ECO102 Lecture Notes - Lecture 18: Microeconomics, Implicit Function Theorem, Level Set
Document Summary
The following result about the slope of a level curve is often useful to economists. The result pro- vides another reason for working with homogeneous functions and motivates the use of homothetic functions" (to be de ned at the end of the handout). Result: consider the function y = f (x1, x2) and let f (x1, x2) = c, where c is a constant, denote a level curve of f . Suppose that f is homogeneous of degree k (hod(k)) and. Then the slope of the level curve is a function of the ratio x2/x1. It follows that if we let x2/x1 = t, where t is a constant, then the slope of the level curve is also constant and equal to the number g(t). A simple example is the case where f is cobb-douglas. Consider the function f (x1, x2) = ax where a > 0 and 0 < < 1.
