a general equilibrium analysis of property tax incidence

Journal of Public Economics 29 (1986) 113-132. North-Holland

A GENERAL EQUILIBRIUM ANALYSIS OF PROPERTY TAX INCIDENCE

Chuan LIN*

Chung-Hua Institution for Economic Research, 75 Chang-Hsing Street, Taipei, Taiwan 106, Republic of China

Received June 1984, revised version received September 1985

Mieszkowski’s (1972) analysis of the ‘new view’ of property tax incidence dealt with a model of an economy containing only one sector and three factors, in which labor was immobile. Brueckner (1981) incorporated an equal utility condition into his general equilibrium analysis of property tax incidence to take worker mobility into account. His model, however, did not have capital as an input factor and the benefits of public expenditure were ignored. This paper extends previous research by using a general equilibrium model of an economy with two sectors, three factors, and multiple communities. Both capital and labor are assumed to be mobile and Brueckner’s labor mobility condition is modified to include public expenditure effects. While the results of the analysis support the ‘new view’, they qualify the original Mieszkowski studies in many aspects. The model also sheds light on tax incidence in no-tax communities, which was often ignored in earlier studies.

1. Introduction

The traditional view of property tax incidence, which was based on the assumption of a perfectly elastic supply of capital improvements, has been superseded by the ‘new view’, introduced by Mieszkowski (1972). The ‘new view’ explicitly identifies the different effects of local versus nationwide imposition of a property tax. The main conclusion of Mieszowski’s analysis is that a uniform tax on the value of capital improvements would be borne in full by owners of capital goods since capital is fixed in supply for the whole economy. If the property tax is not uniform, tax rate differentials would lead to excise tax effects while the overall return to capital would be depressed by the economy-wide average rate of the tax.’

While Mieszkowski’s contribution was accepted by most economists, ‘. . . the theoretical foundations of the new view are incomplete’ [Aaron (1975, p. 42)]. Mieszkowski himself admits that his analysis of property tax

*This paper is based on part of my unpublished Ph.D. dissertation at the University of Illinois at Urbana-Champaign. I am grateful to Jan Brueckner, my adviser, for guidance and helpful, substantive, as well as editorial, suggestions. Also, I thank two referees for helpful comments. Any errors, however, are my own.

‘See Aaron (1975, pp. 18-55) for an excellent survey of both viewpoints.

0047-2727/86/$3.50 1986. Elsevier Science Publishers B.V. (North-Holland)

114 C. Lin, Property tax incidence

incidence is partial because of the omission of genera1 equilibrium adjust- ments and price changes which occur in the no-tax communities2 A further drawback is that Mieszkowski’s analysis is based on a mode1 with one sector and three factors (capital, labor, and land) in which only capita1 was mobile. Both Aaron (1975) and Courant (1977) agree that a more precise analysis should rely on a two-good, three-factor model where two factors (labor and capital) are mobile between jurisdictions. The results of such a mode1 could differ in important ways from those of Mieszkowski.

The purpose of the present paper is to provide a more genera1 analysis of property tax incidence by focusing on a mode1 which is free of the above deficiencies. Innovations in the model include the assumption of an economy with two sectors (housing and non-housing), three factors (capital, labor and land), and multiple jurisdictions. A complete genera1 equilibrium analysis is carried out under the assumptions that capita1 and labor are fully mobile. In the treatment of labor mobility, the analysis extends the work of Brueckner (1981), who was the first to use equalization of utilities as the appropriate labor mobility condition in a general equilibrium framework. While previous authors, such as McLure (1975) and Mieszkowski ( 1972),3 believed that wage equalization was the appropriate migration equilibrium condition, the possi- bility of cost of living or public service differences between communities means that wage equalization need not generate worker indifferences between jurisdictions. While Brueckner’s analysis also used a genera1 equilibrium approach, his mode1 did not include capital as an input factor and therefore was only weakly connected to the ‘new view’. Another drawback in his framework was the omission of public expenditure effects, which are included in the present ana1ysis.4

The plan of the paper is to present the mode1 and its solution in the next section. Section 3 offers intuitive explanation of the results of the analysis of section 2 and section 4 discusses the difference made by eliminating the labor mobility assumption from the model. The study is summarized in the last

section.

‘Mieszkowski (1972, p. 82). % Mieszkowski’s (1972) paper, the analysis of the property tax effects is composed of two

parts. The first part explains the excise tax effect with a numerical example. The next part demonstrates the capitalization of property taxes and the effects on land values and wage levels by using a one-sector model. While this general model assumes immobility of labor, Miesz- kowski did consider perfect mobility of labor as well as capital in the numerical example dealing with the excise effect of property tax differentials. His labor mobility condition requires that after-tax wage rates are equal in all communities.

41gnoring public expenditure benefits would be appropriate from the point of view of tax incidence studies only if government expenditures were completely wasteful. See Lin (1985) for details.

