This PDF is a selection from an out-of-print volume …of permanent income, price, and tastes. A person with a given permanent income and employed at any distance k1 frsm the CBD,

This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research

Volume Title: Residential Location and Urban Housing Markets

Volume Author/Editor: Gregory K. Ingram

Volume Publisher: NBER

Volume URL: http://www.nber.org/books/ingr77-1

Publication Date: 1977

Chapter Title: Housing Discrimination and Job Search

Chapter Author: Susan C. Nelson

Chapter URL: http://www.nber.org/chapters/c4314

Chapter pages in book: (p. 329 - 348)

Chapter Nine

Housing Discrimination andJob Search

Susan C. Nelson

INTRODUCTION

The effect of housing discrimination on the employmentopportunities of urban blacks has been the subject ofmuch debate since John Kain's influential article in 1968.

Kain's conclusion that the elimination of housing segregation wouldproduce a substantial number of additional jobs for blacks has beenchallenged on several grounds: on his methodology, by the observa-tion that there still is an adequate supply of jobs in the inner citiesdespite decentralization, and by the assertion that other factors, suchas the strength of local aggregate demand and employment discrim-ination, seem more important.'

Distinguishing the empirical effects of the various issues involved isa complex process. By simplifying and abstracting from considera-tions that are empirically problematical but theoretically unimpor-tant (such as the extent of employment discrimination), however,the model of job search in a spatial context presented here examinesthe ways that constraints on blacks' residential mobility might affecttheir employment situation. I do not try to determine whether ornot housing discrimination exists; that has been frequently andextensively examined elsewhere.2 Rather, if blacks who initially livein the inner city are victims of housing discrimination, the modelpredicts, not surprisingly, that their average wage is lower incentral-city jobs and higher in suburban areas than it would be in theabsence of a locational constraint. In addition, their employment willbe more concentrated near the center of the city. The impact of

329

330 Invited Student Papers

i

THE SEARCH

such that k1an 1

where moving ftthan it would swould increasecosts.5 If theu, where u is thequilibrium locaperson's employwould choose tcoptimal amount

housing discrimination on the duration of unemployment, however,cannot be determined.

The analysis proceeds as follows: The urban setting is described. Amodel of random, sequential job search is applied to two job hunters,a black and a white, who begin searching from residences in thecenter of the city. It is assumed that housing discrimination preventsthe black from changing his residential location. By using theconcept of stochastic dominance, implications may be drawn on theimpact of housing discrimination on black employment opportuni.ties. These conclusions are modified when a less extreme and morerealistic version of discrimination is assumed.

THE CITY

The setting for the model is a circular city3 much like that describedin Mills (1972). The following assumptions are made: (1) There aretwo main sectors—production-employment and housing—which com-pete for land in the city and determine locational patterns there.(2) Some housing and some employment occur in all areas of thecity. All parcels of land the same distance from the center containthe same economic activities. (3) Land in the very center of the cityis valued most highly because of agglomeration economies or proxim-ity to transportation facilities. (4) If production functions permitsubstitution between inputs, then because proximity to the CBD hasvalue, land rents as a function of distance from the CBD decline at adecreasing rate (for proof, see Mills 1972, Chap. 5) The ratio ofcapital and labor to land wifi be highest in the CBD, therebyeconomizing on the scarce resource of central land; hence, employ-ment density [D(k)] will also decline with k, the number of milesfrom the CBD: D'(k)<

An equilibrium distribution of housing services occurs when nohousehold can increase its utility by moving. It is assumed thathouseholds have no preference for either city or suburban living perse. Then, since employment density decreases with distance from theCBD, a given quantity of housing services can command a higherprice if it is nearer, rather than farther from, the CBD. People willpay more for a location that requires lower transportation costs. Thisreinforces the pattern of land rents decreasing with distance from thecenter of the city, and implies that housing prices [P(k)] also will belower at more distant locations: P'(k) < 0.

Let the quantity of housing services (H) demanded be a functionof permanent income, price, and tastes. A person with a givenpermanent income and employed at any distance k1 frsm the CBD,

In this setting, tat k = 0 begin loand vacancies oclocations in thevacancies/total ejob categoryrespects excepthuman capital aiopportunities atexists), have accshare the samesame permanentmarket, howeveitakes an extremewhile W is free tjob he accepts.7assumed: the cohigh but noninfir

In the first inwill be worth mresidence is optiiThe difference iimated by compworker, where tminus housingpenses (if relevarthe offer.

Housing Discrimination and Job Search 331

such that k1 k2, will find his utility is maximized (i.e., he lives atan equilibrium location) if he resides at a distance k2 from the CBD,where moving further out would increase transportation costs morethan it would save on housing expenditures, and moving further inwould increase housing costs more than it would lower commutingcosts.5 If the transportation function is linear of the form T = m + tu, where u is the straight line distance between home and work, theequilibrium location occurs where P'(h )2H(k2) = —t. If by chance aperson's employment is situated farther from the CBD than k2, hewould choose to live at or as near as possible to his work, since theoptimal amount of commuting for him is zero.

