There is a principal and an agent. The agent performs two tasks, and chooses efforts e1 and e2. The agent's efforts generate noisy outputs: y1=e1+andy2=e2+ where is a common noise term with E[]=0 and Var[]=2>0. The principal can offer the agent an incentive scheme based on both task outputs: w=+1y1+2y2. The principal is risk-neutral while the agent is risk-averse: Up=E[y1+gy2w]andUa=E[w]2Var[w]21(e12+e22). Note that the parameter g 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 U0=0.) Step 3. The agent chooses e1 and e2. Step 4. Outputs y1 and y2 are realized. The principal pays the agent w. Let's proceed step-by-step to solve the problem. 1. In step 3 , what is the agent's optimal choice of e1 and e2, as a function of 1 and 2 ? 2. Suppose g=0, so task 2 doesn't matter for the principal at all. What is the principal's optimal choice of 1 and 2 ? What are the corresponding effort choices e1 and e2 ? 3. Still supposing g=0, what are the efficient effort choices e1eff and e2eff that a social planner maximizing Up+Ua would impose? Comparing with your answers from (2), you should find that e10. The principal can offer the agent an incentive scheme based on both task outputs: w=+1y1+2y2. The principal is risk-neutral while the agent is risk-averse: Up=E[y1+gy2w]andUa=E[w]2Var[w]21(e12+e22). Note that the parameter g 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 U0=0.) Step 3. The agent chooses e1 and e2. Step 4. Outputs y1 and y2 are realized. The principal pays the agent w. Let's proceed step-by-step to solve the problem. 1. In step 3 , what is the agent's optimal choice of e1 and e2, as a function of 1 and 2 ? 2. Suppose g=0, so task 2 doesn't matter for the principal at all. What is the principal's optimal choice of 1 and 2 ? What are the corresponding effort choices e1 and e2 ? 3. Still supposing g=0, what are the efficient effort choices e1eff and e2eff that a social planner maximizing Up+Ua would impose? Comparing with your answers from (2), you should find that e1