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hw10a - ISyE 4803B Homework 10 1 Consider a principal-agent...

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ISyE 4803B Homework 10 1. Consider a principal-agent framework. An agent can choose from 3 levels of effort (from high to low): e1, e2, and e3. The agent’s utility is U=E[w]-e if she exerts effort level e, and the utility from rejecting the contract is a. The principal has sees the following returns: R(e1)=H with prob 0.7 and L with prob 0.3, R(e2)=H with prob 0.5 and L with prob 0.5, and R(e3)=H with prob 0.1 and L with prob 0.9. Assuming the principal wants the agent to exert a high level of effort, answer the following: a. Write the participation constraints. b. Write the incentive compatibility constraints. c. Assume that the agent is risk averse in that she scales the probabilities of the outcomes down by 10%. Redo parts a. and b. 2. CareLess Industries has two divisions. Division 1 makes cleaning products, and the net worth of this division (PV of cash flows) is 500. Division 2 makes a chemical product and has net worth of 300, absent any potential liability.
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