Please answer the following questions

Question 1 In this problem, we study the consequences of relative performance evaluation when agents are altruistic, i.e., they care about other agents' payoffs. There is one principal and two agents. Agent 1 chooses effort '31 to perform task 1 while Agent 2 chooses effort (:2 to perform task 2. Both agents produce noisy, perfectlycorrelated output: x1 :61 +5, x2 : 32 + s, where E[e] : 0 and VarLs] : 1. Agent 1 is risk averse and maximizes \"1 : IE.[T1] Var[T1]/2 ref/2; Agent 2 is risk neutral but altruistic, and maximizes L12 : thrl] + E[12] 63/2. Notice that y 2 0 captures how altruistic Agent 2 is, i.e., how much he cares about Agent 1's payoff MI. The principal is riskneutral and maximizes 7? : Elx1l+ Elle _IE'[TI] Elrzl- To simplify the problem, we assume that Agent 2's incentive scheme is xed as T2 : Jag/2. Further, Agent 2 will always work for the principal; there is no accept/reject decision for Agent 2. On the other hand, the principal chooses an incentive scheme for Agent 1 which includes a team component, T]: a + 52x1 + 3x2, and Agent 1 chooses whether to accept or reject this olfer. d) 80, the Timing is: Step 1: Principal offers Agent 1 an incentive scheme r1 = a + 5x1 + 8x2. Step 2: Agent 1 accepts or rejects. If she rejects, the game ends and each agent receives zero outside option. Step 3: Agent 1 chooses el and Agent 2 chooses 92. Step 4: The principal pays TI and T2. First, assume for parts [a)(c) that Agent 2 is not altruistic, y = 0. Calculate nonaltruistic agent 2's optimal choice of effort 6; . Calculate Agent 1's optimal choice ofeifort er, as a function of b. Calculate the incentive strengths {3* and 8* that the principal optimally offers Agent 1. Conrm that this corresponds to pure relative performance evaluation, 8* : 49*. (Hint: because only Agent 1 chooses Whether to accept, the usual trick applies only to Agent 1, not to Agent 2.) For the remaining parts, assume that Agent 2 is altruistic, y = 1. Calculate agent 25 optimal choice ofeifort e; , as a function of b and / or B. In words, why does agent 25 effort choice depend on the incentive scheme offered to agent 1? Calculate Agent 1's optimal choice ofelfort ell, as a function ofb. Calculate the incentive strengths if and Bit that the principal optimally offers Agent 1. (Hint: you should nd that the principal does not engage in relative performance evaluation.) Explain, in words, why the principal doesn't engage in relative performance evaluation when agents are sufficiently altruistic