Suppose a person has $20 and likes both rap music (R) and country music (C) with a set of preferences so that $\mathrm { U } = \mathrm { C } ^ { 1 / 2 } \mathrm { R } ^ { 1 / 2 }$. Suppose that the iTunes price of a rap music song is $P _ { R } = 2$ and the price of a country music song is $P _ { C } = 1$. What is the lowest level of $\text { utility that }$ is unaffordable?
A)6
B)7
C) $\sqrt { 50 }$
D)8

Question

Suppose a person has $20 and likes both rap music (R) and country music (C) with a set of preferences so that $\mathrm { U } = \mathrm { C } ^ { 1 / 2 } \mathrm { R } ^ { 1 / 2 }$. Suppose that the iTunes price of a rap music song is  $P _ { R } = 2$ and the price of a country music song is $P _ { C } = 1$. What is the lowest level of $\text { utility that }$  is unaffordable?
A)6
B)7
C) $\sqrt { 50 }$
D)8

Quizplus · Accepted Answer

The budget constraint is $2R + C = 20$. To find the highest affordable utility, maximize $U = C^{1/2} R^{1/2}$ subject to the budget constraint. The highest utility is achieved when $R = 5$ and $C = 10$, giving $U = \sqrt{5 \times 10} = \sqrt{50}$. Therefore, any utility level above $\sqrt{50}$ is unaffordable, making 8 the lowest unaffordable utility level.

Suppose a Person Has $20 and Likes Both Rap Music U=C1/2R1/2\mathrm { U } = \mathrm { C } ^ { 1 / 2 } \mathrm { R } ^ { 1 / 2 }U=C1/2R1/2

Suppose a Person Has $20 and Likes Both Rap Music $\mathrm { U } = \mathrm { C } ^ { 1 / 2 } \mathrm { R } ^ { 1 / 2 }$