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Optimization Models in Mathematical Economics

Author

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  • Mohajan, Haradhan

Abstract

The method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In this paper interpretation of Lagrange multipliers is given by showing their positive values. Three models on optimization are given with detailed mathematical calculations. The Implicit Function Theorem is important for solving a system of non-linear equations for the dependent variables and calculating partial derivatives of these variables with respect to the independent variables. In this paper an attempt has been made to optimize economic models subject to a budget constraint, using Lagrange multipliers technique, as well as, using necessary and sufficient conditions for optimal value.

Suggested Citation

  • Mohajan, Haradhan, 2017. "Optimization Models in Mathematical Economics," MPRA Paper 83185, University Library of Munich, Germany, revised 11 Apr 2017.
    • Handle: RePEc:pra:mprapa:83185
    as

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    File URL: https://mpra.ub.uni-muenchen.de/83185/1/MPRA_paper_83185.pdf
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    References listed on IDEAS

    as
    1. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2010. "Utility Maximization Subject to Multiple Constraints," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 4(1), pages 15-29, December.
    2. repec:ksb:journl:v:4:y:2011:i:1:p:116-128 is not listed on IDEAS
    3. Jamal NazrulIslam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2011. "Output Maximization Subject to a Nonlinear Constraint," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 4, pages 116-128, December.
    4. Pahlaj Moolio & Jamal Nazrul Islam & Haradhan Kumar Mohajan, 2009. "Output Maximization of an Agency," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 39-51, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Lagrange multipliers; optimization; comparative static analysis; necessary and sufficient conditions;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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