Journal of Monetary Economics 4 (1978) 687-713. 0 North-Holland Publishing Company

UTILITY MAXIMIZATION, AGGREGATE LABOR FORCE BEHAVIOR, AND THE PHILLIPS CURVE

John J. SEATER*

Fnirrctl Reww Bmk qf PAiludelpkicl. Plriiadelpkiu. PA 19105, C.S..4.

I. introduction

In this paper. 1 examine aspects of the Phillips curve using a microecon- omit model of labor force behavior developed elsewhere [Seater (1977)]. The model is a unification of the two major approaches to the microfoundations of labor force behavior. The first approach, exemplified by Dale Mortensen’s work (1970a). assumes the individual is an income maximizer with fixed leisure time and examines how the individual divides nonleisure time between labor and job search; the second approach, exemplified by Robert Lucas and Leonard Rapping’s work (1970). assumes the individual is a utility maximizer not engaging in job search and examines how the individual divides his time between labor and leisure.

Each of these approaches ignores an aspect of the individual’s time allocation decision and is therefore deficient when applied to aggregate analysis. The first approach, assuming leisure time fixed, ignores the partici- pation decision and implicitly assumes that the size of the labor force is fixed, an assumption contradicted by empirical observation. The second approach. ignoring job search, implicitly treats unemployment as an unpr0ductiv.e leisure activity, a treatment contradicted by recent theories of job search and which renders difficult a workable definition of unemployment.

By combining these two approaches, the unified model overcomes the deficiencies of each taken separately. In brief, the individual is assumed to be a utility-maximizer, deriving utility from consumption and leisure and capable of engaging in labor. search, and leisure simultaneously. Under certain restrictions on labor supply, the model yields natural and mutually

*This paper is based on the second part of my Ph.D. dissertation at Brown University. I thank Herschel I. Grossman, Harl E. Ryder, and John Kennan, who constituted my dissertatron committee, and also Robert A. Jones for many helpful comments and suggestions on my dissertation. 1 al:. thank Anthony M. Santomero for comments and suggestions on earlier drafts of this pape-. The views expressed herein are not necessarily those of the Federal Reserle System or the Federal Reserve Bank of Philadelphia.

688 J.J. Seatcv. Utility maximixtiort

consistent definitions of employment, unemployment, and nonparticillill icjn. These definitions help illuminate aspects of the Phillips curve heretofore not examined and also show the relationships among the earlier contributions.

In section 2, I summarize the model and the pertinent results. In section 3, I use the model to analyze the response of aggregate employment, unemploy- ment, and nonparticipation to certain exogenous changes. I show that, even though the response of any given individual to an exogenous change may be ambiguous because of income and substitution effects, this ambiguity does not carry over to aggregate employment, unemployment, and nonpartici- pation. The responses of employment and nonparticipation are determinate for the exogenous changes considered herein. The response of unemployment generally is ambiguous but not because of income and substitution effects. The ambiguity arises from unemployment’s position as a ‘middle’ state between employment and nonparticipation. Changes which tend to induce some people to leave unemployment for employment also tend to induce other people to leave nonparticipation for unemployment, leaving the net change in unemployment ambiguous in general. In section 4. I use the model to examine the Phillips curve. 1 show that, under appropriate assumptions about perceptions, the model can generate a negatively-sloped short-run relation between inflation and unemployment. Under most sets of assum- ptions used in earlier contributions, such as those of Friedman (1968) and

Mortensen (1970a). the long-run Phillips curve is vertical. However, under the assumptions used by Lucas and Rapping (1970), the relation between inflation and unemployment is ambiguous in both the short run and the long

run, although the relation betwecsn both employment and nonparticipation and inflation is unambiguous in both the short and long runs. The results on inflation and unemployment differ from those obtained by Lucas and Rapping. In section 5. I summarize the results.

2. Summary of the individual model

The individual derives utility from consumption and leisure. Consumption at any moment t, denoted C(r), is nonnegative and measured in goods per week, Leisure is all time not spent in labor and job search. The rate of leisure at any moment t. measured in hours per week, is 168 -L(f)- S(t), where 168 is the number of hours in a week and L(r) and s(t) are the rates of labor and search at moment t, measured in hours per week. Labor is time spent working on a job, and job search is time spent looking for a higher paying job than that currently held. The rates of labor and search, and also the sum of these rates, must be between zero and 168.

The assumption that the individual gets utility from consumption and leisure implies that his utility depends only on C and the sum L + S, and not on the sizes of the individual terms L and S. Consequently, utility at time r

J.J. Seutcr. Utility muximizntion 6X9

can be expressed as U[C(t),L(t)+ S(r)]. I assume consumption and leisure, is additively separable in C the usual Inada conditions; thus:

that C: is concave in and L + S, and satisfies

c’, >o, U, * -=o,

u2 <o, L’zz co.

c’,2=&* -0.

lim C,=+ Y. lim U, =c). (‘ _- 0 (’ * I

lim Lr2=0. lim Lrz= - x. (,+ :‘-a* I.+S--lhn

The indi\tduiri’s lifetitne budget constraint. as perucited by him at time T. IS

d .4(r)

it i =; L 1 I’* -4(r)+cr.(f’ L(f)--C‘lf). (1 1 P I,

Au-)=.-I,. (2)

.4(D)=O, (3)

.4(t ) =espected total assets at time t. measured in current dollars, r* = the expected real interest rate at time 1. which equals the nominal

intcrest rate r minus the expected rate of inflation rr.

I’*=).-- .

and which in the ahsencc of inflation is assumed by the individual to be constant.

\\*(I I = the expected notninal hourly wage rate at time r, measured in current dollars,

It==the expcctcd price of consumption goods at time 1, which in the absence of inflation is assumed by the individual to be constant.

7’= the present moment. D = the moment of death, known by the individual.

,4,- = the initial value of assets, known by the individual. B

1 assume that all assets are inside. cariable interest rate assets earning the current market rate. I’.

The individual has some control oier the future value of his wage through job search. Assume that:

690 J.J. Seater. Utility nwxinrization

(a, There is a distribution of nominal wages over vacancies, denoted F*. Let S* be the density function associated with F*:

(b) The individual has a perception, denoted by F, of F*. Let -1‘ be the density function associated with F.

(c) The individual adjusts F to F* with a lag. I leave the precise method of adjustment unspecified.

(d) The individual’s nominal wage will not change unless he searches. (e) The lndividual must accept or reject an offer as soon as he receives it. (f) Similarly, if the individual quits his job, he loses all rights to it; should

he later want to return to it, he would have to compete with other applicants for it.

(g) There is no cost to changing jobs. (h) The only costs of search are foregone leisure and foregone earnings.

