducing some distortion 

in the work-leisure choice (p. 132). 

The second part of the orthodox argument against local ability to 

pay taxes is that local governments will be unable to achieve the 

social objective of redistributing income.2 The orthodox view of 

the redistributive potential of local governments has also been 
-2-

stated by Oates (1972): 

Moreover, the movement of the wealthy out of the 

community and the influx of the poor would necessitate 

a rising income-tax rate, which would further hasten 

the departure of the rich and subsequently provide

little advantage for the poor. Consumer mobility

would thus not only introduce allocative 

inefficiencies but would also largely frustrate the 

attempt to attain a more desirable incidence of local 

taxes (p.132). 

Despite the orthodox argument, Oates (1983) has recently 

pointed out that all levels of government use an income tax in 

certain cases. In addition, if property values are positively 

correlated with income, a property tax without the zoning 

restriction suggested by Hamilton (1976) is subject to the same 

type of distortionary location incentives that beset an income 

tax.3 Although an ability to pay tax surely creates the 

incentives suggested by the orthodoxy, the magnitude of the 

welfare loss that results has never been estimated. The results 

of this paper indicate that the welfare loss is likely to be 

small and that some redistribution may occur. Consequently, a 

rethinking of the efficacy of local ability to pay taxes may be 

in order. 

The measurement of the welfare loss from local taxation that 

is described by Oates has never been attempted for three major 

reasons. First, several authors have pointed out the 

difficulties in establishing the existence of an equilibrium in a 

model of local governments. Since the usual measures of welfare 

loss presuppose an equilibrium, this problem needs to be overcome 

to apply the standard tools of,economic analysis. Second, the 

literature has not clearly differentiated between various 
-3-

optimality conditions that arise in an analysis of local 

taxation. Consequently, no generally accepted definition of 

"the" welfare loss resulting from local taxation has emerged from 

the literature. Third, the standard analysis would compare an 

efficient equilibrium with an inefficient equilibrium. Even if 

we can define an efficient equilibrium in theory, data may be 

difficult to obtain if such an equilibrium is not attained in 

reality. 

The first problem, that concerning the existence of an 

equilibrium in models of local finance with mobile consumers, has 

arisen in the past decade from attempts to formalize the Tiebout 

(1956) model. Wheaton (1975) is the first to show that a 

proportional income tax, under certain assumptions, will not lead 

to an equilibrium in which people are satisfied with the 

community in which they live. The driving force behind Wheaton's 

result is that a consumer can obtain a lower tax-price by 

migration to a marginally richer community, while maintaining 

equality between his marginal rate of substitution and the ratio 

of prices he faces. In contrast, Westhoff (1977, 1979) showed 

that, if we consider a finite number of communities and restrict 

preferences, an equilibrium can be shown to exist in a model with 

a proportional income tax. Epple, Filimon, and Romer (1983, 

1984) alter and extend the Westhoff model to incorporate a 

housing market, constant marginal congestion costs, and a 

property tax. 

Besides providing sufficient conditions for the existence of 

an equilibrium, the Westhoff model is important because it 
-4-

explicitly incorporates voting within a community. The Westhoff 

proof therefore establishes two types of equilibria: an 

intercommunity equilibrium, in which everyone is satisfied with 

the community in which they live, and an intracommunity or voting 

equilibrium. This suggests two types of welfare losses that 

might occur: the nonoptimal allocation of people to communities 

and the nonoptimal provision of the public good within a 

community. I will refer to the first as a violation of 

intercommunity optimality and to the second as a violation of 

intracommunity optimality. This division has been recognized by 

Wildasin (1980) and Yinger (1982), and a normative framework 

which encompasses such a categorization is developed in Goodspeed 

(1986). Ying.er, in particular, stresses that "efficiency depends 

on the political process of voting, not just on the market 

process of choosing a community" (p. 938). 

The large literature in local public finance on 

intracommunity optimality has developed, on the whole, separately 

from the literature on migration. Barlow (1970) was the first to 

investigate this type of welfare loss. Bergstrom (1979) added 

the interesting theoretical result that, if incomes are 

symmetrically distributed and a proportional income tax system is 

used, majority rule will satisfy the Samuelson condition; that 

is, the sum of the marginal rates of substitution will equal the 

marginal rate of transformation. In a recent paper, Brueckner 

(1982) used a migration model to test empirically for the 

satisfaction of the Samuelson condition within a community. 

Thus, Brueckner tests for intracommunity optimality. In contrast 
-5-

to the many articles on intracommunity optimality, no one has 

attempted to test for or measure the intercommunity welfare loss 

from local taxation, and it is this type of welfare loss that the 

orthodox argument against the use of ability to pay taxes by 

local governments emphasizes. 

Given the strides recently made which establish conditions 

under which an equilibrium will exist, it is now possible to 

construct a general equilibrium model of a Tiebout world which 

includes both voting and migration. As Shoven and Whalley (1984) 

note in a recent survey, applied general equilibrium models have 

become a useful policy tool in the analysis of federal taxes. 

For instance, Shoven and Whalley (1972) and Shoven (1976) have 

investigated the welfare loss from differential capital taxation. 

Fullerton, King, Shoven, and Whalley (1981) have investigated the 

effect of integrating corporate and personal income taxes in the 

United States. The techniques developed in this literature can 

also be applied to investigate local tax issues. Thus, applied 

general equilibrium models provide a solution to the third 

problem mentioned previously, that an efficient equilibrium might 

not exist in practice. 

