Question please check the attachment 4-1. and there is the answer for this question 4-2. But I do not know to draw the diagram of Poppy’s Marginal Benefit and Marginal Cost curve, Please only draw the MC MB diagram for this question!!
- Attachment 1
- Attachment 2
4. Consider a variant on the Aghion and Tirole (1997) model. Poppy, the principal,and Aiden, the agent, together can decide on implementing a new project, but both areunsure of which project is good and which is really bad. Given this, if no one isinformed they will not do any project and both parties get zero. Both Poppy andAiden can, however, put effort into discovering a good project. Poppy can put in effort E; this costs her effort cost $152 , but it gives her a probability of being informed of E. If Poppy gets her preferred project she will get a payoff of $1. For allother projects Poppy gets zero. Similarly, the agent Aiden can put in effort e at a cost of éei ; this gives Aiden a probability of being informed with probability e. If Aiden gets his preferred project he gets $1. Foj‘ all other projects he gets zero. Note also, thatthe probability that Poppy‘s preferred project is also Aiden’s preferred project is or(this is the degree of congruence is a). It is also the case that u if Aiden chooses hispreferred project that it will also be the preferred project of Poppy. (Note, in thisquestion, we assume that u = [3 from the standard model studied in class.) (a) Assume that Poppy has the legal right to decide (P-formal authority). 1f Poppy isuninformed she will ask the agent for a recommendation; if Aiden is informed he willrecommend a project to implement. First consider the case when both Aiden andPoppy simultaneously choose their effort costs. Write out the utility or proﬁt functionfor both Poppy and Aiden. Solve for the equilibrium level of E and e, and show thatPoppy becomes perfectly informed (E = l) and Aiden puts in zero effort inequilibrium (e = 0). Explain your result, possibly using a diagram of Poppy’smarginal benefit and marginal cost curves. What is Poppy’s expected proﬁt?