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 d any project and both parties get zero. Both Poppy andAiden can, however, put effort into discovering a good project. Poppy can put ineffort E; this costs her effort cost 1 22E , but it gives her a probability of beinginformed 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 costof 1 22e ; this gives Aiden a probability of being informed with probability e. If Aidengets his preferred project he gets $1. For all other projects he gets zero. Note also, thatthe probability that Poppy's preferred project is also Aiden's preferred project is (this is the degree of congruence is ). It is also the case that if Aiden chooses hispreferred project that it will also be the preferred project of Poppy. (Note, in thisquestion, we assume that = from the standard model studied in class.)(a) Assume that Poppy has the legal right to decide (P-formal authority). If 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 = 1) 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?