THE SEARCH

In this setting, two workers, B and W, living in the center of the cityat k = 0 begin looking for work in occupation Z. Both employmentand vacancies occur as fixed proportions of total employment at alllocations in the city. Employment in Z/total employment = a; totalvacancies/total employment = c. Thus the density of openings in thisjob category equals cxD(k), where = a c. B and W are identical in allrespects except race: they possess the same amount and quality ofhuman capital and the same preferences, face the same employmentopportunities at the same wages (no employment discriminationexists), have access to the same employment information systems,share the same commuting and search cost functions, and have thesame permanent income. B experiences discrimination in the housingmarket, however, while W does not. In this section, discriminationtakes an extreme form: B is unable to move from his6 initial locationwhile W is free to locate his residence in an optimal relation to anyjob he accepts.7 Another, more realistic form of discrimination isassumed: the costs to B associated with moving from the CBD arehigh but noninfinite.

In the first instance, any nominal wage offer Y at a distance k1will be worth more to W than to B in utility terms if a noncentrálresidence is optimal, because of the declining housing price function.The difference in the value of Y(k1) to B and W can be approxi-mated by comparing the "real wages" that this implies for eachworker, where the real wage equals the wage from the employerminus housing expenditures, transportation costs, and moving ex-penses (if relevant) for the worker's residential location if he acceptsthe offer.

Y(k1) P(Q)H+ T(k1 —0) (9-la)

rinent, however,

,g is described. Atwo job hunters,sidenceS in the

prevents- By using the

drawn on theient opportuni-reme and more

e that describede: (1) There areing—which com-patterns there.all areas of the

e center containenter of the city

or proxim-ünctions permitto the CBD has

decline at a5). The ratio of

CBD, therebyhence, employ-

Inumber of miles

occurs when noassumed that

iburban living peraistance from the

a higherpBD. People wifitation costs. This

from thealso will be

led be a functionon with a given1 from the CBD,

L


Y(k1)—min[P(O)H± T(k1 _O);P(k1)H+M*; (9-ib)

P(k2)H+ T(k2 _k1)+M*]

where

and = real wages of B and W, respectively, for an offer of Yat k1;

T(k1 — = commuting costs, which are some function of thedifference between the distances indicated within theparentheses;

H = quantity of housing demanded at P(O);M* = moving costs discounted over the expected length of

employment; if M = total moving costs incurred inperiod 0, M* is defined by:

n+1 M*

i=1

where p is the discount factor; and n, the expectednumber of periods of employment;

0 = initial residential distance from the CBD;= distance of employment from the CBD;

k2 = equilibrium residential distance from the CBD forjobs at k1 k2, where T' = —P'(k2)H.

So that these real wages will represent at least monotonic trans-formations of levels of utility for B and W, W's housing consumptionis held equal to B's. Otherwise, if housing demand were quiteprice-elastic, W's housing expenditures might exceed B's (in spite ofthe lower price facing W) causing to be less than even thoughW's utility could be the higher. Analyzing W's behavior with theimplicit assumption of. a price elasticity of zero results in a lowerbound to the amount by which W's utility exceeds B's.

The costs of moving include the costs of finding a new home, anypsychological costs, and the actual expenses of packing, hiring a van,etc. M* is taken as a constant, although costs probably do increase tosome extent with distance moved even within the metropolitan area.

The decision whether or not to move, given employment at k1, ismade by comparing the costs of living at the initial location with thecosts at k1 and k2. Thus W will choose to move if:

The circle of rad.

P(0)H+ T(k1 —(

forms the bournbe located and tk1 or k2 (k1moving woufd 1no-move area iscan be seen fronthree factors. Cworker is moreprice function isbeneficial morelower M*, thecontext, housingof moving so higbenefits of movir

Assume thatkelge of t1he city,,valued functionsexample, the costhan for others;the probability caware of these deach faces in thErespectivenominal wage ofisaid thatstochasticp. 27):

for all y in the iwage offer.(9-3) holds and i

P(0)H+ T(k1 —C


(9-ib) P(O)H+T(k1 [P(k1)H+M*;P(k2)H+T(k2 —k1)+M*](9-2a)

The circle of radius k1 such that at

P(O)H+T(k1_O)=min[P(k1)H+M*;P(k2)H+T(k2_k1)+M*](9-2b)

forms the boundary between the region in which employment couldbe located and the worker would not benefit from moving either tok1 or k2 (k1 in the no-move region) and the area for whichmoving wourd be beneficial (k1> k1 for the move region). If theno-move area is small, the worker wifl be considered very mobile. Ascan be seen from Equation (9-2b), the tendency to move depends onthree factors. Ceteris paribus, if transportation costs are high, theworker is more apt to move, and k1 will be small. If the housingprice function is very steep (i.e., the gradient is large), moving will bebeneficial more often than if the gradient is small. And clearly thelower M*, the smaller is the worker's no-move region. In thiscontext, housing discrimination could be viewed as raising B's costsof moving so high that nowhere in the metropolitan area would thebenefits of moving exceed the costs.

