Question

1. (20 points) Amy has utility function u(x1, x2) = min{2x₁²x₂, x₁x₂²}. De- rive Amy’s demand function for x₁ and x₂. For what values (if any) of m, p₁, and p₂ are the goods gross complements or gross substitutes of each other?

Answer 1

U=min{ x1^2*x2,x1*x2^2}

The optimal bundle will be where

x1^2*x2=x1*x2^2

x1=x2

M=px1*x1+px2*x2

M=px1*x1+px2*x1

X1=M/(x1+x2)

X2=M/(x1+x2)

Gross complement is when x1 price increase , Decrease demand of x2.so x1 and x2 are gross complement.

As demand function shows x1 and x2 are gross complement and for all values more than zero of M,p1 and p2 both are gross complement