#### 15.4.2 Elasticities of substitution: Cobb-Douglas

The Cobb-Douglas production function or Cobb-Douglas
utility function is a special element of the CES- family for
$\sigma =1$. This
property is advantageous in many economic applications. The general form is:
${\mathbb{R}}^{n}\mapsto \mathbb{R},f\left(v\right)=a\left({\prod}_{j=1}^{n}{x}_{j}^{{\alpha}_{j}}\right),n\ge 1$, where
${\sum}_{j=1}^{n}{\alpha}_{j}$
indicates the degree of homogeneity. u represents the production- or utility- level and
a the technology factor. In the above graph, a graph of the Cobb-Douglas function
$u=a{x}^{{\alpha}_{1}}{y}^{{\alpha}_{2}}$ is
drawn for n=2.

(c) by Christian Bauer

Prof. Dr. Christian Bauer

Chair of monetary economics

Trier University

D-54296 Trier

Tel.: +49 (0)651/201-2743

E-mail: Bauer@uni-trier.de

URL:

https://www.cbauer.de