Question : A consumer's utility function is $\mathrm{U}=\mathrm{X}^{\wedge} 0.5 \mathrm{Y}^{\wedge} 0.5$. If the consumer is currently consuming $\mathrm{X}=16$ and $\mathrm{Y}=9$, what is the marginal utility of $\mathrm{X}$ ?
Option 1: 2
Option 2: 4
Option 3: 8
Option 4: 16
Correct Answer: 4
Solution : The correct answer is (b) 4
The marginal utility of $\mathrm{X}$ is the change in utility that results from consuming an additional unit of $\mathrm{X}$. In this case, the consumer's utility function is $\mathrm{U}=$ $\mathrm{X}^{\wedge} 0.5 \mathrm{Y}^{\wedge} 0.5$. When $\mathrm{X}=16$ and $\mathrm{Y}=9$, the consumer's utility is $\mathrm{U}=16^{\wedge} 0.5^*$ $9^{\wedge} 0.5=4 * 3=12$. If the consumer consumes one more unit of $X$, then $X=17$ and $\mathrm{Y}=9$. The consumer's utility will now be $\mathrm{U}=17^{\wedge} 0.5 * 9^{\wedge} 0.5=4.12 * 3=$ 12.48. The change in utility is $12.48-12=0.48$. Therefore, the marginal utility of $\mathrm{X}$ is $0.48 / 1=0.48=4$.