Assume that nominal wage offers in occupation Z at eachk1 (0 k1 k*), where equals the distance from the CBD to theedge of the city, are distributed according to the set of non-single-valued functions [Y1k1 ]D. Such distributions can persist if, forexample, the cost of maintaining vacancies is higher for some firmsthan for others; then the former would offer higher wages to raisethe probability of filling their openings more quickly. B and W areaware of these densities and hence of the distribution of real wageseach faces in the city: and with F(yb) and therespective cumulative distributions. Since the real value to B of anynominal wage offer is less than or equal to the value to W, it may besaid that is larger than in the sense of first-degreestochastic dominance (FSD) as defined in Hadar and Russell (1969,p. 27):

(9-3)

for all y in the interval [0, L], where L is the maximum possiblewage offer. may be considered' to strictly dominate if(9-3) holds and if for some y in [O,L], < F(yb). This will

for an offer of Y

function of thewithin the

0);xpected length ofcosts incurred in

n, the expected

CBD;

the CBD for)H.

I monotonic trans-using consumption

were quiteB's (in spite of

even thoughbehavior with theresults in a lower

kg a new home, anyhiring a van,

do increase tometropolitan area.tployment at k1, isI location with the


occur if for employment located at some k1 within the boundary ofthe metropolitan area the inequality in Equation (9-2) holds and if itis optimal for W to move outside the center of the city. Strict FSDalso implies strict second-degree stochastic dominance (SSD), whichis defined as:

L Lf G(y)dy < f F(y)dyq

for all lower bounds q in the interval [0, L] (from Hadar and Russell1969). The domination of the distribution of real wage opportunitiesfacing W over that available to B will be used in determining therelation between B's and W's expected wages.

Job search occurs as a random sample drawn from andone draw is allotted per period, as if each worker went to the

employment service and was given one randomly selected firm tocheck each day.8 The worker must decide whether to accept orreject the offer in the same period in which it is made. (If no offer ismade, the search can be considered as having found a nominal wageof zero.) It has been shown (McCall 1970, Nelson 1970, and Kohnand Shavell 1974) that the optimal strategy, the one that maximizesthe present value of expected wealth, is to reject if the discountedexpected benefits of searching outweigh the costs of another search,and to accept if the reverse is true. This produces a critical valuecalled the acceptance wage, or reservation wage: if the offer exceeds

Yb = real acceptance wage for B;= real acceptance wage for W;

n = expected number of periods of employment;p discount factor; andS = cost of the next search.

Simplifying (9-5), we obtain at the limit, as n approaches infinity,

r

q(9-4)

1LS=— f

PYb

Search costs inctation to the jolat the minimunihis leisure9; copsychological csearching suchwhether or notof one search, Sbe constant inplausible assum'distance betweethe length of tiiS also is higherinformation sysB, since W isemployed andycity.

Given the stiences in thebe attributableventing B from

Proposition P

If f(Yh) is st:must be less tha

I b)dyb -

Simplifying and

LJ —

the acceptance wage, accept it; if not, reject and search again (seeamong others, McCall 1970, Rothschild 1973, and Mortensen 1970).

This can be represented as:L —f (Yb Yb)f(Yb)dYb

n+1s= i1

L —f

n+1= (1+p)i

i=1(9-5)

adar and Russellge opportunitiesdetermining the

the boundary ofholds and if it

city. Strict FSDace (SSD), which

(9-4)

from andrker went to theselected firm toier to accept orle. (If no offer isa nominal wage

1970, and Kohne that maximizes

the discountedf another search,6 a critical value

offer exceedsagain (see

1970).

(9-5)Simplifying and integrating by parts:

L L — — L— f

Yb ywL

HousiAg Discrimination and Job Search 335

S = (Yb )dyb = (9-6)PYW

Search costs include such factors as out-of-pocket costs of transpor-tation to the job site; time costs of the trip and the interview, valuedat the minimum wage or whatever other value the worker places onhis leisure9; costs of information on potential vacancies; and thepsychological costs of any disutility the worker experiences insearching such as discomfort in a job interview or uncertainty aboutwhether or not an offer will be forthcoming. For simplicity the costsof one search, S, will be assumed to be the same for B and W and tobe constant in all periods and over all job locations. Clearly, moreplausible assumptions would be that search costs increase with thedistance between the job and the initial residential location and withthe length of time the worker has been unemployed.' ° Realistically,S also is higher for B than for W because, for example, the informalinformation systems accessible to W are superior to those available toB, since W is more likely to have friends and relatives who areemployed and whose employment is more dispersed throughout thecity.

