A firm's output is L(100 - L) when it uses L50 units of labor, and 2500 when it uses L> 50 units of labor. The price of output is 1. A union thatrepresents workers presents a wage demand (a nonnegative number w),which the firm either accepts or rejects. If the firm accepts thedemand, it chooses the number L of workers to employ (which youshould take to be a continuous variable, not an integer); if itrejects the demand, no production takes places (L = 0). The firm'spreferences are represented by its profit; the union's preferencesare represented by the value of wL.
a) Formulate this situation as an extensive game with perfectinformation.
b) Find the subgame perfect equilibrium (equilibria?) of thegame.
c) Is there an outcome of the game that both parties prefer to anysubgame perfect equilibrium outcome?
d) Find a Nash equilibrium for which the outcome differs from anysubgame perfect equilibrium outcome.