In labour economics, Shapiro–Stiglitz theory of efficiency wages (or Shapiro–Stiglitz efficiency wage model) is an economic theory of wages and unemployment in labour market equilibrium. It provides a technical description of why wages are unlikely to fall and how involuntary unemployment appears. This theory was first developed by Carl Shapiro and Joseph Stiglitz.
Contents
Introduction
When full employment is achieved, if a worker is sacked, she automatically finds her next job soon. In the circumstances, she does not need to exert her effort in her job, and thus full employment necessarily motivates a worker to shirk provided that she is happy with loafing on the job. Since shirking makes a firm's productivity decline, the firm needs to offer its workers higher wages to eliminate shirking. Then all firms try to eliminate shirking, which pushes up average wages and decreases employment. Hence nominal wages tend to display downward rigidity. In equilibrium, all firms pay the same wage above market clearing, and unemployment makes job loss costly, and so unemployment serves as a worker-discipline device. A jobless person cannot convince an employer that she works at a wage lower than the equilibrium wage, because the owner worries that shirking occurs after she is hired. As a result, her unemployment becomes involuntary.
No-shirking condition
Suppose utility is a function of wages w and effort e like
because the worker is either dismissed or kept employed during the time. The exponential function appears, because the occation of dismiss in the interval is once and Poisson distribution is used for the discount rate. Due to the short interval, we approximate the exponential function by 1-rT
and simple calculation yields
Then we find the fundamental asset equation of a worker:
For a nonshirker the equation is
and for a shirker
where q is the probability per unit time that a worker is caught shirking and sacked. Then we see
The condition
where
Market equilibrium
Let
where
and we call it the aggregate NSC. These two yields
where the unemployment rate is
The aggregate production function
A firm's labour demand is given by equating the cost of hiring an additional employee to the marginal product of labour. This cost consists of wages and future unemployment benefits. Now consider the case where
In equilibrium,
This suggests following things.
Job security rules
The level of employment is changed by rules about job security. Let us consider a firm which consists of an employer and homogeneous employees. Then, suppose the profit of the firm is a function of the level of employment N, the lowest wage
where g(N) is the production function, L is the value of on-the-job leisure from shirking, and p is the probability that an employee is caught shirking and sacked. Assume that the production function has the upper limit and its second derivative with respect to N is negative. Not to mention, the first derivative is positive. That is a reasonable assumption that the function has its upper bound in term of productivity. Consider, for instance, such a function of time as
Obviously its first derivative is positive, and second derivative is negative.
Let R be a measure of the difficulty of dismissing an employee who is caught shirking. Then p is a function of both R and M. The first and second derivatives of the profit with regard to N are:
The condition for the maximum of the profit is
Thus differentiating its both sides with regard to R gives us
It turns out that