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Cost Minimization is Essential for the Sustainable Development of an Industry: A Mathematical Economic Model Approach

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  • Mohajan, Haradhan

Abstract

The method of Lagrange multiplier is a very useful and powerful technique in multivariable calculus. In this study interpretation of Lagrange multiplier is given with satisfactory mathematical calculations and shows that its value is positive. For the sustainable development of an industry, cost minimization policy is crucial. In any industry the main objective is to minimize production cost for maximizing its profit. By considering Lagrange multiplier technique application an attempt has been taken here in cost minimization problem subject to production function as an output constraint. To predict future performance of an industry, mathematical calculations are necessary and all the procedures are given in this paper with detail mathematical procedures. In this study an attempt has been taken to minimize cost by considering three variables capital, labor, and other inputs of an industry by the application of economic models subject to a budget constraint, using Lagrange multiplier technique, as well as, using necessary and sufficient conditions for minimum value.

Suggested Citation

  • Mohajan, Haradhan, 2021. "Cost Minimization is Essential for the Sustainable Development of an Industry: A Mathematical Economic Model Approach," MPRA Paper 106924, University Library of Munich, Germany, revised 04 Feb 2021.
    • Handle: RePEc:pra:mprapa:106924
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    References listed on IDEAS

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    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. Arrow, Kenneth J. & Dasgupta, Partha & Goulder, Lawrence H. & Mumford, Kevin J. & Oleson, Kirsten, 2012. "Sustainability and the measurement of wealth," Environment and Development Economics, Cambridge University Press, vol. 17(3), pages 317-353, June.
    3. Haradhan Kumar MOHAJAN, 2018. "Qualitative research methodology in social sciences and related subjects," Journal of Economic Development, Environment and People, Alliance of Central-Eastern European Universities, vol. 7(1), pages 23-48, March.
    4. Pahlaj Moolio & Jamal Nazrul Islam, 2008. "Cost Minimization of a Competitive Firm," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 2(2), pages 148-160, December.
    5. Mohajan, Haradhan, 2017. "Optimization Models in Mathematical Economics," MPRA Paper 83185, University Library of Munich, Germany, revised 11 Apr 2017.
    6. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531925, April.
    7. MOHAJAN, Haradhan Kumar, 2017. "Two Criteria For Good Measurements In Research: Validity And Reliability," Annals of Spiru Haret University, Economic Series, Universitatea Spiru Haret, vol. 17(4), pages 59-82.
    8. 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.
    9. Arrow, Kenneth J. & Dasgupta, Partha & Goulder, Lawrence H. & Mumford, Kevin J. & Oleson, Kirsten, 2012. "Sustainability and the measurement of wealth," Environment and Development Economics, Cambridge University Press, vol. 17(3), pages 317-353, June.
    10. Dixit, Avinash K., 1990. "Optimization in Economic Theory," OUP Catalogue, Oxford University Press, edition 2, number 9780198772101.
    11. Mohajan, Haradhan, 2020. "Quantitative Research: A Successful Investigation in Natural and Social Sciences," MPRA Paper 105149, University Library of Munich, Germany, revised 15 Nov 2020.
    12. Mohajan, Haradhan, 2015. "Sustainable Development Policy of Global Economy," MPRA Paper 82815, University Library of Munich, Germany, revised 30 Mar 2015.
    13. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262032899, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Lagrange multiplier; cost minimization; mathematical economical models; sustainability;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models

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