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 e'orts el and e2. The agent's eorts generate noisy outputs: y1=el+c and y2 =ez+c where e is a common noise term with ]E[s] = 0 and Var[e] = 02 > 0. The principal can oer the agent an incentive scheme based on both task outputs: 1=a+b1yl+b2y2. The principal is risk7neutral while the agent is risk7averse: A n = lE[yl + gyz 7 T] and u = lE['r] 7 EVarh'] 7 5 (2% + 2%). 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 g : 0.) Step 3. The agent chooses el and 22. Step 4. Outputs yl and y2 are realized. The principal pays the agent 'r. Let's proceed step-by-step to solve the problem. a) In step 3, what is the agent's optimal choice of :21 and e2, as a function of 171 and b2? b) Suppose g = 0, so task 2 doesn't matter for the principal at all. What is the principal's optimal choice of b; and b; ? What are the corresponding effort choices e: and e; ? c) Still supposing g = 0, what are the efcient effort choices 9?\" and e? that a social planner maximiz ing 71 + u would impose? Comparing with your answers from (b), you should nd that e;