One can also show that if ftrms do not change their wages, for reasonable cases their incentive to adjust their prices is also small. If wages are completely flexible, however, the incentive to adjust prices is not small. With greater than Ueq, each firm wants to pay less than other firms are paying (see [10.15]). Thus if wages are completely flexible, they must fall to zero-or, if workers have a positive reservation wage, to this reservation wage. .As a result, firms labor costs are extremely low, and thus their incentive to cut prices anc increase output is high. Thus in the absence of any barriers to changing wages, small cosi to changing prices are not enough to prevent price adjustment in this model.

"In fact, in a competitive labor market, an individual firms incentive to reduce wages other firms do not is even larger than the fall in the equilibnum wage. If other firms do n cut wages, some workers are unemployed. Thus the firm can hire workers at an arbitrarL small wage (or at workers reservation wage).

Dickens, Katz, Lang, and Summers (1989) document the importance of worker theft ar.= shirking m the United States and argue that these phenomena are essential to understanding the labor market.

Suppose that /3 = 0.06 and fo = 1, so that ueq = 6%. Suppose, however, that unemployment rises to 9% and that other firms do not change their wages. Equations (10.20) and (10.21) imply that this rise lowers Cfixed by 2.6% and Cadi by 3.2%. Thus the firm can save only 0.6% of costs by cutting its wages. For /3 = 0.03 and fo = 0.5, the declines in Cfixed and Cadj are 1.3% and 1.5%; thus in this case the incentive to cut wages is even smaher.

In a competitive labor market, in contrast, the equilibrium wage faUs by the percentage fall in employment divided by the elasticity of labor supply. For a 3% fall in employment and a labor supply elasticity of 0.2, for example, the equilibrium wage falls by 15%. And without endogenous effort, a 15% fall in wages translates directly into a 15% fall in costs. Firms therefore have an overwhelming incentive to cut wages and prices in this case.

Thus efficiency wages have a potentially large Impact on the incentive to adjust wages in the face of fluctuations in aggregate output. As a result, they have the potential to explain why shifts in labor demand mainly affect employment in the short run. Intuitively, in a competitive market firms are initially at a corner solution with respect to wages: firms pay the lowest possible wage at which they can hire workers. Thus wage reductions, if possible, are unambiguously beneficial. With efficiency wages, in contrast, firms are initially at an interior optimum where the marginal benefits and costs of wage cuts are equal.

10.4 The Shapiro-Stiglitz Model

The source of efficiency wages that has probably received the most attention is the possibility that firms limited monitoring abilities force them to provide their workers with an incentive to exert effort. This section presents a specific model, due to Shapiro and StigUtz (1984), of this possibility.

Presenting a formal model of imperfect monitoring serves three purposes. First, it allows us to investigate whether this idea holds up under

Assumptions

The economy consists of a large number of workers, L, and a large number of firms, N. The workers maximize their expected discoimted utilities, and firms maximize their expected discoimted profits. The model is set in continuous time. For simplicity, the analysis focuses on steady states. Consider workers first. The representative workers lifetime utility is

e-pfumt, p>0. (10.22)

u(f) is instantaneous utility at time f, and p is the discount rate. Instantaneous utility is

w(t) - e(t) if employed u(f) = - (10.23)

0 if unemployed.

w is the wage and is the workers effort. There are only two possible effort levels, e = 0 and e = e. Thus at any moment a worker must be in one of three states: employed and exerting effort (denoted "£"), employed and not exerting effort (denoted "S," for shirking), or unemployed (denoted "L/").

A key ingredient of the model is its assumptions concerning workers transitions among the three states. First, there is an exogenous rate at which jobs end. Specifically, if a worker begins working in a job at some time fo (and if the worker exerts effort), the probability that the worker is still employed in the job at some later time t is

Pit) = e-<-f"\ b > 0. (10.24)

(10.24) implies that Pit + )/ ( ) equals e and thus that it is independent of t: if a worker is employed at some time, the probability that he or she is still employed time later is e" regardless of how long the worker has already been employed. This lack of time dependence simplifies the analysis greatly, because it implies that there is no need to keep track of how long workers have been in their jobs. Processes like (10.24) are known as Poisson processes.

An equivalent way to describe the process of job breakup is to say that it occurs with probability b per imit time, or to say that the hazard rate for job breakup is b. That is, the probability that an employed workers job ends

scrutiny. Second, it permits us to analyze additional questions; for example, only with a formal model can we ask whether government policies can improve welfare. Third, the mathematical tools the model employs are useful in other settings.

The Values of E, U, and S

Let Vi denote the "value" of being in state i (for z =E,S, and U). That is. \ is the expected value of discounted lifetime utihty from the present momenl forward of a worker who is in state /. Because transitions among states are Poisson processes, the V; s do not depend on how long the worker has beee in his or her current state or on his or her prior history. And because we are focusing on steady states, the V, s are constant over time.

To find Ve, Vs, and Vu, it is not necessary to analyze the various par the worker may follow over the infinite future. Instead we can use dynani,, programming. The central idea of dynamic programming is to look at onl> a

in the next dt units of time approaches bdt as dt approaches zero. To see that our assumptions imply this, note that (10.24) implies P{t) = -bP{t).

The second assumption concerning workers transitions between states is that firms detection of workers who are shirking is also a Poisson process. Specihcally, detection occurs with probability q per tmit time, q is exogenous, and detection is independent of job breakups. Workers who are caught shirking are fired. Thus if a worker is employed but shirking, the probabihty that he or she is stiU employed time later is (the probability that the worker has not been caught and fired) times e (the probabihtv. that the job has not ended exogenously).

Third, imemployed workers find employment at rate a per unit time. Each worker takes a as given. In the economy as a whole, however, a is determined endogenously. When firms want to hire workers, they choose workers at random out of the pool of unemployed workers. Thus a is determined by the rate at which firms are hiring (which is determined by the number of employed workers and the rate at which jobs end) and the number of unemployed workers. Because workers are identical, the probabihtv of finding a job does not depend on how workers become unemployed or on how long they are unemployed.

Eirms behavior is straightforward. A firms profits at t are

Mt) = Fimt)) - witmt) + Sit)], F{-)>0. F"(-)<0, (10.23

where L is the number of employees who are exerting effort and 5 is the number who are shirking. The problem facing the firm is to set w sufficienth high that its workers do not shirk, and to choose L Because the firms deo-sions at any date affect profits only at that date, there is no need to anah ze the present value of profits: the firm chooses w and L at each moment tc maximize the instantaneous flow of profits.

The final assumption of the model is eFieL/N) > e, or F(eL/N) > 1. This condition states that if each firm hires 1/ of the labor force, the marginal product of labor exceeds the cost of exerting effort. Thus in the absence of imperfect monitoring, there is fuU employment.