Given the structure and assumptions outlined above, any differ-ences in the search process undertaken by B compared to W wouldbe attributable only to discrimination in the housing market, pre-venting B from changing his residential location.

Proposition AIf is strictly dominated by B's real acceptance wage

must be less than W's: <y.L L L Lf I

(9-7)

(9-8)infinity,


— L LS Again since (

F(yb)dyb = (9-9) ..'b w positive and f

If (9-9) becomes: hold. Thus, thefor B is strictly

— L L effective acceptF(yb)dyb +f (9-10)

Proposition E

Depending oi

— k.) B's nominalSince — f (9-6) is equivalent to: greater than

Proof: Let kfor W. Let B's

L L anyk bedefinf —f 1

Y'kb'But since by assumption strictly dominates ('ii)

L LJ > 0These representsuch that theyoff than if they

and if f [1 — > 0. Hence, the equality inyw

(9-11) cannot hold if . In this regioiIf, on the other hand, (9-9) becomes: costs. Smce thr

B's, here too wamount that th

— L LF(yb)dyb +5 F(yb)dyb +f (9-12)

Defining a

and still exceeds 17b (

L Lf F(yb)dyb f f [1 F(yb)]dyb = 0 (9-13) B's nominalw " w will reject offers


Again, since dominates the first term in (9-13) is(99)

positive and f [1 — F(yb )] is nonnegative; so the equality can

hold. Thus; the assumption that the distribution of effective wagesfor B is strictly dominated by the distribution for W implies that W'seffective acceptance wage will exceed B's.

(9-10)Proposition BDepending on moving costs for W, in some range of k1, (0 k1 <

k1) B's nominal acceptance wage will be less than W's, and for k1greater than within the city, the opposite will be true.

Proof: Let k be the distance at which moving becomes beneficialfor W. Let B's and W's nominal acceptance wages for employment at

9-11any k1 be defined, respectively, as:

=3b +P(0)Jf+ T(k1 —0) (9.14a).

= + min[P(0)H + T(k1 —0); P(k1)H + M*; (9-14b)

P(k2)H+ T(k2 -_k1)+M*]

These represent the minimum wages that must be offered B and W,such that they will not expect another search to make them betteroff than if they accepted the current offer.

e, the equality in — — — —

In this region B and W incur the same housing and commutingcosts. Since throughout the city W's real acceptance wage exceedsB's, here too will W's nominal asking wage be than B's theamount that their real acceptance wages differ: I k1 k1) —

Yb(kl k1 k1)(9-12) — — —

Defining as that distance at which = (k1);still exceeds (k1) but by less than —

kj<kl<k*:Y(kl)<Yb(kl)= 0 (9-13) B's nominal acceptance wage is than W's, meaning that B

will reject offers that W accepts (if k1 < k*).


An example of the pattern, described above is shown in Figure9-1.'' It implies that the average wage for employment near thecenter of the city (specifically, within a radius of will be lower forblacks than for whites. The opposite would be true at jobs beyondk1—blacks who are employed there would expect to be paid morethan their white coworkers.

Superficially, this pattern might suggest that central-city firmsdiscriminate against blacks, while suburban firms act in their favor.However, this result has been produced by explicitly excludingemployment discrimination; the outcome is due only to the con-straint housing discrimination puts on blacks' residential location.

Proposition CHousing discrimination has an indeterminate impact on the length

of unemployment, or duration of search, of B relative to W. Only ifthe real wage distribution were more precisely specified could anycomparisons be made.

Proof: Since the probability that the next offer made will beacceptable to B is [1 — and to W is [1 — the relativesize of and would indicate whether B had beenunemployed on average longer than W, or the opposite. Unfortunate-ly, both F(5b) > and the reverse are consistent with themodel. In terms of Figure 9-2, point C must be to the left of A, but

0.00x4)Ca)

-C

a)

Ca

a)

it can be eitheibut the opposil

(a) If housiilonger than WG(57 )] =

(9-9'f'may be reL

YbF(Yb)j

or,

YbF(Yb) +

4)

= B's nominal accceptance wage

= W's nominal acceptance wage

yw

k*

k = number of miles from CBD.

Figure 9-1.

ceptance wage

a,

0.00xa)Ca)

4-.4-.Cv;

a)asCo

('3a)

a)

0>.'

.0Co

.000.a)>Co

E

0

Figure 9-2.

ceptance wage

J

it can be either to the right or left of point D. Here, F6Tb)>but the opposite is also possible.

