JOURNAL OF HOUSING ECONOMICS6,293–317(1997)
ARTICLE NO.HE970219
Job Decentralization with Suburban Housing
Discrimination:An Urban Equilibrium Modelext
of Spatial Mismatch
Richard W.Martin
Department of Economics,Agnes Scott College,141E.College A v enue,
Decatur,Georgia30030
Received January13,1997
The spatial mismatch hypothesis,with its roots in the work of Kain(1968,Quart.
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J.Econ.82(2),175–197),has received much recent attention from empirical re-
春节用英语怎么说archers.Its basic premi is that differences in job access between black and
white workers have contributed to increasing racial inequality in urban labor mar-
kets.While the initial evidence was ambiguous,recent studies have established that
differences in job accessibility have worned the labor market outcomes of minority
workers.This paper develops an urban equilibrium model which allows for the
analysis of the impact of job decentralization and suburban housing discrimination
on the welfare of workers in a city.©1997Academic Press
I.INTRODUCTION
Rearchers have given much attention to measuring and explaining racial differences in labor market outcomes.Most studies have ud differ-ences in relative skills and the returns to marketable skills between black and white workers to explain the differences that exist(Bound and Freeman (1992),Katz and Murphy(1992),Juhn,Murphy,and Pierce(1991)).Re-cently,however,there has been a
resurgence of interest in the possibility that there is a spatial dimension to the problem.The suggestion that spatial factors play a role in the racial inequality that is characteristic of American urban labor markets was originally formulated by Kain(1968)and is known as the spatial mismatch hypothesis.The basic idea of this hypothesis is that differences in the spatial distribution of black and white residences,relative to the spatial distribution of employment,increa inequality by granting whites better access to job opportunities than black workers.1
The ideal respon of black workers to the suburbanization of employ-1See Kain(1992)and Holzer(1991)for surveys of the empirical work on the spatial mismatch hypothesis.
293
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294RICHARD W.MARTIN
ment would be to shift their residences toward the suburbs.However,if there are barriers that prevent black entry into suburban residential areas, black workers will not be able to adjust their places of residence as they would like in respon to the changing spatial distribution of employment opportunities.In extreme cas,black workers will have to maintain their original residences in the central city where they must choo between scarce,low wage jobs in nearby central city locations and higher wage jobs in the distant suburbs.If high commuting costs deter a large number of workers from eking work in the suburbs,unemployment in the central city will result if central city wages do not fall sufficiently to absorb the relatively high supply of labor.Additionally,if central city wages fall to a low enough level,some black workers may drop out of the labor force as the wage falls below their rervation wages.2
This paper eks to contribute to the spatial mismatch discussion by helping to build an underlying analytical framework that has been largely abnt in the empirical work that exists on the subject.In particular,this paper eks to extend the work started in Brueckner and Martin(1995) by more fully developing a model that can display the wage effects of spatial mismatch that are propod in the empirical literature.Section II develops the model withfixed wages and Section III us the model to derive the welfare effects of spatial mismatch when wages arefixed.Section IV expands the model to
include an explicit labor market,while Section V derives the effects of spatial mismatch on welfare,wages,and inequality in the city when wages are determined within the model.Section VI provides conclusions and suggestions for future rearch.
II.THE BASIC MODEL
A.The Monocentric City
The model ud in this paper is a simplified version of a standard mono-centric urban economic model extended to include a suburban employment center.The city is populated by N b black workers and N w white workers. Residents consume two goods,land and a numeraire nonland good,e.In equilibrium,the amount of nonland consumption must be equal within each group.
The primary simplification in the model is that land consumption is assumed to befixed for both groups of workers.In standard urban economic models,residents substitute land for nonland consumption as their place 2Juhn(1992)finds that reduced market opportunities have contributed to the lower labor force participation rates of less-educated black men.
URBAN SPATIAL MISMATCH295 of residence moves away from the CBD becau per-unit land rent falls
to compensate them for their incread commuting costs.In this model,
however,no such substitution takes place.Workers within a particular
group consume the same amount of land regardless of their residential
distance from the CBD.Whites consume one unit of land while blackmozella
workers consumeunits withϽ1.3For the sake of simplicity,the city is assumed to be located on a rectangular island of unit width so that the
amount of land necessary to hou the entire population of the city is
N wϩN bϵx,which is assumed to be the length of the island.Later it will be en that the rectangular island assumption allows a cond employ-
ment center to emerge without concerns about whether residents relocate
to land that is not part of the original city and is near to the new employ-
ment center.
If distance to the CBD is given by x,the budget constraint for white
workers is
y wϪtxϭr w(x)ϩe w.(1) Rearranging this expression yields the white bid-rent curve:
深圳unity3d培训r w(x)ϭy wϪtxϪe w.(2) Similarly,the budget constraint for black workers is
y bϪtxϭr b(x)ϩe b(3) and their bid-rent curve is
r b(x)ϭ1
(y bϪtxϪe b).(4)
Note that the slopes of the white and black curves with respect to x are Ϫt andϪt/,which implies that the black curve is steeper.
