Question

at sallys current consumption bundle, if the amount of good x increases by 0.13, her utility would increase by 0.2 utils; if the amount of good y increases by 0.07, her utility would increase by 0.4 utils. please find her mrs of x for y at her current consumption bundle. in other words, at her current consumption bundle, a unit of good x is just as good as ____ units of good y.
hints/example

question 2
2 pts
at a consumers current - consumption bundle, the marginal utility of good x is 3.7 utils/unit. if the amount of good x increases by 0.12, the consumers utility would increase by ____ utils.
hints/example

Explanation:

Question 1

Step1: Recall MRS formula

$MRS_{X for Y}=\frac{MU_X}{MU_Y}$
We can find $MU_X$ and $MU_Y$ from the given information. $MU_X=\frac{\Delta U_X}{\Delta X}$ and $MU_Y = \frac{\Delta U_Y}{\Delta Y}$.

Step2: Calculate $MU_X$

$MU_X=\frac{0.2}{0.13}\approx 1.54$

Step3: Calculate $MU_Y$

$MU_Y=\frac{0.4}{0.07}\approx 5.71$

Step4: Calculate MRS

$MRS_{X for Y}=\frac{MU_X}{MU_Y}=\frac{\frac{0.2}{0.13}}{\frac{0.4}{0.07}}=\frac{0.2\times0.07}{0.13\times0.4}=\frac{0.014}{0.052}\approx 0.27$

Step1: Recall marginal - utility formula

The formula for marginal utility is $MU_X=\frac{\Delta U_X}{\Delta X}$. We know $MU_X = 3.7$ utils/unit and $\Delta X=0.12$.

Step2: Rearrange the formula to find $\Delta U_X$

$\Delta U_X=MU_X\times\Delta X$

Step3: Substitute values

$\Delta U_X = 3.7\times0.12 = 0.444$

Answer:

$0.27$

Question 2