Question

Consider the following scenario for questions 21-23. In a market with 100 people who want to sell their used
cars and 100 people who want to buy a used car, everyone knows that 50 of the cars are “plums” and 50 are
“lemons”. The current owner of each car knows its quality. The owner of a lemon is willing to part with it for
$1000 and the owner of a plum is willing to part with it for $2000. The buyers of the car are willing to pay
$2400 for a plum and $1200 for a lemon.
21. If prospective buyers can observe the quality of the cars, then there will be __ cars sold in total.
a) 0 b) 50 c) 100 d) None of the above
22. If prospective buyers cannot observe the quality of the cars, then there will be __ cars sold in total.
a) 0 b) 50 c) 100 d) None of the above
23. If prospective buyers cannot observe the quality of the cars, which of the following is a possible price
that lemons could sell at?
a) $0 b) $500 c) $1000 d) None of the above

Answer 1

A) 100 cars sold:

This is because when quality is observable, the buyers would know what kind of car they are buying and thus offer money accordingly. In this case, to buy a "lemon", they would pay something between 1200 and 1000 while to buy a plum, they would pay somewhere between 2400 and 2000. Thus, due to perfect information, all 100 cars would be sold.

B) 50 cars sold

In this case, due to asymmetric information, the quality of the car is not visible. Thus, a buyer on average would be ready to pay (1/2)*1200 + (1/2)*2400 = 1800. As his expected bid price is lower than the value of the "plum", those cars would not be sold but because it is higher than the value of the "lemon", those cars would be sold.

C) $1000 is a prospective price

Following from the above explanation, the buyer would be willing to pay $1800 for a car. But in this case, he is sure that no "plums" would be sold and all he can get is "lemons". Thus, he would be willing to pay something between

1000 <= price <= 1200 as he values the "lemon" not more than 1200. Thus, all values between 1000 and 1200 are possible values at which the car can be sold and thus 1000 is a possible price.