Problem
Efficiency wages and bargaining. (Grain and Martin, 2000.) Summers (1988, p. 386) states, "In an efficiency wage environment, firms that are forced to pay their workers premium wages suffer only second-order losses. In almost any plausible bargaining framework, this makes it easier for workers to extract concessions." This problem asks you to investigate this claim.
Consider a firm with profits given by π = [(eL)α/α] - wL, 0< α < 1 and a union with objective function U = (w -x )L, where x is an index of its workers' outside opportunities. Assume that the firm and the union bargain over the wage, and that the firm then chooses L taking was given.
(a) Suppose that e is fixed at 1, so that efficiency-wage considerations are absent.
(i) What value of L does the firm choose, given w? What is the resulting level of profits?
(ii) Suppose that the firm and the union choose w to maximize Uγ π1-γ, where 0 <>< α indexes the union's power in the bargaining. what level of w do they>
(b) Suppose that e is given by equation (10.12) in the text: e = [(w- x )/x]β for w > x, where 0 < β><>
(i) What value of L does the firm choose, given w? What is the resulting level of profits?
(ii) Suppose that the firm and the union choose w to maximize U γ π1-γ, 0 < α. what level of w do they choose? (hint: for the case of β="0," your answer should simplify to your answer in part [a ][ii>
(iii) Is the proportional impact of workers' bargaining power on wages greater with efficiency wages than without, as summers implies? Is it greater when efficiency-wage effects, β, are greater?