Question: A consumer allocates income (M) between two goods (x and y) and has the utility function: \(U={{x}^{a}}{{y}^{b}}\). The goods are priced at p_x and p_y respectively. Show that the utility maximizing consumption of the goods (assuming no saving from income) yields demand functions of the form:

\(x=\frac{a}{a+b}\frac{M}{{{p}_{x}}}\)

\(y=\frac{b}{a+b}\frac{M}{{{p}_{y}}}\)