2. Suppose, as in class, that the utility function of a worker is U(w, e)=√w-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?

2. Suppose, as in class, that the utility function of a worker is U(w, e)=√w-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?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter20: The Problem Of Adverse Selection Moral Hazard

Section: Chapter Questions

Problem 2MC

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Suppose there are two types of people, high ability and low ability. A high-ability person's productivity is valued at wH = $100,000, while a low-ability person's productivity is valued at wL = $50,000. Assume that the employer does not know the ability of a job applicant, but knows that the probability of an applicant being high ability is 50%. Assume next that only high ability applicants can send a signal, i.e., obtain a degree. The employer pays the expected wage. i. What is the wage oer in a pooling equilibrium (no applicant attains a degree)? ii. What is the wage oer in a separating equilibrium (only high-ability applicants attain a degree)? iii. Suppose now both types can attain a degree, but it is costlier to attain for low-ability people and costs them cL = $60,000, while it costs high-ability people cH = $40,000. Is a separating equilibrium where only high-ability people send education as a signal possible? Explain.
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?
a. On a graph with the probability of injury on the x-axis and the wage level on the y-axis plot two indifference curves, labeled UA and UB, so that the person associated with UA is less willing to take on risk relative to the person associated with UB. Explain what it is about the indifference curves that reveals person A is less willing to take on risk relative to person B. b. Consider a third person who doesn’t care about the risk associated with the job. That is, he doesn’t seek to limit risk or to expose himself to risk. On a new graph, draw several of this person’s indifference curves. Include an arrow on the graph showing which direction is associated with higher levels of utility. c. Consider a wage-risk equilibrium that is characterized by an upward-sloping hedonic wage function. Now suppose there is a government campaign that successfully alters people’s perception of risk. In particular, each worker adjusts her preferences so that she now needs to be more highly compensated…
Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .
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Give typing answer with explanation and conclusion 1. If wH=100 and wL=36 and U(w)=w^1/2. Further, let the reservation utility be 7. (a) What is the minimum probability for which the wage earner accepts the contract? (b)Let p=3/4. What is the maximum cost of effort for which the tenant accepts the contract?
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, and you are considering a self-employment opportunity that may pay $10,000 per year or $40,000 per year with equal probabilities. What certain income would provide the same satisfaction as the expected utility from the self-employed position? a) $22,500 b) $15,000 c) $27,500 d) $25,00
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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 manaаger has an outside wage of 1. Calculate the optimal wage schedule under high and low realized profits.
A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)
There are 50 workers in the economy in which all workers must choose to work a safe or a risky job. When it comes to accepting a risky job, Worker 1’s reservation price is $5; worker 2’s reservation price is $6, worker 3's reservation wage is $7, and so on. Assume there are exactly 12 risky jobs. (a) What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm? (b) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of $1, worker 2’s reservation price is $2, and so on. There are still only 12 risky jobs. What is the new equilibrium wage differential? c) What is the maximum the firm should be willing to pay for its ad campaign?