Suppose that a worker interacts with a firm as follows:The workerfirst decides how much to invest in developing his skills. Letxdenote the worker’sinvestment, and suppose that the investment entails a personal cost to the worker of x^2; assume x≥0. If the worker works in the firm, then his investment generatesreturnaxfor the firm. If the worker decides to work on his own (separate fromthe firm), then his investment generates a return ofbxthat he keeps. The numbersaandbare positive constants satisfying a > b(which means that the investmentis more productive in the firm). After the worker chooses his investment, the firmobserves it. Then the firm offers the worker a wagew, and the worker accepts orrejects it (ultimatum bargaining). If the worker accepts the wage, then he works inthe firm. If he rejects the wage, then he works on his own.

a. Draw the game tree. Find and report the subgame perfect equilib-rium of this game. What investment level is selected?
b. Consider a variant of the game in which the worker gets to makethe wage offer (and the firm accepts or rejects the offer).What investmentlevel will prevail in equilibrium?