2. Consider a corporate manager who lives forever, and who has a discount factor that is equal to e (0, 1) . The manager works for each firm for only one period. When she works for a firm, she can choose to either work hard or slack off. Slacking off is costless, but working hard results in a cost to the manager of $25. The manager's objective is to maximize the discounted difference between what she gets paid and her cost of effort. The manager is paid by her employer every period, but this compensation cannot depend on her effort in the current period. However, firms who hire the manager know what she has done for other firms in the past. A manager who has always worked hard is considered trustworthy and is paid $100. A manager who has slacked off at some point in the past, on the other hand, is paid only $25. In the first period, the manager is paid $100. a) Suppose for a minute that the manager lives for only one period. What would her optimal effort level be? Explain your answer. b) Suppose instead that the manager lives forever. Derive the conditions under which it is optimal for her to work hard in every period. You must prove your answer. ) Explain the economic intuition behind your answer in part b). d) Suppose that firms can observe the manager's past effort level only at a cost. Explain what this would do to the manager's incentive to work hard. You do not have to make any calculations