Question

Samantha has $7 to spend on apples and bananas and wants to
maximize her utility on her purchase. Based on the data in the
table, how many apples and bananas should Samantha purchase, and what is her total utility from the purchase? Does the
utility-maximizing rule hold true for her purchase? Explain.

Answer 1

Samantha's marginal utility per dollar for bananas and apples.

Bananas Marginal utility Quantity of apples Marginal utility 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;

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

Samantha'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;

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

The table with Samantha'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.

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