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Question 3 In this question, we'll consider a problem with multiple (misaligned) performance measures. There are three tasks. The principal benets only from the rst and third tasks: 7': = x to where x = 361 + 63. The agent has payoff function u = w g (e? + e: + (2%); he chooses effort in each task. (Effort in each task can be negative.) There are two available performance measures, y = e1 + 32 and z = 32 + 33. The principal can offer the agent an incentive scheme of the form to = a + By + yz. The timing is as usual: step 1. Principal oers agent an incentive scheme of the form to = a: + [3 y + yz. step 2. Agent may accept or reject the offer, If he rejects, he receives zero outside option. step 3. If agent accepts, then he chooses el, 62, and 63. step 4. Principal pays agent 1.0 = a + y + yz. We'll go through the problem step-by-step. a) For step 3, given the principal's o'er (w = a + y + yz), write down the agent's maximization problem, and calculate his payoff-maximizing effort choices e1, 22 and as as a function of a, and y. b) For step 1, write down the principal's maximization problem, and calculate his payoff-maximizing choice of incentive strengths ([3 and )2). What effort levels does this incentive scheme induce in the agent? c) Explain, in words, why the principal chooses an incentive scheme that induces the agent to produce negative output in task 3