At any moment t, the rate at which the individual contacts vti:.ancies is a function of the rate of search at moment t. Let N be this function, so that at any moment the rate of contact is N[S(r)]. which has the units of vacancies per week. Other possible arguments of N. such as the vacancy and unemployment rates or transportation technology, are suppressed. I assume that I&’ is concave in search:

N’(S)>O, N”(S)<O.

and that N’ has the following limit properties:

lim N’(S)= + Y,, lim !V’(S)=O. S-O s-+1

Under these assumptions, N’ is bounded away from zero for Ss 168. Suppose an individual earning wage MI(~) decides to look into a vacancy

chosen at random. His estimate of the probability that he fails to improve his wage is F[w(t)J. Suppose the individual searches for a length of time At, and suppose N[S(t)J is constant over At. The total number of vacancies the individual can conta,ct is N[S(t)]At. His estimate of the probability that he will fail to improve his wage during the entire period Jr is

Denote the density function associated with (F[r~(t)])“l”“‘l“’ by js,,,[~(~ )].

J.J. Seater, Urility maximizution

At time I, the expected improvement in the wage over WWl, is

ECdw(t11=S~,r,Cw-w(t)l~.,,,(o)d~~

=j::,,,(l - [F(w)]Ni”“‘ld’ do ,

69 I

the period dt. denoted

where G is the maximum wage attainable. The expected rate of change w(t) at time t, denoted E[r+(t)], is obtained by taking the appropriate limit dt goes to zero:

E[G(t )] = -N[S(t)]S~,,,lnF(o.,)dwhO.

I define

E[W )] = g[w(t), S(t)],

where

g&O, g,,.2:0, -

g&O* gs, 5 09

g,,, 50.

of as

(4)

Relation (4) is the individual’s best estimate of the ftiture rate of nominal wage improvement. I assume that the individual treats it as the rate that actually will occur and write’

The rate of change of real wages is simply’

d w(t)

[ 1 g[H’(f). SW] N sip= -_- n. P P

(5)

The individual’s utility over his remaining lifetime is3

J’:!U[C(t),L(r)+S(t)]dr. (6)

‘This assumption implies certainty equivalence and Ignores behavior toward risk. In m) I earlier paper (19771. I discuss the implications of this assumption and also show by an indirect method how some of the stochastic elements of the individual’s maximization problem can be analyzed.

‘I assume rhar the rate of wage inflation always equals the rate of price inflation. which is why R appears in (5).

‘Insertion into (6) of the usual discount factor e -” would not alter the results substantially.

However, when the time horizon IS hnown and finite. the discount rate neither is needed to guarantee existence of the integral nor has the natural interpretation that arises when the time horizon is infinite.

692 J.J. Seater, Utility maximization

The individual’s problem is to maximize (6) subject to his budget constraint -.- given by (l), (2), and (3)-and his real wage i,- lprovement constraint - given by (5) together with the initial condition

W(T)=W,, (7)

where M”~ is known by the individual. The solution, or optimal control, is obtained by applying Pontryagin’s maximum principle. The Hamiltonian is

H=U[C(t),L(t)+S(t)]+9(t) L A(t) w(t) r* -j--+---j- L(f)-C(t) 1

+ j&(t) ( gCJ4f ), w )I w __-____._ _ 71 .

P P ) If a control is optimal. then

d A(t) ?H A(r) W(f) _ -...- = -_ = dt P cl)

r*----+-- L(t)-C(r), P P

.Y

.dj.(Il= =(-rH= -IL(f)L(r)-E.(t)(R,~[M,(1),S(f)]-~). dt ;(\yp)

(11 I

An optimal control also must satisfy initial conditions (2), (3). and (7); furthermore. by the transversality cc>ndition, it must satisfy

/.( D ) = 0. (12)

Finally. an optimal control must satisfy the following marginal condiiions:

J.J. Seder, Utility maximization 693

The Inada conditions imply that consumption and leisure always will be positive. Consumption continuously rises such that the marginal utility of consumption falls at a rate equal to r.

Because UL = Us = U2, equality in both (14) and (15) would imply that

However, the left side of (16) is bounded away from zero, so equality cannot be attained for small values of \): ;ln particular, for M’ equal to zero). In such’ cases, L is set equal to zero and S is positive. Thus in the early part of his life, when \V is very low. the individual specializes in search (but still takes some leisure).

When the individual is not working, (14) holds as an inequality. Relations (13) and (15) hold as equalities; totally differentiating then yields the following implicit functions:

C=C($,, f-1

S= S(i. iv).

I+ N-- 1

(17)

(18)

where the sign ander a variable is the sign of the partial derivative with respect to that variable. Small changes in +, i.. and 1%. have no effect on L. so its partial derivatives are all zero.

A positive value of S implies growth of \v. As \V grows, equality tends to come about in (16); but until it does, L remains equal to zero.’ At the moment T* that ( 16) begins to hold as an equality, so does ( 14) and L becomes positive, Relations (13).( 15) now ali hold as equalities and yield the following implicit functions:

C-C(t),. t-1

(19)

“This raises a complication needing explanation. It is clearly sensible t3 talk about the indlvidtldis wage growmg when he is working. However, when the individual IS searching but not working. he earns no wage. What sense. then. is there in talking about wage growth? Consider an individual at‘ initial time T formulating his optimal plan. Suppose he plans to commence work at time T* and at an expected wage of w(T*). Consider a time T’ earlier than TV. The wage w(T’I is the expected value of the wage the individual could earn if he followed the same pattern of search but commenced work at i’:rne T’ instead of T*. Clearly, w(T*) exceeds w(T’). It IS in this sense that the wage grows when the,individual is searching but not working. For further discussion. see my earlier paper (1977).

694 J.J. Seater. Utility maximixtinn

L= L (tj, i.. M’).

(+w--I(+)

s=s ($b, i., M’) ,

c-)(+)(-4

L+S=(L+S) ($, M’).

(+)(+)

(11)

(22 )

Two regions have been defined :

Interior: Relations (13). (14), and (15) all hold as equalities, and C, L. and S are all positive. L=O Corner: Relation (IS) is a strict positive.

inequality and L =O; C and S are

There is no region in which S equals zero, so that the individual always searches. Furthermore. the individual never stops working once he has started: in particular, he never retires. These results arise from the absence of differential costs in the model. To make labor force nonparticipation possible. consider a particular differential cost a restriction on hours worked.

So far, the individual has been able to work any number of hours bctwecn 0 and 168. A consequence is that the individual nevzr sets both I. and S equal to zero at once and therefore never is a labor force nonparticipant. In reality, however, most jobs require that an individual work some minimum number of hours. For convenience, I take this minimum to be uniform at 40 hours because that seems to be about average. However, any number will do. It is only the existence and not the value of the minimum that matters. This restriction on hours worked makes retirement and nonparticipation in the labor force possible. It also leads to natural. precise definitions of cmploy- ment, unemployment. and nonparticipation.

