### What is the smallest amount for which he would sell the deal

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Question: Buying and selling prices for risky investments obviously are related to CEs. This problem, however, shows that the prices depend on exactly what is owned in the first place! Suppose that Peter Brown's utility for total wealth (A) can be represented by the utility function U(A) = ln(A). He currently has \$1,000 in cash. A business deal of interest to him yields a reward of \$100 with probability 0.5 and \$0 with probability 0.5.

a. If he owns this business deal in addition to the \$1,000, what is the smallest amount for which he would sell the deal?

b. Suppose he does not own the deal. What equation must be solved to find the greatest amount he would be willing to pay for the deal?

c. For part b, it turns out that the most he would pay is \$48.75, which is not exactly the same as the answer in part a. Can you explain why the amounts are different?

d. (Extra credit for algebra hotshots.) Solve your equation in part b to verify the answer (\$48.75) given in part c.

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