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Question 2 In this problem, we will consider a multitasking problem where the principal can only incentivize the agent on one task, but where there is a \"crowding-in\" effect: the agent's effort in one task reduces the agent's marginal cost of eifort in the other task. There are two tasks (task 1 and task 2). The principal benets from the agent's effort in both tasks: at = x1 +x2 w . 1 2 2 where x1 = e1 and x2 = ez. The agent has payoff function u = w 5(el + e2 8182). (Note that the agent may choose negative effort levels, potentially resulting in negative output.) The principal cannot reward the agent for total output; instead, he can only reward the agent for his performance in the rst task. That is, the principal can offer the agent an incentive scheme of the form to = a + )3 y, where y=x1. The timing is as usual: step 1. Principal offers agent an incentive scheme to = a: + [i y. step 2. Agent may accept or reject the offer, If he rejects, he receives an outside option of zero. step 3. If agent accepts, then he chooses e1 and e2. step 4. Principal pays agent to = a + y. We'll go through the problem step-bystep. a) For step 3, given the principal's offer (10 a + By), write down the agent's maximization problem, and calculate his payoif-maximizing effort choices 31 and 62 as a function of a and i? b) For step 1, write down the principal's maximization problem, and calculate his payoff-maximizing choice of incentive scheme (a and 3). c) What effort levels does this incentive scheme induce in the agent? d) Calculate the efcient effort levels (i.e. the effort levels 81,82 that maximize total payoffs 7': + u). e) Explain, in words, why your answers to (c) and (d) diifer (if they indeed differ)