1. Assume the market for used cars is set up as in the table below. There are tw
ID: 1133313 • Letter: 1
Question
1. Assume the market for used cars is set up as in the table below. There are two types of cars: lemons and peaches. Peaches are more reliable than lemons and thus have a higher value to both buyers and sellers. Sellers know the quality of their cars, but buyers cannot distinguish between the two. Buyers are risk neutral and only care about the average quality of the cars on the market. Assume that the seller has more bargaining power and cars will sell at the buyer’s value. Everyone has the information in the table, but the buyers only know the percentage of cars that are lemons.
Suppose 30% of the cars are lemons. At what price will cars sell? Input only your numerical answer below. Give the number only with no dollar sign.
Answer:
Question 2
Suppose now that 75% of the cars are lemons. At what price will cars sell?
Input only your numerical answer below. Give the number only with no dollar sign.
Question 3.
Again, suppose now that 75% of the cars are lemons. In the previous question you gave the selling price for cars in this market. In the space below, describe the deadweight loss, if any, in this market.
Answer:
Question 4.
Given the information in the table, what is the highest percentage of lemons in the used car market that will produce an equilibrium where all used cars are sold?
Input your numerical answer here. Give the number only with no percent sign (i.e., 10% is written as 10).
Explanation / Answer
Answer 1. The buyer’s value for a random car is
0.7*30,000+0.3*20,000 = 27,000
Since the cars are sold at the buyer’s value, sales will occur at this price.
Answer 2.
The buyer’s value for a random car is
0.25*30,000+0.75*20,000 = 22,500
Since the cars are sold at the buyer’s value, sales will occur at this price.
Answer 3.
The sellers of lemons have no reason to charge a price lower than this, as it would hurt their revenues, whereas the sellers of peaches are not able to charge a price higher than this, as buyers cannot differentiate between cars. At this price, buyers would understand that no seller would sell a peach, so only lemons should be sold on the market for 20,000. Thus, there is a 4,000 deadweight loss per peach, so thus there is a 1,000 deadweight loss per car.
Answer 4.
All used cars can be sold only when the buyer’s average value of the used car (no matter peach or lemon) is 26,000 or higher. Suppose that x is the proportion of peaches in the market, the average value to a buyer of a car is
(x)*30,000 + (1-x)*20,000 = (10,000x + 20,000)
Hence, the minimum x should solve:
10,000x + 20,000 = 26,000
10,000x = 6,000
x = 60%
Meaning that the highest proportion of lemons can be 40% in the market, so that the market that will produce an equilibrium where all used cars are sold.
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