So assume now that the individual cannot work less than 40 hours a week: if he supplies less than 40 hours of labor, no one will hire him. In addition. assume that if an individual holding a job decides to supply less than 40 hours of labor per week. he loses his job and his wage becomes zero. For simphcity. continue to assume that the individual can work any amount over 40 hours.

Under these assumptions, the wage earned depends on the number of hours of labor supplied. Let I be the wage rate associated with a terrain job but which will be paid only if the individual works at least 40 hours a week. Thc;n the wage actually earned, denoted M’,, is

N+,(t)= i

n(t) if L(t)240

0 if L(t)<40.

J.J. Srarrr, Utility muximization 695

The model of individual behavior is changed somewhat by the presence of the restriction on hours worked. The Hamiltonian becomes”

H=U(C,L+S)+l) r*$+-(y +;1 ( ) ( g(w,S) NJ ‘r --_71 ,

P P /

and eqs. (12~( IS) become

A(t) M’, =r* -p--+-,-L(r)-C(t), ‘0

g[H’O 1. S(r )I M = ._- ._ -. _--____ II P P ’

(9’)

The original endpoint conditions (2). (3 ). (7). and (12) still hold. Relations (13) (IS) become

U,.=$(t 1. (13’)

Suppose ~(r ) were large enough to satisfy (14’) as an equality if there were no restriction on hours worked. The equality relation represents what the individual would like to achieve: it is the relation that would m.lximize his utility in the absence of the constraint. When the restriction on hours worked is present. however, equality in (14’) cannot always be attained-in particular. whenever the individual would like to work a positive amount less than 40 hours. The individual then must choose between working 40 hours. which is more than the unconstrained optimum. and not working at all. which is less than the unconstrained optimum.” In either case. his utility is

‘The pertinent expression for making this choice is

ILrr,~~.:CI:!t!..S,rr)l-_C’[Clrl.JO+S,(rl] 40

where S,(r 1 is the amount of search that would be undertaken if L(t) were set equal to zero and S?(r) 15 the amount of search if L(r) were set equal to 40. If the left side exceeds the right. the individual bets L(t) equal to 40; if the right side exceeds the left. the individual sets L(r 1 equal to 0: and If the two sides are equal. he is indifferent between haling L(t) equal 40 and 0.

696 J.J. Seater, Urilit~ maximietition

less than in the unconstrained case. Also, (14’) is satisfied as an inequality. As long as labor is positive, :arch is positive, too; when labor is zero, search

may be positive or zero. 6 Thus there are four possible states the individual can be in:

Interior: L 2 40, S > 0. The hours restriction is not binding, and ( 13’)-( 15’) are satisfied as equalities. The individual’s behavior is described by (19)-(22). Type 1 Corner: L =40, S >O. The hours restriction is binding, and the individual chooses to work. Small changes in +, i,, and w have no effect on L, so the partial derivatives of L all are zero. Relation (14’) can be ignored and the resulting system of (13’) and (15’) give the implicit functions (17) and (18). Type 11 Corner: L - -0, S > 0. The restriction on hours worked is binding, and the individual chooses not to work now but plans to work later. As at the Type I Corner, L is not affected by small changes I,$, i.. and W, and eqs. (17) and (18) again apply. rvpe 111 Corner: L =0, S =O. The restriction on hours worked is binding, and the individual chooses not to work now or in the future. Neither L nor S is affected by small changes in 1(1, E,, or W; and all the partial derivatives of both L and S are zero. Relation (14’) and (15’) can be ignored, and relation (13’) gives ( 17) as the implicit function for C.

Solution of the individual’s problem provides optimal paths for C. L, and S; together, these paths constitute the individual’s optimal plan. Should there be unanticipated exogenous changes in the value of a parameter or variable. the individual must formulate a new plan.’ The following direction of the initial changes in C, L, S, and L + S in exogenous changes for an individual in the interior?

CE=CE (,4, r--II, N, if. p)

+ +(--I + +(+I -

equations show the response to sew-al

(23)

‘The indrvidual sets both L and S equal to zero (i.e., retires from the labor force) if and lmly

if

maxjyL[C,(r), O]dt 2 max j:’ b’[C~f). L(r)+ S(r)]dr,

where the maximum on the left side is taken over all paths of consumption (‘,, consistent HIIII endpoint condition (3) mhen L and S are zero from T’ to D and where the maximum on the right side is taken over all paths of C. L. and S consistent with (2). (3), (7). (8’). (1 I’) and (12). In the absence of the hours restriction. the above inequality cannot be satisfied because the individual always finds it worthwhile to devote at least a small amount of trme to labor and is allowed to do so.

-One can think of the individual as making a new plan at every instant. If at time T all variables have changed as anticipated at time T - dr, then the plan chosen at time T coincides on the interval [T. D] with the plan chosen at time T -dr. However. if some variable has changed in an unanticipated way, then the plan adopted at Twill differ from that adopted at 7-- dt.

*See my earlier paper for the derivation of these relations.

J.J. SPuter. Utilif!, maxinlixtiorl

f!=L! (.4, I’---, N, ~7, p)

- -(+) - ?(?, ?

697

(24)

s”=s” (A, r-Jr N. . . p) - --(+I -(+) ?;‘-, ?

(L+S)“=(L+S)” (A, r-;L. N, \r. p) - -(+) - ?(?) +

where

(25)

(26)

(0

(ii)

. . . (111)

(iv)

the sign under a variable is the sign of the partial derivative with respe,-t to that variable; The variable N signifies all changes in the function N that change the values of N[S(r)] and N’[S(r)] in the same direction; the sign outside parentheses assumes dominance of the income effect of such changes and the sign inside parentheses assumes dominance of the substitution effect; the sign under r - n outside parentheses assumes dominance of the income effect of changes in r -n and the sign inside parentheses assumes dominance of the substitution effect; the sign under w outside parentheses is the result for an equipropor- tional change in all wages when the individual correctly perceives that wages other than his own have changed, and the sign inside parentheses is the result when the individual believes that only his own wage has changed.”

The superscript E’s are a reminder that the results shown pertain to exogenous changes in the variables in question.

Note that when the individual is in a corner, some of the changes indicated in (23H26) may not occur. For example, suppose the individual is in the Type II Corner when his assets unexpectedly fall. The individual has a tendency to increase his labor, as shown by the negative sign under A in eq. (24). However. in order to increase his labor at all, the individual must incrcasc it to at least 40 hours a week. He may not be willing to do this and consequently may continue to supply no labor at all, in which case L(T) will not have been affected by the change in A(T). Similar results hold for labor in the Type I and Type III Corners and for search in the Type III Corner. Thus, for any pivcn indi\,idual in a corner, the effects described by (23). (26), tend to csror but these effects may not be realized if their realization requires

“When the individual correctly perceives that wages other than his own have changed equiproportionally to his own, he perceives no change in the position of his nominal wage relatrve to other nominal wages. whereas when the individual does not percelke that other wages have changed. he does perceive a change in the relative position of his nominal wage. The individual’s perception of his returns to search depends on the relatke position of his nominal wage. SO it is necessary to distinguish between the two cases.

