In this question, we'll consider a model with a risk-averse multi-taslting agent where the tasks have correlated noise. There is a principal and an agent. The agent performs two tasks. and chooses etforts e1 and e1. The agent's efforts generate noisy outputs: p1=e1+e and p2=e1+e where e is a common noise term with IE[e] = and Var[e] = o1 :- [L The principal can otter the agent an incentive scheme based on both task outputs: 1' = '1 "' 51h + be)\":- The principal is risk-neutral while the agent is risk-averse: l 1 a 2 re: E[y'1+'t_:;|-'2 w] and u = E[1'] EVarh] E (e] +e3). Note that the parameter 3 represents the importance oftask 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. [lfhe rejects. the game ends and he each receive outside option 3 = D.) Step 3. The agent chooses e] and e2. Step 4. ICIIutpnts 3:1 and y; are realized. The principal pays the agent r. Let's proceed step-bystep to solve the problem. a) In step 3, what is the agent's optimal choice of e, and ez, 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 bj and by ? What are the corresponding effort choices e; and e ? c) Still supposing g = 0, what are the efficient effort choices e," and ez that a social planner maximize ing or + u would impose? Comparing with your answers from (b), you should find that el