4. Consider the following problem discussed in class:• workers with productivity 0 E {1, 2} with respective probabilities p and 1 – p,• education choice e e {0, 1}• costs for the two types are c(1) = and c(2) = ?,• market pays expected wages.Let s denote the equilibrium probability with which type 0 will choose e = 1.(a) Construct an equilibrium with s† = s = 0.(b) Under what conditions does the above equilibrium fail the CKIC?

(a) Equilibrium with s₁ = s₂ = 0: In this scenario, neither type of worker chooses education (e =…

4. Consider the following problem discussed in class: • workers with productivity 0 € {1,2} with respective probabilities p and 1 P, education choice e = {0, 1} • costs for the two types are c(1) = and c(2) = ¾¼, • market pays expected wages. Let s denote the equilibrium probability with which type will choose e = 1. (a) Construct an equilibrium with st = s₂ = 0. (b) Under what conditions does the above equilibrium fail the CKIC?

4. Consider the following problem discussed in class: • workers with productivity 0 € {1,2} with respective probabilities p and 1 P, education choice e = {0, 1} • costs for the two types are c(1) = and c(2) = ¾¼, • market pays expected wages. Let s denote the equilibrium probability with which type will choose e = 1. (a) Construct an equilibrium with st = s₂ = 0. (b) Under what conditions does the above equilibrium fail the CKIC?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

2. Suppose, as in class, that the utility function of a worker is U (w, e) = Vw - e, where w is the wage and e € {0, .8} is the level of effort. Suppose the reservation utility is 1. Suppose the outcome is $10 or $0 and that the probability of the $10 outcome is .6 if the worker works hard and .2 if the worker chooses low effort. (a) If you could costlessly monitor the worker's effort, would you want the worker to work hard? What payments would you offer and for what effort?
3. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is: v(w)-g(e), where v(w)= Jw and g(e)=e/2 The agent can choose one of two possible effort levels, e¡ = 4 or e, = 6 . If the agent chooses effort level e, = 4 the project yields 100 with probability 1/4 and 0 with probability 3/4. If he chooses e, = 6 the project yields 100 with probability ½ and 0 with probability ½. The reservation utility of the agent is 0. (a) Suppose the effort level chosen by the agent is observable by the principal. Find the contract chosen by the principal. Show graphically in terms of contingent utilities v(w,00) and v(w.)
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.
Suppose that the expected value of weekly profits for an ice cream shop, before paying the manager, Amy, is where e is Amy's weekly avertime hours. Amy is risk-neutral but incurs a cost for working overtime. Thus, tatal expected surplus is What level of effort maximizes total surplus? The value of overtime that maximizes total surplus is e-hours. (Enter your response rounded to one decimal place.) E(x)=500+10c C(e)=² E(S)-[(x)-C(e).
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
When the second order derivative of a function is greater than zero than the agent is risk lover. question; Asses the risk attitude of an agent represented by the expected utility function u(x)= 2x2-5. However my course material writes that this agent is risk neutral because it is affine. My question is that whys is this so despite the fact that the second order derivative is '4' which is >0. Kindly explain this to me with complete steps.
1. Consider the following utility functions, u(w) and v(w), which are functions of wealth w and the parameter p, where 0
Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much money as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. 1. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. 2. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent.
Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?
1. Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply. A. 9% B. 18% C. 17% D. 10% 2. Alternatively, the city could hold the number of officers constant and discourage parking violations by raising the fine for illegal parking. Suppose the average probability of getting caught for parking illegally is currently 10% citywide, and the average opportunity cost of parking is, again, $12. The fine that would make the average person indifferent between searching for parking and parking illegally is ____ , assuming that people will not…
1. All potential criminals are alike. Each has a benefit B of committing a crime, where B = $10,000. The cost, to the criminal, of being punished is T=$1,000 for each year spent in prison. The probability of a criminal being caught and punished is p. Let S represent the number of years spent in prison (i.e., the sentence). Suppose there are 100 potential criminals. Each chooses whether to commit this crime which has a social harm cost of $100,000. Suppose criminals are caught with a 15% probability. The cost of prison is $5,000 per prisoner, per year. (a) Write down the condition for a rational criminal to commit a crime. What is the optimal choice of sentence, S? What is the total social cost associated with this choice!-
Suppose a college athlete is deciding on when to turn pro (right out of high school, or after 1/2/3/4 years of college). If they go to college, their potential earnings increase by rate r (which is different for every year spent in college). But they have to postpone their earnings by 1 more year and pay discount rate i. What is the general decision rule for staying in school for one more year vs turning pro?