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Utility maximization analysis of an emerging firm: a bordered Hessian approach

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  • Mohajan, Devajit
  • Mohajan, Haradhan

Abstract

In this paper, method of Lagrange multipliers is used to investigate the utility function; subject to two constraints: budget constraint, and coupon constraint, and to verify that the utility is maximized. An economic model of an emerging firm has been developed here by considering four commodity variables. In the study, determinant of the 6×6 bordered Hessian matrix is operated to verify the utility maximization. Two Lagrangian multipliers are used here, as devices of optimization procedures, during the mathematical calculation. In this article, an attempt has been taken to achieve optimal result by the application of scientific method of optimization.

Suggested Citation

  • Mohajan, Devajit & Mohajan, Haradhan, 2022. "Utility maximization analysis of an emerging firm: a bordered Hessian approach," MPRA Paper 115838, University Library of Munich, Germany, revised 25 Sep 2022.
    • Handle: RePEc:pra:mprapa:115838
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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. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    3. ROY, Lia & MOLLA, Rashed & MOHAJAN, Haradhan Kumar, 2021. "Cost Minimization Is Essential For The Sustainable Development Of An Industry: A Mathematical Economic Model Approach," Annals of Spiru Haret University, Economic Series, Universitatea Spiru Haret, vol. 21(1), pages 37-71.
    4. Mohajan, Haradhan, 2022. "Four Waves of Feminism: A Blessing for Global Humanity," MPRA Paper 114328, University Library of Munich, Germany, revised 09 Jul 2022.
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    6. MOHAJAN, Haradhan Kumar, 2021. "Estimation Of Cost Minimization Of Garments Sector By Cobb-Douglas Production Function: Bangladesh Perspective," Annals of Spiru Haret University, Economic Series, Universitatea Spiru Haret, vol. 21(2), pages 247-267.
    7. 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.
    8. repec:sph:rjedep:v:3:y:2017:i:6:p:27-46 is not listed on IDEAS
    9. Mohajan, Devagit & Mohajan, Haradhan, 2022. "Profit Maximization Strategy in an Industry: A Sustainable Procedure," MPRA Paper 114675, University Library of Munich, Germany, revised 21 Jun 2022.
    10. Haradhan Kumar MOHAJAN, 2017. "Roles Of Communities Of Practice For The Development Of The Society," Journal of Economic Development, Environment and People, Alliance of Central-Eastern European Universities, vol. 6(3), pages 27-46, September.
    11. Mohajan, Devajit & Mohajan, Haradhan, 2022. "Importance of Total Coupon in Utility Maximization: A Sensitivity Analysis," MPRA Paper 115553, University Library of Munich, Germany, revised 17 Sep 2022.
    12. George J. Stigler, 1950. "The Development of Utility Theory. I," Journal of Political Economy, University of Chicago Press, vol. 58, pages 307-307.
    13. Mohajan, Haradhan, 2017. "Optimization Models in Mathematical Economics," MPRA Paper 83185, University Library of Munich, Germany, revised 11 Apr 2017.
    14. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531925, December.
    15. 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.
    16. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Political Economy and Social Welfare with Voting Procedure," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 2, pages 42-66, December.
    17. 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.
    18. 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.
    19. Mohajan, Haradhan, 2013. "Poverty and economic development of Kenya," MPRA Paper 51072, University Library of Munich, Germany, revised 06 Jul 2013.
    20. Mohajan, Haradhan, 2014. "Improvement of Health Sector in Kenya," MPRA Paper 58420, University Library of Munich, Germany, revised 10 Aug 2014.
    21. Mohajan, Haradhan, 2021. "Utility Maximization of Bangladeshi Consumers within Their Budget: A Mathematical Procedure," MPRA Paper 109993, University Library of Munich, Germany, revised 20 Jul 2021.
    22. 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.
    23. Mohajan, Devajit & Mohajan, Haradhan, 2022. "Sensitivity Analysis among Commodities and Coupons during Utility Maximization," MPRA Paper 115554, University Library of Munich, Germany, revised 04 Oct 2022.
    24. Mohajan, Haradhan, 2022. "Cost minimization analysis of a running firm with economic policy," MPRA Paper 114951, University Library of Munich, Germany, revised 04 May 2022.