C. Lin, Property tax incidence 115

2. The model

2.1. Basic assumptions

The economy described in the model contains multiple communities. Each community has both housing and non-housing sectors. Housing is assumed to be non-traded, while non-housing, which is viwed as a composite good, is tradeable among regions. Transport costs are neglected, which implies a uniform non-housing price in all communities. The economy is endowed with three input factors: capital, labor and land, which are all fixed in supply. For

analytical convenience, each sector is assumed to use only two factors. We assume housing is produced by capital and land, and non-housing by labor and land.5 In addition, product and factor markets are perfectly competitive, and factors receive the value of their marginal products. Production functions are identical across communities and are assumed to be homogeneous of degree one.

Each resident owns only one kind of income resource. Residents with the same income resource receive the same amount of income (i.e. endowments are identical for all capital owners; the same is true for workers and landlords). Both capital and labor are assumed to be perfectly mobile among communities at zero cost, so that rates of return on capital and workers’ utility levels must be uniform across communities (workers must live and work in the same community). Capital owners and landlords, however, are assumed to be immobile. Residents are assumed to have identical homothetic preferences. In addition, local governments will enforce a balanced budget by returning to each of their residents a lump-sum amount equal to taxes paid.6

Population densities of workers, capital owners and landlords are uniform across communities. There are n (n 22) communities with equal fixed land areas. The property tax is imposed on housing services as an ad valorem tax.7 The economy starts in equilibrium with a zero tax rate in every community, and the effect of an increase in the property tax rate in community 1 is analyzed.

‘Mieszkowski (1972) assumes that housing is produced by capital only and that the property tax is imposed on all types of capital. The current model goes beyond this restrictive assumption through the incorporation of a land input into housing production. While the omission of a labor input from the housing sector and a capital input from the non-housing sector seems suspect, the justification is based on the fact that housing production is capital intensive and non-housing production is labor intensive. The model considers the extreme case of capital and labor intensitivity by eliminating the less important labor input from the capital-intensive housing sector and the less important capital input from the labor-intensive non-housing sector. As long as the production of housing is relatively capital intensive, qualitative analysis under the current model will not be misleading.

6The advantages of this assumption in tax incidence analysis are widely recognized. For instance, see Tresch (1981, p. 380).

‘In a more realistic model the tax would also be levied on the land used in non-housing production.


Since the analysis relies heavily on the symmetry of the initial equilibrium, the assumption of equal land areas might appear to be crucial. The results derived, however, also apply in the absence of this assumption. This is due to the fact that increasing the size (land area and population) of a community increases total endowments proportionally within that community, which leaves all marginal productivities and prices unchanged (recall that production exhibits constant returns). Therefore, a big community is equivalent to a combination of several small communities. Essentially, we consider the case where the taxed community has a land area equal to l/n of the total land area of the economy, with no-tax communities containing the remaining (n-1)/n of the land (the approtionment of this area among communities is irrelevant).

2.2. The structure of the model

The variables in the model are defined as follows. The wages, rates of capital return, land rents, and housing prices (gross of tax) in each jurisdiction are, respectively, Wi, Si, li, pi, i = 1,2,. . . n. AS Harberger and his followers have done, we choose units of labor, capital, land, and housing such that all the above prices are initially equal to one. Xi, which represents the non-housing good produced in community i, is taken to be the numeraire, with its price set to unity. Housing services in community i are represented by Hi. The production functions of Hi and Xi, which are

identical across regions, are written as Hi=F(Ki, 1H) and Xi= G(Li, I;), respectively, where Ki, Li, 1H, and 1; are the capital input to housing production, the labor input to non-housing production, the land input to housing production, and the land input to non-housing production, respectively, in community i.

The capital constraint for the economy is K 1 + K, + ... + K,= nK, where nK equals the total fixed stock of capital (note that K, = ... = K,= K will hold initially because of symmetry). Total differentiation of this constraint

yields:

dK,+dK,+ ... +dK,=O. (1)

Because of the symmetry assumption of equal size communities, the effect of the property tax imposed in community 1 is identical for the n- 1 other communities. This means that dK, + dK, + . . . + dK, = (n - 1) dK,. Letting an asterisk (*) indicate a natural logarithm, so that dKT =dKJK, eq. (1) reduces to

dK:+(n-l)dK;=O. (la)


The economy’s labor force constraint, and the land constraints in each community, are L, + L, + . . . + L, = nL and 1; + 1: = 1, respectively (total land area 1 is the same for each community). Total differentiation yields:

dLT+(n-l)dL,*=O, (2)

lHdl”*+lXdl~*=O, i=l,..., Iz. (3)

Note that eq. (3) incorporates the symmetry assumptions since ly=ly=lH

and 1; = 1; = 1”.

