Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U (w, e) = 100 - (10/w) - c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. Assume for this question that the principal wants to achieve the good effort and that effort is not contractible. Assume the principal offers an optimal 2 part contract {ws, Wf}, where we is paid if there are no defects and Wf is paid if there are any defects. What is the principal's expected profit under the optimal contract in this case? Answer to at most 2 decimal places (rounded), do not include a dollar sign in your answer. Answer:

Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U (w, e) = 100 - (10/w) - c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. Assume for this question that the principal wants to achieve the good effort and that effort is not contractible. Assume the principal offers an optimal 2 part contract {ws, Wf}, where we is paid if there are no defects and Wf is paid if there are any defects. What is the principal's expected profit under the optimal contract in this case? Answer to at most 2 decimal places (rounded), do not include a dollar sign in your answer. Answer:

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.2P

See similar textbooks

Similar questions

A firm’s board of directors wants to maximize its profits. If the firm’s manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%. The utility functions of both the board of directors and the manager are identical and are simply u(b)=b. High effort for the manager costs 2. The manager has an outside wage of 1. Calculate the optimal wage schedule under high and low realized profits.
A company decides whether and how to induce a manager to put in high effort to increase the changes that the project succeeds. Unfortunately, the manager's effort is unobservable. the value of a successful project is $2 million; the probability of success given high effort is 0.4; the probability of success given low effort is 0.2 The manager's utility is the square root of compensation (measured in millions of dollars) and his disutility from exerting high effort is 0.1. The reservation wage of the manager is $160000. To induce HIGH effort, the company should pay the manager $______ in case of a successful project and $______ in case of an unsuccessful project.
A risk-neutral manager is attempting to hire a worker. All workers in the market are of identical quality but differ with respect to the wage at which they are willing to work. Suppose half of the workers in the labor market are willing to work for a salary of $40,000 and half will accept a salary of $38,000. The manager spends three hours interviewing a given worker and values this time at $300. The first worker the manager interviews says he will work only if paid $40,000. Should the firm manager make him an offer or interview another worker?
Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.
Imagine a signaling model where there are two types of workers, low-productivity workers with a productivity of 10, and high-productivity workers with a productivity of 30. The proportion of low-productivity workers is .5. Firms are competitive and obtain profit equal to the productivity of the worker they hire. Workers can obtain one of three levels of education: e1, e2, and e3. Workers get utility equal to their wage minus the cost of education. Wages must be between 10 and 30. The cost of getting an education for low-productivity workers is e1 = 0, e2 = 9, e3 = 18. The cost of getting an education for high-productivity workers is e1 = 0, e2 =4, e3 = 8. Are there any separating equilibria in this model? If so, find them, if not show why they do not exist.
Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R 5 250: 2$200, 2$100, $0, $100, $200, $300, $400, $500
For constants a and b, 0 < b, b 1, and expected profit E(p), the expected utility function of a person who is risk-neutral can be written as E(U) = Which one: a+b^p a + (E(p))^b. a - bE(p). a + bE(p). a + (E(p))^(-b).
Many police officer positions require the applicant to have a college degree, even though the tasks of a police officer rarely call upon college course material. Suppose two individuals who do not have college degrees are considering applying to the police force. Ginny is considering applying for an officer position and plans on working for the police force for a period of time, over which she would earn approximately $500,000 (in present discounted value) in earnings while in the position. Kenji is also considering applying, and plans on working as an officer for a period of time, over which he would earn approximately $10,000 (in present discounted value) in lifetime earnings while in the position. Also suppose that present value of obtaining a college degree, which is required to submit a job application to the police department, is $100,000. Use the following table to indicate whether each individual would likely apply, or not, given the cost of obtaining a college degree.…
When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
For an output level exactly at QEQE, the value of a unit to a buyer is equal to the cost of a unit to a seller. Suppose a firm that produces for this market employs a private security force that makes town residents, many of whom have no business with the company, feel safer. This scenario is characterized by , which is an example of
A seller sells a good of quality q at a price t. The cost of producing at quality level q is given by q2/2. There is a buyer who receives a utility of Xq − t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility of zero. X can take two values X1 = 1 and X2 = 4. (a) Suppose the seller can observe X. Derive the profit maximizing price-quality pairs offered when the type is X1 = 1 and when the type is X2 = 4. (b) Show that the full information price-quality pairs are not incentive compatible if the seller cannot observe X.
In a standard economic model, we generally assume the individual only cares about their own payoff. So, for example, utility of individual i is given by u = pi, where pi is the individual’s payoff. Suppose the individual is playing a dictator game with another partner j. How would you modify the utility function to explain the non-zero allocations to the partner that are typically observed?