698 J.J. Seuter, Utility masimizntinn

moving across the boundary of a corner. However, if we consider the total of all individuals in a particular corner, it seems safe to assume that an exogenous change that tends to push individuals across the corner boundary in fact will do so for some individuals, Thus if we consider a ‘representative’ individual, functions (23)-(25) should apply.

Note that if individuals are assumed to maximize income with leisure time fixed, the model reduces to that of Siven (1974), which is a continuous time, variable search and !abor version of the McCall (1970)-Mortensen (1970b) model. If instead individuals are assumed to engage in no job search, the model reduces to that of Friedman (1968) and Lucas and Rapping (1970). Thus the model developed above is quite general and contains most earlier models as special cases.

3. Aggregate behavior

The foregoing model yields natural definitions of employment, unemploy- ment, and nonparticipation:

(i) Employmen?: L >O, S ~0. An individual is employed if he is either in the Interior or the Type I Corner.

(ii) Unemplo_rment: L=O, S >O. An individual is unemployed if he is in the Type II Corner.

(iii) Nortparticiparion: L=O, S =O. An individual is nonparticipating if he is in the Type III Corner.

Aggregate employment, unemployment, and nonparticipation are simply the collections of all employed, unemployed, and nonparticipating individuals. respectively.

In this section, I examine the qualitative responses of employment. unemployment. and nonparticipation to various exogenous shocks to the economy. The procedure is first to examine the effects of a shock on individuals within each state and then to sum over states to obtain the net aggregate impact of the shock on each state. This procedure treats labor market phenomena as strictly supply determined; demand is ignored. Undeniably, such a procedure is deficient. However. this deficiency is shared by virtually all papers in this field; they, too, treat the aggregate labor market phenomena as supply determined.“-) Because the purpose of the

‘“See Friedman (1968), Gronau (1971). Lucas (1971. 1973). and McCall (1970). for example. Lucas and Rapping (1970) mention demand. but do not use it in their analysis of the Phillips curte. Mortensen (197Oa) is the only author to attempt a genuine full analysis of the labor market. However, his demand side is flawed in several ways. and in any case, employment still turns out to be supply-determined. Moreover. the restrictions simplified by Mortensen’s formulation of labor demand apparently do not alter the qualitative behavior of employment. unemployment. and nonparticipation.

J.J. Srotcr. G’iilirj, mffrim xliorl 699

present paper is to synthesize the earher contributions and then examine how their results depend on their particular assumptions. I make no attempt to extend the analysis in the direction of including demand; I confine myself to examination of supply. Inclusion of demand would be a worthwhile extension. .r

An exogenous change may hate different effects in the early and later periods of individuals’ lives. For example. an increase in the interest rate may cause individuals to increase their labor supply in the early period of their time horizons but to reduce it later. I confine my discussion to the earlier period. W’irhirl this early period. I will distinguish between long and short runs. during which certain adjustments have or have not taken place. The adjustments concerned will be clear from context.

Subsections 3.1. through 3.h. contain a detailed analysis of certain exog- cnous shocks of interest in examining the Phillips curve; the results are collected and discussed in subsecticjn 3.7.

Because ali assets are inside. there can he no changtz in aggregate asvzt holdings. Assuming that creditors and debtors are equally distributed among emp,loyment. unemployment. and nonparticipation. there are no asset effects on the three states of participation.

3 ’ _ ._. Sowimd raft' (?I illic*rcW t

Suppose that I’ falls at time T and x is unchanged. so that the real in+e&.est rate I** falls. Because all wealth is inside. there are no aggregate income cflects. Ho\vc\er. there are aggregate substitution effects. Eys. (23) -(Zh) shou that individuals increase C( 7’) and decrease L( T1. S(T). and L(T) + S( T 1. The effects on the apgrcgate states of participation are as folhwvs:

(il Employed indiiiduals reduce both labor and search. They may continue to suppYy enough labor to remain employed. may reduce labor en!.qh to become unemployed: or may reduce labor and search enough to become nonparticipatinp. On average. there will be people reacting in each of these ways so that wme people shift from employment to unemp1oymcnt and nonparticipation.

(ii) Unemployed individuals reduce time devoted to search. They may keep search positike and remain unemployed. or they may stop searching altogether and become nonparticipating. On average. some people shift from unemployment to nonparticipation.

(iii) Nonparticipating individuals have no tendency to increase either labor or search and therefore remain nonparticipating. There is no shift out of nonparticipation.

The net results are a decrease in employment, an ambiguous change in unemployment, and an increase in nonparticipation.

The ambiguity in the response of unemployment arises from

unemployment’s being a ‘middle‘ state between employment and non-

participation. Changes which cause some people to enter unemployment from employment also cause some people to leave unemployment for non- participation. This same ambiguity in the response of unemployment will arise in most of the subsequent exogenous changes to be examined.

The results for an increase in I’ are not merely reversals of those for a decrease. Although individuals may leave employment instantly, they cannot enter it instantly; they must spend some time searching for a job. Consider the immediate effects of an increase in I’.

(i) Employed individuals increase their labor supply and therefore remain employed, There are no shifts out of employment.

(ii) Unemployed individuals increase their search and desire to increase their labor. The increase in search means that no unemployed people become nonparticipating. The desire to increase labor means that unemployed individuals want to start work sooner than before the increase in r: however, in the first instant. none of them can start work because they have not yet found jobs. Therefore, at the initial instant that r increases, there is no shift out of unemployment into either employment or nonparticipation.

(iii) Nonparticipating individuals may remain nonparticipating or may com- mence searching and become unemployed. Like unemployed individuals, they do not become employed immediately because search is required to obtain employment. There is a shift from nonparticipation to unemployment .

The initial results are no change in employment, an increase in unemploy- ment. and a decrease in nonparticipation, However, as soon as time begins to pass, the flow from unemployment to employment increases because of the increased desire of unemployed individuals to commence work. This in- creased flow tends to reduce unemployment. Eventually, the equilibrium levels of employment. unemployment, and nonparticipation are reached. Employment will be higher than before the increases in I’, and non- participation will be lower. The change in unemployment will be ambiguous, depending on the relative magnitudes of the initial shift into unemployment from nonparticipation and the total flow out of unemployment into employ- ment. These final results are the opposite of those for a decrease in r. A\suming that the new equilibrium levels of the three aggregates are reached L)uickIy. these final results can be considered the aggregate effects of an increase in I’.

