Question 2 In this problem, there is one principal and two agents. Agent 2 does not directly produce useful output, but can make an investment which reduces the \"cost of effort'= of agent 1. The principals payoif function is U], = Etc11:1 mg] with s: = e1+ where E [E = 0], Vas] = 02. Agent 1 chooses effort in; his payo' function is U1 = Ehsl] AlVarhul] @ef e122). Agent 2 chooses the costsaving investment 22; his payoff function is U2 = E [11.12] :iA2Varhng] zj The principal offers agent 1 an incentive scheme of the form an = (11 + {31:13, and offers agent 2 an incentive scheme of the form mg = 0:2 + 323:. The timing is as usual: Step 1: Step 2: Step 3: Step 4: Principal offers each agent an incentive scheme. Each agent may accept or reject the offer. If either agent rejects, then both agents receive zero outside option. If both agents accept, then: Agent 2 chooses 22., after which Agent 1 chooses e1. [Agent 1 observes agent 2's choice of 22, and makes his choice of (31 accordingly.) We'll go through the problem stepbystep. 3) b) For step 4, given the principal's oifer to agent 1, and given agent 2's choice of costsaving investment 22, write down agent 1's maximization problem. Calculate agent 1's payoff maximizing choice of e1. For step 3, given the principal's offer to agents 1 and 2, and given your answer to part (a), write down agent 2's maximization problem. Calculate agent 2's payoffmaximizing choice of .52. For step 1, write down the principal's maximization problem, and calculate his payoff maximizing choice of incentive strengths (+31 and {32} How does expected output E[J:] change as agent 1 becomes less risk averse (A1 decreases)? Explain, in words, the logic behind this result. How does expected output E[s:] change as agent 2 becomes less risk averse (A2 decreases)? Explain, in words, the logic behind this result