Step 1: Step 2: Step 3: Step 4: a) b) C) d) 8) Question 3 In this problem, there is one principal and two agents. The principal interacts rst with Agent 2, then with Agent 1. The two agent's efforts are complements: the effect of agent 1's effort on output is higher when agent 2 puts in more effort, and vice versa. However, the only available performance measure is output in task 1. Specically: the principal's payoff function is 11' = x w1 wz with x = e] + 2122. The available performance measure is y = 21. Agent 1 chooses 81; his payoff function is u] = w1 i212. Agent 2 chooses 82; his payoff function is u; = w; 2%. Both agents have outside option of zero. The timing is as follows: Principal offers Agent 2 an incentive scheme w: = (x2 + [32 y, which he can accept or reject. Ingent 2 accepts, then he chooses 22. Principal offers Agent 1 an incentive scheme m1 = a1 + [31 y, which he can accept or reject. Ingent 1 accepts, then he chooses 21. (Agent 1 observes Agent 2's choice of 32, and makes his choice of e] accordingly.) We'll go through the problem step-bystep. For step 4, given the principal's offer to agent 1, write down agent 1's maximization problem. Cal- culate agent 1's choice of e] . For step 3, given the principal's offer to agents 1 and 2, and given your answer to part (a), write down the principal's maximization problem as a function of [31. Given the principal's offer to agent I, calculate the principal's payoff-maximizing choice of [31. For step 2, given the principal's offer to agent 2, and given your answers to (a) and (b), write down agent 2's maximization problem. Calculate agent 2's choice of 32. For step 1, given your answers to (a)(c), write down the principal's maximization problem. Cal- culate the principal's payoff-maximizing choice of [32. Show that the equilibrium effort levels 3; and e; are inefciently low. (That is, total utility Umltal can be raised by increasing effort levels above 2; and a: .) Explain, in words, why this is the case