J.J. Serrw. I'filifv nmxirnixtion 701

Henceforth, 1 examine exogenous changes in one direction only. The final results for changes in the opposite direction are always exactly the opposite. although the paths followed may not be simple reversals of each other.

Changes in the complicated g function can arise in many ways and can be quite difficult to analyze. I discuss only two of them. The first kind arises from changes in the function IL’ such that both N[S(r)] and .%“[.S(r)] increase for all values of S(r) .. in other bvords. from any change that increases both the number of vacancies and the marginal number of tacancies that an individual can contact with a given z:mount of search. An improvement in information or transportation technology ~;.~rlld be such a change. The second kind of change arises from an equiproportional increase in all images; such a change ‘expands the density function of tvages ,f’*. I

discuss the second kind of change in the next subsection. Suppose .4,’ changes such that ,V[Slt )] and .Y’[S(r )] both increase. The

aggregate effects are the following:

(i) Some employed individuals, perceiving an incre;ise in the return to search relative to the return to labor, may quit work to search for a better job and thereby become unemployed.’ I There is a shift o\;t of employment to unemployment. No one becomes nonparticipating. t,f course, because to do so would make it impossible to capture the benefits of the change in S.

(ii) Unemployed individuals remain unemployed. Like employed individuals. they do not become nonparticipating. They do not become employed because their wage is still zero. There i:re no shifts out of unemployment.

(iii) Nonparticipating individuals may be induced by the improved returns to search to become unemployed. Like unemployed individuals. they do not become employed. There is a shift from nonparticipation to

unemployment.

The net results are a decrease in employment, an increase in unemployment.

and a decrease in ilonparticipiltion. One could argue that these results are not the final ones. The change in 3’

mukcs it easier to find a job paying any given wage rate. Therefore, does not the change in N reduce the duration of unemployment. implying Ibat as time begins to pass the flow from unemployment to employment increases. leaking the final new equilibrium le\,els of employment and unemployment am-

biguous’? It is true that the change in N makes it easier to find a job paying any given wage: ho\vever, as P have shown in my earlier paper. the change in .V also induces people to increase their acceptance wage. which tends to increase the duration of unemployment. The net change in the duration of unemployment is ambiguous. For simplicity, I assume tlxre is no change in the duration of unemployment so that the results of the preceding paragxph are the final results of a change in N.

Suppose there is an equiproportional increase in all nominal wages. The reactions of employment, unemployment. and nonparticipation depend on whether or not individuals perceive the general nature of the wage increase. Suppose first that they do.

41) Employed individuals perceil e equiproportional increases in their real \vage and real returns to search. ’ ,’ Some employed individuals probably would be induced to lea\-e employment for unetnployment. but it seems safe to assume the number of people so induced to bc negligible. No one becomes nonparticipating because to do so would make it impossible to capture the benefits of the wage increase. There are no shifts out of employment.

(ii) llnemployed individuals percei1.e an increase in their real returns to search. Whether untmplqed individuals increase or decrease their search time is ambiguous because of income and substitution effects: but. as I ha1.e argued irl ml- earlier paper. the duration of unemployment can be expected to fall becau>e of the increased attractivcncss of holding a job. Ho\ve\-er. unemployed indil,iduals do not become employed immediateI>- because their own ~.age is still zero: an 1. like employed individuals. they do not become nonparticillatiny. There are no shifts out of unemploxnient.

(iii) Nonparticipating indi\,iduals also percei\,e an increase in their real

returns to search and may become unemployed. Like unemployed individuals. they do not hccomc rmplo!~cd immcdiatcly. Thcrc is a shift from nonparticipation to unenip~oymcnt.

The initial results arc no chanpc in emplo~mcnt. an increase in uncmplo>- ment. and a decre;r?;c in nonpal.ticipation. As time passes. howcvcr. there is an increased fiou from unemployment to employment because of the decreased duration of unemployment. Consequently. employment ultimately

J.J. Secrtrr. L’tiliry maximi.xrtion 703

rises. Whether unemployment ends up higher or lower than before the equiproportional increase in wages is ambiguous because of the shift into unemployment from nonparticipation. Therefore, the final results are an increase in employment, an ambiguous change in unemployment, and a decrease in nonparticipation.

Now suppose individuals perceive only the increase in their own nominal wage.

(i) Employed individuals perceive an increase in their real wages and a decrease in their real returns to search.13 They remain employed. and there is no shift out of employment.

(ii) Unemployed individuals feel no impact of the wage increase because their own wage of zero is unchanged and they perceive no change in their returns to search. They are completely unaffected by the wage increase initially, and there is no shift out of unemployment.

(iii) Nonparticipants are in the same position as unemployed individuals. There is no shift out of nonparticipation.

The initial results are no changes in employment. unemployment, or non- participation. However, as time begins to pass, two things happen. First, people engaging in search experience unexpectedly high wage offers. Not knowing that all wages have increased equiproportionr-illy and that the wage distribution has been expanded, they belie1.e these wage offers to be relatively high in the wage distribution and to be a ‘once in a lifetime’ bit of good luck. Some unemployed people accept employment earlier than they had anti- cipated, thereby increasing employment and reducing unemployment. Second, people begin to learn of the equiproportional increase in wages and the increased returns to search. As this happens, the aggregate results approach those of the case where people perceived the increase in all wages immediately. Once perceptions have caught up to reality, the results for the two cases are the same. Employment is higher, the change in unemployment is ambiguous, and nonparticipation is lower.

First suppose the price level rises once and for all. Real wages and real returns to search are reduced equiproportionally, This reduction has the same effects on participation as if it were caused by an equiproportional decrease in all nominal wages. Employment falls. the change in unemploy- ment is ambiguous, and nonparticipation rises.

lJln this cast. Individuals perceive no rxpanswn of the distnbution F. Consquentl~. eack individual pcrcelvc~ an increase in his norn~nal wage relative to all others; this reduces the return to search. as can be seen from (5 t.

704 J.J. Seater. Utility nmirnization

Now suppose there is an equiproportional increase in all prices and nominal wages. It seems reasonable to assume that the individual perceives immediately the increase in his own nominal wage, if he is earning one. However, he may or may not perceive immediately that all other wages have risen by the same proportion as his. He also may or may not perceive immediately that the price level has risen, There are four possibilities to consider. Individuals may perceive at the instant they occur:

Case (a ). Both the increase in the price level and the increase in nominal wages other than their own. Perceived real wages and returns to search are unchanged. and there are no changes in employment, unemployment, or nonparticipation.

