3. Suppose that a worker interacts with a firm as follows: The worker first decides how much to invest in developing his skills. Let r denote the worker's investment, and suppose that the investment entails a personal cost to the worker of 2; assume r 0. If the worker works in the firm, then his investment from the firm), then his investment generates a return of bx that he keeps. The numbers a and b are positive constants satisfying a > b (which means that the investment is more productive in the firm). After the worker chooses his investment, the firm observes it. Then the firm offers the worker a wage w, and the worker accepts or rejects it (ultimatum bargaining). If the worker generates return ar for the firm. If the worker decides to work on his own (separate accepts the wage, then he works in the firm. If he rejects the wage, then he works on his own. (a) Draw the game tree. Find and report the subgame perfect equilibrium of this game. What investment level is selected? (b) Consider a variant of the game in which the worker gets to make the wage offer (and the firm accepts or rejects the offer). What investment level will prevail in equilibrium