In this paper, I will use a model developed in Goodspeed 

(1986) that is similar to the Epple, Filimon, and Romer 

extension, but which incorporates a proportional income tax 

rather than a property tax and endogenizes land rents. I use the 

income tax as an example of an ability to pay tax. The model 

incorporates a housing market and so accounts for the 

capitalization of income taxes into the price of housing. By 
-6-

comparing the equilibrium that occurs under the income tax to the 

"counterfactual" head tax equilibrium, I compute the equivalent 

variation (EV) and compensating variation (CV) for any one 

c~nsumer.~The EV and CV can be used to shed light on both the 

equity and the efficiency arguments of the orthodoxy. 

Assuming that the head tax is optimal and that the social 

marginal utility of income is the same for all people, an 

aggregation of the EVs or CVs over all people provides a measure 

of the welfare loss from local income taxation. The generally 

accepted wisdom of the literature is that a head tax is socially 

optimal.6 For instance, Oates and Mills (1975) write that ''a 

head tax would be the simplest perfect benefit tax." (p. 5) The 

assumption that social marginal utilities of income are equal is 

probably not valid so that a simple aggregation of EVs or CVs may 

not correspond to an increase in social welfare. However, there 

is no easy solution to this problem. I present both the EV and 

CV figures as estimates of the change in welfare. In addition, 

the EV or CV for any one consumer gives a measure of how much 

better or worse off he is under a head tax as opposed to an 

income tax. This can be used to judge the redistributive 

potential of the local income tax. 

The rest of the paper will be organized as follows. The 

second section presents an overview of the model and the 

assumptions that are needed to establish an equilibrium. The 

third section presents further assumptions that are used in the 

simulation exercise. The fourth section presents simulation 

results for benchmark parameters of the Stone-Geary utility 
-7-

function. The fifth section presents the results of a 

sensitivity analysis of the model. The sixth section gives a 

summary and conclusions. 

11. The Model 

The model that I will use is an extension of Westhoff's 

(1977) model and is similar to that used by Epple, Filimon, and 

Romer (1984). The additions to the Westhoff model are constant 

marginal congestion costs and a housing market. The differences 

from the Epple, Filimon, and Romer model are that a proportional 

income tax is used rather than a property tax and land is owned 

endogenously. I will present an overview of the model here. A 

more detailed discussion is contained in Goodspeed (1986). 

Following Epple, Filimon, and Romer (1984), housing is 

assumed to be competitively produced from capital and land 

according to a Cobb-Douglas production function: 

H-K (l-B)L(B) = Lk(1-B) (1) 

where L is land, K is capital, and k = K/L. I assume that there 

is an exogenous number of communities, J. Each community is 

assumed to have an identical and fixed land area, L'. Capital is 

perfectly elastically supplied to the metropolitan area. 

Consequently, the price of capital is exogenous to the model. 

Housing producers solve the following profit maximization 

problem: 

where Ph is the price of housing, PK is the price of capital, and 
-8-

PL is the price of land. The first order condition can be 

rearranged to obtain the demand for K. The supply function for 

housing, which is the same in all communities, is found by 

substitution and is equal to 

where E = (l-B)/B. The price elasticity of supply of housing is 

equal to E. 

Income is composed of two parts: a continuous and exogenous 

distribution of income, f(Y), and endogenously determined land 

rents. Land rents in the metropolitan area are defined as the 

sum over communities of producer surplus, and are assumed to be 

equally divided among the fixed number of people in the 

metropolitan area. Thus, an individual's share of land rents, D, 

is given by 

where N is the fixed total number of people in the metropolitan 

area and PhJ is the equilibrium price of housing in community j, 

which is determined by equating the demand and supply of housing 

as described later. I also assume that an individual can be 

characterized by his income, y = Y + D. 

An individual's preferences can be represented by the utility 

function U(x, G, h), but it will prove useful to represent 

preferences by the indirect utility function 

V(G,t,Ph,y) = Max u(X, G, h) S.t. y(1-t) X + phh (5)

h,x 

where x is the private good, G is the public good, h is housing, 

and t is the tax rate. M(G,t,Ph,y) will denote the marginal rate 
--- 

-9-

of substitution between G and t, holding Ph constant. That is, 

dt I = -vG M(G,t,Ph,y) = --I --- I uG (6) 

dG IIdV=dPh=dy=O Vt yux 

The public good in community j is assumed to be produced 

according to a production function which exhibits constant 

returns to scale in capital and constant negative returns to 

scale in the population of community j, Nj: 

GJ = b(K/NJ). (7) 

This functional form is often used in the literature and is 

supported by many empirical studies, beginning with Bergstrom and 

Goodman (1973). For a recent argument, see Hamilton (1983b). 

The cost function associated with this production function is 

CJ(G,NJ) = (PK/b)GNJ (8) 

where PK/b is the constant per person per unit cost of G. 

A complete equilibrium consists of an intercommunity 

equilibrium and intracommunity equilibrium in each community and 

can be characterized by three sets of equations, which will be 

described in turn. The first set of equations comprises an 

intercommunity equilibrium: for given values of the price of 

housing in each community, per-capita land rents, the level of 

public good in each community, and the tax rate in each 

community, we must partition the distribution of people so that 

everyone is satisfied with the community in which they live. To 

obtain this result in a model without a housing market, Westhoff 

makes an assumption that restricts preferences. As shown in the 

Appendix, Westhoff's assumption is equivalent to 
------ 

-10-

E 

GfY > 1 (9) 

IcG,Pl 

where E GtP 

is the price elasticity of demand for G and E GfY is 

the income elasticity of demand for G. 

