Consider a market for used cars. There are many sellers and even more buyers. A seller values a high quality car at 800 and a low quality car at 200. For any quality, the value to buyers is m times the value to sellers, where m > 1. All agents are risk-neutral. Sellers know the quality of their own car, but buyers only know that 2/3 of the cars are low quality and the remaining 1/3 of them are high quality. For what values of m do all sellers sell their used cars?

Consider a market for used cars. There are many sellers and even more buyers. A seller values a high quality car at 800 and a low quality car at 200. For any quality, the value to buyers is m times the value to sellers, where m > 1. All agents are risk-neutral. Sellers know the quality of their own car, but buyers only know that 2/3 of the cars are low quality and the remaining 1/3 of them are high quality. For what values of m do all sellers sell their used cars?

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

Chapter19: The Problem Of Adverse Selection

Section: Chapter Questions

Problem 10MC

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[Adverse Selection] Two firms, Gord and FM, sell cars. Suppose 50% of thenew cars in the market are made by Gord and 50% are made by FM. Gord has superiortechnology so it produces higher quality cars, and the cost of producing a car is $90 for Gord.FM produces low quality cars at a unit cost of $50. Consumers value high quality cars at $120and low quality cars at $80. Suppose consumers are willing to pay any price at or below theirvalues. Sellers can either accept or reject offers depending on whether an offered price isabove or below the car’s cost.a. Assume there is imperfect information such that consumers know one companyproduces high quality cars and the other produces low quality cars, but they do notknow which company produces high quality cars. What is the equilibrium price of cars?b. How does your answer in part (a) change when the cost of producing a car forGord is $105 (instead of $90)?c. Back to the setting in part (a). Suppose we have the following dynamicgame. First, each…
Show that expectation damages are efficient with respect to breach, but not efficient with respect to reliance.
A drug dealer knows whether his supply is high quality (@ = H), mediocre (@ = M), or low quality (@ = L). He values his product at $30 if it is high quality, $20 if it is mediocre, and $10 if it is low quality. A potential buyer values the drugs at $30 + x if they are high quality, $20 + x if mediocre, and $10 + x if low quality, where 0 < x < $5. The buyer does not know the quality of the product - he only knows that each quality is equally likely : Pr(@ = H) = Pr(@ = M) = Pr(@ = L) = 1/3. The buyer offers a price p for the drugs, which the dealer can either accept or reject. Assume if the dealer is indifferent, then he accepts. 1. In equilibrium, which drug qualities are sold, and at what price? 2. Now, suppose Pr(@ = H) = Pr(@ = L) = 1/4, while Pr(@ = M) = 1/2. Find the values of x for which mediocre drugs will be sold?
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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)
Suppose that every driver faces a 2% probability of an automobile accident every year. An accident will, on average, cost each driver $14,000. Suppose there are two types of individuals: those with $112,000.00 in the bank and those with $3,500.00 in the bank. Assume that individuals with $3,500.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is . Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $112,000.00 in the bank likely buy insurance, and those with $3,500.00 in the bank likely buy insurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.) Suppose a state law has been passed…
Suppose that every driver faces a 1% probability of an automobile accident every year. An accident will, on average, cost each driver $15,000. Suppose there are two types of individuals: those with $90,000.00 in the bank and those with $3,000.00 in the bank. Assume that individuals with $3,000.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is . Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $3,000.00 in the bank likely buy insurance, and those with $90,000.00 in the bank likely buy insurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.) Suppose a state law has been passed…
The value of a successful project is $420,000; the probabilities of success are 1/2 with good supervision and 1/4 without. The manager is risk neutral, not risk averse as in the text, so his expected utility equals his expected income minus his disutility of effort. He can get other jobs paying $90,000, and his disutility for exerting the extra effort for good supervision on your project is $100,000. (a) Show that inducing high effort would require the firm to offer a compensation scheme with a negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme. (b) How might a negative base salary be implemented in reality? (c) Show that if a negative base salary is not feasible, then the firm does better to settle for the low-pay, low-effort situation.
Suppose that there is asymmetric information in the market for used cars. Sellers know the quality of the car that they are selling, but buyers do not. Buyers know that there is a 30% chance of getting a "lemon", a low quality used car. A high quality used car is worth $30,000, and a low quality used car is worth $15,000. Based on this probability, the most that a buyer would be willing to pay for a used car is $___
Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. f) Now we turn to social otimality rather than equilibrium. Consider the value judgement that the optimal level of care is…
Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. A) Draw a game tree to represent this model.
Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ?…