The basic factor demand condition for the housing industry is’

aH(ds;-dr;)=dl”*-dK,*, i=l,...,n, (4)

where &’ represents the elasticity of substitution between capital and land in housing production. In addition, the assumption of linear homogeneous production functions and competitive factor markets means that equilibrium is also characterized by the next two conditions in housing production:

dH:=f,dK;+f,dl”*, i=l,..., n, (5)

dpT=dti+ fkdsF+fidrr, i=l,..., n, (6)

where fk and fi are the initial factor shares of capital and land in the housing sector, and ti is the property tax rate on housing consumption in community i (fk and fi are identical across communities because of the symmetry of the initial equilibrium).

Conditions similar to (4) and (6) for the non-housing sector are

cr”(dwf-drf)=dl;*-dLT, i=l,..., n, (7)

and

O=g,dwT+g,drl, i= l,..., II, (8)

respectively, where ox is the elasticity of substitution between labor and land in non-housing production, and g, and g, are the initial factor shares of labor and land-in non-housing production. The right-hand side of (8) is zero because the non-housing good is numeraire. An equation analogous to (5) for the non-housing sector is unnecessary since the non-housing market is ignored by Walras’ law.

‘The derivation of eq. (4), as well as eqs. (5) and (6) below, can be found in Shoven and Whalley (1972) and in McLure (1975).


The capital mobility condition gives:

dsT=dsT=ds*, i,j=l,..., n and i#j, (9)

where si(sj) indicates the capital return in community i (j), and s the common capital return.

The equal utility condition for workers is less familiar than those above. In its basic form, the condition requires:

I/(~,+tib,p,,pi)=I/(~~+tjb~p~,~~), i,j=l,..., n,and ifj, (IO)

where I/ is the common indirect utility function, and bi (bj) is individual housing consumption by workers in community i( j).9 The term (wi + t,b,p,) in the utility function represents the total income received by individual workers, which includes wage income (wi) and the government’s lump-sum return of taxes paid (t,b,p,) (recall the balanced budget assumption). By Roy’s Identity, dl//api= -biYL, where YL is marginal utility of income. With a property tax imposed only in community 1 and all prices being initially equal to one, differentiation of eq. (10) and use of Roy’s Identity yields:

dw:+bdt,-bdpT=dw:-bdp,*, i=Z,...,n, (104

where b= b, = bi because of the symmetry of the initial equilibrium (the YL

terms cancel by symmetry). To close the model, a housing sector demand condition is needed. Since

preferences are assumed to be homothetic, each resident in the community spends fixed proportions of his income on housing and non-housing goods. Aggregate housing demand in the community therefore depends directly on the community aggregate income and the housing price. Furthermore, we have already seen that local governments maintain balanced budgets by returning to each of their residents a lump-sum amount equal to taxes paid. This assumption produces the same implication as Harberger’s assumption that the government spends its tax revenue in the same way as does the private sector (aggregate demand is the same regardless of whether the

government returns the tax revenues or spends them as a consumer). The income effect of the tax change is eliminated by either of these assumptions. There is, however, a substitution and migration effect on aggregate demand (the migration effect results from worker movement among communities). The housing demand condition thus may be written (see appendix A) as

dHF=Edp*+MdL*, i=l,..., n, (11)

‘Note that non-housing price is not included in the indirect utility function because the non- housing good is numeraire.


where E, which is negative, is the income-compensated elasticity of demand for housing, and M, which is positive, is the elasticity of community housing

demand with respect to worker population. Because of the symmetry assumptions, both E and M have the same values over communities at the initial equilibrium. Finally, note that a demand condition for the non- housing sector is redundant by Walras’ law.

The system described above can be simplified. Eq. (9) is eliminated with substituting ds* for ds,* in (4) and (6). Furthermore, due to the symmetry assumptions, the property tax in community 1 produces equal effects in the rest of the communities. We therefore drop communities 3 through n from consideration. With two communities left, the system thus contains 17 equations (la), (2), (3), (4), (5), (6), (7) (8), (lOa), and (11) to solve for the 17 unknowns dKT, dLT, dir*, dl;*, dHT, dr?, dw:, dp:, and ds*, i= 1,2.

2.3. The implications of the labor mobility condition

To solve the system, we first substitute (6) and (8) into the labor mobility equation (10a). After eliminating dp?, and dw:, the equation reduces to

dr: = dr; = dr*, (lob)

where dr* represents the common change of land rent in all communities. It follows immediately that dw: =dwz =dw*, where dw* is the common change of the wage rate in all communities.

