In this problem, there is one principal and two agents. The principal interacts first 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. Specifically: the principal's payoff function is = 1 2 with = 1 + 1 2 . The available performance measure is = 1 . Agent 1 chooses 1 ; his payoff function is 1 = 1 1 2 2 1 . Agent 2 chooses 2 ; his payoff function is 2 = 2 2 2 . Both agents have outside option of zero. The timing is as follows: Step 1: Principal offers Agent 2 an incentive scheme 2 = 2 + 2, which he can accept or reject. Step 2: If Agent 2 accepts, then he chooses 2 . Step 3: Principal offers Agent 1 an incentive scheme 1 = 1 + 1, which he can accept or reject. Step 4: If Agent 1 accepts, then he chooses 1 . (Agent 1 observes Agent 2's choice of 2 , and makes his choice of 1 accordingly.) We'll go through the problem step-by-step. a) For step 4, given the principal's offer to agent 1, write down agent 1's maximization problem. Calculate agent 1's choice of 1 . 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 1 . Given the principal's offer to agent 1, calculate the principal's payoff-maximizing choice of 1 . c) 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 2 . d) For step 1, given your answers to (a)-(c), write down the principal's maximization problem. Calculate the principal's payoff-maximizing choice of 2 . e) Show that the equilibrium effort levels 1 and 2 are inefficiently low. (That is, total utility total can be raised by increasing effort levels above 1 and 2 .) Explain, in words, why this is the case.