Hugh’s income is currently $5,000. His utility function is shown in the accompanying table.
Income Total utility (utils)
$0…………………………….. 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
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 will lose $3,000, and with a probability of 0.5 he will win $5,000. 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 will lose $1,000, and with a probability of 0.5 he will win $3,000. 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?