MARKET FORLEMONS Task: There are 100 people who would like to sell a used car, a
ID: 1138865 • Letter: M
Question
MARKET FORLEMONS
Task: There are 100 people who would like to sell a used car, and 100people who would be interested in buying one. Cars are either Good or Bad. The quality of a car is known by the seller. A buyer cannot determine the quality of any particular car but does know how many cars of each type are being marketed. The reservation price of a potential seller is $1000 if the car is Bad and $3000 if the car is Good. The reservation of a potential buyer is $2000 if the car is Bad and $4000 if the car is Good. (For a car of unknown quality, the buyer is willing to pay (1q)2000 +q4000 where q is the probability that the car is Good.) Let n be the number of cars, out of the 100, that are good. Assume that n is common knowledge.
1. Derive a function for q in terms of n.
2. When n= 1, for which prices p of used cars will the market clear?
3. When n= 99, for which prices p of used cars will the market clear?
4. For which values of n are there market equilibria in which Good cars are traded?
Explanation / Answer
1. Since q is the probability that the car is good, q = n/100
2. When n=1, q = 1/100
Thus, prices of used car for market clearing = (1 - 0.01)*2000 + 0.01*4000 = $2020
3. Wnen n=99, q = 99/100
Thus, prices of used car for market clearing = ( 1 - 0.99)*2000 + 0.99*4000 = $3980
4. For market equilibria in which Good cars to be traded, the buyer should be willing to pay atleast $3000 for car of unknown quality.
Thus, (1 - n/100)*2000 + n/100*4000 >= 3000
-> 2000 + 20*n >= 3000
-> n >=50
Thus, for n as (50 to 100), market equilibria for trading of Good cars exist.
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