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 $\mathrm { I } = \$ 100 , \mathrm { P } _ { \mathrm { x } } = \$ 25$ and $\mathrm { P } _ { \mathrm { y } } = \$ 10$ be the initial set of prices and income. Now, let $\mathrm { P } _ { \mathrm { x } }$ fall to $\$ 10$ . What is the approximate compensating variation for this change in prices?

A) 24
B) 30
C) 34
D) 40