EXERCISE 177.1 (Firm-union bargaining) A firm's output is L(100 – L) when it uses L≤ 50 units of labor, and 2500 when it uses L> 50 units of labor. The price of output is 1. A union that represents workers presents a wage demand (a nonnegative number w), which the firm either accepts or rejects. If the firm accepts the demand, it chooses the number L of workers to employ (which you should take to be a continuous variable, not an integer); if it rejects the demand, no production takes place (L = 0). The firm's preferences are represented by its profit; the union's preferences are represented by the value of wL. a. Formulate this situation as an extensive game with perfect information. b. Find the subgame perfect equilibrium (equilibria?) of the game. c. Is there an outcome of the game that both parties prefer to any subgame perfect equilibrium outcome? d. Find a Nash equilibrium for which the outcome differs from any subgame perfect equilibrium outcome.

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