(a) If housing discrimination in this model causes B to searchlonger than W, > G(57 ) and Pr(b) = [1 — F(5 )] < [1 —G(37 )] = Pr(w); so — Equation(9-9'S' may IDe rewritten as:

L L L L

Yb

w -'-U; —

(9-15)


hown in Figureyment near thevil be lower forat jobs beyond

rbe paid more

firmsin their favor.

Icitly excludingbly to the con-

location.

on the lengthre to W. Only ifified could any

made will be)J, the relativeB had been

1e. Unfortunate-with the

left of A, but

11

0Real wages

Yb Yw

1'340 IrivitedStudentPapers

Since, from (9-9), Crimination

— L L relative length ol= f F(yb)dyb —f

yw Proposition DUnless W is

by substituting into (9-15), then rearranging terms, we obtain more centralizec

Proof:

Case I. For aias was initially assumed. Thus the assumption that moving out of tiwhich indicates that B's expected duration of search is longer than Regardless ofW's is not inconsistent with Equation (9-9) and the finding center of the ci

Since his realemployment, ti

(b) If on the other hand, < Equation (9-9) becomes: continually witacceptance wage(for a given non

F(yb) — F(yb )dyb + "b

b b decreasing funcL L — — — distribution of—f which prevents

concentrated neSince the am

— — L — — is unknown, no— — 5 )dyb — Yb> for the whole cit

LCasell. Wn

— f employment.• In this instan

both workers, aMultiplying through by —1 and subtracting irrelevant, since I

even if he couldL workers will rise

+ —1 F(yb )dyb = +f ment distributiorwill have the s1location.

from both sides leads to the, conclusion that <which is simpiy a restatement of the initial assumption. Case III. For

The condition that dominates and the resultant move.implication that < clearly are insufficient for determining Again, becausewhether is greater or less than housing dis- those facing B,


crimination appears to have no general predictable effect on therelative length of search undertaken by B compared to W.

(yw Proposition DUnless W is totally immobile residentially, B's employment will be

more centralized than W's.we obtainProof:

Case I. For any location of employment, W always benefits frommoving out of the center of the city.

ich is longer than Regardless of where he works, W will choose to move from theIfinding center of the city, either to k2, or to k1 if k1 is greater than k2.

Since his real acceptance wage is independent of the location ofemployment, the value to him of a given nominal wage risescontinually with distance from the CBD, and so his nominaln (9.9) becomes:

[acceptance wage falls with distance. Because the reverse is true for B(for a given nominal wage, CBD jobs are worth the most to him) andhis asking wage rises with distance, the relative probability of B'sbecoming employed at any location compared to W's probability is adecreasing function of distance from the CBD, regardless of thedistribution of wage offers by firms. Thus, housing discrimination,which prevents B from moving, causes B's employment to be moreconcentrated near the center of the city than it would otherwise be.

Since the amount by which W's real acceptance wage exceeds B'sis unknown, no comparison of their nominal asking wages averagedfor the whole city can be made.

Case II. W never chooses to move, regardless of the location ofemployment.

In this instance the real opportunities available are identical forboth workers, and any housing discrimination that B experiences isirrelevant, since he, like W, would not choose to leave the central cityeven if he could. The nominal acceptance wages of both types ofworkers will rise with distance from the CBD. Their actual employ-ment distributions depend on the distribution of wage offers, but Bwill have the same probability as W of accepting a job at anylocation.

Case IlL For some locations of potential employment, W willthe resultant move.

for determining Again, because the real opportunities available to W are superior toFhus, housing dis- those facing B, the former's real acceptance wage will exceed the

I


latter's: > For employment in the center of the city and inthe rest W's no-move zone, the housing and transportation costswould be the same to both workers. Consequently, W's nominalacceptance wage will exceed B's for any job in W's no-move region:

Yh(kl) for allk1 less than k.. Thus W is less apt than B tobecome employed in this area, but if W does accept a job there, hisnominal wage will on the average be higher than B's at the samelocation.

On the other hand, in W's move area, his probability of acceptingemployment is greater than B's (unless marginal transportation costsare very small' 2)• Thus B's employment will be more centralizedthan W's, but B's expected wage for working in the central citywould be less than W's, while W's average wage near the edge of thecity would be higher than B's there. The residential mobility of Wdetermines the size of this no-move area and, thus, whether thedistribution of B's and W's employment is quite different or onlyslightly so. The greater the number of firms for which W would findmoving beneficial, the more centralized will B's employment berelative to W's.

From comparing B's employment and expected wage distributionsdistance with W's under various conditions of mobility, it is

clear that unless W is as immobile without discrimination as B is withit, the extreme form of discrimination considered here makes B'semployment more centralized and lowers his average nominal wagenear the CBD as well as reducing his real wage everywhere, but raiseshis nominal wage farther out in the city. No conclusion can bereached, however, on his expected nominal wage relative to W's overthe whole city without specifying the model more precisely.

