N U M E R I C A L P R O B L E M S
1. The table shows the total utility Joseph derives from eating pizza in the evening while studying.
Pieces of pizza/evening Total Utility
0 0
1 30
2 48
3 60
4 70
5 78
6 80
7 76
a. How much marginal utility does Joseph derive from the third piece of pizza?
b. After eating how many pieces of pizza does marginal utility start to decline?
c. If the pizza were free, what is the maximum number of pieces Joseph would eat in an evening?
d. On separate diagrams, construct Joseph’s total utility and marginal utility curves for pizza. Does
the law of diminishing marginal utility hold? How do you know?
2. Suppose the marginal utility of good A is 20 and its price is $4, and the marginal utility of good B is 50 and
its price is $5. The individual to whom this information applies is spending $20 on each good. Is he or she
maximizing satisfaction? If not, what should the individual do to increase total satisfaction? On the basis of
this information, can you pick an optimum combination? Why or why not?
3. John and Marie settle down to watch the evening news. Marie is content to watch the entire program,
while John continually switches channels in favor of possible alternatives. Draw the likely marginal utility
curves for watching the evening news for the two individuals. Whose marginal utility curve is likely to be
steeper?
4. Li, a very careful maximizer of utility, consumes two services, going to the movies and bowling. She has
arranged her consumption of the two activities so that the marginal utility of going to a movie is 20 and
the marginal utility of going bowling is 10. The price of going to a movie is $10, and the price of going
bowling is $5. Show that she is satisfying the requirement for utility maximization. Now show what
happens when the price of going bowling rises to $10.
5. The table shows the total utility (TU) that Jeremy receives from consuming different amounts of two
goods, X and Y, per month.
Quantity TUX MUX MUX/PX TUY MUY MUY/PY
0 0 0
1 50 75
2 88 117
3 121 153
4 150 181
5 175 206
6 196 225
7 214 243
8 229 260
9 241 276
a. Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and
the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X
and Y is $3. Be sure to use the “midpoint convention” when you fill out the table.
b. If Jeremy allocates $30 to spend on both goods, how many units will he buy of each?
c. How much will Jeremy spend on each good at the utility maximizing combination?
d. How much total utility will Jeremy experience by buying the utility-maximizing combination?
e. Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize
his utility now?
f. Draw Jeremy’s demand curve for good Y between the prices of $6 and $3
1. The table shows the total utility Joseph derives from eating pizza in the evening while studying.
Pieces of pizza/evening Total Utility
0 0
1 30
2 48
3 60
4 70
5 78
6 80
7 76
a. How much marginal utility does Joseph derive from the third piece of pizza?
b. After eating how many pieces of pizza does marginal utility start to decline?
c. If the pizza were free, what is the maximum number of pieces Joseph would eat in an evening?
d. On separate diagrams, construct Joseph’s total utility and marginal utility curves for pizza. Does
the law of diminishing marginal utility hold? How do you know?
2. Suppose the marginal utility of good A is 20 and its price is $4, and the marginal utility of good B is 50 and
its price is $5. The individual to whom this information applies is spending $20 on each good. Is he or she
maximizing satisfaction? If not, what should the individual do to increase total satisfaction? On the basis of
this information, can you pick an optimum combination? Why or why not?
3. John and Marie settle down to watch the evening news. Marie is content to watch the entire program,
while John continually switches channels in favor of possible alternatives. Draw the likely marginal utility
curves for watching the evening news for the two individuals. Whose marginal utility curve is likely to be
steeper?
4. Li, a very careful maximizer of utility, consumes two services, going to the movies and bowling. She has
arranged her consumption of the two activities so that the marginal utility of going to a movie is 20 and
the marginal utility of going bowling is 10. The price of going to a movie is $10, and the price of going
bowling is $5. Show that she is satisfying the requirement for utility maximization. Now show what
happens when the price of going bowling rises to $10.
5. The table shows the total utility (TU) that Jeremy receives from consuming different amounts of two
goods, X and Y, per month.
Quantity TUX MUX MUX/PX TUY MUY MUY/PY
0 0 0
1 50 75
2 88 117
3 121 153
4 150 181
5 175 206
6 196 225
7 214 243
8 229 260
9 241 276
a. Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and
the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X
and Y is $3. Be sure to use the “midpoint convention” when you fill out the table.
b. If Jeremy allocates $30 to spend on both goods, how many units will he buy of each?
c. How much will Jeremy spend on each good at the utility maximizing combination?
d. How much total utility will Jeremy experience by buying the utility-maximizing combination?
e. Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize
his utility now?
f. Draw Jeremy’s demand curve for good Y between the prices of $6 and $3
