Adverse Selection Problems

Economics 1

1. Residents of the town of Los Carburetors currently own 15

"lemons" and 30 good used cars. A lemon is worth $100 to its

current owner and a good car is worth $2,500 to its current

owner. The only buyer for used cars is a used car dealer who

happens to be a monopolist. The dealer can not tell good cars

from lemons when he buys them, but as soon as he buys them and

brings them into his shop, he will know. A lemon is worth $600 to

the used car dealer and a good car is worth $5,000 to the used

car dealer. In order to be able to buy a car from its current

owner, the car dealer must pay at least $1 more than its value

to its current owner. If the used car dealer offers to buy used

cars at a price of $101, how much profits will she make?

(a) $7,485

(b) $154,455

(c) $82,455

(d) $1,500

(e) $750

2. Suppose that the monopoly used car buyer in Los Carburetors

decides to offer $2,501 for every used car that she buys. How

much profits will she make?

(a) $154,455

(b) $82,455

(c) $74,970

(d) $46,455

(e) None of the above.

3. In Sparkplug, Nevada, there are many used car buyers and

the market is highly competitive. There are currently 40 good

used cars and 60 lemons in the hands of local residents. The

current owners of good used cars will sell their cars if and only

if they can get at least $2,000 for them and the current owners

of lemons will sell their used cars if and only if they can get

at least $0 for them. The value of a good used car to a used car

buyer is $4,000 and the value of a lemon to a buyer is $300.

Used car buyers can not tell good cars from lemons until after

they have purchased them. In the used car market in Sparkplug

(a) there is an equilibrium with self-confirming beliefs in which

everyone believes that all used cars will be sold by their

original owners and the price of a used car is approximately

$1,780.

(b) the only equilibrium with self-confirming beliefs is one in

which only the lemons are sold by their original owners and

the price is $300.

(c) the only equilibrium with self-confirming beliefs is one in

which only the lemons are sold by their original owners and

the price is $0.

(d) there is an equilibrium with self-confirming beliefs in which

everyone believes that only the good used cars will be sold

by their original owners and the price of a used car is

approximately $4,000.

(e) there is an equilibrium with self-confirming beliefs in which

everyone believes that all used cars will be sold by their

original owner and the price of a used car is approximately

$800.

Answer Key

1. A

2. D

3. B