The problem that one faces when trying to establish an 

intercommunity equilibrium is that a consumer has an incentive to 

move to a richer community in order to obtain the public good at 

a lower price. The role of Westhoff's assumption is illustrated 

in Figure 1 for the two-community case for a particular consumer. 

This consumer obtains the quantity given by his demand curve 

evaluated at price P1 in community 1, and must weigh the costs 

and benefits of residing in community 1 with the lower 

price-.higher quantity option available in the wealthier community 

2. The benefit of residing in community 2 as compared to 

community 1 is area A, the increase in consumer surplus obtained 

* 

from consuming all units up to G at the lower price of community 

2. The cost of residing in community 2 as opposed to community 1 

is equal to area B, the decrease in consumer surplus from 

* consuming units G to G2 for which price is greater than marginal 

benefit. The consumer will reside in community 1 (community 2) 

if area A is less than (greater than) area B. Westhoff's 

assumption implies that, in equilibrium, there will be a person 

for whom area A is just equal to area B. Furthermore, for all 

those poorer (richer) than this indifferent person, area A will 

be less (greater) than area B. 

Since inequality (9) is an important assumption, it is 

worthwhile examining its validity. A survey by Inman (1979) 
-11-

Figure 1 

An Illustration of the Role of Westhoff's Assumption 

$ 

1 

P 

2 

P 

\

I' D 

1 * 2 

G G G G 
-12-

indicates that the income elasticity of demand for local public 

goods has generally been estimated to be greater than the 

absolute-value of the price elasticity. In addition, Hamilton 

(1983a) has argued that income elasticities for local public 

services have been underestimated. This tends to strengthen the 

validity of Westhoff's assumption. 

With the addition of a housing market, the analog to 

Westhoff's assumption is shown in the Appendix to be equivalent 

to 

where &h rY is the income elasticity of the demand for housing. 7 

Intuitively, the housing market acts as a further deterent to 

migration because the consumer may face a higher price for 

housing in a richer community as well as an excessive quantity of 

the public good. In a survey of housing demand studies, Mayo 

(1981) concludes that the income elasticity of demand for housing 

is below one. Thus, in terms of actual elasticity estimates, a 

less restrictive condition can be used to establish an 

intercommunity equilibrium when a housing market is included. 

The importance of the assumption given by inequality (10) is 

that it implies that any equilibrium must be characterized by 

communities that are composed of a single interval of incomes. 

Further, if we rank communities from poorest to richest according 

to mean income, there will exist a border person who is 

indifferent between any two adjacent communities. For the two 

community case, all those richer than the border person will 
-13-

locate in one community, and all those poorer will locate in the 

other. Consequently, the first set of equations that 

characterize a complete equilibrium describes an intercommunity 

equilibrium, and can be stated as 

v(Gj,tJ,PhJ,yJ) V(G j+l,tJ+l"h J+',yj) for j = 1, ...,J-1 (11) 

where yJ = YJ + D denotes the income of the border person between 

communities j and j+l. 

The second and third sets of equations describe 

intracommunity equilibrium: for a given partition of people to 

communities, we must determine the level of public good and the 

price of housing in each community. The prices of housing are 

determined by equating supply and demand in communities 1 to J. 

The supply function is the same in each community. For a given 

partition of people to communities, equilibrium in the housing 

where the signifies that the consumer takes G and t as fixed. 

Equations (12) constitute the second set of equations that 

characterize a complete equilibrium. 

The level of public good is determined by a voting procedure 

in each community. I will assume that the preference of the 

median voter is satisfied. The median voter must satisfy the 

budget constraint of the community. As illustrated in figure 2, 

for a given price of housing and per-capita land rent, a tangency 

of the median voter's indifference curve.and the community's 

budget constraint in the (G,t) plane determines the level of 
-14-

Figure 2 

The Level of Public Good and Tax Rate of Community j 

t 

j

t 
-15-

public good and the tax rate in a given community. Thus, the 

third set of equations that characterize a complete equilibrium 

where med denotes median and m denotes mean. 

Although the three sets of equations (11)-(13) are all that 

is needed to solve the model, other variables of interest are 

found through a set of identities. In particular, the tax rate 

in each community is computed by an identity given by the 

community's budget constraint, 

tj = ((PK/b)/Y mj )Gj (14) 

per-capita land rent is given by equation (4), and the aggregate 

quantity of housing is given by equation (3). Thus, the income 

tax model consists of 5J equations and 55 endog,enous variables, 

GI, tj, HI, Phj for j = 1, ...I J, 

Yj for j = 1, ..., J-1, 

and D. 

The head tax model is similar, and also consists of 5J 

equations: 

v(Gj,cj,PhJ,yj) V(G j+lfCj+l,Phj+l

,y

j for j - 1, ..., J-1 (15) 

for j = 1, ...#J (16) 
-16-

where Cj is the head tax in community j. The endogenous 

variables for the head tax case are 

Yj 

for j = 1, ..., J 

for j = 1, J-1 

D. 

