The Cobb-Douglas Function : Simple Derivations and How Students Might Accept Strange Dimensional-Properties

The Cobb Douglas production function is a central element in economic growth theory and Microeconomics. Its popularity in economics stems from certain convenient mathematical properties. Some of these properties describe a set of (partial) differential equations. Although the Cobb Douglas function is very popular, there exists a discussion in the literature if its analytical form makes sense from a dimensional point of view.This paper provides two interesting aspects: First it supplies two relatively simple derivations of the Cobb Douglas function given the before-mentioned set of (partial) differential equations. Furthermore one classroom-friendly derivation is provided. Thereby this paper gives a simple mathematical argument for perceiving the Cobb Douglas function as a mathematical consequence of assumptions, rather then assuming an ad hoc analytical form of the production function. Second, by perceiving the Cobb Douglas function as the solution of differential equations, the paper sheds some light on the "dimension and economics" discussion. It shows that the Cobb Douglas function has to be meaningful in a units-of-measurement sense given the underlying assumptions. Thus the derivation of the Cobb Douglas function should help students avoid similar misunderstandings