Efficiency wages: employment versus welfare.

• Author: Carter, Thomas J.

1. Introduction

   This paper analyzes the effects of government policies in an efficiency wage model. In such a model, wages exceed market clearing rates. Firms may pay high wages for many reasons; Levine gives thirteen motivations for efficiency wages [12].(1) In the model used here, high wages prevent shirking by workers. The model is similar to those of Shapiro and Stiglitz, Sparks, Fairris and Alston, and others [15; 17; 7].

   Efficiency wage models are often viewed as providing the microeconomic foundations of involuntary unemployment and Keynesian economics [1; 2]. Unemployment is also emphasized in many discussions of government policies [3; 4; 11].

   A major example is that of Johnson and Layard [9]. They find that a per capita employment subsidy financed by an ad valorem wage-rate tax would reduce unemployment. They conclude that this policy would benefit a country because of the employment effect.(2)

   Yet, this paper shows that the employment effect is misleading. Here, a policy that causes employment to rise (fall) also must cause income net of effort to fall (rise). So, total welfare falls (rises). The policy implications discussed by Johnson and Layard and others are therefore reversed.

   The result holds because there is a trade-off between employment and the utility of employed workers. The trade-off is such that national welfare rises when worker utility and unemployment rise. One could also view this trade-off as being between employment and productivity. A policy that encourages low wages (a wage-rate tax used to finance an employment subsidy) raises employment. The lower wages, however, reduce worker incentives to provide effort and so reduce efficiency or productivity. The results show that productivity falls so much that income net of effort falls when employment rises.(3)

   Section II considers wage-rate (ad valorem) and employment (per capita) taxes and subsidies in an efficiency wage model with endogenous effort and productivity. With a government budget constraint, one can find a trade-off between employment and the welfare of employed workers. Section III finds that, given this trade-off, total welfare can only increase if employment falls. Section III also considers distribution. Some agents gain, but no agents suffer first order decreases in their expected utility as a result of an employment-reducing policy. One such policy is a wage-rate subsidy financed by an employment tax. Section IV considers some extensions of the basic model.

2. An Efficiency Wage Model of Shirking

   The model used is a moral hazard or shirking model similar to that of Shapiro and Stiglitz but with endogenous effort [15]. There are three key assumptions in such models. First, workers find disutility in working, that is, leisure on the job brings utility. Second, firms cannot perfectly monitor their workers. Third, firing is the worst punishment workers may suffer if caught shirking; there is no bonding or blackballing. Under these assumptions, firms must pay wages that exceed the worker's opportunity cost. If they did not, firing would carry no penalty and all workers would shirk. Without other complications, this implies involuntary unemployment.

   To begin the mathematical presentation, consider the workers. All workers are identical and receive utility from income but suffer disutility from effort. Specifically, the instantaneous utility of a worker is as shown below:

   U = w - F(e).

   Here, w is wage income and e is effort. F(e) is the disutility of effort. F(O) is the disutility of having a job at which one shirks or provides no effort. Assume that ([Delta]F/[Delta]e) [greater than] 0 and so F(e) [greater than] F(0).

   The firms choose w and a minimum acceptable effort standard to ask of their workers. If workers do not provide this level of effort, if they shirk, they are at risk of being discovered and fired. Assume that q is the exogenous rate at which firms discover and fire workers. Workers must choose either to provide effort or to shirk. Assuming risk neutrality, the discounted utilities of shirkers and non-shirkers are as in equations (1A) and (1B). Shapiro and Stiglitz provide derivations of these equations.

   r[V.sub.ES] = w - F(0) + (b + q)([V.sub.U] - [V.sub.ES]) (1A)

   r[V.sub.EN] = w - F(e) + b([V.sub.u] - [V.sub.EN]) (1B)

   [V.sub.ES] and [V.sub.EN] are the utilities of employed shirkers and non-shirkers while [V.sub.U] is the utility of unemployed workers, r is the discount rate. b is the exogenous rate at which workers choose to leave employment? e is the effort the firm asks of its workers.(5)

   Notice that (1A) and (1B) are similar to some equations in the finance literature. They show the discounted value as equal to the flow benefits plus the expected change in the value of the stock. The worker uses (1A) and (1B) to make the decision to shirk or not.

   Assuming that zero effort yields zero output, the firm must choose w and e to keep workers from shirking. That is, the firm must set [V.sub.EN] [greater than or equal to] [V.sub.ES]. Using (1A) and (1B), one can find this non-shirking condition. It is shown in (2A) as an equality because there is no gain for the firm in increasing wages or reducing the minimum acceptable effort level beyond the levels necessary to eliminate shirking. (2B) is another relationship that will be useful below. It shows that the gain from shirking, the disutility of effort avoided, equals the expected cost of shirking. (2B) is also derived from (1A) and (1B). Since [V.sub.EN] = [V.sub.ES] in equilibrium, I simplify the notation by using [V.sub.E] to denote the utility of an employed worker.

   [F(e) - F(0)] [r + b] = q[w - F(e) - r[V.sub.U]]. (2A)

   F(e) - F(0) = q([V.sub.E] - [V.sub.U]) (2B)

   (2A) gives e as an implicit function of [V.sub.U] and w. A higher wage or a lower [V.sub.U] raises the utility cost of being fired. So, both allow firms to ask greater effort of their workers without a shirking response.

   Now consider the firms in more detail. These perfectly competitive firms use labor as the only input to produce some good. With constant returns to scale, the firm can maximize profit by maximizing profit per worker, [Pi]. Profits per worker are the value of output per worker minus the cost of the worker. These profits are driven to zero in equilibrium.(6)

   [Pi] = Q(e) - [w(1-[S.sub.W]) - [S.sub.E]] = 0 (3)

   where Q is output per worker. It is a function of effort; greater effort leads to more output. The price of the good is the numeraire. [S.sub.E] and [S.sub.W] are employment and wage-rate subsidies. [S.sub.E] is paid per capita; [S.sub.W] is paid ad valorem. These are the only government policies available.(7)

   From (3), one can find the first order condition:

   ([Delta][Pi]/[Delta]w) = ([Delta]Q/[Delta]e)([Delta]e/[Delta]w) - (1 - [S.sub.W]) = 0. (4A)

   From (2A),

   ([Delta]e/[Delta]w) = q/[(r + b + q)([Delta]F/[Delta]e)].

   So, (4A) becomes (4B):

   [Epsilon]Qq/[(r + b + q)([Delta]F/[Delta]e)e] = (1 - [S.sub.W]) (4B)

   where [Epsilon] = ([Delta]Q/[Delta]e)/(e/Q), the elasticity of Q with respect to e. Assume that [Epsilon] is constant.

   In the non-shirking condition (2A), the zero profit condition (3), and the first order condition (4B), there are three equations with three unknowns, e, w, and [V.sub.U]. So, one can solve for these variables here, independent of the employment level.

   It is now possible to find the comparative statics results of the two labor subsidies. To begin, notice that in (4B), Q and ([Delta]F/[Delta]e) are functions of e. So, (4B)...