Microeconomics 2nd Edition by Douglas Bernheim

Exercise 3

Martin, from Problem 10, now has the opportunity to buy any fractional share, S , of the Yankees t-shirt business. For example, if S = 0.5, he pays $400 for the business, which provides him with a net gain of $200 if the Yankees win and a net loss of $200 if they lose. Write a formula for his expected utility as a function of the share purchased. Find the share that maximizes his expected utility. What fraction of the business should he purchase