Question 2 a) In step 3, what is the agent's optimal choice of e, and e2, 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 In this question, we'll consider a model with a risk-averse multi-tasking agent where the tasks have choice of by and b2? What are the corresponding effort choices e, and ez ? correlated noise. There is a principal and an agent. The agent performs two tasks, and chooses efforts e, and e2. The c) Still supposing g = 0, what are the efficient effort choices e," and ez" that a social planner maximize agent's efforts generate noisy outputs: ing it + u would impose? Comparing with your answers from (b), you should find that el 0. d) Now, suppose g = 1, so task 1 and task 2 matter equally for the principal. What is the principal's optimal choice of by and b2 ? What are the corresponding effort choices e, and ez ? The principal can offer the agent an incentive scheme based on both task outputs: e) (1 point) Still supposing g = 1, what are the efficient effort choices e," and ez" that a social planner T = a + bly1 + 62yz. maximizing it + u would impose? f) Comparing your answer for e, from (d) to your answer for e, from (b), you should find that the The principal is risk-neutral while the agent is risk-averse: principal induces the agent to exert less effort in task 1 when g = 1 than when g = 0. In words, 7 = E[y1 + gy2 -T] and u = [r] - >Var - ? (e; + ez). explain why the principal chooses to weaken incentives on task 1 when g (the importance of task 2) increases. Note that the parameter g represents the importance of task 2 to the principal; it can be positive, g) For what value of g would the principal optimally offer an incentive scheme that induces the agent negative, or zero. to exert efficient levels of effort, el = el" and ez = e2"? (You do not necessarily have to perform The timing is as usual: the detailed calculations for this question; it is sufficient to explain in words the reasoning for your answer.) Step 1. The principal chooses the incentive scheme. Step 2. The agent decides whether to accept or reject the offer. (If he rejects, the game ends and he each receive outside option u = 0.) Step 3. The agent chooses e, and ez. Step 4. Outputs y, and y2 are realized. The principal pays the agent T. Let's proceed step-by-step to solve the