## Rules for Maximizing Utility

1.

• No. She would have to sacrifice two slot machine games to play a single game of pinball, which would cause her total utility to decline.
Incorrect. We do not know the marginal utility of the second-to-last slot machine game, so cannot predict whether the utility from the last two slot machine games exceeds that of a single pinball game.
• We cannot determine the answer with the given information.
Correct! To determine whether Sandy should play a game of pinball we must know whether the combined marginal utilities of the second-to-last and last slot machine games is less than that of a single pinball game. The marginal utility of the second-to-last slot machine game is unknown.
• Yes. The marginal utility per dollar of the first pinball game exceeds the marginal utility per dollar of the last slot machine game.
Incorrect. Sandy must give up two slot machine games to play one round of pinball, and the marginal utility of the second-to-last slot machine game is unknown.

2.

• 100
Incorrect. If the marginal utility from the sixth can of beans was 100 then Thomas would net a higher total utility by consuming more beans and less ramen.
• 10
Incorrect. If the marginal utility from the sixth can of beans was only 10 then Thomas would net a higher total utility by consuming more ramen and less beans.
• 50
Correct. Using the utility-maximizing rule, you find that at this value, the ratio of prices equals the ratio of marginal utilities.

3.

• 5 pizzas and 5 pepsis
Incorrect. This consumption bundle lies outside of Hector’s budget constraint.
• 4 pizzas and 5 pepsis
Correct! At this bundle the marginal utility per dollar of both goods are equal and the budget is exhausted.
• 5 pizzas and 3 pepsis
Incorrect. At this consumption bundle the marginal utility per dollar of pepsis exceeds the marginal utility per dollar of pizzas. Hector could increase his total utility by shifting away from pizzas towards pepsis.

4.

• 126
Incorrect. This is the total utility associated with consuming 4 X and 2 Y At this point the marginal utility per dollar of Y exceeds the marginal utility per dollar of X, so the consumer should purchase more Y and less X to maximize their total utility.
• 156
Correct! The utility-maximizing consumption bundle is 3 X and 4 Yt at which point the marginal utilities per dollar for both boods are equal and the budget is exhausted. Summing the marginal utilities for the two goods finds the total utility.
• 57
Incorrect. While the utility-maximizing consumption bundle is 3 X and 4 Y, 57 is the sum of the marginal utilities per dollar and not marginal utilities. You must add up the marginal utilities to obtain the total utility.