Answer to Question #125602 in Microeconomics for Mr. Sal

Question

Suppose utility function is given by U(x,y) = x0.3y0.7 subject to budget constraint I= Pxx + Pyy. Further suppose that the prices for those goods given by Px=1 Py=2 & I=2. Derive demand function of good x and good y.

Answer 1

$$\frac {\delta U}{\delta x}=0.3(\frac{y}{x})^{0.7}$$

$$\frac {\delta U}{\delta y}=0.7(\frac{x}{y})^{0.3}$$

$$\frac {\frac {\delta U}{\delta x}}{\frac {\delta U}{\delta y}}=\frac {p_x}{p_y}$$

$$\frac {x}{y}=\frac{6}{7}$$

$$x=\frac {6}{7}y$$

$$\frac {6}{7}y+2y=I$$

Thus, the demand function for a set of two products has the form

$$y=\frac{7}{20}I$$

$$x=\frac{3}{10}I$$