9. Differentiation: Functions of Several Variables

In this chapter we shall extend the concept and methods of differentiation to functions of several variables. Most economic relationships involve more than one variable and their analysis require the methods of this chapter. In addition, many economic models consist of several equations. Tracing the effect of a change in one variable in an equation throughout the model is a preoccupation of economics. In later sections we shall learn how to solve such problems. Differentiation plays an important role in statistics and econometrics as well. In particular, derivation of least squares and maximum likelihood estimators rely on differentiation. Differentiation of functions of several variables brings up the issues of continuity and differentiability. We discussed these subjects in the previous chapters and their extension to the case of functions of several variables, using notations developed in this chapter, is straightforward. Therefore, we will not revisit these topics in this chapter.