The labor mobility condition, with the incorporation of (8) (the condition of the equal price of the non-housing good) therefore implies equalized factor returns not only to labor but also to land in spite of the immobility of land. These results follow from two facts. First, due to the presence of the tax rebate, the impact of the tax component of the gross housing price is fully offset by the extra benefit received from the public expenditure. Changes in workers’ utility levels, therefore, are determined only by changes in the wage rate and the net price of housing services. Furthermore, since the change in the net price of housing services depends entirely on the change in the land rent and capital return according to (6), and since capital returns are equalized in equilibrium, worker utility level differences between communities are ultimately determined by changes in wages and land rents [the equal utility condition of (10a) reduces to dwf-bf,drT =dwg-bfdr~]. Secondly, the’ fi~ct that the non-housing good is tradeable means that its price must be equal across communities, so that g,dw:+g,dr: =g,dwg +g,drg =O.” To see the implication of these facts,. suppose dw: >dwq. From (lOa), equal utilities would then require dr:>drf. But these inequalities together imply

“The zero value of g,dw: +g,drr indicates that the non-housing good is numeraire.


that the non-housing price in community 1 must increase relative to its price in community 2 (that is, g,dwT +g,drf >g,dwT +g,dr;), an impossibility. Thus, dw:>dwg is ruled out. A situation where dw: <dw; is ruled out by an identical argument.

Several additional points related to (lob) deserve note. First, while all the results of the present analysis would be unchanged under the naive assumption that migration responds to wage, not utility, differences (so that the fundamental equilibrium condition is dw: =dw$), this would not be true in a more complex model. Suppose, for example, that the property tax also were also applied to the land input in the non-housing sector. This would change eq. (8) to g, dw: +g, dr: +g, dt, = 0, which means that the reduced equal utility condition (lob) would be replaced by [(gJgL) + bfi] dr: + (gJgJ dt 1 = [(gJgJ + bfi] dr”;. In this case, changes in land rents and wage rates will not be equal across communities. The equal untility and the equal wage rate conditions therefore are not generally equivalent.

A second point is that when labor mobility is taken into account, there is no reason to confine residents, other than workers, to immobility. In equilibrium, the mobility of capital owners and landlords requires that their utilities be equalized in all communities. Making this change in the assumptions of the model, however, leads to no change in the results derived. The mobility of capital owners and landlords implies V(s + t, hp,, pl) = V(s, p2) and V(r, +tlqp,,p,)= V(r,,p,), where h and q equal individual housing consumption by capital owners and landlords, respectively. With total differentiation and simplification, these conditions reduce to nothing but (lob). Therefore, equalization of worker utilities guarantees equalized utilities of capital owners and landlords in all communities. The labor mobility assumption of our balanced budget general equilibrium model is therefore

equivalent to general residential mobility.

2.4. Comparative static solution

To further simplify the system, we eliminate the variables dLT, dl”*, dlf*,

dHT, dw?, and dp: by substituting (3), (4), (5), (6), (7), (8), and (lob) into (la), (2), and (11) (see appendix B). The resulting four-equation system in dr*, ds*, dKT, and dK; is then solved. The solution yields:‘l

“Referring to the definitions of B, F, R, and J in appendix B, we can write Q=BF-RJ. The sign of 0 is determined through the following simplifications:

g=[fioH-E~~+M(J/n)]F-[f,aH+Ef,+M(F/n)]/

=W”-%)F-_(f#+Ef,)J

= W” - fTk)bJ + no”U +(g,/gJl} -(f@ + J%)J = -%J+(fiaH--Ef,)nu’C1 +(sJg31 -%J =no”ll +(&lgJIU?JH--Ef,) -EJ =n{o”[l +(gl/gL)](froH--~~)--uH(IH/lx)} >o.


dr* EaH(iH/l”) -= dt, n{dIl +kt/g,)l(~Hh-%) -EWV”))

(note the value of Q in the denominator is positive by inspection), as well as

and

ds* ---=

dt, E{o’Tl+ WgJl + Q~V”P”)) <o

lh >

dKT (n- l)E

__ = n[l + IM(P/Z”)] < O, dt,

dK; E

dt, n[l + M(P/P)] ‘O. (15)

The effects of the property tax change on the other variables can be derived from the agove results. Complete solutions include:

dw* _=- dt, 0

!L d’x>o g, dt, ’

(16)

-_= 1 +Ek”Cl +(g~/gL)lfk+aH(lH/lx)) >. dp: dt, nSZ

> (17)

dP: -z.z

dt, E@“Cl +hh.).h + oHVH/W <o

n!2 2

dHT _ dKT I f,EoHo”C1 + (i&)1 <o dt, dt, Q

dH; _ dKT I f,EoHa”C1 + WgJl > o dt, dt, 52

< 2

dl:* dKT

dt, dt,

+ EaHW + k&.)1 52

<o >

dl:* dKT ; EflW1+ klkL)l > o _ _ dt, dt, Q < 2

(18)

(19)

(20)

(21)

(22)


dLT lH dK:’

0 - ->o,

dt,= - P dt,

dL; lH dK; -_=- - dt, 0

----<o. 1” dt,

(23)

(24)

(25)

(26)

3. The incidence of the property tax

3.1. Property tax efects in the taxed community

The above results are now discussed. Unless otherwise specified, we are considering the general case where n is a finite value and E is negative.

