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3. We consider the principalagent problems. Now, assume there are 91. possible outcomes [11,. .. 12:\"). The agent can take one of two actions, a. or 51 which inuence the probability of occurrence of the outcomes. Thus, we let in]. be the probability that I; is observed if the ag-t chooses action a, and in, be the probability that I.- is observed if the agent chooses action h. Let s,- = 5:11;} be the payment from the principal to the agent if I,- is observed. Then the expected prot of the principal if the agent chooses the action :5, say, is Elli} lm As for the agent, let us suppose that he is risk-averse and seeks to maximize V011 NeumarmMorgenstern utility function of the payment, can and the cost ofhis action is c,I ifa is chosen1 and ob ifh is chosen. {a} Show the IC condition which has to be satised if agent chooses the action I!) even if the choice of action is not observable for principal. {b} Suppose that if the agent does not participate, he gets utility t1. Show the IR condition. {c} Suppose there's no asymmetric information problem1 and the prin cipal chooses the action b for an agent. In this case, the agent chooses b. Show the rst order condition of the prot maximization problem with respect to s,- by the principle