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Solving the production cost minimization problem with the Cobb – Douglas production function without the use of derivatives

Vedran Kojić ; Faculty of Economics and Business, University of Zagreb
Zrinka Lukač orcid.org/0000-0003-2986-6345 ; Faculty of Economics and Business, University of Zagreb

Abstract

In this paper, we propose a new original method to solve the production cost minimization problem with Cobb-Douglas production function by using the weighted arithmetic-geometric-mean inequality (weighted AM-GM inequality). Instead of using derivatives or the Lagrange multiplier method, the minimum costs and global minimizers in the case of the Cobb-Douglas production function are derived in the direct way. The result is first derived for the case of two inputs and then generalized for the problem with n inputs.

Keywords

global optimization; Cobb-Douglas technology; without derivatives; arithmetic mean; geometric mean

Hrčak ID:

136629

URI

https://hrcak.srce.hr/136629

Publication date:

2.6.2014.

Article data in other languages: croatian

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