Sensitivity Analysis between Lagrange Multipliers and Consumer Coupon: Utility Maximization Perspective

Mohajan, Devajit and Mohajan, Haradhan (2022): Sensitivity Analysis between Lagrange Multipliers and Consumer Coupon: Utility Maximization Perspective. Published in: Frontiers in Management , Vol. 2, No. 1 (17 January 2023): pp. 14-25.

Abstract

Sensitivity analysis is a vital concept in optimization models. From this analysis an economist can predict on the outcome of an economic model by the use of certain range of input variables. Utility maximization policy is essential for the sustainability of the economic organizations. This study takes an attempt to discuss sensitivity analysis between Lagrange multipliers and consumer coupon, where utility maximization is analyzed with detail mathematical analysis. In the study method of Lagrange multipliers is used to investigate the utility function; subject to two constraints: budget constraint, and coupon constraint. Moreover, two Lagrange multipliers are used here with four commodity variables.

• Item Type: MPRA Paper
• Language: English
• Keywords: Coupon, consumers, Lagrange multipliers, sensitivity analysis, utility maximization
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models; L - Industrial Organization > L7 - Industry Studies: Primary Products and Construction

References

Baxley, J. V., & Moorhouse, J. C. (1984). Lagrange Multiplier Problems in Economics. The American Mathematical Monthly, 91(7), 404-412.

Bentham, J. (1780). An Introduction to the Principles of Morals and Legislation. CreateSpace Independent Publishing Platform.

Coleman, J. S. & Fararo, T. J. (1992). Rational Choice Theory. Nueva York: Sage.

Eaton, B., & Lipsey, R. (1975). The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition. Review of Economic Studies, 42(1), 27-49.

Ferdous, J., & Mohajan, H. K. (2022). Maximum Profit Ensured for Industry Sustainability. Annals of Spiru Haret University. Economic Series, 22(3), 317-337.

Hu, Y., Imkeller, P., & Müller, M. (2005). Utility Maximization in Incomplete Markets. The Annals of Applied Probability, 15(3), 1691-1712.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2009a). Preference of Social Choice in Mathematical Economics. Indus Journal of Management & Social Sciences, 3(1), 17-38.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2009b). Political Economy and Social Welfare with Voting Procedure. KASBIT Business Journal, 2(1), 42-66.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2010). Utility Maximization Subject to Multiple Constraints. Indus Journal of Management & Social Sciences, 4(1), 15-29.

Islam, J. N., Mohajan, H. K., & Moolio, P. (2011). Output Maximization Subject to a Nonlinear Constraint. KASBIT Business Journal, 4(1), 116-128.

Islam, J. N., Mohajan, H. K., & Datta, R. (2012). Stress Management Policy Analysis: A Preventative Approach. International Journal of Economics and Research, 3(6), 1-17.

Kirsh, Y. (2017). Utility and Happiness in a Prosperous Society. Working Paper Series, No. 37-2017, Institute for Policy Analysis, The Open University of Israel.

Kothari, C. R. (2008). Research Methodology: Methods and Techniques (2nd Ed.). New Delhi: New Age International (P) Ltd.

Mohajan, D., & Mohajan, H. K. (2022a). Profit Maximization Strategy in an Industry: A Sustainable Procedure. Law and Economy, 1(3), 17-43. https://doi:10.56397/LE.2022.10.02

Mohajan, D., & Mohajan, H. K. (2022b). Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure. Law and Economy, 2(1), 1-15.

Mohajan, D., & Mohajan, H. K. (2022c). Utility Maximization Investigation: A Bordered Hessian Method. Annals of Spiru Haret University. Economic Series, Manuscript Submitted.

Mohajan, D. & Mohajan, H. K. (2022d). Sensitivity Analysis among Commodities and Prices: Utility Maximization Perspectives (Unpublished Manuscript).

Mohajan, D. & Mohajan, H. K. (2022e). Sensitivity Analysis among Commodities and Coupons during Utility Maximization. Frontiers in Management Science, 1(3), 13-28.

Mohajan, D., & Mohajan, H. K. (2022f). Importance of Total Coupon in Utility Maximization: A Sensitivity Analysis. Law and Economy, 1(5), 65-67.

