Question

Suppose that there are two types of houses for sale: those with solid foundations and those with cracked foundations. In all other respects, the two types of houses are identical. Houses with solid foundations are worth $200,000, while those with cracked foundations are worth $200,000 minus the $20,000 to fix the crack, or $180,000. Sellers know which type of house they have, but buyers cannot detect whether the foundation has a crack. Suppose that 80 percent of the houses for sale have a solid foundation and 20 percent of the houses for sale have a cracked foundation. If buyers are risk-neutral and know the that 80 percent of the houses for sale have a solid foundation while 20 percent have a cracked foundation, then the owners of houses with a solid foundation will find that:

A. potential buyers are offering more than $200,000.

B. potential buyers are offering $200,000.

C. potential buyers are offering $180,000.

D. it is not worthwhile to sell their houses.

Answer 1

Here buyers know that 80% of the houses have solid foundation and 20% have cracked foundation.

So, when they go to buy house they will apply this expectation in there willingness to pay.

They will calculate a weighted average of the prices of both type with the probabilities being the weight.

Therefore, Buyers willingness to pay will be = $200,000 x 0.80 + $180,000 x 0.20 = $196,000

Since buyers dont know the actual qaulity of house they will be pay a maximum of $196,000, but the sellers of house with solid house have complete knowledge about their house and so they will not be willing to sell it below its true worth i.e. $200,000.

Thus, Answer is (D) it is not worthwhile to sell their houses