16.8 Following in the spirit of the labor market game described in Example 16.6, suppose the firm’s total revenue function is given by R ¼ 10l % l 2

and the union’s utility is simply a function of the total wage bill:

Uðw, lÞ ¼ wl:

a. What is the Nash equilibrium wage contract in the two-stage game described in Example 16.6?

b. Show that the alternative wage contract w0 ¼ l 0 ¼ 4 is Pareto superior to the contract identified in part (a).

c. Under what conditions would the contract described in part

(b) be sustainable as a subgame-perfect equilibrium?