Question

Assume that a good second-hand car worths $10 to the seller and $12 to the buyer, an ordinary second-hand car worths $7 to the seller and $9 to the buyer, and a bad second-hand car worths $5 to the seller and $3 to the buyer. Assume that one third of the cars are good, one third are ordinary, and one third are bad.

a. If the buyer can tell good or ordinary or bad, will the good cars sell? Will the ordinary cars sell? Will the bad cars sell?

b. Now assume that the buyer cannot tell good or ordinary or bad but knows that the probabilities of a good, ordinary, and bad car are 1/3, respectively. How much will a risk neutral buyer be ready to pay?

c. Will the seller keep the good cars in the market?

d. Understanding this, now the buyer sees a car in the market. What are the probabil- ities that this car is good, ordinary, and bad, respectively?

e. How much will the buyer be ready to pay now?

f. Will the seller now keep the ordinary cars in the market?

g. Understanding this, now the buyer sees a car in the market. What is the probability that this car is good, or ordinary, or bad?

h. How much will the buyer be ready to pay now?

i. Will the seller now keep the bad cars in the market?

j. Will any car be sold?

Answer 1

if buyer can tell good or ordinary or bad car , then only good and ordinary cars will be sold , while the bad cars will be left untold.
Since the buyer cannot distinguish between the type of car , he will be ready to pay average price for the car, that is

   1/3(12) + 1/3(9)+ 1/3(3). Where 1/3 is the probability of each type of car being sold

   = $ 8

So buyer will be ready to pay only $8 for the car

C) Since the amount that buyer is willing to pay Is less than the even the worth to seller , sellers will remove their good cars from the market.

D )Given the above scenario, probabilities for good cars = 0

probabilities for ordinary cars = 1/2

probabilities for bad cars = 1/2

E) Given the change in probabilities, buyer will be willing to pay

   = 1/2(9) +1/2(3)

= $6

F) Sellers will. Not keep the ordinary car in the market since the amount buyer is willing to pay is less than worth to seller.

G) Given the above scenario, probabilities for good cars = 0

probabilities for ordinary cars = 0

probabilities for bad cars = 1

H) Buyer will be willing to pay only $3 for the bad car

sellers will keep the bad cars in the market.

J) No car will be sold as all cars are of bad quality