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

Vedran Kojić () and Zrinka Lukač ()
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Vedran Kojić: Faculty of Economics and Business, University of Zagreb
Zrinka Lukač: Faculty of Economics and Business, University of Zagreb

No 1403, EFZG Working Papers Series from 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 (search for similar items in EconPapers)
JEL-codes: C61 C65 D24 (search for similar items in EconPapers)
Pages: 11
Date: 2014-06-02
New Economics Papers: this item is included in nep-eff
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http://web.efzg.hr/repec/pdf/Clanak%2014-03.pdf First version, 2014 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:zag:wpaper:1403

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