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10.2 A Generic Efficiency-Wage Model

Potential Reasons for Efficiency Wages

The central assumption of efficiency-wage models is that there is a benefit as well as a cost to a firm of paying a higher wage. There are many reasons that this could be the case. Here we describe four of the most important (see Yellen, 1984, and Katz, 1986, for surveys and references).

First, and most simply, a higher wage can increase workers food consumption, and thereby cause them to be better nourished and more productive. Obviously this possibility is not important in developed economies. Nonetheless, it provides a concrete example of an advantage of paying a higher wage. For that reason, it is often a useful reference point.

Second, a higher wage can increase workers effort in situations where the firm cannot monitor them perfectly. In a Walrasian labor market, workers are indifferent about losing their jobs, since identical jobs are inmie-diately available. Thus if the only way that firms can punish workers who exert low effort is by firing them, workers in such a labor market have no incentive to exert effort. But if a firm pays more than the market-clearing wage, its jobs are valuable. Thus its workers may choose to exert effort even if there is some chance they will not be caught if they do not. This idea is developed in Section 10.4.

Third, paying a higher wage can improve workers ability along dimensions the firm cannot observe. Specifically, if higher-abihty workers have higher reservation wages, offering a higher wage raises the average quality

The third way the firm can respond to the unemployed workers offer is to say that it does not accept the premise that the unemployed worker is identical to the firms current employees. That is, heterogeneity among workers and jobs may be an essential feature of the labor market. In this view, to think of the market for labor as a single market, or even as a large number of interconnected markets, is to commit a fundamental error. Instead, according to this view, each worker and each job should be thought of as distinct; as a result, the process of matching up workers and jobs occurs not through markets but through a complex process of search. Models of this type are known as search models, or search and matching models, or the flow approach to labor markets. They are discussed in Section 10.8.

Finally, the firm can accept the workers offer. That is, it is possible that the market for labor is approximately Walrasian. In this view, measured unemployment consists largely of people who are moving between jobs, or who would like to work at wages higher than those they can in fact obtain. Since the focus of this chapter is on unemployment, we will not develop this idea here. Nonetheless, it is important to keep in mind that this is one view of the labor market.



Other Compensation Schemes

This discussion imphcitly assumes that a firms financial arrangements with its workers take the form of some wage per unit of time. An important question is whether there are more complicated ways for the firm to compensate its workers that allow it to obtain the benefits of a higher wage less expensively. The nutritional advantages of a higher wage, for example, can be obtained by compensating workers partly in kind (such as by feeding them at work). To give another example, firms can give workers an incentive to exert effort by requiring them to post a bond that they lose if they are caught shirking.

If there are cheaper ways for firms to obtain the benefits of a higher wage, then these benefits lead not to a higher wage but just to complicated compensation policies. Whether the benefits can be obtained in such ways depends on the specific reason that a higher wage is advantageous. For that reason, we wiU not attempt a general treatment. The end of Section 10.4 discusses this issue in the context of efficiency-wage theories based on imperfect monitoring of workers effort. In this section and the next, however, we simply assume that compensation takes the form of a conventional wage, and investigate the effects of efficiency wages under this assumption.

Assumptions

We now turn to a model of efficiency wages. There is a large number, JV, of identical competitive firms. The representative firm seeks to maximize its real profits, which are given by

When ability is observable, the firm can pay higher wages to more able workers; thus observable ability differences do not lead to any departures from the Walrasian case.

See Problem 10.5 for a formalization of this idea. Three other potential advantages of a higher wage are that it can reduce turnover (and hence recruitment and training costs, if they are borne by the firm); that it can lower the likelihood that the workers will unionize; and that it can raise the utility of managers who have some ability to pursue objectives other than maximizing profits.

We can think of the number of firms as being determined by the amount of capital in the economy, which is fixed in the short run.

of the applicant pool, and thus raises the average ability of the workers the firm hires.

Finally, a high wage can build loyalty among workers, and hence induce high effort; conversely, a low wage can cause anger and desire for revenge, and thereby lead to shirking or sabotage. Akerlof and Yellen (1990) present extensive evidence that workers effort is affected by such forces as anger, jealousy, and gratitude. For example, they describe studies showing that workers who believe they are underpaid sometimes perform then work in ways that are harder for them in order to reduce their employers profits.



= Y -wL, (10.1)

where is the firms output, w is the real wage that it pays, and L is the amount of labor it hires.

A firms output depends both on the number of workers it employs and on their effort. For simplicity we neglect other inputs and assume that labor and effort enter the production function multiplicatively. Thus the representative firms output is

Y = F(eL), FC)>0, F"C) < 0, (10.2)

where e denotes workers effort. The crucial assumption of efficiency-wage models is that effort depends positively on the wage the firm pays. In this section we consider the simple case (due to Solow, 1979) where the wage is the only determinant of effort. Thus,

e = e(w), eC) > 0. (10.3)

Finally, there are I identical workers, each of whom supplies one unit of labor inelastically.

Analyzing the Model

The problem facing the representative firm is

maxF(e(w)L) - wL. (10.4)

If there are unemployed workers, the firm can choose the wage freely. If unemployment is zero, on the other hand, the firm must pay at least the wage paid by other firms.

When the firm is unconstrained, the first-order conditions for I and w are

F(e(w)L)e(w) - w = 0, (10.5)

F{e(w)L)Le(w) -1 = 0. (10.6)

We can rewrite (10.5) as

F(e(w)L) = . (10.7) e(w)

Substituting (10.7) into (10.6) and dividing by L yields

= 1. (10.8) e(w)

We assume that the second-order conditions are satisfted.



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