Question

Given that utility function=10x1^0.6,x2^0.4, where U=f(x1,x2) given Px1=10 ,px2=20, and Px3=1000 are units of proces x1 and x2,while B is money income.Required,Interpret the utility function,Construct budget constraint function,derive demand curvea for x1 and x2and prove they are actually demand curves then compute maximum utility given the income and prices of x1 and x2

Answer 1

Solution

$U=10x_1^{0.6}+x_2^{0.4}$

$MUx_1=6x_1x_2^{0.4}$

$MUx_2=4x_1^{0.6}x_2^{1.4}$

Px₁=10 Px₂=20 Px₃=1000

Constrain function

$1000=10x_1+20x_2$

$100=x_1+2x_2$

$MRS=\frac{6x_1^{1.6}x_2^{0.4}}{4x_1^{0.6}x_2^{1.4}}$

$(\frac{3}{2})(\frac{x_2}{x_1})=\frac{10}{20}$

$x_2=0.33x_1$

$100=x_1+0.66x_2$

x₁= 60.24

x₂=19.88