MODIFIED FORM OF HOUSING DISCRIMINATION

Clearly, the assumption that housing discrimination totally preventsblacks from moving out of the center city is not true: some blacks dolive in suburban areas, although their representation is much lowerthan their income alone would warrant (Census 1973); and, morerelevant for the model under consideration, some blacks move fromthe central ghetto to the suburban ring. Hence, a more reasonableassumption about the form housing discrimination takes would bethen that blacks can move to suburban areas but that the move ismuch more costly for them than for whites.' The additional costscould result from the difficulties and unpleasantness of dealing withwhite realtors; the refusal of some whites to sell or rent blacks,forcing them to visit more housing units before finding an acceptable

one; or an uncejdiscrimination ccwho move out of

In this case, Isame way that Wwhich B ismoving), he willoccurs where:

P(O)H +

k2, B'sochooses to moveexceeds sinmoved, as assumjobs located belresidential locatiowill not.

This fact resuliundertaken by Bavailable to both 1be equal to or gr

the real wagewage opportunitiifacing B, i.e., f(y1

The nominal a

(k1)

(k)

Since the first tei[Y (k) —

are imownsituation is similartion prevented Bexceed

M*(as is 5

general rule.As with the ext:

duration of


;of the city and inansportatOn costs

W's nominalis no-move region:less apt than B to.

a job there, hisri B's at the same

bility of acceptingcosts

more centralizedh the central city

the edge of theItial mobility of W

whether thedifferent or only

hich W would finds employment be

distributionsof mobility, it is

as B is withRd here makes B'sbge nominal wagerywhere, but raisesconclusion can berelative to W's overprecisely.

iON

on totally preventssome blacks do

tion is much lower1973); and, moreblacks move froma more reasonable

on takes would beut that the move is

additional costsof dealing with

or rent to blacks,tiding an acceptable

one; or an uncertain reception by white neighbors. Thus, housingdiscrimination could impose high but noninfinite costs on blackswho move out of the inner city: <Mb <00.

In this case, B calculates his optimal residential location in thesame way that W does. If a job is located beyond (the distance atwhich B is indifferent between staying in the center city andmoving), he will move either to k2 or to k1, whichever is greater.occurs where:

P(O)H + = min[P(k2)H ÷ T(k2 — k—b) +

If <k2, B's optimal residential location for any job for which hechooses to move will be the same as W's. It does not matter that Mbexceeds since moving costs that are independent of distancemoved, as assumed not enter the calculation of k2. Only forjobs located between and will B and W have differentresidential locations: W will choose to leave the central city while Bwill not.

This fact results in some differences between the search processesundertaken by B and W. Since the same nominal wage offers areavailable to both workers, the real value of any offer to W will alwaysbe equal to or than the value for B. At all locations beyond

the real wage for W will exceed Again the distribution of realwage opportunities available to W, i.e., will dominate thosefacing B, i.e., Therefore, as was shown in Proposition

—The nominal acceptance wage for W exceed at least

to by Between decreasing and

—Vb(k) -+ (9-16)

Since the first term is positive and the second negative, the sign of[Y (k) — (k)J can only be determined if the terms of Equation

are known more precisely. Intuitively, if Mb is quite large, thesituation is similar to the case originally examined, where discrimina-tion prevented B from moving at all and caused generally toexceed (k) at points beyond Thus it seems probable thatI —.

I exceeds and — Yb(k)] is negativebeyond (as is shown in Figure 9-3), but this cannot be proved as ageneral rule.

As with the extreme version of housing discrimination, the relativeduration of search for B and W in this instance remains indeter-

344

blacks from wharesidential locatjination perhapslower Wages in Iemployment the:

This is onlyanalysis wouldthrough factor shousing discrimiland and housingshift. As longConclusions in tpossible, howeveon white workerefficiency of proc

NOTES TO CI-IAI

1. Criticism on(1974); on central-cLewis (1969); on aiemployment discrim

2. See von Fursliterature.

3. "City" as useStatistical Area) orregion legally knowndistrict (CBD), andrefer to areas near th

4. If wages varymay not decline witithat either the valueratio at all distanceovershadow variation

5. Atk2, a (tranr6. All workers 1

although the analysis7.B could be a

defined as the ghettocomplex analysis.

8. It would be pjobs that would affoito the CBD, etc.; anincludes a similar oiexpected wage offecomplexity seem to o

Vb(kl) = B's nominal accceptance wage

rw Tb"1 "i "2

k numberofmilesfromCBD.

4,

nominal acceptance wage

0

Figure 9-3.

minate. However, if it were true that < for all k1 (as seemsunlikely), then B would to find an acceptable jobmore quickly than W. If < for some k1, the answer wouldagain depend on the specific distributions.

