b) d) 8) In this question, we will consider a model of incentives and disagreement where the principal can either choose to give the agent an order, or persuade the worker. Unlike the model covered in class. orders are binding. There is a (P}rincipal and an (A}gent. A works on a project: he chooses effort e at cost gel and a binary decision :1 (either 1 or 1). There is a binary state of die world 9 [eidrer l or 1) that is not known until after the agent makes his choices. The project is successful if and only if the action matches the state (:1 = 8). in which case the principal receives revenue 9 = Be. where B > 0. Otherwise, if the project fails, then die principal receives 0 = D. and the principal also incurs an additional cost of c = l. P can offer A an incentive scheme of the form r = bu. So, the principal's and agent's payoffs are 1 if the project fails 0 if the project succeeds n = E[o] E[r]{ u = E[-r] 4232. P and A disagree on how likely each state of die world is. P believes mat 3 = 1 occurs with proba- bility 1; A believes that 3 = 1 occurs with probability U3. At the start of the game, P chooses one of two options. P can give A an orderr' (either 1 or 1). HA receives an order. he cannot disobey. and must choose at = 1'; however. he can choose any effort level he likes. Dr, P can persuade A. If P chooses to persuade, ien she is successful 50% of the time: A changes his mind. and believes (like P} that \"8 = 1 will occur with probability 1\". The oier 50% of the time. persuasion fails: A continues to believe that \"3 = 1 will occur with probability 1 3": The game proceeds as follows: Step 1. The principal chooses whedier to give the agent an order i, or to persuade the agent. Ifthe principal chooses to persuade die agent, then she learns whether persuasion was successful. Step 2. The principal offers the agent an incentive contract 1' = bu. Step 3. The agent chooses a decision d, and an effort level e 2 D. If the principal gave an order. the agent must obey. Step 4. The state of the world is revealed. and die project succeeds or fails (based on whether the agent chose the correct action}. The principal pays the agent his wage r. We'll work this out stepbystep: Suppose the principal chooses to give A an order. What order does P choose? What effort level does the agent exert in step 3, given the principal's choice of incentive strength b in step 2? What incentive strength 5' does the principal optimally choose in step 2? Suppose die principal chooses to persuade A, and that persuasion succeeds. What effort level does the agent exert in step 3, given the principal's choice ofincentive strength b in step 2? What incentive strength b' does re principal optimally choose in step 2? Suppose the principal chooses to persuade A, and that persuasion fails. What effort level does the agent exert in step 3. given the principal's choice of incentive strength b in step 2? Show that the principal will always receive the same payoff, regardless of the choice of incentive strength. For what values of B does the principal choose to persuade the agent, rather than order the agent? Explain, in words, why the principal prefers to persuade the agent [rather than order the agent} when 3 is large