Eqs. (13) and (14) indicate that an increase in the local property tax in community 1 causes an outward flight of capital and depresses the overall capital return, results which coincide with the ‘new view’. The impact on land rent in the taxed community derived in (12), however, is not exactly

equivalent to the result derived from Mieszkowski’s one-sector, three-factor model. Mieszkowski stated that the change in land rent in the taxed community is uncertain but that r probably tends to decrease as the property tax rate increases. Eq. (12), however, shows a definite decrease in land rent. The reason for this discrepancy is that Mieszkowski’s property tax is a tax on capital, one of three factors of production. In his model, a higher property tax causes substitution away from capital, which tends to raise other factor prices (including land rent), while at the same time depressing output and reducing demand for all factors. The net effect on land rent is ambiguous. In the present model, the property tax is a tax on a commodity (housing) produced with land, so that a higher tax depresses the derived demand for land in housing production, leading to lower land rent (the transfer of land between sectors is discussed further below).

The property tax increase in community 1 also results in an excise effect, as Mieszkowski suggested. Eq. (17) indicates this effect, While the after-tax housing price in community 1 tends to increase as a result of the excise effect, unless income-compensated housing demand is perfectly inelastic (E=O), or the number of communities is infinite, the percentage increase in the housing price is less than the increase in the tax rate. Consequently, the net-of-tax housing price is depressed. Eq. (17) therefore implies that the property tax will be shifted both forward and backward.


If income-compensated housing demand is perfectly inelastic (which means

the indifference curves are right-angled), then dp:/dt, = 1 and the property tax is fully shifted forward. In addition, this case implies that all the solutions from (12) to (26) other than (17) reduce to zero. There is no capital movement between communities, no transfer of land between sectors, and therefore no change in output in each sector and each community. The property tax becomes a neutral tax which only enhances the housing price.

Eq. (16) predicts a rise in the wage rate in community 1 with the imposition of the property tax. This result strikingly contradicts the ‘new view’. Justification, however, is straightforward. Since the property tax increase causes land to be transferred from the housing sector to the non- housing sector, as indicated by (21) and (23), it reduces the labor-land ratio and therefore increases the marginal productivity of labor in non-housing production, which implies a higher wage rate and lower land rent. This, however, violates the equal utility condition (10). As explained above, worker utility level differences between communities are determined by changes in wages and land rents. The rise in the wage level and the fall in the land rent in the taxed community together imply that the community workers are better off. This means that workers will migrate from outside communities into the taxed community, as shown by (25) and (26), until labor-land ratios (and thus wage rates and land rents) in non-housing production are equalized across communities. The inflow of labor buffers the rise in the wage rate and the fall in land rent in the taxed community. The final equilibrium will be established with a higher wage rate and a lower land rent across communities. As the number of communities becomes large, the labor-land ratio in non-housing production becomes stable in response to the shifting use of the land input in the taxed community. Changes in the wage rate and land rent will be small. Eq. (12) indicates this.

It is worth recalling that the economy under Mieszkowski’s analysis contains only one sector. A capital tax, which represents a property tax, results in the substitution of other inputs for capital. A significant difference, however, emerges when a model with two or more sectors is considered, and when the property tax is imposed on housing services instead of capital. In the current model, a tax on the housing sector produces an output effect through demand reduction, as mentioned above. Both capital and land, as the housing inputs, suffer a loss on their returns. There is no production substitution effect between capital and land which favors one input factor (land) and disfavors the other (capital). Nevertheless, there is a ‘substitution effect’ between sectors within the taxed community. Since non-housing goods become relatively cheaper with an increase of the housing price, demand for non-housing goods increases. Note that the expansion of the non-housing sector is made possible by the transfer of land from the housing to the non- housing sector, as indicated by (21) and (23), and the immigration of workers


from the no-tax communities to the taxed community, as indicated by (25) and (26).

Finally, recall that Mieszkowski believed that the level of economic activity in the taxed community would be decreased by the property tax.” This, however, is not true in the current model. Although eq. (14) indicates an outward flight of capital from the taxed community, there is labor immigration generated by the tax. With less capital input in the withered housing sector and more labor input in the expending non-housing sector, the change in total economic activity in the taxed community is indeterminate.

3.2. Property tax effects in the no-tax communities

The tax effects in the no-tax communities were ignored in Mieszkowski’s analysis and in much of the ‘new view’ literature.13 This omission is justifiable in the current model when the economy contains infinitely many communities. In this case, the taxed community is tiny relative to the whole economy, and the capital flowing into (and labor flowing out of) each no-tax community will be a trivial amount and no distinct effect will be observed. The solutions derived from the model indicate that, when n tends to infinity, changes in all prices (in all communities), except for pi, approach zero and the property tax shifts fully forward (that is, dprf/dt, = 1). This is exactly the result suggested by the traditional view, which says the local property tax produces an excise tax effect.

