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

Multiple Choice

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 $= - 1.3$