question 2

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2.Consider a relationship between a principal and an agent in which only two levels of production, valued at $50,000 and $25,000, respectively, are possible. The outcome of production depends on both the effort level of the agent and a random component. The agent can choose one of three effort levels: low, medium and high. The probability of each outcome given each level of effort is given in the following table. _ Output = $25,000 Output = $5 0,000 High effort Let denote output and the payment to the agent. The principal's utility lnction is and the agent's utility function is where denotes the disutility of effort. The disutility of effort is 40 when effort is high, 25 when effort is medium and 5 when effort is low. a) Given these utility functions, how would you characterize the principal's attitude towards risk? How would you characterize the agent's? Briey explain why. Suppose effort is observable. b) Explain the constraint(s) the contract must satisfy if the principal wants the agent to provide i) high effort and ii) medium effort. c) Derive the rst best contract inducing high effort. Now suppose that effort is not observable. d} What additional constraints must the contract satisfy for the agent to provide high effort? e) Briey explain how the contract that induces high effort is affected by the asymmetric information. What will be the effects on the principal and the agent? (NOTE; you do not need to solve for the optimal contract under asymmetric information, merely provide a verbal explanation