The bid-rent curves show the land rent that keeps every member of a particular group equally well off at every point in the city.The slope of each group’s bid-rent curve reveals the amount that land rent must fall to compensate a worker for a one-unit increa in commuting distance.A one-unit incre
a in commuting distance rais commuting cost by t for both black and white workers.This means that the total amount that black
3The lower black land consumption is a result of land being a normal good and black incomes being lower than white incomes.
296RICHARD W.MARTIN
and white workers spend on land must fall by t if their commute increas by one unit and they are to be just as well off.Becau white workers consume one unit of land,this means that their per-unit land rent must fall by t.Black workers,on the other hand,consumeunits of land,which is less than one.This means that their per-unit land rent must fall by t/Ͼt if they are to be fully compensated for the incread commute.Therefore, the black bid-rent curves are steeper than their white counterparts. Initially,all employment is in the CBD,located at xϭ0.The steeper bid-rent curve for black workers implies that they occupy the land clost to the CBD.4Therefore the residential pattern of the monocentric city has black workers living from xϭ0to xϭN b and white workers living from xϭN b to xϭx.This is shown in Fig.1.
The equilibrium conditions for the monocentric city are
y wϪtxϪe wϭ0(5)
1
N bϪe b)ϭy wϪtN bϪe w.(6)kid
(y bϪt
Equation(5)states that at the city’s boundary,x,the rent paid must be equal to the land’s opportunity cost in agriculture,which is assumed to be zero.Equation(6)states that the bid-rents of the two groups must be equal atN b.
Equations(5)and(6)can be solved for e w and e b,the white and black nonland consumption levels in the monocentric city.Doing so yields
e wϭy wϪtx(7)
e bϭy bϪt(N wϩN b).(8) B.The Decentralized City
Job decentralization is modeled by allowing workers to work either at the CBD or at a suburban busi
ness district(SBD)located at xϭx,the other end of the island.Although multiple commuting patterns are possible,
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4It is a standard result in urban economic models that when two groups with different levels of land consumption occupy a city,the lower land consumption group is able to outbid the higher land consumption group for the land clost to the employment center.This is due to a steeper bid-rent curve for the group with the lower land consumption.However, this may not be the ca if the higher income group has a higher opportunity cost of time spent commuting.This would imply that the higher income group would have a higher commuting cost parameter and might have a steeper bid-rent curve and be able to bid away the land clost to the employment center.
ever since
URBAN SPATIAL MISMATCH297
FIG.1.The monocentric city.
the discussion in this paper will be limited to the ca in which both groups work in both employment centers.5
Two cas of the decentralized city will be analyzed.Thefirst will be the unrestricted ca,in which black residents are not hindered in their choice of a place of residence.The cond is called the restricted ca,and will include the restriction that black workers are not allowed to relocate in respon to job decentralization.
beautiful girlsWith job decentralization,workers choo to work in the employment 5For a detailed discussion of the different types of commuting patterns that are possible, e Brueckner and Martin(1997).
298RICHARD W.MARTIN
center that pays them the highest wage net of commuting cost.The bid-rent curves for the four types of workers(white CBD,white SBD,black CBD,and black SBD)are given by
r c w(x)ϭy c wϪtxϪe w(9)
r s w(x)ϭy s wϪt(xϪx)Ϫe w(10)
r c b(x)ϭ1
(y c bϪtxϪe b)(11)
r s b(x)ϭ1
[y s bϪt(xϪx)Ϫe b],(12)
where the subscripts b and w refer to black and white workers and the superscripts c and s refer to CBD and SBD workers.
1.The unrestricted ca.When there are no restrictions on where resi-dents can live,the form of the decentralized equilibrium is as shown in Fig.
2.Note that the size of the city does not change in respon to job decentralization becau of the island city assumption.Rather,job decen-tralization leads to a change in the land-u pattern within the existing city. Black CBD workers occupy the land between xϭ0and x˜c,white CBD workers occupy the land between x˜c and xˆw,white SBD workers live be-tween xˆw and x˜s,and black SBD workers live from x˜s and x.The equilibrium
conditions for this ca are
y c wϪtxˆwϪe wϭy s wϪt(xϪxˆw)Ϫe w(13)
y c wϪtx˜cϪe wϭ1(y c bϪtx˜cϪe b)(14) y s wϪt(xϪx˜s)Ϫe wϭ1[y s bϪt(xϪx)Ϫe b](15)
y c wϪtxˆwϪe wϭ0(16)
x˜sϪx˜cϭN w.(17)
Equation(13)states that bid-rent curves for white workers must interct at the point where white workers are indifferent between the two employ-ment centers,xˆw.Equation(14)says that the rent paid by white CBD and black CBD workers must be equal at the border between their residential areas,x˜c,while(15)states that the rent paid by white SBD and black SBD workers must be equal at x˜s.Equation(16)says that the lowest rent paid in the city,which occurs at xˆw,must be equal to the land’s opportunity
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