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Homework answers / question archive / Consider a market in which there are many potential buyers and sellers of used cars
Consider a market in which there are many potential buyers and sellers of used cars. Each potential seller has one car, which is either of high quality (a plum) or low quality (a lemon). A seller with a low-quality car is willing to sell it for $4,500, whereas a seller with a high-quality car is willing to sell it for $8,500. A buyer is willing to pay $5,500 for a low-quality car and $10,500 for a high-quality car. Of course, only the seller knows whether a car is of high or low quality.
Suppose that 85% of sellers have low-quality cars. Assume buyers know that 85% of sellers have low-quality cars but are unable to determine the quality of individual cars.
(a.) If all sellers offer their cars for sale and buyers have no way of determining whether a car is a high-quality plum or a low-quality lemon, the expected value of a car to a buyer is_. (Hint: The expected value of a car is the sum of the probability of getting a low-quality car multiplied by the value of a low-quality car and the probability of getting a high-quality car multiplied by the value of a high-quality car.)
(b.) Suppose buyers are willing to pay only up to the expected value of a car that you found in the previous question. Since sellers of low-quality cars are willing to sell for $4,500, while sellers of high-quality cars are willing to sell for $8,500, which type will be willing to participate in this market at that price?
(c.) The dilemma in this problem is an example of which of the following economic concepts: moral hazard; adverse selection; screening; or signaling?
(a.) The expected value of a car to a buyer is $6,250 and is determined as follows
value = (probability of a low value car)(value of a low value care) + (probability of a high value car)(value of a high value care) = (.85)($5,500) + (.15)($10,500) = $6,250.
(b.) With a maximum selling price of $6,250, only sellers of low value cars will be willing to participate in the market.
(c) The dilemma in this problem is an example of adverse selection, which arises as a form of market failure when there is an asymmetrical distribution of product information. As in this example, adverse selection most commonly arises in situations in which sellers have more complete information than buyers.
