Ellen works for a firm. She contributes to the firm's profits so that she can obtain a bonus if the firm gets outstanding results. The firm pays Ellen a baseline wage of 160 if no outstanding results are observed, and of 160(1+a) if outstanding results are observed, with > Parameter a captures the wage increase. The firm therefore hopes to stimulate Ellen's efforts. Ellen's utility is√xe where 'x' is labour income and 'e' is effort. Ellen can choose to make no effort at all, eq = 0, and the probability of making outstanding results would be p₁ = 0 (option 0). Alternatively, she can exert efforts e₁ = 1.2 and the probability of outstanding results would be p₁ = 0.5 (option 1). ep1 b) What is the wage increase 'a' that the firm has to implement to make Ellen exert some efforts (option 1)? Suppose Ellen can work even more. She can make efforts 2-3.2 and make sure that the firm makes outstanding results, p₂ = 1 (option 2). c) What is the wage increase 'a' that the firm has to implement to induce Ellen to work hard (option 2) versus working a little bit (option 1)? Show that, under this new wage increase, Ellen prefers option 2 to option 0. Ellen generates a production revenue of 320 for the firm in normal times, and an outstanding revenue of 240. d) Write the expected profits of the firm as a function of the wage increase 'a' and the probability of oustanding results 'p'. Suppose for the rest of the exercise that the firm can only fix a =0a=0.45 or a=0.75 (these are not the answers to the previous questions). Explain what would happen in these three cases, and conclude on the best choice for the firm. e) Suppose the firm can pay a manager to monitor Ellen's efforts, preventing her from shirking. Ellen would not be able to choose option 0 anymore. What is the maximum price the firm would pay for these monitioning activities?