Question 1 In this problem, we will consider a principal-agent model with an agent who dislikes the principal. The principal's utility function is, as usual: 7'! = xT where x = e. The agent has payoff function u = T )me2 / 2. The term in in the agent's payoff function captures the agent's dislike of the principal: all else equal, the agent prefers outcomes where the principal gets a lower payoff, independently of how well he does himself. The parameter A is xed and represents the how much the agent dislikes the principal. Assume that the principal cannot charge the agent a participation fee or any other xed payment. That is, the principal offers the agent an incentive scheme of the form r = bx. The timing is: Step 1. Principal chooses 5. Step 2. Agent chooses e. Step 3. Principal pays agent '1' = bx. We'll go through the problem step-by-step. a) For step 3, given the principal's offer (T = bx), write down the agent's maximization problem, and calculate his payoff-maximizing effort choice e* as a function of b. How does the agent's effort choice change with his dislike )t of the principal for a given level of b? b) For step 1, write down the principal's maximization problem, and calculate his payoff-maximizing choice of incentive scheme (19). Does the principal offer stronger or weaker incentives (19*) to an agent who dislikes the principal more (higher )L)? c) Show that the effort level of the agent does not change with his dislike of the principal. d) In words, why does the effort level remain constant even as incentives strengthen when the agent dislikes the principal more intensely? Why does the principal choose to strengthen incentives as the agent dislikes him more