kindly do all parts. need all parts solution

Question 4 Consider a firm run by an "incumbent" manager. Suppose the incumbent manager has the opportunity to invest in one of two different projects, Project 1 or Project 2. The incumbent manager has a higher ability in managing Project 1 rather than Project 2. Also, if the incumbent is fired by shareholders, she is replaced by an "alternative" manager whose ability to manage Project 1 is lower than the incumbent's ability. Suppose the investment in a project is irreversible, and the shareholders' choice of the incumbent manager salary (as well as their decision on whether to fire her) is taken after the investment is made. Also, assume the incumbent manager has a stake in the firm she runs, but she does not fully control it. (a) Suppose none of the projects gives the manager a direct utility. According to Shleifer and Vishny (1989), which of the two projects should the incumbent manager choose? What is the economic rationale behind this choice? Explain. (30% of the marks) (b) Suppose the incumbent manager chooses the size of the investment in her preferred project. Do you expect the manager to select the investment size that maximizes the firm's market value? If not, does the manager over-invest or under-invest with respect to the efficient investment size? Explain your answer. (40% of the marks) (c) Suppose now that, unlike in Shleifer and Vishny (1989), the manager's compensation is a fixed salary w, which does not vary with the size of the investment chosen either by the incumbent manager or by the alternative manager. Suppose also that the manager owns a positive fraction # e (0, 1) of the shares of the company, but she does not fully control it (that is, 0