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

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

$$\frac {\delta U}{\delta y}=0.7(\frac{x}{y})^{0.3}=2 \lambda$$

$$0.7(\frac{x}{y})^{0.3}=2\times 0.3(\frac{y}{x})^{0.7}$$

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

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

$$1\times x+2\times y=I$$

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

The demand function of good x and good y

$$x=0.3I$$

$$y=0.35I$$