Q3. Consider a market for used cars. There are 1,000 used cars, 500 of which are
ID: 1122688 • Letter: Q
Question
Q3. Consider a market for used cars. There are 1,000 used cars, 500 of which are bad and 500 of which are good. The current owners of the used cars know their cars’ types. Those with bad cars have reservation price $5,000 for selling, while those with good cars have reservation price $8,000 for selling. There are 1,500 identical, risk-neutral potential buyers of used cars. They would be willing to pay up to $6,000 for a bad used car if they knew it were bad. They would be willing to pay up to $9,000 for a good used car if they knew if were good. There are no guarantees or warranties.
(a) Suppose buyers could determine each car's type before purchase. What is the resulting competitive equilibrium? What is the corresponding total surplus? Now assume the buyers do not know the type of any individual car though they do know the overall distribution of used car types.
(take note on the number of buyers and cars available. how will the price equilibrium will change?)
Explanation / Answer
(a) Suppose buyers could determine each car’s type before purchase. Buyers would be ready to pay $9000 for good car which they know, are 500 and for bad cars, they are ready to pay $6000. Those with bad cars have reservation price $5,000 for selling, while those with good cars have reservation price $8,000 for selling. Since the buyers valuation exceeds the valuation of the car owner, all the cars will be sold. The price for good cars will lie between $9000 and $8000 and that of a bad car will lied between $5000 and $6000.
Total surplus = (Max reservation price 0 minimum reservation price)*car quantity
= (9000 – 8000)*500 + (6000 – 5000)*500 = $1 million.
Now assume the buyers do not know the type of any individual car though they do know the overall distribution of used car types. This implies that they will place an expected price on each car type. With the knowledge of 50% of cars being bad, the expected price is 6000*0.5 + 9000*0.5 = $7500. When buyers are paying only $7500, all good car owners who have a higher reservation price at $8000, will leave the market and the resulting competitive equilibrium has only bad car sellers. Once buyers realize this, they will pay inly $6000 which is acceptable to owners of lemons. Hence, only bad cars are sold.
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