In Rustbucket, Michigan, there are 200 used cars for sale, half of them are good

Question

In Rustbucket, Michigan, there are 200 used cars for sale, half of them are good and half of them are lemons. Owners of lemons are willing to sell them for $300. Owners of good used cars are willing to sell them for prices above $1,300 but will keep them if the price is lower than $1,300. There is a large number of potential buyers who are willing to pay $600 for a lemon and $2,100 for a good car. Buyers can’t tell good cars from bad, but original owners know.                                                 

The answer is: There will be an equilibrium in which all used cars sell for $1,350.

Could you provide a step-by-step solution! Thanks :)

Explanation / Answer

Expected value of the willingness to pay = 0.5 x 600 + 0.5 x 2100 = $1350

Since, $1350 > reservation price of the owners willing to sell good/bad used cars, there will be an equilibrium in which all used cars sell for $1350.

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