111. Further Assumptions 

To investigate the welfare loss and redistribution that occur 

from the use of ability to pay taxes by local governmentsp a 

functional form for utility must be specified. Because of the 

assumption that restricts preferences that has been made to 

establish the existence of an equilibrium, certain simple 

functional forms are ruled out. For instance, the Cobb-Douglas 

utility function does not satisfy inequality (10); for this 

function income elasticities are one and price elasticities are 

minus one. A simple function that, for certain restri,ctions on 

the parameters,8 satisfies the crucial assumption used in the 

existence proof is the Stone-Geary utility function: 

U( G,h,x) = ( G-A1 ) B1( x-A2 ) B2 (h-A3 ) B3. (21) 

Choosing h and x to maximize (21) subject to y(1-t) = x + Phh 

yields the demand functions for h and x given income tax 

financing: 

h = A3 + (1/Ph)(83/(1-Bl))(y(1-t)-A2-PhA3) (22) 

X A2 + (B2/(l-Bl))(y(l-t)-A2-PhA3). (23) 

Substituting (22) and (23) back into (21) yields the indirect 

utility function V(G,t,Ph,y). Similarly, demand functions can be 
-17-

derived for the head tax case by maximizing (21) subject to y = x 

+ phh + C, which, upon substitution, yields V(G,C,Ph,y). 

To obtain an estimate of the welfare loss for an individual 

from local income taxation, I implicitly define the compensating 

variation and equivalent variation, respectively, for an 

individual with income Y through the indirect utility 

function :

9 

V(t 0 0 ,G ,Pho,Y+Do) - V(G 1,Phl,C1,Y+D1-CV) = O (24) 

V(t 0 0 ,G ,Pho,Y+D0+EV) - V(G 1,Phl,cl,Y+D1) = 0. (25) 

The arguments of the indirect utility function that are 

superscripted "0" indicate the levels attained by the consumer 

under an income tax, while those superscripted "1" indicate the 

levels attained under a head tax. I will assume that the income 

tax equilibrium is the initial state and that the head tax 

equilibrium is the new, or counterfactual, state. The CV is the 

amount of money one would have to take away from the consumer 

after the change to a head tax to leave the consumer at the same 

level of utility that he had attained under an income tax. The 

EV is the amount of money one would have to give the consumer 

before the change to a head tax that would just allow him to 

achieve the level of utility he would have attained under a head 

tax. Thus, both the EV and the CV will be positive if the 

consumer is better off under a head tax and negative if the 

consumer is worse off. 

To obtain an estimate of the welfare loss for society that 

results from local income taxation, I approximate the integral of 

the functions EV(Y) and CV(Y) over Y. lo This presents the well 
-18-

known problem that, unless one-consumer equivalence can be 

invoked, a positive value for the simple sum of EVs or CVs may 

not correspond to an increase in social welfare. A sum of the 

EVs or CVs. is the most widely used measure of welfare loss, and I 

will present the results of such an exercise. But, since it is 

important to further identify the gainers and losers, I will 

supplement the value of the integral of EV(Y) and CV(Y) with an 

identification of the winners and losers by income. 

I must also make an assumption concerning the exogenous 

distribution of income in the metropolitan area. I will assume 

that income in the metropolitan area is uniformly distributed 

between 1 and 2: 

O,Y<1 

f(Y) = 1, 1 1. Y 5 2 

0, Y > 2. 

This assumption implies that, for any partition of the 

distribution f(Y) described previously, the median voter in a 

community will also be the mean voter. From Bergstrom (1979), 

this implies that the quantity of G supplied in each community 

will satisfy the Samuelson condition, whether the tax system is a 

proportional income tax or a head tax. Therefore, the aggregate 

measure of welfare loss that I obtain will' be due solely to the 

nonoptimal distribution of people to communities. 
-19-

IV. Simulation Results for Benchmark Parameters 

For a benchmark case, I selected the parameter values to 

reflect estimated values for the income and price elasticities of 

demand for public services, the income elasticity of demand for 

housing, the share of income spent on housing, the share of 

income spent on local public services, and the price elasticity 

of supply for housing. The parameter values chosen were A1=.04, 

A2=.1, A3=.1, Bls.02, B2=.78, B3=.2, L'=.Ol, and E=3. The choice 

of 3 for E, the price elasticity of supply of housing, follows 

Epple, Filimon, and Romer (1984) and reflects an underlying share 

of expenditure on housing costs that accrues to land of .25. 

Other elasticities and budget shares are calculated from the 

simulation results and are discussed below. The other parameter 

values have been chosen to obtain elasticities and budget shares 

that are consistent with the literature. Those elasticities and 

budget shares that differ across incomes are calculated for the 

median income in the respective community. 

