Implicit Functions and Implicit Differentiation Consider a consumer with utility function

u(x1,x2) = x1x2

3b. Write down an identity relating x1, x2(x1) and u*. Implicitly differentiate it and solve for dx2/dx1. Compare your answer to the answer to part a.

3c. The Implicit Function Theorem (Simon and Blume, Theorem 15.1): Let G(x,y) be a continuously differentiable function such that G(x0,y0) = c, and consider the expression G(x,y) = c. If G/y(x0,y0) 0, then there exists a continuously differentiable function y = y(x) defined near (x0,y0) such that:

(1) G(x,y(x)) = c

(2) y(x0) = y0, and

(3) dy/dx = - G/x / G/y at x = x0 and y = y0.

Use the implicit function theorem to derive the slope of an indifference curveubstitution?