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There are 100 people who want to sell their used cars. Everybody knows that fraction q of these cars are "peaches" and the remaining (1-q) fraction of these cars are "lemons". Only owners know the quality of their cars. Owners of lemons will be happy to get rid of their cars for any price greater than $1000. Owners of peaches will be willing to sell them for any price greater than $2000, but will keep them if they can't get $2000. There is a large number of buyers who would be willing to pay $3000 for a peach, but would pay only $500 for a lemon. When these buyers are not sure of the quality of the car they buy, they are willing to pay the expected value of the car. (a) What is the smallest fraction of peaches required for the existence of an equilibrium in which both types of cars are traded? (b) Now suppose that 45 out of these 100 cars are lemons, and 55 cars are peaches. Describe all possible equilibria that exist, including prices and quantities for each type of cars.

There are 100 people who want to sell their used cars. Everybody knows that fraction q of these cars are "peaches" and the remaining (1-q) fraction of these cars are "lemons". Only owners know the quality of their cars. Owners of lemons will be happy to get rid of their cars for any price greater than $1000. Owners of peaches will be willing to sell them for any price greater than $2000, but will keep them if they can't get $2000. There is a large number of buyers who would be willing to pay $3000 for a peach, but would pay only $500 for a lemon. When these buyers are not sure of the quality of the car they buy, they are willing to pay the expected value of the car. (a) What is the smallest fraction of peaches required for the existence of an equilibrium in which both types of cars are traded? (b) Now suppose that 45 out of these 100 cars are lemons, and 55 cars are peaches. Describe all possible equilibria that exist, including prices and quantities for each type of cars.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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There are 100 people who want to sell their used cars. Everybody knows that fraction q of these cars are "peaches" and the remaining (1-q) fraction of these cars are "lemons". Only owners know the quality of their cars. Owners of lemons will be happy to get rid of their cars for any price greater than $1000. Owners of peaches will be willing to sell them for any price greater than $2000, but will keep them if they can't get $2000. There is a large number of buyers who would be willing to pay $3000 for a peach, but would pay only $500 for a lemon. When these buyers are not sure of the quality of the car they buy, they are willing to pay the expected value of the car. (a) What is the smallest fraction of peaches required for the existence of an equilibrium in which both types of cars are traded? (b) Now suppose that 45 out of these 100 cars are lemons, and 55 cars are peaches. Describe all possible equilibria that exist, including prices and quantities for each type of cars.
Transcribed Image Text:There are 100 people who want to sell their used cars. Everybody knows that fraction q of these cars are "peaches" and the remaining (1-q) fraction of these cars are "lemons". Only owners know the quality of their cars. Owners of lemons will be happy to get rid of their cars for any price greater than $1000. Owners of peaches will be willing to sell them for any price greater than $2000, but will keep them if they can't get $2000. There is a large number of buyers who would be willing to pay $3000 for a peach, but would pay only $500 for a lemon. When these buyers are not sure of the quality of the car they buy, they are willing to pay the expected value of the car. (a) What is the smallest fraction of peaches required for the existence of an equilibrium in which both types of cars are traded? (b) Now suppose that 45 out of these 100 cars are lemons, and 55 cars are peaches. Describe all possible equilibria that exist, including prices and quantities for each type of cars.
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