informed of E. If Poppy gets her preferred project she will get a payoff of $1. For all other projects Poppy gets zero . Similarly , the agent Aiden can put in effort e at a cost 1 of me"; this gives Aiden a probability of being informed with probability e. If Aiden gets his preferred project he gets $1. For all other projects he gets zero . Note also , that the probability that Poppy's preferred project is also Aiden's preferred project is a (this is the degree of congruence is a). It is also the case that a if Aiden chooses his preferred project that it will also be the preferred project of Poppy . (Note , in this question , we assume that a = p from the standard model studied in class .) (a) Assume that Poppy has the legal right to decide (P-formal authority ). If Poppy is uninformed she will ask the agent for a recommendation :if Aiden is informed he will recommend a project to implement . . First consider the case when both Aiden and Poppy simultaneously choose their effort costs . Write out the utility or profit function for both Poppy and Aiden . Solve for the equilibrium level of E and e, and show that Poppy become: perfectly informed (E = 1) and Aiden puts in zero effort in equilibrium (e = 0). Explain your result , possibly using a diagram of Poppy's marginal benefit and marginal cost curves . What is Poppy's expected profit ? (b) Now consider the case when the agent Aiden has the formal decision making rights (Delegation or A- formal authority ). In this case , if Aiden is informed he will decide on the project if he is informed ; if not he will ask Poppy for a recommendation . Again calculate the equilibrium levels of E and e. c) Consider now the case when Poppy can decide to implement a different timing sequence . Assume now that with sequential efforts first Aiden puts in effort e into finding a good project . If he is informed , Aiden implements the project he likes . If Aiden is uninformed he reveals this to Poppy , who can then decide on the level of her effort E. If Poppy is informed she then implements her preferred project . If she too is uninformed no project is implemented Draw the extensive form of this game and calculate the effort level Poppy makes in the subgame when the Agent is uninformed . Now calculate the effort that Aiden puts in at the first stage of the game . Calculate the expected profit of Poppy in this sequential game and show that it is equal to (1 - a)a +- 2 ECO53003 Problem set 3 of 3