Microeconomics Question?

Question

There are 10,000 buyers and 8,000 sellers of used cars. Each seller has one car, which is either high quality (a "plum") or low quality (a "lemon"). A seller with a low-quality car will be willing to sell it for $5,000, while a seller with a high-quality car will be willing to sell it for $10,000. Of course, only the seller knows whether a car is high or low quality. A buyer is willing to pay $8,000 for a low-quality car and $13,000 for a high-quality car.

Suppose that 75% of cars in the market are low quality. That is, 75% of sellers have low-quality cars.

If all sellers offer their cars for sale, what is the expected value of a car to a buyer?

A. $6,750

B. $8,000

C. $13,500

D. $9,250

In my opinion, it's probably D...I mean, the buyer has no clue whether the car is high or low quality....so the price I'd expect the car to be is around 9250$ to offset the confusion - i guess. anyone have a different approach?

Answer 1

Q1: - D. $9,250

Q2: - D. Only low-quality sellers

Q1:

You should use weighted average approach here:

Price x Probability = Value

8000*75% = 6000

13000*25%=3250

6000+3250=9250

Q2:

Sellers will be willing to sell only starting from (and up) market price - since price is fixed at 9250 then only 6000 low-level cars will be sold (with demand up to 10'000 cars)

P.S. Though there could be mistake in methodology - but this is just simplest method.