Question 2 In this question, we'll consider a model with a risk-averse 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 ez. The agents e'orts generate noisy outputs: y] =e1+e and JV2 =e2+e where e is a common noise term with ]E[e] = 0 and Var[e] = 0'2 > O. The principal can offer the agent an incentive scheme based on both task outputs: r=a+b1y1+bzy2. The principal is risk-neutral while the agent is risk-averse: A 1 it = ]E[y1+ 9W2 T] and u = lE['r] EVarh'] E (e? + e3). 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: 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 E = 0.) Step 3. The agent chooses e1 and e2. Step 4. Outputs yl and y2 are realized. The principal pays the agent T. Let's proceed step-by-step to solve the problem. a) In step 3, what is the agent's optimal choice of e, and e2, as a function of b, and by? b) Suppose g = 0, so task 2 doesn't matter for the principal at all. What is the principal's optimal choice of by and by ? What are the corresponding effort choices el and ez? c) Still supposing g = 0, what are the efficient effort choices ef" and ez" that a social planner maximiz ing it + u would impose? Comparing with your answers from (b), you should find that er