Solutions to the system of equations (3), (4), (11)-(14) and 

(15)-(20) were obtained for the cases of 2, 6, and 12 communities 

using the TSP statistical package. l2 TSP uses a variant of 

Newton's method to solve a system of nonlinear equations. As 

Tables lA, lB, and 1C show for the 2, 6, and 12 community cases 

respectively, the benchmark results are characterized by income 

elasticities for the public good that range from about .4 to -55 

and price elasticities for the public good that range from -.32 

to -.48. These are consistent with the estimates surveyed by 
46 .54 

-.35 -.45 

.65 e 72 

&h,Y 

Housing Share .3f .28 

-20-

Table 1A 

Benchmark Case, 2 Community Model 

2 Cormunity Model, Head Tax 

1 

G .06067 

’h 2.20320 

H .lo695 

Y’ 1.5517 

D <-

46 

-.35 

.65 &h,Y

Housing Share .3f 

Public Good Share .044 

Share of Population .55 

conununity 2 

.07067 

2.20475 

.lo717 

.11798 -> 

.54 

-.45 

e 72 

.28 

037 

.45 

Aggregate Tax Revenue = .06515 

2 Comity Model, Income Tax 

1 

G ,06039 

t .04392 

’h 2e 1544 

H. .loo0 

Y’ 1.5137 

D <-

.45

‘G,y -.35 ‘G.P 

.66 ‘h,y

Housing Share .30 

Public Good Share .044 

Share of Population .51 

Coxtununity 2 

07020 

.03744 

2.24984 

.1139 

.11791 -> 

.53 

-.44 

.71 

e 28 

.037 

.49 

Aggregate Tax Revenue = .06392 * 

Aggregate CV = .57% of tax revenue

Aggregate Ev = .64% of tax revenue 
-21-

Table 18 

Benchmark Case, 6 Community Model 

6 Community Model, Head Tax 

Community 

1 2 3 4 

G .0581 .0620 .0655 .0688 

’h 1.6298 1.6299 1.6300 1.6301 

H .0433 .0433 .0433 .0433 

Y’ 1.2051 1.3894 1.558.1 1.7147 

D < -_I .lo590 

‘G,y 42 .45 .48 .51 

E

G,P 

&h,Y 

-.33 

.70 

-.37 -.40 -.43 

.73 .75 .77 

Housing Share .28 .27 .26 .26 

public Good Share .048 ,044 .041 .039 

Share of Population .20 .18 .17 .16 

Aggregate Tax Revenue = ,06606 

5 6 

.0718 .0747 

1.6301 1.6301 

.0433 .0433 

1.8615 

> 

.53 .54 

-.45 -.47 

0 79 .80 

.25 .25 

.038 .037 

.15 .14 

5 6 

.0712 .0743 

.0381 ’ .0367 

6 Community Model, Income Tax 

Community 

1 2 3 4 

.OS79 ,0613 .0647 .0679 

.0486 .0449 .0421 .0399 

G 

t 

‘h 

H 

Y3 

D 

‘G,y

E

GtP 

‘h,Y

Housing Share 

Public Good Share 

Share of Population 

1.5534 1.5893 1.6197 1.6459 1.6689 1.6893 

.0375 .0401 .0425 .0446 ,0465 .0482 

1.1739 1.3453 1.5137 1.6790 1.8410 

< .lo582 > 

.41 .45 .47 .50 .52 .55 

-.32 -.36 -.39 -.43 -.45 -.47 

.71 .73 .75 .77 .78 .79 

.31 .30 .29 .28 .27 .27 

.049 .045 ,042 ,040 .038 .037 

.17 .17 .17 .17 .16 .16 

Aggregate Tax Revenue - .06606 * 

Aggregate CV - .89% of tax revenue

Aggregate EV = .99% of tax revenue 
-22-

Table 1C 

Benchmark Casep 12 Community Model 

G 

'h 

E 

Yj 

D 

'G,y 

CG,P 

%Y 

-lnity 

1 2 3 4 5 6 7 8 9 10 11 12 

.OS76 .OS% .0616 .0635 .0652 .0669 .06L)S .0701 .0716 .0730 .0745 .0758 

1.351 1.351 1.351 1.351 1.351 1.351 1.351 1.351 1.351 1.351 1.351 1.351 

.0247 .0247 .0247 .0247 .0247 .0247 .0247 .0247 .0247 .0247 ,0247 .0247 

1.1072 1.2078 1.3027 1.3929 1.4790 1.5615 1.6408 1.7173 1.7913 1.8629 1.9324 

e .lo0027 > 

.40 .42 .44 .46 .47 .48 .50 .51 .52 .53 .54 .55 

-.32 e.34 -.36 -.38 -.40 -.dl -.I3 -.44 -.45 --46 -.47 -.40 

-74 .76 .77 .78 .79 .80 .81 .82 .82 .83 .03 .04 

wing Shere .27 .26 .26 .25 .25 .25 .25 .24 .24 .24 .24 .24 

Public Geod Share .OS0 .047 .045 .044 .042 .041 .040 .039 .039 .038 .037 .037 

Share of -ation .11 .10 

- .09 .09 .09 .08 .08 .08 .07 e 07 .07 .07 Aqgregatr Tax Rmvann .066498 

1 2 3 4 5 6 7. 8 9 10 11 12 

G .OS75 .OS92 .0609 .0626 .0643 .0659 .0676 .0692 .0708 .0724 .074O .0756 

e .OS03 .OM1 .0463 .0446 .0432 .0420 .0408 .0398 .ON9 .0381 .0373 .0367 

'h 1.274 1.292 1.308 1.322 1.336 1.348 1.360 1.371 1:381 1.390 1.399 1.400 

H .0207 .a215 .0224 .0231 .02N .0245 .0252 .02S .0263 .0269 .0274 .0279 

Yj 1.087 1.174 1.260 1.345 1.430 1.514 1.597 1.679 1.760 1.841 1.921 

D c .099955 > 

'Goy .40 .91 .43 .IS .46 .(o .49 .SO .51 .52 .53. .54 

'G,P -.32 -a34 -e36 -.37 -.39 -.40 -.42 -.43 -.IS -.46 -.47 -.40 

%Y .75 .76 .77 .78 .79 .80 .80 .81 .82 .82 .a2 .83 

Bavinq YYrr .26 .26 .26 .26 .25 .IS .25 .25 .24 .24 .24 .24 

Public Good Shrr .OS0 .048 .046 .045 .043 .042 .041 .040 .039 .038 .037 ,037 

share of population .09 .09

- .09 .09 .08 .Q .08 .08 .08 .08 .08 .00 Aqgrwt. Tu RMnw .0665034 

Aqqrrg.te CV - 1.14% of tu rm" 

