1. Utility Maximization Problem Set
Chapter 7

2. Assume the price of pizza is $2. 00 and the price of pop is $1
Assume the price of pizza is $2.00 and the price of pop is $1.00 and that at your current levels of consumption, the Marginal Utility from pizza is 10 and the Marginal Utility from pop is 6. True or false: You can increase total utility by buying more pop and less pizza.
Calculate the marginal utility per dollar from each of the goods

3. True
Pizza: MU/$ = 10/2 = 5
Pop: MU/$ = 6/1 = 6

4. The price of steak is $7 per pound, and the price of chicken is $2 per pound. Your mother currently receives a marginal utility of 14 from consuming steak this week and 6 from consuming chicken this week. The marginal utility of chicken is therefore less than that of steak. Does this imply that your mother should buy less chicken this week? Explain.

5. No, the marginal utility per dollar is 2 from steak and 3 from chicken, therefore mom can increase total utility by spending more money on chicken and less on steak.

6. ? ?

7. At 4 races and 1 musical, the marginal utility per dollar is equal across the goods, so this is the utility-maximizing combination. Note that this exactly uses up Bob’s $300 income (4 races at $50 each = $200 and 1 musical at $100 each = $100).

8. If the price of musicals doubles, what will happen to Bob’s consumption of the two goods? Explain.

9. Now we see that the equimarginal principle is satisfied at 5 races and 2 musicals, but Bob cannot afford this combination with available income and prices. So, in this case, he will purchase 5 races and 0 musicals and have $50 left over (he can buy a mark martin hat and tee shirt at the races). To see how this is found, simply spend the income one purchase at a time, and for each purchase, always buy the good that yields the highest marginal utility per dollar.

10. Assume that UB40 CD’s are a normal good for you, and that you regularly purchase these CD’s. Following is a decrease in the price of UB40 CD’s:
You will consume fewer CD’s because there is no income effect.
You will consume more CD’s because both the income and substitution effect dictate that you do so.
You will consume more CD’s because both the income effect always outweighs the substitution effect for normal goods.
Your consumption of CD’s will not change because the substitution effect and income effect will offset each other.
You can’t be sure whether you will increase or decrease consumption of CD’s without knowing the relative sizes of the income effect and substitution effect.

11. B

12. Matt eats five slices of pizza on a Saturday night but admits each slice of pizza doesn't taste as good as the previous one. This suggests that for Matt:
The marginal utility of a slice of pizza is positive but decreasing.
The marginal utility of a slice of pizza is negative.
The total utility of slices of pizza is declining.
The total utility of slices of pizza is increasing by larger and larger increments.
The law of diminishing marginal utility does not hold for Matt

13. A