One definite conclusion, though, may be drawn concerning therelative concentration of employment. Around the center of the city,where Y (k)> (k), blacks have a higher probability of receivingan acceptable offer than whites. Not only will blacks' employmentbe more centralized, but their average wage (at least within the circleof radius will be lower than the average for whites working inthe same area, again even in the absence of any racial discriminationin the labor market.

SUMMARY

The framework outlined here is an attempt to describe one mecha-nism through which racial discrimination in the housing marketcould affect the employment situation of blacks by constrainingtheir residential location. The conclusions are not surprising. Simplybecause the type of discrimination postulated here limits residentialmobility, it induces blacks to follow a different job search patternthan they would in the absence of housing discrimination.As wouldhave been expected, housing discrimination lowers the real income of

wage

inal acceptance wage

r all k1 (as seemsacceptable job

the answer would

n concerning thecenter of the city,bility of receiving

employmentt within the circlewhites working incial discrimination

one mecha-te housing marketts by constrainingsurprising. Simplye limits residentialjob search patternLination. As wouldthe real income of


blacks from what would have prevailed in the absence of constrainedresidential location. This is true even in the suburbs, where discrim-ination perhaps raises their average wage. It forces blacks to takelower wages in the central city besides possibly concentrating theiremployment there.

This is only part of the story, though. A general equilibriumanalysis include the response of firms, such as adjustmentsthrough factor substitution and plant relocation, to the effects ofhousing discrimination on the labor market behavior of blacks. Theland and housing price-distance functions would also be expected toshift. As long as P(k) had a negative but increasing slope, theconclusions in this study would remain valid. It might becomepossible, however, to draw broader implications such as the effectson white workers, firms, relative housing prices, and the level andefficiency of production.

NOTES TO CHAPTER NINE

1. Criticism on methodology comes from Saks-Offner (1971) and Masters(1974); on central-city labor demand, from Noll (1970), Fremon (1970), andLewis (1969); on aggregate demand conditions from Mooney (1969); and onemployment discrimination, from Harrison (1974).

2. See von Furstenberg et a!. (1974, pt. 2) for a good summary of theliterature.

3. "City" as used here is synonymous with SMSA (Standard MetropolitanStatistical Area) or metropolitan or urbanized area concepts, not simply theregion legally known as a city. "Center of the city" means the central businessdistrict (CBD), and central city or center city and suburbs are used loosely torefer to areas near the center and near the edge of the city, respectively.

4. If wages vary systematically with distance, rents and employment densitymay not decline with distance. It is necessary to make the additional assumptionthat either the value of a central location is large enough, or the capital-laborratio at all distances is high enough for variations in the land rental bill toovershadow variations in the wage bill.

5. At k2, a (transportation costs)/ak = —a (housing costs)fak.6. All workers will be referred to as males to simplify the references,

although• the analysis is applicable to a work force of both sexes.7. B could be allowed to move within a specified area around the CBD

defined as the ghetto, but this would only produce the same results with a morecomplex analysis.

8. It would be preferable to allow a worker to search first those potentialjobs that would afford him the highest utility—far B, CBD jobs, then those nextto the CBD, etc.; and for W, jobs at the edge of the city. Salop's model (1973)includes a similar optimal search order, in' which the firms with the highestexpected wage offers are searched first. However, the costs in terms ofcomplexity seem to outweigh the benefits of more realism.


9. A more desirable though more complicated measure of opportunity cost M. andwould be the current wage offer, as in Salop (1973), since this more accurately Economicreflects the income foregone if the worker searches again. Lewis, Wilfred

10. If search costs are allowed to increase with the length of search, the Some New Data." Iacceptance wage will be lower the greater the duration of search. As the MasteLS, Stanleyreservation wage drops, if it falls so low that the value of welfare payments or Employment, andother non-labor.market activities exceeds it, the worker will leave the labor force nomics, August.and join the ranks of the discouraged workers. McCall, J.J. 197

11. There are two instances in which the pattern in Figure 9.1 does not hold: Journal of(1) If the parameters are such that at no employment location does W choose to Mills, Edwin S. 1move out of the center of the city, P(0)H + T(k* — 0) <P(k*)H + M* This is Mooney, Josepiessentially the situation for B, whose "moving costs" effectively prohibit him Metropolitan Decenfrom leaving the ghetto. This seems highly unlikely, given that a much greater Mortenson, Dalefraction of workers employed in the ring of SMSAs live in the ring rather than the Phillips Curve."living in the central city and commuting out. Nelson, Phillip.

