Question

After a car crash Mr Magoo wants to buy a used car. Just like all other buyers of used cars on

the perfectly competitive market he is willing to pay 20000 USA for a lemon (a bad used car)

and 50000 USA for a plum (a nice used car). The sellers are prepared to sell lemons for a

minimum of 10000 SEK and plums for 40000 USA. The buyers cannot distinguish the lemons

from the plums when purchasing a car while the sellers know what they are selling. The buyers’

and the sellers’ valuations of the cars are common knowledge.

a) Assuming that the proportion of lemon cars is 10% (the buyers know this), what would

the market equilibrium price for a used car be? Is the market outcome efficient? Explain!

b) Assume now that the proportion of lemon cars is 50% (the buyers know this), what

would the market equilibrium price be for a used car? Is the market outcome efficient? Explain!

c) Can you give an example of how sellers of plums might convince buyers that they are actually selling a plum? Explain!

d) If the buyers actually could distinguish lemons from plums, what would the market price be for each type of car? Would this be an efficient market outcome?

Answer 1

A) Proportion of lemon cars in market= 10%

Therefore, Proportion of plum cars in market= 90%

Expected value of car= (proportion of lemon car)*(buyer willingness to pay for lemon car)+(proportion of plum car)*(buyer willingness to pay for plum car)

= 0.10*20,000+0.9*50,000 = 47,000

So, when a buyer cannot differentiate between a lemon and a plum, but he knows that only 10% of total car in market is lemon, he's willing to pay 47,000 USD. Since, At this price both the owners of plum(expecting value of 40,000) and lemon(expecting value of 10,000) are willing to sell their car. This is an efficient market outcome because both types of cars will be traded in market.

B) Proportion of lemon cars in market= 50%

Therefore, Proportion of plum cars in market= 50%

Expected value of car= (proportion of lemon car)*(buyer willingness to pay for lemon car)+(proportion of plum car)*(buyer willingness to pay for plum car)

= 0.5*20,000+0.5*50,000= 35,000

But, obviously, the owner of a lemon will be willing to sell his car at the price of 35,0000. because he's willing to sell his car at 10,000. Therefore, this is not an efficient market outcome because at this price only lemons will be traded in the market.

C) There are many ways that a seller of plum can use to convince the buyer that he's selling the plum. One of them is by building a good reputation in the market, the other is by giving them test drives.

D) If it is easy to distinguish a plum from a lemon,that is, when no asymmetric problem exist, there will be no problems in the market. Then lemons will sell at some price between 10,000(Seller's price) and 20,000(Buyer's price), and in the same way, plums will sell at some price between 40,000 and 50,000.

Yes, this will be an efficient market outcome because both types of car will be traded in this situation.