Consider the following principal-agent model. With equal probabilities, the agent is either low cost (0-1) or high cost (62). The agent chooses effort e, and output is equal to In e. The cost of effort to the low cost agent is e² = e². The cost of effort to the high cost agent is ee² = 2e2. The reservation utility of the agent is zero. The principal pays a salary w to the agent. The utility of the principal is equal to Ine-w. The utility of the agent is w-cost of effort (salary minus cost of effort). The principal chooses the wage function (w), while the agent chooses effort. Assume symmetric information, that is, the type and effort of the agent are known to the principal. Find the optimal contract for the principal. The contract must specify the salary (w) and effort (e) for each type of agent.
Consider the following principal-agent model. With equal probabilities, the agent is either low cost (0-1) or high cost (62). The agent chooses effort e, and output is equal to In e. The cost of effort to the low cost agent is e² = e². The cost of effort to the high cost agent is ee² = 2e2. The reservation utility of the agent is zero. The principal pays a salary w to the agent. The utility of the principal is equal to Ine-w. The utility of the agent is w-cost of effort (salary minus cost of effort). The principal chooses the wage function (w), while the agent chooses effort. Assume symmetric information, that is, the type and effort of the agent are known to the principal. Find the optimal contract for the principal. The contract must specify the salary (w) and effort (e) for each type of agent.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the following principal-agent model. With equal probabilities, the agent is either low cost
(O = 1) or high cost (6 = 2). The agent chooses effort e, and output is equal to In e.
The cost of effort to the low cost agent is 0,e? = e².
The cost of effort to the high cost agent is 6ye? 2e?.
The reservation utility of the agent is zero.
The principal pays a salary w to the agent.
The utility of the principal is equal to In e-w.
The utility of the agent is w-cost of effort (salary minus cost of effort).
The principal chooses the wage function (w), while the agent chooses effort.
Assume symmetric information, that is, the type and effort of the agent are known to the principal.
Find the optimal contract for the principal. The contract must specify the salary (w) and effort (e)
for each type of agent.
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