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An alternative approach to solving cost minimization problem with Cobb–Douglas technology

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  • Vedran Kojić

    (University of Zagreb)

  • Zrinka Lukač

    (University of Zagreb)

Abstract

We propose a new method for solving the production cost minimization problem with Cobb–Douglas technology. The method is based on weighted arithmetic–geometric-mean inequality (weighted AM–GM) and it does not use calculus. In comparison to methods which use calculus (like substitution method or the Lagrange multiplier method), our method derives the global minimum costs and unique global minimizer in case of the Cobb–Douglas production function in a new and easier manner. Another benefit of this method is that it derives the exact formula for the optimal level of inputs as well as the formula for minimum costs in general case of $$n>2$$ n > 2 inputs. Also, it is important to emphasize that our method does not require checking the first and the second order conditions, which is a necessary step in methods using calculus. The result is first derived for the case of two inputs and then generalized for the problem with $$n>2$$ n > 2 inputs.

Suggested Citation

  • Vedran Kojić & Zrinka Lukač, 2018. "An alternative approach to solving cost minimization problem with Cobb–Douglas technology," 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. 26(3), pages 629-643, September.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:3:d:10.1007_s10100-017-0519-2
    DOI: 10.1007/s10100-017-0519-2
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    References listed on IDEAS

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    1. R. J. Duffin, 1962. "Cost Minimization Problems Treated by Geometric Means," Operations Research, INFORMS, vol. 10(5), pages 668-675, October.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    3. 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.
    4. 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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