Question 2 In this question, we'll consider a model with a riskaverse multi-tasking agent where the tasks have correlated noise. There is a principal and an agent. The agent performs two tasks, and chooses efforts el and e2. The agent's efforts generate noisy outputs a) In step 3, what is the agent's optimal choice of 21 and e1, as a function of b, and b2? b) Suppose g = 0, so task 2 doesn't matter for the principal at all. What is the principal's optimal y 1 = 21 + 5 \"Id 72 = '32 + 3 choice off); and 112'? What are the corresponding e'or't choices el' and e; ? c) Still supposing g = 0, what are the efficient effort choices ef and egg that a social planner maximiz- ing 11 +14 would impose? Comparing with your answers from (b), you should nd that e; 04 The principal can offer the agent an incentive scheme based on both task outputs: T=Ix+blyl +b2y2. d) Now, suppose g = 1, so task 1 and task 2 matter equally for the principal. What is the principal's The principal is risk-neutral while the agent is riskaverse: optimal choice of bf and 17;? What are the corresponding effort choices e; and 51'? e) (1 point) Still supposing g = 1, what are the efficient eEort choices e?\" and eg\" that a social planner maximizing n + u would impose? A 1 n = E[y1+ gyz w] and u = lE[r] EVarh] i (e: + cg). f) Comparing your answer for 5i from (d) to your answer for e; from (b), you should nd that the principal induces the agent to exert less e'ort in task 1 when g = 1 than when 9 = 0. In words, explain why the principal chooses to weaken incentives on task 1 when 9 (the importance of task 2) increases. Note that the parameter 9 represents the importance of task 2 to the principal; it can be positive, negative, or zero. The timing is as usual: g) For what value of 9 would the principal optimally offer an incentive scheme that induces the agent Step 1' The principal chooses the incentive scheme. to exert efcient levels of effort, a: = 6:5 and e; = :5\"? (You do not necessarily have to perform the detailed calculations for this question; it is suicient to explain in words the reasoning for your Step 2. The agent decides whether to accept or reject the offer. (Ifhe rejects, the game ends and answer) he each receive outside option g = 0.) Step 3. The agent chooses el and e2. Step 4. Outputs y] and y2 are realized. The principal pays the agent 1. Let's proceed step-by-step to solve the