When the economy contains only a finite number of communities, the property tax rate increase in community 1 will produce considerable effects in the no-tax communities. Eqs. (16) and (12) show that the tax increase enhances the wage level and depresses the land rent in the no-tax communities as well as in the taxed community. Since the capital return and land rent are reduced in all communities, the housing price in the no-tax communities falls, as indicated in eq. (18). While the reduced housing price increases individual demand for housing services, the change in aggregate demand and hence production in each no-tax community is indeterminate, as

indicated in eq. (20), because of the outward migration of workers. Since the signs of (22) and (24) are indeterminate, changes in the land

input in both the housing and non-housing sectors in the no-tax communities are also ambiguous. Comparing (12) with (13) we find that as a result of the increase of the property tax and the inflow of capital from the taxed community, the capital return is depressed more than the land rent in the

“Mieszkowski (1972, p. 87). ‘%ourant (1977), using a general equilibrium model with many taxing jurisdictions, did

consider property tax effects in the no-tax communities. However, he analyzed a restrictive one- sector model with capital and land as the factors of production.


no-tax communities. The substitution effect in housing production thus tends to reduce the demand for land at each level of housing output in no-tax communities. On the other hand, the output effect on the demand for land is ambiguous because changes in housing production are indeterminate, as mentioned above. The net effect on the demand for land in the housing sector therefore is ambiguous, as is the change in the land input in the non- housing sector.

3.3. Property tax effects on the utility levels

Now we are able to inquire into our principle subject: What is the incidence of the property tax under the balanced budget assumption of our model? To answer this question we have to inspect the utility changes of different income groups caused by the property tax increase. There are three income groups in the economy: Capital owners, landlords, and workers. Since utilities for each group are uniform across communities as a result of the labor mobility condition, the utility changes in the taxed community can be applied to all no-tax communities. Within community 1, the property tax increase raises the price of housing, which tends to reduce the welfare of consumers, while differentially affecting the incomes of different groups (wage income rises, while the incomes of capital owners and landlords fall). However, each resident receives the benefit of public expenditure equal to the amount of the property tax paid. Balanced budget incidence, therefore, depends on the net effect of income, housing price, and public expenditure changes.

To calculate these changes, we use the indirect utility functions of capital owners, landlords, and workers, which are V: = V(s + t, hp,, PI), Vi = V(r + t,qpl, pl), and Vf = V(w + t,bp,p,, pl), respectively. Differentiating the utility functions of each income group with respect to t, gives:14

dV: p= Y“ dt,

:(I-hh)-hl;; <o, 1 1 1 (27)

141n deriving eq. (27), eq. (6) and the relationship aV:/ap,= -hYk are used. The same equations are used in deriving (28) and (29). In addition. the sign of eq. (27) is determined by in\pccting the budget constraint of capital owners at the initial equilibrium, which implies that s= I >hp, >O or l>h>O. This means (1-h~~)>(h-h/;)=hf;>O. Since ds*/dt, is negative, we have (ds*/dt,)hfi>(ds*/dt,)( -I&). Thus:

Because (ds*/dt, -dr*/dt,) is negative, the sign of dV:/dt, is negative


dV; -= Y' dt,

>o,

(28)

(29)

where Yj is the marginal utility of income of group j, j=k, 1, and L. The imposition of the property tax causes a deterioration of capital owners’ utility and an improvement of workers’ utility in all communities. On the other hand, the change in landlords’ utility is ambiguous.

These results are not surprising. As we mentioned above, under the balanced budget assumption the utility change of residents attributable to the tax component of the gross housing price is fully offset by the extra benefit received from the public expenditure. Changes in residents’ utility levels depend only on changes in their factor returns and the net price of housing services. While the reduced net housing price benefits all the residents, income changes determine the final outcome. The increase in the wage level clearly implies a net increase in the utility level of workers. Capital owners, however, turn out to be worse off because their gain from the reduced net housing price is offset by a lower income. The net effect on landlords is indeterminate and depends both upon the magnitudes of the decreases of the net housing price and land rent, and also upon the proportion of their income used in housing consumption.

All the preceding results are summarized in table 1, with three cases presented: E is zero, E is non-zero with n being finite, and E is non-zero with n being infinite,

4. The model without labor mobility

As pointed out above, the current analysis extends Mieszkowski’s work mainly in two respects. First, it analyzes property tax incidence by using a general equilibrium approach with the assumption of an economy containing two sectors, three factors, and multiple communities. Secondly, it incorporates the labor mobility condition into the model under a balanced budget assumption. An interesting contrast with the current results would be those derived from the same model without labor mobility.

