potential determinants of these variables we examine wage and employment determination with two types
of labour.
We assume that wages for the two types of workers are determined in different ways. For skilled
workers, we suppose that imperfect information on the part of the firm about whether or not employees
are shirking forces the former to pay wages above the market clearing level, which in turn lead to
unemployment, as in the efficiency wage model of Shapiro and Stiglitz (1985). For unskilled workers, we
model the wage and employment determination process as the outcome of wage bargaining between a
single union and a single firm in a right-to-manage framework. The union bargains over unskilled wages
with the firm, and then the latter sets employment. 5
Efficiency wages for skilled workers
Consider a simple, one-period efficiency wage model. Suppose skilled agents receive a net wage
w~s = (1 - τ)ws , where τ is the tax wedge paid to the government as employer and employee
contributions. Workers are assumed to be risk-averse with utility U(wi) = wiρ , with 0 < ρ ≤ 1 . Then,
the utility of shirking is simply U S = (1 - p)((1 - τ)ws )ρ + pBρ and that of not-shirking
UN = ((1 - τ)ws - e)ρ , where p is the probability of being caught if shirking, B is the unemployment
benefit (or the monetary equivalent of leisure if the latter is unavailable), and e is the monetary cost of
effort.6 The resulting efficiency wage, Ws, is given by the solution to
((1 -τ)ws - e)p= (1 - P)((1 -τ)ws )p+ PBp (6)
Simple differentiation shows that Ws is increasing in B and e, and decreasing in p . Given Ws and the
level of unskilled employment, the inverse demand for skilled labour, equation (2c), determines skilled
employment, H .
Union bargaining and the unskilled wage
Consider now the determination of the unskilled wage and employment level. We assume that the union
represents only the unskilled, and that it has a utilitarian utility function of the form
V = i[LU(Wu)+(L - L)U(B)] (7)
L
where L is the unskilled labour force, U(.) is the workers’ utility function, U(Wi ) = Wip, and the net
wage is given by w~u = (1 - τ)wu . The bargaining process is then governed by
5 All our results can be obtained if instead of having efficiency wages for the skilled we had a single union that
represented both types of workers and bargained simultaneously over both wages.
6 It would be straightforward to allow for the dynamic flows into and out of employment. For simplicity, we assume
here that labour markets are separated by skills, such that an unemployed skilled worker cannot work as unskilled.
Note that B goes untaxed, as in most institutional set-ups.