4 Consider a variant on the Aghion and Tirole (1997) model. Poppy, the principal, and Aiden,...

 

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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 are unsure of which project is good and which is really bad. Given this, if no one is informed they will not do any project and both parties get zero. Both Poppy and Aiden can, however, put effort into discovering a good project. Poppy can put in effort E; this costs her effort cost E², but it gives her a probability of being 2 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 of fe; 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 = ß 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 becomes 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? 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 are unsure of which project is good and which is really bad. Given this, if no one is informed they will not do any project and both parties get zero. Both Poppy and Aiden can, however, put effort into discovering a good project. Poppy can put in effort E; this costs her effort cost E², but it gives her a probability of being 2 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 of fe; 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 = ß 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 becomes 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? 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 are unsure of which project is good and which is really bad. Given this, if no one is informed they will not do any project and both parties get zero. Both Poppy and Aiden can, however, put effort into discovering a good project. Poppy can put in effort E; this costs her effort cost E², but it gives her a probability of being 2 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 of fe; 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 = ß 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 becomes 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?

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Answer The given question has Poppy the principal and Aiden the agent Poppy can put in effort E this ... View the full answer