The absence of labor mobility eliminates eqs. (2) and (lOa) from the original model. It also requires replacement of eqs. (7) and (11) by

#(dw:-dr*)=dl;*, i=l,2, (30)

and

dHT=Edpr, i=l,2, (31)


Balanced

Table 1

budget incidence of an increase in community l’s property tax rate with the model of mobile capital and labor.

Prices

E=O +o 0 0 0 0 0 0 E # 0, n is finite + - + + - - - -

E # 0, n is infinite +o 0 0 0 0 0 0

Inputs

E=O 0 0 0 0 0 0 0 0 E # 0, n is finite ‘? +? -

-b + -

E #O, n is infinite +o A+0

outputs

E=O 0 0 0 0 E # 0, n is Iinite ? +? E # 0, n is infinite _ 0 +o

Utilities

E=O 0 0 0 0 0 0 E#, n is finite 7 7

E # 0, n is infinite Ebboo

respectively. The modified model therefore contains 15 unknowns with an equal number of equations to solve. The quantitative solutions to this modified model are not presented here because the procedures are parallel to those of the original solution (derivations and solutions are available on request). The qualitative results, however, can be found in table 2.

It is interesting to note that the absence of labor mobility does not change the qualitative results appreciably. When E=O, the results for both models are identical. In the case where E is negative and n is finite, the modified model, however, indicates that H2 increases and changes in w2, r2, Vi, and V: become indeterminate. In this case, the absence of labor mobility leads to an expansion of the housing sector in no-tax communities. Remember that, in the original model, the migration of workers weakens the aggregate demand for the housing services in no-tax communities. This situation does not appear in the modified model. Moreover, the local property tax induces

128 C. Lin, Property tax inculence

Table 2

Balanced budget incidence of an increase in community l’s property tax rate with the model of mobile capital and immobile labor.

Prices

E=O +o 0 0 0 0 0 0 E#O, n is finite +--+? -? --

E # 0, n is infinite +o +o -0 0 0

Inputs

IH IH 1 2 1” 1” 1 z K Kz I

E=O 0 0 0 0 0 0 E # 0, n is finite - ? +? -+ E #0, n is infinite - 0 +o -0

outputs

E=O 0 0 0 0 E # 0, n is finite - + + ? E # 0, n is infinite - 0 to

Utilities

Vf v:: v: v: v: vi

E=O 0 0 0 0 0 0 E # 0, n is finite f???? - E # 0, n is infinite +o -0 +o

an inflow of capital into no-tax communities and reduces housing prices. The reduced housing price in each no-tax community stimulates the demand for housing services and therefore expands housing production, as indicated in table 2.

The expansion of housing production in no-tax communities further produces an output effect which increases the demand for land. On the other hand, the depressed capital return leads to a capital-intensifying of housing production. This means more capital will be employed per unit of land input at each level of housing output. Since this substitution effect works in the opposite direction to the output effect, the final changes in land inputs in both sectors are indeterminate and depend on the elsasticities 8, CJ~+, and E.

Since the labor-land ratio in non-housing production determines the wage rate and the land rent, and since labor is fixed in the modified model, changes in the wage rate and the land rent in each no-tax community


therefore depend totally on changes in the land input in the non-housing sector. Changes in the land inputs, however, are ambiguous, as just discussed. The indefinite changes in w2 and r2 thus are understandable. Furthermore, because the change in w2 is indeterminate, the utility change of workers in no-tax communities also becomes indeterminate.

In the taxed community, the depressed capital return and net-housing price produce opposite effects on the utility level of capital owners. Since neither effect is decisive, the change in capital owners’ utility is unknown.

Eliminating labor mobility also leads to different qualitative results in the case where E is negative and n is infinite. The explanation of these differences, however, is not new and is left to the reader.

5. Summary

This paper has analyzed property tax incidence in a model of a two-sector economy with multiple communities. In the case with non-zero income- compensated elasticity of housing demand and a finite number of communities, the local property tax imposed on the housing sector produces a forward-shifting as well as a backward-shifting effect. Within the taxed community, the depression of the capital return caused by backward shifting is moderated by a reduction of the capital input in the housing sector. Capital flees to no-tax communities until its return is equalized throughout the economy. In addition, the land input in housing production also is reduced, moderating the fall of land rent caused by the backward shifting of the property tax. This results in a lower labor-land ratio in non-housing production, which increases the wage rate. The increase in the wage rate, however, is moderated by the immigration of workers from no-tax communities. The larger the number of communities, the more effective is the moderation of the backward-shifting effect on factor prices, and the higher the increase of the gross housing price through forward shifting. As long as the economy contains a finite number of communities, the final equilibrium established in taxed community will have a higher gross housing price and wage as well as a lower net housing price, rent, and capital return.

