Question

BANANAS APPLES
Quantity (pounds) Marginal utility per dollar Quantity (pounds) Marginal utility per dollar
1 30 1 40
2 24 2 34
3 18 3 24
4 12 4 16
5 6 5 8
6 0 6 0

The table above gives Sam's marginal utility schedule for bananas and apples. Sam's fruit budget is $10.
a) If bananas cost $1 per pound and apples cost $2 per bag, what is Sam's marginal utility per dollar for all quantities of both goods?
b) What is the utility maximizing combination of bananas and apples for Sam?
c) If the price of bananas increases to $2 per pound, how does Sam's marginal utility per dollar for bananas change?
d) At the banana price of $2 per pound, what is the new utility maximizing combination of bananas and apples for Sam?
e) List two points on Sam's demand curve for bananas.

Answer 1

a)     The table below has Sam's marginal utility per dollar for bananas and apples.

Bananas Marginal utility Quantity of apples Marginal utility per dollar

(Quantity in pounds) per dollar

1 30 1 20

2 24 2 17

3 18 3 12

4 12 4 8

5 6 5 4

6 0 6 0

Where;Pb=1 for marginal utility of bananas $m_u/p_o$

$=\frac{30}{1}=30,\frac{24}{1}=24,\frac{18}{1}=18,\frac{12}{1}=12,\frac{6}{1}=6,\frac{0}{1}=1$

Where;Pb=2 marginal utility will be;

$=\frac{30}{2}=15,\frac{24}{2}=12,\frac{18}{2}=9,\frac{12}{2}=6,\frac{0}{2}=0$

For apples marginal utility will be;

$=\frac{40}{2}=20,\frac{34}{2}=17,\frac{24}{2}=12,\frac{16}{2}=8,\frac{8}{2}=4,\frac{0}{2}=0$

b)  Sam's utility maximizing combination of bananas and apples is 4 pounds of bananas and 3 bags of apples. This quantity allocates (spends) his budget and equates the marginal utility per dollar from bananas and apples.

This is because utility is maximized where;

$\frac{mu_b}{p_b}$ $=\frac{mu_a}{p_a}$

c)  The table with Sam's new marginal utility per dollar for bananas is below.

Bananas

Quantity(pounds) Marginal utility

1 15

2 12

3 9

4 6

5 3

6 0

$\frac{mu_b}{p_b}$$=$ $\frac{mu_b}{p_b}$ $=12$ when the number of bananas is 2 and the number of apples is 3.

Budget constraint is also satisfied $(2)(2)+(2)(3)=$ income.

New utility maximizing combination of 2 bananas and 3 apples.

d) Sam's new utility maximizing combination of bananas and apples is 2 pounds of bananas and 3 bags of apples.

e) When the price of a pound of bananas is $1, the quantity demanded is 4 pounds and when the price rises to $2, the quantity demanded decreases to 2 pounds.