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 'H' = x \"'1 mg with x = '31 + 6162. The available performance measure is y 2 el. Agent 1 choos es 81; his payoff function is ul 2 w1%e%. Agent 2 chooses 62; his payoff function is u; = mg e. Both agents have outside option of zero. The timing is as follows: Step 1: Principal offers Agent 2 an incentive scheme LUZ = a2 + {32)}, which he can accept or reject. Step 2: If Agent 2 accepts, then he chooses 92. Step 3: Principal offers Agent 1 an incentive scheme ml 2 a1 + {31;}, which he can accept or reject. Step 4: If Agent 1 accepts, then he chooses 61. (Agent 1 observes Agent 2's choice of 82, and makes his choice of 81 accordingly.) We'll go through the problem stepbystep. a) For step 4, given the principal's offer to agent 1, write down agent 1's maximization problem. Calculate agent 1's choice ofel. b) 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 1, calculate the principal's payoffmaximizing choice of l