The mobility of capital and labor leads factor returns in the no-tax communities to change in the same direction as in the taxed community. While the reduced housing price would increase the aggregate demand for housing services, the migration of workers reduces it. The net effect on housing production, and therefore on the land inputs in both sectors, is unknown and depends on various elasticities.

The model further enables us to explore balanced budget incidence by evaluating utility changes for different income groups. Higher wages together with depressed net housing prices across communities imply that workers are better off. In addition, capital owners are worse off because their gain from


reduced housing prices is more than offset by their income loss from capital. The change in the utility level of landlords is indeterminate and depends on the magnitudes of the changes in the net housing price and land rent as well as on the proportion of their income used in housing consumption.

Appendix A: Derivation of the housing demand condition

We assume that each capital owner owns one unit of capital. Letting ai be the number of capital owners in community i, it follows that a,=K. Since capital owners are assumed to be immobile, ai is constant and capital income for community i is up. Recalling that preferences are homothetic, it then follows that housing demand in each community can be represented by Hi = D(p,, $J, where D is the demand function and $i = wiLi +rili + uis + pitiHi

(r,l is the aggregate income of landlords in community i). Since prices are initially equal to one and the tax rate is initially equal to zero, totally differentiating the housing demand function gives:

where E = aDlap and m is the marginal propensity to consume (m = aD/arl/). Since absolute price changes equal percentage changes (e.g. dpi = dp:), we find using(6) that 1~dri+Uid~i+H~dt~=H~[(I~/H~)dr,*+(K~/H~)ds~+dti]=H~dp~. Using (8), we find that Li dwi + 1: dri = Xi[(Li/Xi) dwr + (If/Xi) dr:] = 0. Eq. (Al), therefore, reduces to

dHT = E dp,*/H, + m(H, dp: + dLi)/H

= [(E + mHi)/Hi] dp: +(mLi/Hi) dLT

=Edpr+MdLT, i=l,..., n,

where E = [(t: + mHi)/Hi] and M = (mLJHi).

Appendix B: Simplification of the system

Since dry =drT = dr*, (4) becomes:

dl”*=dK*+oHds*-oHdr*. (Bl)

Also, we knaw from (8) and (3) that dw: = -(gJgJdr: and dl; = -(lH/P) dlF*,


respectively. Eq. (7) therefore can be written as

dL; = 0°C 1 + (g,/gL)] dr* - (ZH/ZX) dlF*. 032)

Substituting (Bl) into (B2) and regrouping the variables gives:

dLT=(F/n)dr*-(J/n)ds*-QdKF, (B3)

where F = n{oH(ZH/lx) + oX[l + (g,/g,)]} > 0, J = noH(lH/l”) > 0, and Q =

(P/1”) > 0. Also, substituting (Bl) into (5) yields:

dHT =dK; + fro” ds* - fia” dr*. (B4)

With eqs. (B4) and (B3), we can solve the system by rewriting (11) and (2) in terms of dr*, ds*, and dKT. Substituting (B4), (6), and (B3) into (11) yields:

Rdr*-Bds*-ZdKT= -Edt,, i=l,2, (B5)

where R = fioH + Efi + M(F/n) >< 0, B = f * ,o”-E&+M(J/n)>O, and Z=l+

MQ>O. Also, substituting (B3) into (2) yields:

Fdr*-Jds*-QdKT-(n-l)QdKz=O. (B6)

With dt,=O and i= 1,2, eqs. (la), (B6), and (B5) constitute the following

four-equation system in ‘matrix form:

-dr* _

ds*

dKT

dK; _

The system can be solved by Cramer’s rule.

=

0

0

-Edt,

0

References

Aaron, H.J., 1975, Who pays the property tax: A new view (Brookings Institution, Washington, DC).

Brueckner, J.K., 1981, Labor mobility and the incidence of the residential property tax, Journal of Urban Economics 10, 173-182.

Courant, P., 1977, A general equilibrium model of heterogeneous local property taxes, Journal of Public Economics 8, 313-328.

Harberger, A.C., 1962, The incidence of the corporation income tax, Journal of Political Economy 70, 2 1 S-240.


Lin, C., 1985, Labor mobility and the incidence of the residential property tax: A comment, Journal of Urban Economics 18, 28833.

McLure, C.E., 1975, General equilibrium incidence analysis - the Harberger model after ten years, Journal of Public Economics 4, 125-161.

McLure, C.E., 1977, The new view of the property tax: A caveat, National Tax Journal 30,69979. Mieszkowski, P.M., 1967, On the theory of tax incidence, Journal of Political Economy 75,25f&262. Mieszkowski, P.M., 1972, The property tax: An excise tax or a profit tax? Journal of Public

Economics 1, 73-96. Shoven, J.B. and J. Whalley, 1972, A general equilibrium calculation of the effects of differential

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Texas).

a general equilibrium analysis of property tax incidence

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