Let $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \sqrt { x y }$ with $\mathrm { MU } _ { \mathrm { x } } = \frac { \sqrt { y } } { 2 \sqrt { x } }$ and $\mathrm { MU } _ { \mathrm { y } } = \frac { \sqrt { x } } { 2 \sqrt { y } }$. Let $\mathrm { I } = \$ 100 , \mathrm { P } _ { \mathrm { x } } = \$ 10$ and $\mathrm { P } _ { \mathrm { y } } = \$ 10$ be the initial set of prices and income. Now, let $P _ { x }$ rise to $\$ 25$. What are the (approximate) substitution and income effects of this change in prices?
A) Income effect $= - 3.3$; Substitution Effect $= - 2.1$
B) Income effect $= - 2.3$; Substitution Effect $= - 1.7$
C) Income effect $= - 1.3$; Substitution Effect $= - 1.7$
D) Income effect $= - 1.7$; Substitution Effect $= - 1.3$

Question

Quizplus · Accepted Answer

The substitution effect is calculated using the change in consumption due to the change in relative prices, holding utility constant, while the income effect is the change in consumption due to the change in purchasing power. Given the utility function and price changes, the substitution effect is approximately -1.7 and the income effect is approximately -1.3.

Let U(x,y)=xy\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \sqrt { x y }U(x,y)=xy​

Let $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \sqrt { x y }$