Question

Buyer a has offered $20,000 for a painting you are trying to sell. you are about to approach buyer b whose best offer, you believe, might be anywhere between $16,000 and $24,000, with all values in between being equally likely. after hearing b’s price, you will pick the higher of the two offers. your expected price is

a) $20,000.
b) $21,000.
c) $22,000.
d) $22,500.

Answer 1

The question involves calculating the expected value from two potential buyers' offers for a painting. Given the details, the expected price after considering both Buyer A's confirmed offer and Buyer B's potential offer is $22,000. The correct option is d) $22,500.

Step-by-step explanation:

The student is asking a question related to expected value in the context of decision-making under uncertainty. Given that Buyer A has already offered $20,000, and the expected best offer from Buyer B could be between $16,000 and $24,000, we need to calculate the expected price the seller will get after hearing Buyer B's offer.

We can assume that any price below $20,000 from Buyer B is irrelevant since the seller will choose Buyer A's offer of $20,000. The probability distribution for Buyer B's offer is uniform between $16,000 and $24,000, so the expected price can be found by averaging the values from $20,000 to $24,000. Since all values in this range are equally likely, the calculation is simply $(20,000 + 24,000) / 2$, which equals $22,000. Therefore, any offer above $20,000 has an average value of $22,000, and, given Buyer A's offer, this results in an expected price of $22,000. The correct option is d) $22,500.