Suppose the Consumer's Utility Function Is Given By $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \mathrm { x } ^ { 1 / 4 } \mathrm { y } ^ { 3 / 4 }$

Multiple Choice

Suppose the consumer's utility function is given by $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \mathrm { x } ^ { 1 / 4 } \mathrm { y } ^ { 3 / 4 }$ where $M U _ { x } = \frac { y ^ { \frac { 8 } { 4 } } } { 4 x ^ { \frac { 8 } { 4 } } } \quad M U _ { y } = \frac { 3 x ^ { \frac { 2 } { 4 } } } { 4 y ^ { \frac { 1 } { 4 } } }$
The equation for this consumer's demand curve for $x$ is:

A) $x = \frac { I } { 2 P _ { x } }$
B) $x = \frac { I } { 4 P _ { x } }$
C) $x = \frac { I } { P _ { x } }$
D) $x = \frac { 3 I } { 4 P _ { x } }$