Question

Consider a used car market with asymmetric information. The owners of used cars know what their vehicles are worth but have no way of credibly demonstrating those values to potential buyers. Thus, potential buyers must always worry that the used car they are being offered may be a low-quality "lemon." a. Suppose that there are equal numbers of good and bad used cars in the market and that good used cars are worth $13,000 while bad used cars are worth $5,000. What is the average value of a used car? b. By how much does the average value exceed the value of a bad used car? By how much does the value of a good used car exceed the average value? c. Would a potential seller of a good used car be willing to accept the average value as payment for her vehicle? d. If a buyer negotiates with a seller to purchase the seller's used car for a price equal to the average value, is the car more likely to be good or bad? e. Will the used-car market come to feature mostly—if not exclusively—lemons? How much will used cars end up costing if all the good cars are withdrawn?

          Consider a used car market with asymmetric information. The owners of used cars know what their vehicles are worth but have no way of credibly demonstrating those values to potential buyers. Thus, potential buyers must always worry that the used car they are being offered may be a low-quality "lemon." 

a. Suppose that there are equal numbers of good and bad used cars in the market and that good used cars are worth $13,000 while bad used cars are worth $5,000. What is the average value of a used car? 

b. By how much does the average value exceed the value of a bad used car? By how much does the value of a good used car exceed the average value? 

c. Would a potential seller of a good used car be willing to accept the average value as payment for her vehicle? 

d. If a buyer negotiates with a seller to purchase the seller's used car for a price equal to the average value, is the car more likely to be good or bad? 

e. Will the used-car market come to feature mostly—if not exclusively—lemons? How much will used cars end up costing if all the good cars are withdrawn?

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Added by Joseph W.

Principles of Economics

Gregory Mankiw 8th Edition

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Solved by Expert Andrew Davis

07/22/2022

Step 1

- There are equal numbers of good and bad used cars. - Good used cars are worth $13,000. - Bad used cars are worth $5,000. The average value of a used car is calculated as follows: \[ \text{Average value} = \frac{\text{Value of good car} + \text{Value of bad Show more…

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Consider a used car market with asymmetric information. The owners of used cars know what their vehicles are worth but have no way of credibly demonstrating those values to potential buyers. Thus, potential buyers must always worry that the used car they are being offered may be a low-quality "lemon." a. Suppose that there are equal numbers of good and bad used cars in the market and that good used cars are worth $13,000 while bad used cars are worth $5,000. What is the average value of a used car? b. By how much does the average value exceed the value of a bad used car? By how much does the value of a good used car exceed the average value? c. Would a potential seller of a good used car be willing to accept the average value as payment for her vehicle? d. If a buyer negotiates with a seller to purchase the seller's used car for a price equal to the average value, is the car more likely to be good or bad? e. Will the used-car market come to feature mostly—if not exclusively—lemons? How much will used cars end up costing if all the good cars are withdrawn?

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Transcript

00:01 So here we have a market for lemons issues, right? and we've got a whole bunch of questions to answer.

00:05 So let's just get started, right? the average value of the car is just the expected value, right? so if we were just randomly picking between these good and bad cars and they're 50 -50, we have a 50 % chance of getting a car worth 13 ,000, and then we have a 50 % chance of getting a car worth 5 ,000.

00:26 So this is 6 ,500 plus.

00:30 Plus 2 ,500 equals 9 ,000.

00:33 So the average car in this situation is 9 ,000, right? so this leads to some problems.

00:40 At a very, right, so bad cars are worth minus 4 ,000 relative to the average in part b, and good cars are plus 4 ,000, right? they're worth more.

00:58 So on average, cars are worth 9 ,000, but the good cars are worth 4 ,000 more and the bad cars are worth 5 ,000 less, right? so c, sellers of good cars are going to refuse to participate.

01:13 They refuse to deal because the key is the information structure here, right? a good car is known to the seller.

01:24 The seller realizes they have a good car.

01:26 They've been driving it for years.

01:27 They know exactly how good it is.

01:29 So they are from their perspective.

01:30 They say, i have this $13 ,000 car.

01:32 But the average price of cars is only 9 ,000...

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