Consider a market in which there are 10000 potential buyers and 8000 potential s

Question

Consider a market in which there are 10000 potential buyers and 8000 potential sellers of used cars. Each potential seller has one car, which is either of high quality or low quality. A seller with a low-quality car is willing to sell it for $5000 while a seller with a high-quality car is willing to sell it for $10,000. Of course, only the seller knows whether a car is of high or low quality. A buyer is willing to pay $8000 for a low quality car and $13000 for a high quality car. Suppose that 75% of cars in the market are of low quality. That is, 75% of sellers have low-quality cars.
Assume buyers know that 75% of sellers have low-quality cars but are unable to determine the quality of individual cars. If all sellers offer their cars for sale and buyers have no way of determining whether a car is a high quality or low quality, the expected value of a car to a buyer is _________________?

Explanation / Answer

Expected value to a buyer is = 0.75*8000+0.25*13000 = 6000 + 3250 = 9250.

Probability of Low quality * Price of Low quality + Probability of High quality * Price of high quality.

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