) (19 Points) Suppose that in the market for used cars buyers are unable to tell

Question

) (19 Points) Suppose that in the market for used cars buyers are unable to tell the quality difference between cars. The quality of a car can be m easured by q where 0 q 1 with 1 being perfect quality and O being junk ( "lemon"). If buyers knew the quality of the used car, then they would be willing to pay any price ps 19000 q+225. The seller of a used car is willing to accept a price p 2 15100 q+50. While the buyers cannot tell the quality of a given car, they do know the distribution of quality for cars in the market. That is, there is a chance that a car will be q-1, a % chance the car will be q-06, % chance a car will be q-03, and chance a car will be q-o since buyers cannot tell the quality there will be a single price in the market using the average quality of the cars Q. Analyze the market given that buyers cannot tell the quality but know the distribution. Make sure to go through each case and show whether there exists any trades between buyers and sellers for each case.

Explanation / Answer

If the buyer is aware of the quality of a car, the price he/she is willing to pay can be easily calculated using the price function p<= 19000*q + 225 and substituting the value of q in the function. This is calculated below:

If q = 1

Buyer will be willing to pay <= 19000*1 +225 = 19225

If q = 0.3

Buyer will be willing to pay <= 19000*0.3 +225 = 5925

If q = 0

Buyer will be willing to pay <= 19000*0 +225 = 225

Now, since the buyer does not have information on the quality of the car, he/she will base his willingness to pay on the average quality of the cars which is based on the distribution of quality. There is 0.25 chance that q=1, 0.25 chance that q=0.3 and 0.25 chance that q=0. Therefore, the buyer will be willing to pay:

<= (0.25*19225) + (0.25*5925) + (0.25*225) = 6343.75

Now, from the sellers' perspective, the price they would be willing to sell at would depend on the price function p>=15100*q + 50

For seller with q = 0

p >= 15000*0 + 50 = 50

Since the buyer is willing to pay a maximum amount of 6343.75, he/she will be willing to pay an amount >50 and hence trade will take place

For seller with q = 0.3

p >= 15000*0.3 + 50 = 4500

Since the buyer is willing to pay a maximum amount of 6343.75, he/she will be willing to pay an amount >4500 and hence trade will take place

For seller with q = 1

p >= 15000*1 + 50 = 15050

Since the buyer is willing to pay a maximum amount of 6343.75, he/she will be not be willing to pay an amount >15050 and hence trade will not take place

The above phenomemnon is called adverse selection due to asymmetric information. If the buyer was fully aware of the quality of the car, trade would have taken place for the highest quality car (q=1) since he/she would be willing to pay 19225 maximum. Since information is imperfect or asymmetric, the buyer is willing to offer an average price for any quality of car. At this lower price, only sellers of low quality cars or lemons will be willing to trade and the buyer will end up making an adverse selection.

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