CUW (6). Neither the increase in the price level nor the increase in nominal wages other than their own. The only people to feel any immediate effects are the employed. They immediately perceive the increase in their own nominal wages: because they do not immediately perceive the increase in the price lev,el. they perceive the increase in their nominal wages to be an increase in their real wages. Consequently, there are no initial changes in employment, unemployment. or nonparticipation. As time begins to pass, two things happen. First. people engaged in search begin to receive un- expectedly high nominal wage offers. This inducts an increase in employment and a decrease in unemployment. Second, everyone begins to learn of the equiproportional increase in nominal wages and prices. Assume that all participants revise their perceptions of wage and price levels at an equal rate. Then it is reasonable to assume that nonparticipants revise their perception of wage levels more slowly than their perception of prices. Presumably, nonparticipants engage in as much consumption. on average, as participants; therefore they acquire information on prices at the same rate as participants. However. nonparticipants engage in no search and acquire information on wages more slowly than participants. Consequently, during the period of adjustment of perceptions, nonparticipants perceive real wages to be 10~s.~ than before “the equiproportional increase in nominal wages and prices, Nonparticipants therefore will have no incentive to leave the state of nonparticipation. and as a result nonparticipation will not be affected by the equiproportional change in wages and prices, Eventually, everyone’s per- ceptions catch up to reality. and employment and unemployment return to their original levels.

Cuss 1~). The increase in the price level but not the increase in wages other than their own. Employed individuals perceive no change in their real wages. All individuals perceive a decrease in their real returns to search. Employed individuals perceive that the real return to work has risen relative to the real

J.J. Sratrr. Utility nwxin~i~ution 705

returns to search: presumably, they remain employed. Unemployed in- dividuals perceive only the decrease in the real returns to search, and some become nonparticipants. Nonparticipants remain as such. Therefore, there is initially no change in employment, a decrease in unemployment, and an increase in nonparticipation. As time begins to pass, individuals engaged in search receive wage offers higher than expected and accept employment sooner than planned. Consequently, employment rises and unemployment falls still more. Eventually, however, people learn that wages have risen by the same proportion as price; emplot-ment and unemployment return to their original levels.

Case (d). The increase in wages other than their own but not the increase in the price level. Before perceptions adjust, the effect is as if only nominal wages were increased. As explained in section 3.4. the result is an increase in employment, an ambiguous change in unemployment. and a decrease in nonparticipation. Once people learn of the increase in the price level, employment, unemployment, and nonparticipation return to their original levels.

Suppose there is an increase in the expected rste of inflation IL If t!le nominal rate of interest I’ adjusts fully and instantaneously to changes in T: so that the real rate r* remains constant, then there are no effects on anyone’s behavior. Consequently, there are no changes in employment, unemployment, or nonparticipation. Suppose instead that r dots not immediately make full adjustment to changes in IL Then I * MS when 71 rises. As explained in section 3.2, the result is a decrease in employment, an ambiguous change in unemployment, and an increase in nonparticipation.

Consider now an increase in the actual rate of inflation z*. Initially. people’s perceived rate of inflation II lags behind R*, so that people continuously experience unexpected increases in all prices and nominal wages. The results for employment, unemployment, and nonparticipation are the same as when the levels of prices and wages unexpectedly increase once and for all. as described in subsection 3.5. Thus if individuals perceive at the moment they occur:

(a) Both the increases in the price level and the increases in nominal wages other than their own, there will be no effects on employment, unemploy- ment, and nonparticipation.

(b) Neither the increases in the price level nor the increases in nominal wages other than their own, then at first employment rises, unemploy-

v-1

Id)

ment falls, and nonparticipation is unchanged; ultimately employment and unemployment return to their original levels, The increases in the price level but not the increases in wages other than their own, the results are as in case (b) above, except that non- participation increases. The increases in nominal wages other than their own but not the increases in the price level, then at first employment rises, the ‘change in unemployment is ambiguous, and nonparticipation falls; ultimately, employment, unemployment and nonparticipation return to their original levels.

If the actual rate: of inflation IT* gradually increases f.om an initial level to a higher level. the results are again the same as for a once and for all increase in the levels of wages and prices.

3.7. Summary

The following equations summarize the net results of the exogenous changes analyzed above:

EM=EM(W, p. zv,r-71). +-- - (13)

UE = C;E(w, p,N, r-n), ? ‘? + ? (14)

NP=NP(w. p, NJ-71), -+- + (151

where EM, C’E, and NP stand for employment, unemployment, and non- participation and where changes in variables are assumed to be in the same direction and proportion for all individuals.”

The most striking thing is the almost complete ambiguity of the behavior of unefnploymcnt; only improvements in the search process. through the N function, have definite effects on unemployment. The reasons the nther changes have ambiguous effects is that unemployment is a ‘middle’ state between employment and nonparticipation; changes which cause people to leave unemployment for employment also cause other people to leave nonparticipation for unemployment, and vice versa. The change in unem- ployment is ambiguous as a result. Note that the ambiguity in the behavior of unemployment does not arise from any income or substitution effects. For

“Note that (13H15) give the final results only; temporal patterns are suppressed. For example. the ultimate results for an equiproportional increase in all nominal wages and prices are the same irrespective of how people initially perceive these challges, whereas the temporal patterns of EM. L’E. and .VP do depend on initial perceptions.

J.J. Serrtcv. L:tilrt\. mtl.rimixtion 707

example, the ambiguity arises whether one assumes dominance of the income or substitution effects of wages. These results are not found in the earlier literature. Earlier models. by not allowing the individual to choose his labor. search, and leisure simultaneously and vary them continuously, were able to define only two states of participation - either employment and unemploy- ment, as in Mortensen (1970a). or employment and nonparticipation, as in Lucas and Rapping (1970).‘” There is no natural third state of participation. obviously making it impossible for unemployment to be a middle state and have the characteristic ambiguities of a middle state.

4. The Phillips curve

Recent microfoundations models of the Phillips curve can be divided into three groups. First. these models can be divided between those that assun:~ the individual to be an income maximizer whose leisure time is fised and who does engage in search (Group I models)‘h and those that assume the individual to be a utility maximizer whose leisure time is \,ariable but who does not engage in search. This latter group can be divided between those models in which the individual is concerned with current wages on1y (Group 2 models)’ _1 and those in which the individual speculates on the future levels of wages (Group 3 models).” Phillips curves arise in these models when certain assumptions are made about individuals’ perceptions of the levels and rates of change of prices and nominal wages.

In this section. I examine what happens when these same assumptions are applied to the more general model de\,eloped in this paper, which contains the earlier models as special cases (see section 2). This exercise confirms the results of the Group 1 models and therefore strengthens them by obtaining them in a more general framework. modifies the results of the Group 2 models and therefore makes them more precise, and contradicts some of the results of the Group 3 models and therefore corrects those resulth. As kvill be seen quickly, all results are evident from the discussion in section 3.