Aqgceg8te W - 1.25% of tax rw" 
-23-

Inman (1979) that pertain to total expenditure. The benchmark 

income elasticities for housing range from about .65 to about 

.84. These are within the range of estimates surveyed by Mayo 

(1981). The budget share for housing ranges from about .24 to 

about .31. Finally, the budget share for the public good ranges 

from about .037 to about .05, which is consistent with data 

presented by Gold (1986) that indicate a share of .043 and the 

.05 figure cited by Gramlich (1985). 

Comparing the head tax and income tax equilibria, the most 

interesting endogenous variables are the income of the border 

person between communities and the price of housing within each 

community. From the equilibrium value of the border incomes, I 

computed the proportion of the population that lives in each 

community. These proportions can be compared for the head and 

income tax cases. For the two community income tax case, about 

51 percent of the population live in the poor community and about 

49 percent live in the rich community. For the two community 

head tax case, about 55 percent of the population live in the 

poor community, 4 percent higher than the income tax case, and 

about 45 percent live in the rich community. For the 6 and 12 

community cases, a pattern emerges which continues to show a 

greater proportion of people living in poor communities under a 

head tax. The reason for this is that the lower price for the 

public good that an individual can obtain by residing in a richer 

community under an income tax makes richer communities more 

attractive relative to the head tax case. As noted earlier, the 

two factors that act to counter the lower price effect are the 
-24-

higher than preferred level of public good and the higher price 

of housing in rich communities. 

The price of housing exerts a strong influence on the pattern 

of migration. This is clear from the results of both the head 

and income tax cases. In the head tax case, the price of housing 

is practically identical in all communities. The price of 

housing can differ among communities only because of demand. 

Thus, with equal populations and a positive income elasticity, 

richer communities would have higher aggregate demand and 

therefore higher prices for housing. Other things equal, this 

tends to make poorer communities more attractive. Consequently, 

in the head tax case, people tend to move to the community with a 

lower price for housing until an equilibrium is established in 

which housing prices are equalized. In the income tax case, rich 

communities are more attractive than poor communities, relative 

to the head tax case. Consequently, the price of housing is 

lower in poor communities and higher in rich communities in the 

income tax case as compared to the head tax case. The strong 

influence of the housing market is probably due to the fact that 

people spend a substantial proportion of their budget on housing. 

To obtain a measure of the welfare loss to society from using 

an income tax on the local level, I computed the aggregate EV and 

the aggregate CV as described in footnote 10. Both measures rise 

with the number of c~mmunities,'~but are small for all cases 

using the benchmark parameter values. For the 2 community model, 

both the EV and the CV are slightly over one half of one percent 

of tax revenue aggregated across communities. For the 6 
-25-

community model, both measures rise to just under one percent of 

tax revenue. The 12 community model yields an EV of about 1.25 

percent of tax revenue and a CV of about 1.14 percent of tax 

revenue. Thus, I find consistently small values for the welfare 

loss from local income taxation. 

The reason for the small loss in welfare is that the budget 

share of the public good relative to the budget share of housing 

is small. To understand why this is an important determinant of 

the magnitude of the welfare loss, recall the incentives faced by 

a consumer under an income tax. The consumer will be better off 

in a richer community under an income tax as compared to a head 

tax because he can obtain a lower price per unit of the public 

good. However, the consumer may have to consume a higher 

quantity of G than he demands at the lower price and also may 

face a higher p,rice for housing. If housing consumes a large 

share of income relative to the public good, then the price of 

housing will be the more important influence on the consumer. 

But, since changes in the price for housing are caused by a 

pecuniary rather than a technological externality, such price 

changes do not cause a change in aggregate welfare. Thus, if the 

budget share for housing is high relative to the budget share for 

the public good, we should observe a small loss in welfare. 

Further results that demonstrate this are presented in the next 

section. 

Although I find that the welfare loss from local income 

taxation, measured by either a sum of the EVs or a sum of the 

CVs, is small, does this mean that the change in welfare for any 
-26-

individual is small? The answer is of course ''no" since some of 

the EVs (CVs) are positive and some are negative. Figure 3 plots 

the EV for some values of income for the 6 community case. The 

poorest person, who has an income of 1, is worse off under a head 

tax by about .02. The tax that he pays constitutes about five 

percent of his budget, or .05. Thus, the welfare gain to the 

poorest individual from the income tax is about 40 percent of the 

tax paid by him. Still, his gain in welfare is small relative to 

his income since the local public good takes up only a small 

proportion of his budget. 

As another illustration of the redistribution that may occur 

from the local income tax, let those with income net of land rent 

above 1.5 be called "rich" and those with income below 1.5 be 

called "poor.II The total gain in welfare for the poor in the 6 

community EV case is .0048, aggregate tax revenue is .06606, and 

the aggregate EV is .00065. Thus, for each dollar in aggregate 

tax revenue, the poor gain on average about $.07 and society 

loses on average about $.01. The local income tax appears to 

have some potential as a redistributive tool in a system of local 

governments. 

