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: Up = :1: is Where :1: : 361 + E3. The agent has payoff function LI" = w % (e? + 6% + 8.3;}; he chooses effort in each task- {Effort in each task can be negative.) There are two available performance measures, 3; 2 :21 + 82 and z 2 :22 + 83. The principal can oer the agent an incentive scheme of the form in = (1 + y + 72;. The timing is as usual: 1. Principal offers agent an incentive scheme of the form is = or + y + '12. 2. Agent may accept or reject the o'er. If he rejects, he receives zero outside option. 3. If agent accepts, then he chooses e1, 122, and eg. 4. Principal pays agent in = 4'1 + y + 7s. We'll go through the problem step-hy-step. a) For step 3, given the principal's offer (in 2 1'1 + y+1rz}, write down the agent's maximization problem, and calculate his payeH-maicimizing effort choices :21, :92 and .93 as a function of a, fiandqt. h) For step 1, write down the principal's maximization problem, and calculate his payoif- maximizing choice of incentive strengths (f3 and Tl- What e'ort leveLs does this incentive scheme induce in the agent? c) Explain, in words, Why,r the principal chooses an incentive scheme that induces the agent to produce negative output in task 3