Question

an art dealer and a buyer negotiate over the price of a painting. However, unlike the question above, assume that the valuations are independent, i.e. how a buyer and a seller values a painting is entirely personal and does not depend on each other’s valuation. The probabilities are such that the buyer values the painting £4,000 with probability q and £20,000 with probability (1-q). Moreover, the painting is worth to the seller £2,000 with probability (1-q) and it is worth £16,000 with probability q.

Hence, under what circumstances would trade occur? Why?

How does the probability that the gains from trade exist depend on q? What does this imply?

Hint: Think of the general situation where trade should occur. Also, remember that the valuations are independent. For example, a seller can value a painting £2,000 but a buyer may value it £20,000 and so forth.

Answer 1