Consider an economy with two goods $X$ and $Y$. Let the utility function be given by $u(x,y) = A\sqrt{xy}$ where $A > 0$, $x \geq 0$ and $y \geq 0$. The budget constraint is $P_X x + P_Y y \leq M$, with $M > 0$. Let $P_X = P_Y > 1$ and let $(x^*, y^*)$ denote the utility maximizing bundle. Then,