#### 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: ${ℝ}^{n}↦ℝ,f\left(v\right)=a\left({\prod }_{j=1}^{n}{x}_{j}^{{\alpha }_{j}}\right),n\ge 1$, 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