Answer to Question #232844 in Macroeconomics for Jon

Question

Suppose 100 cars will be offered on the used-car market. Let 50 of them be good cars, each worth $10,000 to a buyer, and let 50 be lemons, each worth only $2,000.

A. Compute a buyer’s maximum willingness to pay for a car if he or she cannot observe the car’s quality.

b. Suppose that there are enough buyers relative to sellers that competition among them leads cars to be sold at their maximum willingness to pay. What would the market equilibrium be if sellers value good cars at $8,000? At $6,000?

Answer 1

Given:

Number of cars offered=100

Number of good cars=50

Probability of good car$=\frac{50}{100}\times 100=50 \space or \space 0.50$

Worth of good car=$10,000

Number of bad cars=50

Probability of lemon$=\frac{50}{100}\times 100=50 \space or\space 0.50$

Worth of bad car=$2000

a)

The maximum willingness of the buyer to pay for a car if he or she could not observe the quality of the car:

Given that the probability for each car is 0.50.

Computation of maximum willingness of buyer:

$=(Probability \space for\space good \space car\times Worth\space of\space good\space car)+(Probability\space for\space bad\space car\times Worth\space of\space bad \space car)\\=\$ (0.50\times 10,000)+(0.5\times 2000)\\=\$ (5000+1000)\\=\$ 6000$

Hence, the maximum willingness of the buyer to pay is $6000.

b)

The market equilibrium if sellers value good cars at:

• $8000

When the quality s not observable and the sellers tend to value the car at $8000 being more than the maximum willingness of the buyer to pay, then only lemons would be sold at $\$(8000−6000)=\$2000$

• $6000

When the quality s not observable and the sellers tend to value the car at $6000 being more than the maximum willingness of the buyer to pay, then both good cars and lemons would be sold at $6000.