Problem 2.

Problem 2. Tough negotiations A rms revenue function when it uses L units of labor is given by R(L) = x/f A union that represents workers presents a wage offer 20 to the rm. The rm observes the offer and either accepts or rejects it. If the rm accepts the offer, it then chooses the number L of workers to employ (which, for simplicity, you should take to be a continuous variable). If it rejects the offer, no one is hired. The revenue of rm and workers is then 0. (a) Write down the rm's prot function. Suppose that the union cares both about the total number of employees hired L and the wage they each receive w. More precisely the union maximizes the following payoff function: U(w,L) = (w 1)L The payoff of the union is also 0 if no one is hired. (b) Find the subgame perfect equilibrium (equilibria?) of this game. (c) Can you nd one outcome of the game that both parties prefer to any subgame perfect equilibrium outcome? Interpret