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

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

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