7. Hugh’s income is currently $5,000. His utility function is shown in the accompanying table.

a. Calculate Hugh’s marginal utility of income. What is his attitude toward risk?

b. Hugh is thinking about gambling in a casino. With a probability of 0.5 he loses $4,000, and with a probability of 0.5 he wins $4,000. What is the expected value of Hugh’s income? What is Hugh’s expected utility? Will he decide to gamble? (Suppose that he gets no extra utility from going to the casino.)

c. Suppose that the “spread” (how much he can win versus how much he can lose) of the gamble narrows, so that with a probability of 0.5 Hugh loses $2,000, and with a probability of 0.5 he wins $2,000. What is the expected value of Hugh’s income? What is his expected utility? Is this gamble better for him than the gamble in part b? Will he decide to gamble?

Income $0 Total utility (utils) 0 1,000 100 2,000 140 3,000 166 4,000 185 5,000 200 6,000 212 7,000 222 8,000 230 9,000 236 10,000 240