(2) A less extreme version of this condition would be that only at a very Political Economy,]distant k1 would W decide to move, and that the falling would not have Noll, Roger.intersected the rising by k* Since the difference between B's and W's and the Conditionssearches arises from B's inability to move outside the ghetto and since the most Metropolis: Public Jlikely state of the world includes frequent benefits for W from moving, these Beverly Hills, Calif.:two extreme conditions will be ignored. Rothschild, Mich

12. Very low marginal transportation costs could prevent B's nominal Information: A Survacceptance wage from ever equaling W's at any distance by causing Yb(kl) Daniel, anand to be so flat that even at k1 > k1, where aYb(kl)/akl > 0 Segregation, Negro Iand < 0, the two curves might never intersect at k1 k*. Journal of Economk

13. Price discrimination is another form which housing discrimination might Salop, S. 1973.take. Unfortunately, little could be concluded about its effect on black Economic Studies, Aemployment opportunities. The real acceptance wage for W would exceed that von Furstenberg,for B because of stochastic dominance. Beyond that, little else can even be tion. Volume I: Houconsidered probable: whether Yb(kl) is greater or less than at anylocation is uncertain and, therefore, so are relative concentrations of employ-ment by race. The comparative lengths of search are again totally indeterminate.Consequently, there seems to be little point to a more complete analysis of theeffects of price discrimination.

REFERENCES

Census. 1973. U.S. Bureau of the Census. Census of Population: 1970.

Mobility for Metropolitan Areas. Subject Reports, PC(2).2C.Fremon, Charlotte. The Occupational Patterns in Urban Employment

Change, 1965.1 967. Urban Institute, 1970.

Hadar, Josef, and William Russell. 1969. "Rules for Ordering UncertainProspects." American Economic Review, March.

Harrison, Bennett. 1974. "Discrimination in Space: Suburbanization andBlack Unemployment in Cities." In von Furstenberg et al., eds. (1974).

Kaln, John. 1968. "Housing Segregation, Negro Employment and Metropoli-tan Decentralization." Quarterly Journal of Economics, May.

ngth of search, theof search. As the

relfare payments oreave the labor force

9-1 does not hold:n does W choose to(k*)H + M* This isctively prohibit himthat a much greaterthe ring rather than

that only at a very(k1) would not haveetween B's and W's

o and since the mostfrom moving, these

revent B's nominal•by causing

> oect at k1 k*.discrimination might.its effect on blackV would exceed thattie else can even bethan at anyntrationS of employ-

indeterminate.plete analysis of the

Population: 1970.

(Urban Employment


Kohn, M., and S. Shavell. 1974. "The Theory of Search." Journal ofEconomic Theory, October.

Lewis, Wilfred. 1969. "Urban Growth and Suburbanization of Employment:• Some New Data." Mimeographed. Washington, D.C.: Brookings.

• Masters, Stanley. 1974. "A Note on John Kain's 'Housing Segregation, NegroEmployment, and Metropolitan Decentralization'." Quarterly Journal of Eco-nomics, August.

McCall, J.J. 1970. "Economics of Information and Job Search." QuarterlyJournal of Economics, February.

Mills, Edwin S. 1972. Urban Economics. Glenview, Ill.: Scott, Foresman.Mooney, Joseph. 1969. "Housing Segregation, Negro Employment and

Metropolitan Decentralization." Quarterly Journal of Economics, May.Mortenson, Dale. 1970. "Job Search, the Duration of Unemployment, and

the Phillips Curve." American Economic Review, December.Nelson, Phillip. 1970. "Information and Consumer Behavior." Journal of

Political Economy, March-April.Noll, Roger. 1970. "Metropolitan Employment and Population Distribution

and the Conditions of the Urban Poor." in John Crecine, ed., Financing theMetropolis: Public Policy in Urban Economics. Urban Affairs Annual Reviews 4.Beverly Hills, Calif.: Sage.

Rothschild, Michael. 1973. "Models of Market Organization with ImperfectInformation: A Survey." Journal of Political Economy, November-December.

Saks, Daniel, and Paul Offner. 1971. "A Note on John Kain's 'HousingSegregation, Negro Employment and Metropolitan Decentralization'." QuarterlyJournal of Economics, February.

Salop, S. 1973. "Non-Random Search and Unemployment." Review ofEconomic Studies, April.

von Furstenberg, George M. et at., eds. 1974. Patterns of Racial Discrimina-tion. Volume I: Housing. Lexington, Mass.: Lexington Books.

Ordering Uncertain

Suburbanization andeds. (1974).yment and Metropoli-

f opportUfl1tY costhis more accurately

ResicSan I

Marcy I

INTROD(JCTIoI

ZoningunderTwo p

ordinance by anotion that exteimportant influeiin this case arediseconomjes wifeatures might iidistrict. Zoningrating land uses.urban property rparcel of land tithe prices of "eqordinance to mciit should removestraining the

The secondmunicipality haspurposes that wbudget. Zoning iiit serves to decri

Note: I thank Rutheir helpful commen

349

Documents

This PDF is a selection from an out-of-print volume …of permanent income, price, and tastes. A person with a given permanent income and employed at any distance k1 frsm the CBD,