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Solving the utility maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities

Author

Listed:
  • Vedran Kojić

    (Faculty of Economics and Business, University of Zagreb)

Abstract

This paper presents a new, non-calculus approach to solving the utility maximization problem with CES utility function, as well as with Cobb-Douglas utility function in case of n≥2 commodities. Instead of using the Lagrange multiplier method or some other method based on differential calculus, these two maximization problems are solved by using Jensen's inequlity and weighted arithmetic-geometric mean (weighted AM-GM) inequality. In comparison with calculus methods, this approach does not require checking the first and the second order conditions.

Suggested Citation

  • Vedran Kojić, 2015. "Solving the utility maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities," EFZG Working Papers Series 1504, Faculty of Economics and Business, University of Zagreb.
    • Handle: RePEc:zag:wpaper:1504
    as

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    File URL: http://web.efzg.hr/repec/pdf/Clanak%2015-04.pdf
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    References listed on IDEAS

    as
    1. 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

    Utility maximization problem; CES and Cobb-Douglas utility function; mathematical inequalities; without calculus;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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