Question : A consumer's utility function is $\mathrm{U}=\mathrm{X}+2 \mathrm{Y}$. If the consumer is currently consuming $X=4$ and $Y=6$, what is the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$ ?
Option 1: 1/2
Option 2: 2/3
Option 3: 3/2
Option 4: 6/4
Correct Answer: 1/2
Solution : The correct answer is a) $1 / 2$
To find the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$, we need to calculate the ratio of the marginal utility of $\mathrm{X}$ to the marginal utility of $\mathrm{Y}$.
The utility function is $\mathrm{U}=\mathrm{X}+2 \mathrm{Y}$. To find the marginal utility of $\mathrm{X}$, we differentiate the utility function with respect to $\mathrm{X}$ : $ \partial \mathrm{U} / \partial \mathrm{X}=1 $
To find the marginal utility of $\mathrm{Y}$, we differentiate the utility function with respect to $\mathrm{Y}$ : $ \partial \mathrm{U} / \partial \mathrm{Y}=2 $
Now we can calculate the MRS:
$ \begin{gathered} \mathrm{MRS}=(\partial \mathrm{U} / \partial \mathrm{X}) /(\partial \mathrm{U} / \partial \mathrm{Y}) \\ =1 / 2 \end{gathered} $
Therefore, the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$ is $1 / 2$.
Question : A consumer's utility function is $U=X+2 Y$. If the consumer is currently consuming $\mathrm{X}=4$ and $\mathrm{Y}=6$, what is the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$ ?
Question : A consumer's utility function is $U=X+2 Y$. If the consumer is currently consuming $\mathrm{X}=5$ and $\mathrm{Y}=3$, what is the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$ ?
Option 4: 5/3
Question : A consumer's utility function is $\mathrm{U}=\mathrm{X}^{\wedge} 2+\mathrm{Y}^{\wedge} 2$. If the consumer is currently consuming $X=3$ and $Y=4$, what is the marginal rate of substitution (MRS) of $\mathrm{X}$ for $\mathrm{Y}$ ?
Option 1: 3/4
Option 2: 4/3
Option 3: 9/16
Option 4: 16/9
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