Why does redistribution occur in the model, contrary to the 

orthodoxy? There are two reasons for this result. First, the 

orthodox view does not take account of the housing market. 

Second, because of the limited number of communities, the rich 

may not have a better alternative to their present community. To 

assess the redistribution result thus requires an assessment of 

these underlying assumptions. Surely, the inclusion of the 
-27-

Figure 3 

The EV(Y) Function for the 6 Community, Benchmark Case 

Ev 

.02 

.01 

0 1 

I 

6 1.7 1.8 1.9 2.0 Y 

-.01 

0.02 
-28-

housing market improves our understanding of local finance. The 

assumption of a fixed number of communities is more 

controversial. While some authors (e.9. Rose-Ackerman, 1979) 

have argued in favor of this assumption, others (e.9. Henderson, 

1985) have argued against it. I find the assumption plausible, 

especially in the older industrial cities of the northeast United 

States. 

Two major conclusions have emerged from an analysis of the 

results of the benchmark case that diminish the force of the 

orthodox arguments against the use of ability to pay taxes by 

local governments: the welfare loss suggested by the orthodoxy 

is small and some redistribution may occur. However, before 

jumping to policy conclusions, it is wise to consider the 

robustness of the results. 

V. Sensitivity Analysis 

Sensitivity analysis is conducted by varying the parameters 

of the model, recalculating the results, and observing whether 

the results have changed. To make the analysis economically 

meaningful, I present the results of the sensitivity analysis in 

terms of the relevant elasticities and budget shares, which are 

computed from the simulation results, rather than in terms of the 

parameters directly. As indicated in section 2, certain 

assumptions concerning the income and price elasticities of 

demand for the public service and the income elasticity of demand 

for housing are important in establishing an equilibrium. One 
-29-

might expect that changing the benchmark elasticities would 

influence the magnitude of the welfare loss. I did not find this 

to be the case.l5 Rather, the most important influence on the 

size of the welfare loss is the budget share of the public good 

relative to the budget share for housing. 

Case a of Table 2 summarizes the results from increasing the 

budget share of the public good, while leaving the budget share 

for housing at the benchmark level. The aggregate EV and CV rise 

for this case as compared to the benchmark case, but remain small 

when the budget share of the public good is increased to about 10 

percent. For the 12 community case, the welfare loss as measured 

by the EV is only 2.8 percent of aggregate tax revenue. The 

primary reason for this result is that, although the budget share 

of the public good is higher than the benchmark case, it remains 

less than the budget share'for housing. To demonstrate the 

change in the welfare loss when the budget share of the public 

good relative to housing is high, case b of Table 2 summarizes 

the results for the case of (approximately) the benchmark budget 

share for the public good, ranging between .039 and .056, and an 

almost equal budget share for housing. For parameter values that 

yield these budget shares, the aggregate EV in the 12 community 

case rises substantially to about 8.8 percent of tax revenue. 

VI. Summary and Conclusions 

This paper examines the orthodox argument that local 

governments should abstain from the use of ability to pay taxes 

'. 
-30-

Table 2 

Sensitivity Results 

Case a (High Share of Public Good) 

&GfY -

& GtP 

‘hfy 

Share of housing 

Share of public good 

* 

EV (CV): 2 community model 

* 

EV (CV): 6 community model 

* 

EV (CV): 12 community model 

Case b (Low 

‘G,y 

& GtP 

‘hfy 

Share of housing 

Share of public good 

* 

EV (CV): 2 community model 

EV (CV): 6 community model* 

* 

EV (CV): 12 community model 

* 

Share of Mousing) 

-40 - .55 

-.32 - -.48 

-81 - .83 

.24 - .25 

.09 - .12 

1.7% (1*5%) 

2.6% (2.3%) 

2.8% (2.5%) 

-36 - .51 

-.32 - -.47 

-75 - -82 

-036 - .040 

,039 - .056 

5.0% (4.9%) 

7.9% (7.8%) 

8.8% (8.6%) 

All EVs and CVs are given as a percentage of aggregate tax 

revenue in the metropolitan area. 
-31-

such as an income tax. Using an applied general equilibrium 

framework, the efficiency and equity parts of this argument are 

quantified. The local income tax is found to cause a nonoptimal 

allocation of people to communities, but the welfare loss is 

found to be small for benchmark parameter values. This is due 

primarily to the the small budget share of the local public good 

relative to housing. Changes in the price of housing result from 

a pecuniary externality and therefore do not lead to efficiency 

losses, but such price changes are the primary deterrent to 

migration when the budget share for housing is high relative to 

the budget share for the public good. Thus, the model results 

suggest that the efficiency part of the orthodox argument may not 

be quantitatively important. Furthermore, as long as the budget 

share for housing remains high relative to the budget share of 

local public services, the welfare loss is likely to remain 

small. That is, even if local governments increase their 

expenditures to 10 percent of an individual's budget, the welfare 

loss is likely to remain small as long as people continue to 

spend 25 to 30 percent of their income on housing. In addition, 

some redistribution is found to take place. This is due to the 

inclusion of a housing market and the assumption of a limited 

number of communities. These results suggest that local 

governments can use ability to pay taxes that result in some 

redistribution without serious efficiency consequences. 

