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

Author

Listed:
  • Vedran Kojić

    (Faculty of Economics and Business, University of Zagreb)

  • Zrinka Lukač

    (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.

Suggested Citation

  • Vedran Kojić & Zrinka Lukač, 2014. "Solving the production cost minimization problem with the Cobb – Douglas production function without the use of derivatives," EFZG Working Papers Series 1403, Faculty of Economics and Business, University of Zagreb.
    • Handle: RePEc:zag:wpaper:1403
    as

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    References listed on IDEAS

    as
    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. Liang-Yuh Ouyang & Chun-Tao Chang & Philip Shum, 2012. "The EOQ with defective items and partially permissible delay in payments linked to order quantity derived algebraically," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 141-160, March.
    3. Teng, Jinn-Tsair, 2009. "A simple method to compute economic order quantities," European Journal of Operational Research, Elsevier, vol. 198(1), pages 351-353, October.
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    More about this item

    Keywords

    global optimization; Cobb-Douglas technology; without derivatives; arithmetic mean; geometric mean;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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