You are engaged by the owner of a small rm to recommend a one-year compensation contract for the rm's top manager. She is concerned about cash ow and feels that, in previous years, the manager may have been shirkmg. You ascertain that if the manager works hard (al), the rm's ultimate cash ow 'om current year operations will be one of $576 or $144 (before manager compensation) with probability 0.6, 0.4, respectively. Ifthe manager shirks (a2), cash ow will be $576 or $144 with probability 0.2, 0.8, respectively. Cash ow, however, will not be known until aer the manager's one-year contract has expired. As an expert in GAAP, you know that if cash ow is going to be 5576, net income for the year will be $625 with probability 0.7 and $121 with probability 0.3. If cash ow is going to be $144, net income will be $625 with probability 0.2 and $121 with probability 0.8. You recommend that the manager's contract be based on reported net income. You interview the manager and nd that he is rational, risk averse with utility for money equal to the square root of the amount of money received, and effort averse with disutility of effort of 2 if he works hard and 1.5 if he shirks. The manager's reservation utility is 4. Required at. What percentage of net income must the manager be offered so that he will accmt the contract and work hard? b. Suppose that all information given in the question is unchanged except in the scenario that the manager shirks, and cash ow is 3144, net income will be $625 with probability 0.3 and $100 with probability 0.7. What contract would you then recommend? Show calculations and explain your contract choice. c. The owner is risk neutral, with utility equal to the dollar amormt of the cash ow, not of the manager's compensation. What is the agency cost of the contract in part a? Show calculations. (The agency cost if the loss in owner's expected utility, compared with part b)