w = e+ \p + =

L-NL

(10.391

Equation (10.39) is the no-shirking condition. It shows, as a function of the level of employment, the wage that hrms must pay to induce workers to exert effort. The more workers who are employed, the smaller is the pool ol unemployed workers and the larger is the number of workers leaving their jobs, and so the easier it is for unemployed workers to find employment. The wage needed to deter shirking is therefore an increasing function ot employment. At full employment, unemployed workers find work instanth. and so there is no cost to being hred and thus no wage that can deter shirking. The set of points in (NL, w) space satisfying the no-shirking condition (NSC) is shown in Figure 10.2.

Closing the Model

Firms hire workers up to the point where the marginal product of labor equals the wage. From equation (10.25) for prohts, this condition is

eF(eL) = w.

(10.40)

L NL

FIGURE 10.2 The Shapiro-Stiglitz model

L NL

FIGURE 10.3 The effects of a rise in q in the Shapiro-Stiglitz model

The set of points satisfying (10.40) (which is simply a conventional labor demand curve) is also shown in Figure 10.2.

Labor supply is horizontal at ¸ up to the number of workers, L, and then vertical. In the absence of imperfect monitoring, equilibrium occurs at the intersection of labor demand and supply. Our assumption that the marginal product of labor at full employment exceeds the disutihty of effort {F(eL/N) > 1) implies that this intersection occurs in the vertical part of the labor supply curve. The Walrasian equilibrium is shown as Point in the diagram.

With imperfect monitoring, equilibrium occurs at the intersection of the labor demand curve (equation [10.40]) and the no-shirking condition (equation [10.39]). This is shown as Point E in the diagram. At the equilibrium, there is unemployment. Unemployed workers strictly prefer to be employed at the prevailing wage and to exert effort, rather than to remain unemployed. Nonetheless, they cannot bid the wage down: firms know that if they hire additional workers at slightly less than the prevailing wage, the workers will prefer shirking to exerting effort. Thus the wage does not fall, and the unemployment remains.

Two examples may help to clarify the workings of the model. First, a rise in q-an increase in the probabiHty per unit time that a shirker is detected-shifts the no-shhking locus down and does not affect the labor demand curve. This is shown in Figure 10.3. Thus the wage falls and employment

Implications

The model imphes the existence of equilibrium imemployment, and suggests various factors that are hkely to influence it. Thus the model has some promise as a candidate explanation of unemployment. Unfortunately, the model is so stylized that it is difficult to determine what level of unemployment it predicts or to use it to derive specific predictions concerning the behavior of unemployment over time.

L NL

FIGURE 10.4 The Shapiro-Stiglitz model without turnover

rises. As q approaches infinity, the probability that a shirker is detected in any finite length of time approaches 1. As a result, the no-shirking wage approaches ¸ for any level of employment less than full employment. Thus the economy approaches the Walrasian equilibrium.

Second, if there is no turnover (b = 0), unemployed workers are never hired. As a result, the no-shirking wage is independent of the level of employment. From (10.39), the no-shhking wage in this case ise + pe/q. Intuitively, the gain from shirking relative to exerting effort is ¸ per unit time. The cost is that there is probability q per umt time of becoming permanently unemployed and thereby losing the discounted surplus from the job, which is (w - ¸)/ . Equating the cost and benefit gives w = ¸ + ¸/q. This case is shown in Figure 10.4.