An art dealer\'s client is willing to buy a painting for exist100,000. The deale

Question

An art dealer's client is willing to buy a painting for exist100,000. The dealer can buy the painting for exist80,000 today (and make a profit of exist20,000) or wait a day and buy it (if it has not been sold) for exist70,000 (and make a profit of exist30,000). The dealer can wait another day and buy the painting (if it has not been sold) for exist50,000 (and make a profit of exist50,000). At the end of the 3rd day, the painting will no longer be available for sale. Each day the painting has a 0.55 probability that the painting will be sold to another client and the dealer will not be able to make any profit on reselling the painting. What strategy maximizes the dealer's expected profit? What should the dealer do?

Explanation / Answer

Expected profit on day i is found using the above table.
It's seen that expected profit is maximum if the painting is purchased on day 1.
Hence the dealer should purchase the painting on the same day.

Table for expected profit Day of pruchase Profit(xi) Probability of profit(Pi) Expected value(xiPi) 1 20000 1 20000 2 30000 1-0.55=0.45 30000*0.45=13500 3 50000 0.45*(1-0.55)=0.2025 50000*0.2025=10125

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