Consider a principal-agent problem with three exogenous states of nature, 8, 62, and 6; two effort...

 

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Consider a principal-agent problem with three exogenous states of nature, 8, 62, and 6; two effort levels, a, and a; and two output levels, distributed as follows as a function of the state of nature and the effort level: State of nature Probability 05 8 0.25 0.5 0.25 Output un ra 18 18 1 Output under a 18 1 The principal is risk neutral, while the agent has utility function w when receiving monetary compensation w, minus the cost of effort, which is nor- malized to 0 for a, and to 0.1 for a,,. The agent's reservation expected utility is 0.1. 1. Derive the first-best contract. 2. Derive the second-best contract when only output levels are observable. 3. Assume the principal can buy for a price of 0.1 an information system that allows the parties to verify whether state of nature 8, happened or not. Will the principal buy this information system? Discuss. Consider a principal-agent problem with three exogenous states of nature, 8, 62, and 6; two effort levels, a, and a; and two output levels, distributed as follows as a function of the state of nature and the effort level: State of nature Probability 05 8 0.25 0.5 0.25 Output un ra 18 18 1 Output under a 18 1 The principal is risk neutral, while the agent has utility function w when receiving monetary compensation w, minus the cost of effort, which is nor- malized to 0 for a, and to 0.1 for a,,. The agent's reservation expected utility is 0.1. 1. Derive the first-best contract. 2. Derive the second-best contract when only output levels are observable. 3. Assume the principal can buy for a price of 0.1 an information system that allows the parties to verify whether state of nature 8, happened or not. Will the principal buy this information system? Discuss.