The results also have implications that extend beyond the 

question of the efficacy of the use of ability to pay taxes by 

local governments. To the extent that the property tax suffers 
-32-

from the same distortionary location effects, the results suggest 

that the question of whether the property tax is a pure benefit 

tax may have been given too much weight since the magnitude of 

the welfare loss resulting from nonbenefit taxation is small. 

Other inefficiencies created by the property tax and in the 

supply of public services should be given more emphasis in future 

research. 
-33-

Footnotes 

1. Oakland (1983) has expressed dissatisfaction with the orthodox 

view by suggesting that the mobility argument has been given too 

much weight. 

2. Two notable exceptions to the orthodox treatment of the 

distribution function are Pauly (1973) and Tresch (1981). 

3. This is not meant to render a judgement on whether zoning

restrictions conform to the Hamilton type, but rather to suggest

that the results of this paper have implications that extend 

beyond the use of traditional ability to pay taxes by local 

governments. 

4. Gordon (1983) is an exception to this. He provides a 

categorization of various externalities resulting from local 

decision making. However, he does not differentiate between 

intracommunity and intercommunity optimality as defined in this 

paper. 

5. Kay (1980) has suggested that the EV is a better measure 

because the compensation is valued at the prices that actually 

occur rather than at the counterfactual prices. Consequently,

different policy alternatives can be compared if the EV measure 

is used, but not if the CV measure is used. In the present 

context, the income tax equilibrium is taken as the status quo

and the head tax case as the counterfactual equilibrium. Since 

there is only one policy alternative, the Kay argument does not 

apply directly. Still, it is interesting to see both the EV and 

CV measures since they are different numbers and I include both 

in the analysis. 

6. Wildasin (1986, p.15) disputes the neutrality of a local head 

tax. However, the assumption made in this paper concerning the 

production function for the local public good negates Wildasin's 

objection. 

7. Burstein (1980) and Bucovetsky (1981) suggest similar 

conditions in different models. 

8. The restrictions are derived in Goodspeed (1986) and are 

available upon request. 

9. Just, Hueth, and Schmitz (1982, p.95) provide a nice 

explanation of the implicit relationship between the CV and the 

indirect utility function. 

10. To calculate the aggregate CV and EV, I solved equations (24)

and (25) for CV and EV, respectively. The next step is to 

integrate over incomes. Some of the CVs and EVS are positive and 

some are negative. However, a priori, one does not know which 

incomes are associated with positive values and which with 
-34-

negative values. Therefore, I approximated the area under the 

functions CV(Y) and EV(Y) by the trapezoidal method. I 

calculated and summed the area of 1000 trapezoids. 

11. Tresch (1981, pp. 81-85) outlines conditions for which 

one-consumer equivalence holds. Unfortunately, these conditions 

are not satisfied for the assumptions of this paper. 

12. Westhoff (1979) cautions against policy conclusions partly on 

the basis that, if there is a unique equilibrium, it is 

necessarily unstable. This suggests that multiple stable 

equilibria might occur in the simulation. I varied the initial 

values of the endogenous variables and always converged to the 

same equilibrium for given parameter values. Thus, although

Westhoff shows that a unique equilibrium must be unstable in a 

model without a housing market, the possible problem of multiple

stable equilibria does not arise in the simulation exercise. 

13. A priori, it is not clear whether the CV should rise or fall 

as the number of communities is increased. More people change

communities as the number of communities rises. Since more 

people are induced to alter their behavior because of the income 

tax, the CV should rise. However, people move to the next 

richest community, which differs from the initial community by

less and less as the number of communities rises. Thus, although 

more people alter their behavior, each person experiences a 

smaller change so that the aggregate effect is ambiguous.

Another way to look at this is that as the number of communities 

rises the head tax equilibrium moves closer to a situation in 

which communities are homogeneous and each consumer obtains his 

unconstrained optimal amount of G. This tends to increase the CV 

as the number of communities is increased. However, the income 

tax equilibrium is also changing, and may be closer to or farther 

from the optimum. 

14. Graphs of the cases for 2 and 12 communities for the EV and 

the CV cases are similar. 

15. Results for these cases are available from the author on 

request. 
-3 5-

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--- 

------ 

-38-

Appendix 

Derivation of Elasticity Conditions 

To derive the elasticity condition that corresponds to 

Westhoff‘s (1977) assumption, define the indirect utility

function 

V(G,t,Y) U(G, Y(1-t)) A(1) 

and define the marginal rate of substitution between t and G 

dt I 

M(G,t,Y) --I = -vG 3 ---uG 

dG I1 dV-0 Vt yuX 

Define P = UG/Ux as the shadow price of G and G = G(PG, Y, t) as 

the demafid function for G. Totally differentiating the demand 

function and setting dG = dt = 0 yields 

Westhoff‘s assumption is 

From A(2) and A(3), 

& 

Thus A(4) holds iff GfY > 1. 

When the housing market is included, the indirect utility

function becomes 
-39-

. 

V(G,t,Ph,y) = Max U(x,G,h) S.t. y(1-t) Phh + X. 

x,h 

Totally differentiating V(G,t,Ph,y) yields 

where the * denotes the optimal value and P = U /U is the 

shadow price of G. The assumption used in Eoodsjee8 (1986) to 

establish an equilibrium is 

1 

I 

LdPh IdV=dt=dpO I

Using A(6) and A(3), 

1

I 

&G Thus , A( 7) holds iff ---lx- > &h,y'

I'G,PI