Q2. The profit of the firm depends on effort of the agent e and a random component (economic conditions) e. The profit of the firm is π = e + 0.5€. The principal observes the profit, but does not know effort e. The only available information about economic shock for the principal is that E€ = 0. The principal maximizes his utility which is up (π, w) = E(T -w), where w is wage paid to the agent. The agent maximizes ua (w, e) = E(w) - c(e), where c(e) are costs of putting effort e. Suppose that c(e) = 0.5e². (a) Suppose that the principal observes effort. Design the first best contract. (b) Suppose now that effort is unobservable. Consider only linear contracts. Design the second best contract. Discuss the intuition of your results.

Q2. The profit of the firm depends on effort of the agent e and a random component (economic conditions) e. The profit of the firm is π = e + 0.5€. The principal observes the profit, but does not know effort e. The only available information about economic shock for the principal is that E€ = 0. The principal maximizes his utility which is up (π, w) = E(T -w), where w is wage paid to the agent. The agent maximizes ua (w, e) = E(w) - c(e), where c(e) are costs of putting effort e. Suppose that c(e) = 0.5e². (a) Suppose that the principal observes effort. Design the first best contract. (b) Suppose now that effort is unobservable. Consider only linear contracts. Design the second best contract. Discuss the intuition of your results.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1) Consider observable effort. Assume that if the Agent does not accept the wage the Principal offers his outside option gives him a net utility of v =2. The probability of high profit under e=1 is %, the probability of high profit under low effort is 1/4. Calculate the minimum wage that the agent will accept to work and supply the asked effort when the Principal asks him to supply e=0, and e=1. Let us call these wages wo and wi. Now, assume that instead of offering him a flat wage, the Principal is offering the agent a wage schedule (, w) where the agent receives when the (gross) profit is High and w when the (gross) profit is low. Calculate all the lowest cost wage schedules the agent will accept to supply e=1, and e=D0. Does the principal's expected net profit change when he pays the minimum cost wage schedule instead of the flat wage minimum cost wage? Explain the intuition for your answer.
A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e e [0, 0). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 where E(R|e) and Var(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: W-α + βR, and so the employee is guaranteed a payment a and then a bonus payment BR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: 1 Eu(w\e) = E(w\e) - jeV ar(w\e) – c(e) pV. where E(wle) and Var(w|e) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the…
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Q) Suppose that utility for a worker is u(w)=w^.5. If the wage (w) offered is $64, there is a 50% chance of being fired, and switching costs are $28. What is the expected utility for the worker? Explain it early
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