    25. repec:ksb:journl:v:2:y:2009:i:1:p:42-66 is not listed on IDEAS
    26. Ivan Moscati, 2013. "Were Jevons, Menger, and Walras Really Cardinalists? On the Notion of Measurement in Utility Theory, Psychology, Mathematics, and Other Disciplines, 1870-1910," History of Political Economy, Duke University Press, vol. 45(3), pages 373-414, Fall.
    27. Read, Daniel, 2004. "Utility theory from Jeremy Bentham to Daniel Kahneman," LSE Research Online Documents on Economics 22750, London School of Economics and Political Science, LSE Library.
    28. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262032899, December.
    29. Mohajan, Haradhan, 2011. "Green marketing is a sustainable marketing system in the twenty first century," MPRA Paper 50857, University Library of Munich, Germany, revised 16 Feb 2012.
    30. Mohajan, Haradhan, 2021. "Product Maximization Techniques of a Factory of Bangladesh: A Sustainable Procedure," MPRA Paper 108094, University Library of Munich, Germany, revised 15 May 2021.
    31. Islam, Jamal & Mohajan, Haradhan & Datta, Rajib, 2012. "Stress management policy analysis: a preventative approach," MPRA Paper 50698, University Library of Munich, Germany, revised 02 Mar 2012.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint," MPRA Paper 116879, University Library of Munich, Germany, revised 12 Feb 2023.
    2. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Various Problems Arise in Industrial Economics If Wage Rate Increases: A Study for Nonlinear Budget Constraint," MPRA Paper 117553, University Library of Munich, Germany, revised 04 Apr 2023.
    3. Mohajan, Devajit, 2023. "Mathematical Analysis of an Industry When Cost of Principal Raw Materials Increase: A Nonlinear Budget Constraint Attempt," MPRA Paper 118933, University Library of Munich, Germany.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons," MPRA Paper 117077, University Library of Munich, Germany, revised 06 Jan 2023.
    5. Mohajan, Devajit & Mohajan, Haradhan, 2022. "Sensitivity Analysis among Commodities and Prices: A Utility Maximization Perception," MPRA Paper 116232, University Library of Munich, Germany, revised 15 Dec 2022.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases," MPRA Paper 117453, University Library of Munich, Germany, revised 22 Mar 2023.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "The Responses of an Organization for the Increase in Wage Rates: Profit Maximization Cases," MPRA Paper 118238, University Library of Munich, Germany, revised 10 Jun 2023.
    8. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science," MPRA Paper 117017, University Library of Munich, Germany, revised 20 Feb 2023.
    9. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Effects of Various Inputs for Increased Interest Rate of Capital: A Nonlinear Budget Constraint Consideration," MPRA Paper 118134, University Library of Munich, Germany, revised 06 May 2023.
    10. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Broca Index: A Simple Tool to Measure Ideal Body Weight," MPRA Paper 116852, University Library of Munich, Germany, revised 18 Jan 2023.
    11. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    12. Mohajan, Devajit & Mohajan, Haradhan, 2023. "An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint," MPRA Paper 118176, University Library of Munich, Germany, revised 05 May 2023.
    13. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    14. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case," MPRA Paper 116907, University Library of Munich, Germany, revised 19 Feb 2023.
    15. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget," MPRA Paper 117299, University Library of Munich, Germany, revised 17 Mar 2023.
    16. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Obesity and Its Related Diseases: A New Escalating Alarming in Global Health," MPRA Paper 116797, University Library of Munich, Germany, revised 05 Feb 2023.
    17. Mohajan, Devajit & Mohajan, Haradhan, 2022. "Sensitivity Analysis between Commodity and Budget: Utility Maximization Case," MPRA Paper 116495, University Library of Munich, Germany, revised 20 Dec 2022.

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    More about this item

    Keywords

    bordered Hessian; commodity; Lagrange multipliers; utility maximization;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • 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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