708 J.J. Seater. Utility mtr.ximi:atiou

4.1. Group I models

Assume as in the Group 1 models that changes in individuals’ perceptions of nominal wages other than their own lag behind changes in nominal wages themselves. The analysis can be divided into two cases, depending on how the individual is assumed to perceive changes in the current price level. It may be assumed that the individual perceives immediately any change in the current price level, or it may be assumed that his perceptions lag behind. (The models of Group 1 make neither assumption, ignoring altogether the problem of how people perceive changes in the price level. These models can do SO because they assume people are income maximizers. Changes in the price level affect real income, but real income is maximized if and only if nominal income is maximized; and nominal income is independent of the price level. Consequently, an income maximizer’s behavior -in particular, the amount of search he undertakes -is independent of how he perceives the current price level. Because employment and unemployment are assumed to be functions of the amount of search undertaken, they, too, are independent of the individual’s price perceptions.)

As it turns out, the qualitative behavior of employment and unemploy- ment, but not nonparticipation, is unaffected by how the individual perceives changes in the price level, which is a somewhat surprising result, as I explain momentarily. The first possibility - that individuals immediately perceive changes in the current price level -is case (c) of the discussion in section 3.6; the second possibility- that individuals’ perception of the current price level lags behind the actual level is case (b) of the discussion in section 3.6.

In both cases, an increase in the rate of inflation at first causes an increase in employment and a decrease in unemployment. I_lltimately, however, employment and unemployment return to their original levels once people’s perceptions have caught up to actuality. Consequently, an increase in the rate of inflation reduces unemployment in the short run, which is the Phillips relation; however, in the long run, unemployment is unaffected by the rate of inflation so that the long-run Phillips curve is vertical. These results agree with and therefore strengthen those of the Group 1 models; in particular, see Mortensen ( 1970a).

It is interesting that the qualitative results do not depend on the accuracy of people’s perceptions. As 1 mentioned above, it is natural that price perceptions do not matter in the Group 1 models because of income maximization. However, in the present model the individual is assumed to be a utility maximizer whose behavior has been shown to depend on real income and therefore on perceptions of the price level. Why does the behavior of employment and unemployment not also depend how individuals perceive the price level? The reason is that these two states of participation are not functions of the amount of time individuals devote to labor, search, and leisure. If people misperceive the distribution of nominal wages, they

receive unexpectedly high nominal wage offers, which induce them to acct’p,t employment. They may work fewer hours if they perceive that the price level has risen than if they think it has not; but they have a greater tendency to accept employment nonetheless, and that is all that matters.

Assume as in the Group 2 models that changes in the individual’s perceptions of the current wage and price level lag behind changes in the current price level. Then as actual inflation causes the current wage and price levels to rise, individuals’ perceptions of the current wage and price levels lag behind. The behavior of employment, unemployment, and nonparticipation depends on whether or not people fail to perceive that nominal wages other than their own are rising as theirs are. (The models of Group 2 make neither assumption, ignoring altogether the problem of how people perceive changes in other people’s nominal wages. These models can do so because they assume people do not search and therefore do not care about the distribution of nominal wages.)

Ctrse (i). Suppose that individuals do not perceive immediately that no- minal wages other than their own have risen. This situation correspor.Js to cast (b) of the discussion in section 3.6.“’ People receive unexpectedly high nominal wage offers; and at first, employment rises, unemployment falls, and nonparticipation is unchanged. Eventually, people adjust their Derceptions of thl; levels of wages and prices to the true values. Employment and unemploy- m::nt return to their original levels. Consequently, an increase in the rate of inMion reduces unemployment in the short run. which is the Phillips relation; however, in the long run, unemployment is unaffected by the rate of inflation so that the long-run Phillips curve is vertical. These results agree with those of the Group 2 models; in particular, see Friedman (1968).

CNW (ii). Suppose individuals do perceive immediately that nominal wages other than their own have risen. This situation corresponds to case (d) of the discussion in section 3.6. People believe their real returns to search have improved. At first employment increases, the change in unemployment is ambiguous, and nonparticipation decreases. Ultimately. once peiceived and actual inflation became equal again, employment. unemployment and non- participation return to their original levels. Consequently, in this case the short-run effect of an increase in the inflation rate is ambiguous. There may be the usual negative. Phillips-type relation; there may be an unusual positive relation: or there may be no relation at all. In any case, the long-run

result is a vertical Phillips curve. The short-run results differ from those of the Group 2 models. The reason the short-run results in case (ii) imply that both the unemployed and the nonparticipants are affected by the increase in tlhe rate of inflation, whereas in case (i) only the unemployed are affected. The result is that in case (ii) the flows out of unemployment into employ- ment are offset by flows into unemployment from nonparticipation, whereas in case (i) they are not.

Thus the results depend on the assumptions about perceptions. The Group 2 models, by ignoring job search, suppress this dependence. Consequently, the model developed in this paper modifies the results of the Group 2 models.

4.3. Group 3 nto&ls

Assume as in the Group 3 models that individual’s price expectations are based on a return to normality scheme,‘” that the individual misperceives the normal levels of prices and nominal wages, and that the perceived real interest rate is inversely related to the perceived rate of inflation.21 If the actual rate of inflation rises and if this rise is not perceived immediately, individuals at first expect deflation; therefore the perceived real interest rate rises. As explained in section 3.2, a rise in the real interest rate causes a decrease in employment. an ambiguous change in unemployment, and an increase in nonparticipation. Ultimately. people learn of the higher rate of inflation and come to expect inflation rather than deflation. In the long run, the perceived real interest rate falls, causing an increase in employment, an ambiguous change in unemployment, and a decrease in nonparticipation. Consequently, there is no clear relation between inflation and unemployment

‘“A return to normality scheme assumes that people believe there are normal levels to which prices and wages return. The perceived normal levels themselves may be adjusted over time, but onf) ,vlth a lag. Consequently. if prices unexpectedly rise. people then expect them to fall. If prices persist at their new, higher levels. people slowly adjust their perception of the normal lc\cl upward until the discrepancy between actual and perceived normal prices disappears. This scheme has an intcrcstmg implication for changes in the rate of inflation. If the inflation rate rises and this rise is not immediately perceived. then people experience unexpected price increases. However. as just explained. people believe for a while that prices will return to thetr old normal le\cls and therefore will fall. Consequently. for some time after the onset of inflation, people actually expect deflation. Eventually. of course. they learn of the inflation and their expectations change according!y.

“This last assumption really cannot bc justified in the present model because people do WI hold money. When people hold money. the perceived rate of inflation and the perceiled real interest rate will be inversely related through the well-known effect of perceived inflation on the real return on money. However. when there is no money. there seems to be no reason for such an inverse relation to exist. It is extremely difficult analytically to introduce money ir: any meaningful wag into the model presented in this paper. Despite these difficulties, 1 will discuss the implication% of an mlercc relation betnecn the perceived re;lI interest ruts and the perceived inflation r.ite for the sake 01 comparison.

in either the short run or the long run.” However, there are unambiguous relations between both employment and nonparticipation and inflation in

both the short and long run. These results on the behavior of unemployment are considerably different

from those obtained by Lucas and Rapping (1970), who concluded that unemployment was inversely related to inflation in the short run. thus giving a standard short-run Phillips relation. and unrelated to inflation in the long run, thus giving a vertical long-run Phillips curve. The reason for the difference is that the Lucas and Rapping model, like the Group 2 models, ignores job search and therefore has only two genuine states of participation --employment and nonparticipation. The Lucas and Rapping model artificially introduces unemployment in such a way that it is not a middle state between employment and nonparticipation.‘” The results of ttrlz behavior of employment and nonparticipation agree with those obtained b:, Lucas and Rapping.

Thus the model developed in this paper contirms and therefore strengthens some of the results of the Group 3 models but contradicts and therefore corrects other results of those models.

5. Summary

In this paper, I have applied to aggregate ailalysis a model of indi\idua‘. behavior developed elsewhere. The model assumes the individual is a utility maximizer who derives utility from consumption and leisure and who can engage simultaneously in labor, search, and leisure. This model unites two common approaches to the study of the microeconomic foundations of aggregate labor force behavior and contains the earlier models as special cases. It is thus a useful generalization of earlier microeconomic investigations.

In addition. the model offers significant improvements over earlier work in its macroeconomic applications. It provides natural. mutually consistent definitions of all three of the states of employment. unemployment. and nonparticipati~,n. These definitions are given directly in numbers of people rather than in terms of approximating functions of numbers of hours devoted to

“If thele should turn out empirically 10 be ;i relation in the short run. then there \vill be an cjpi>cjsltc relation m the long run bccuuse the heha\ior of the perceibcd real Interest rnte in the long run I\ the opposite of that in the <hart run.

“LUGI!, i\nd Rapp~np define ihc unemplqment rate IO be ;i function of the difference bcturcn actuiil and ‘normal’ employment. Normal employment is the employment that would preba’l if current real wages CqUi~lld normal real wages. Actual employment is the employment that

pre\;lils at the actual current wage. Both normal and actual employment are functions of the real interest rate. As It 1~1*ns out, v.hen one takes the difference .>f actual and normal employment. the real interes; rate term xncels out. so thilt unemployment has the odd feature

of ncbt hcmg a function of tht‘ real interest rate e\en though both actual and nc>rmal emplqment tit-c.

712 J.J. Seater, Utility maximization

labor, search, or leisurli: by a representative individual. These more direct, precise definitions have enabled clarification o; the nature and behavior of the three states of participation and have permitted avoidance of assump- tions regarding dominance of income and substitution effects. The simul- taneous, mutually consistent definitions of all three states of participation have resulted in recognition of unemployment’s position as a middle state between employment and nonparticipation. This middle position generally results in ambiguity in the response of unemployment to various exogenous changes, even though the responses of employment and nonparticipation are unambiguous.

The model also confirms the results of certain recent studies of the Phillips curve-those that assume the individual speculates on the distribution of nominal wages over vacancies, typified by Mortensen’s (1970a) work; mo- difies the results of others-those that assume the individual misperceiyes his current real wage, typified by Friedman’s (1968) work; and contradicts some of the results of still others-those that assume the individual speculates on the future levels of real wages, typified by Lucas and Rapping’s (1970) work. In general, it is possible to obtain an inverse relation between inflation and unemployment in the short run and no relation between them in the long run, but these results depend on the assumptions made about individuals’ perceptions.

References

Alchian. Armen A.. 1970. Information costs, pricing, and resource unemployment, in: Edmund S. Phelps. ed.. Microeconomic foundations of employment and inflation theory (W. Norton, New York 1.

Almonacid, Reuben D., 1971, Nominal income, output, and prices in the short run, Ph.D. dissertation, University of Chicago.

Friedman, Milton, 1968, The role of monetary policy, American Economic Review 58. March, l- 17.

Gamkrelidze, R.V., 1965, On some extremal problems in the theory of differential equations with applications to the theory of optimal control, SIAM Journal on Control 3, Jan., 106128.

Gronau, Reuben, 1971, Information and frictional unemployment, American Economic Review 61, June, 290-301.

Hedrick, Charles F., 1973, Expectations and labor supply, American Economic Review 63, Dec., 968-974.

Lee. E.B., and L. Markus, 1967, Foundations of optimal control theory (John Wiley. New York).

Lucas. Robert E., Jr., 1972, Expectations and the neutrality of money, Journal of Economic Theory 4, April, 103-124.

Lucas, Robert E., Jr., 1973, Some empirical evidence on output-inflation trade-offs, American Economic Review 63, June, 326-334.

Lucas, Robert E., Jr., 1975, An equilibrium model of the business cycle, Journal of Political Economy 83, Dec., 1113- 1144.

Lucas, Robert E., Jr. and Leonard A. Rapping, 1970, Real wages, employment, and inflation, in: Edmund S. Phelps. ed., Microeconomic foundations of employment and inflation theory (Norton, New York).

J.J. Seater, Utility ma.uimization 713

McCall. J.J.. 1970, Economics of information and job search, Quarterly Journal of Economics 84. Feb., 113-126.

Mortensen. Dale T., 197Oa, A theory of wage and employment dynamics. in: Edmund S. Phelps. ed.. Microeconomic foundations of employment and inflation theory (Norton, New York I.

Mortensen. Dale T., 1970b, Job search, the duration of unemployment, and the Phillips cur\e, American Economic Review 60. Dec., 847-862.

Parsons. Donald 0.. 1973, Quit rates over time: k search and information approach, American Economic Rebicw 63, June, 390-401.

Salop, S.E.. 1973, Systematic job search and unemployment, Review of Economic Studies 40, April, 191-202.

Sargent, Thomas J.. 1973, Rational expectations, the real rate of interest, and the natural rate of unemployment. Brookings Papers on Economic Activity 2, April. 429 -472.

Seater, John J.. 1?77. A unified model of consumption. labor supply. and job search, Journal of Economic Theory 14, April, 349 372.

Seater, John J.. 1979. Job research and vacancy contacts, American Economic Review 69. forthcoming.

Siven. Claes-Henric. 1974. Consumption, supply of labor and search activity In an intertemporal perspective, Swedish Journal of Economics 76, March. 44~ 61.

Weiss, Yoram. 1972. On the optimal lifetime pattern of labor supply. Economic Journal 72. Dec., 1293 1315.

Wh;pple. David, 1973, A generalized theory of job search, Journal of Political Economy 81. Sept.. 117& 1188.