Mohajan, H. K. (2012). Green Marketing is a Sustainable Marketing System in the Twenty First Century. International Journal of Management and Transformation, 6(2), 23-39.

Mohajan, H. K. (2014a). Greenhouse Gas Emissions of China. Journal of Environmental Treatment Techniques, 1(4), 190-202.

Mohajan, H. K. (2014b). Improvement of Health Sector in Kenya. American Journal of Public Health Research, 2(4), 159-169.

Mohajan, H. K. (2017a). Optimization Models in Mathematical Economics. Journal of Scientific Achievements, 2(5), 30-42.

Mohajan, H. K. (2017b). Two Criteria for Good Measurements in Research: Validity and Reliability. Annals of Spiru Haret University. Economic Series, 17(3), 58-82.

Mohajan, H. K. (2017c). Roles of Communities of Practice for the Development of the Society. Journal of Economic Development, Environment and People, 6(3), 27-46.

Mohajan, H. K. (2018a). Aspects of Mathematical Economics, Social Choice and Game Theory. PhD Dissertation. University of Chittagong, Chittagong, Bangladesh.

Mohajan, H. K. (2018b). Qualitative Research Methodology in Social Sciences and Related Subjects. Journal of Economic Development, Environment and People, 7(1), 23-48.

Mohajan, H. K. (2020). Quantitative Research: A Successful Investigation in Natural and Social Sciences. Journal of Economic Development, Environment and People, 9(4), 52-79.

Mohajan, H. K. (2021a). Utility Maximization of Bangladeshi Consumers within Their Budget: A Mathematical Procedure. Journal of Economic Development, Environment and People, 10(3), 60-85.

Mohajan, H. K. (2021b). Product Maximization Techniques of a Factory of Bangladesh: A Sustainable Procedure. American Journal of Economics, Finance and Management, 5(2), 23-44.

Mohajan, H. K. (2021c). Estimation of Cost Minimization of Garments Sector by Cobb-Douglass Production Function: Bangladesh Perspective. Annals of Spiru Haret University. Economic Series, 21(2), 267-299.

Mohajan, H. K. (2022a). Cost Minimization Analysis of a Running Firm with Economic Policy. Annals of Spiru Haret University. Economic Series, 22(3), 171-181.

Mohajan, H. K. (2022b). An Overview on the Feminism and Its Categories. Research and Advances in Education, 1(3), 11-26. https://doi.org/10.56397/RAE.2022.09.02

Mohajan, H. K. (2022c). Four Waves of Feminism: A Blessing for Global Humanity. Studies in Social Science & Humanities, 1(2), 1-8. https://doi:10.56397/SSSH.2022.09.01

Mohajan, H. K., Islam, J. N., & Moolio, P. (2013). Optimization and Social Welfare in Economics. Lambert Academic Publishing, Germany.

Moolio, P., Islam, J. N., & Mohajan, H. K. (2009). Output Maximization of an Agency. Indus Journal of Management and Social Sciences, 3(1), 39-51.

Ojo, S. O. (2003). Productivity and Technical Efficiency of Poultry Egg Production in Nigeria. International Journal of Poultry Science, 2(6), 459-464.

Pandey, P., & Pandey, M. M. (2015). Research Methodology: Tools and Techniques. Bridge Center, Romania, European Union.

Pandi, S. N, Torsen, E., Martins, D., & Modibbo, U. M. (2022). Application of the Techniques of Determinants to the Utility Maximization for a 4-Period Age-specific Inter-temporal Budget Constraints: Determinants to the Utility Maximization. Journal of Computational and Cognitive Engineering. https://doi.org/10.47852/bonviewJCCE2202353

Roy, L., Molla, R., & Mohajan, H. K. (2021). Cost Minimization is Essential for the Sustainable Development of an Industry: A Mathematical Economic Model Approach. Annals of Spiru Haret University. Economic Series, 21(1), 37-69.

Samuelson, P. A. (1947). Foundations of Economic Analysis. Harvard University Press, Cambridge, MA.

Zheng, K., & Liu, Y. (2022). Application of Mathematical Models in Economic Variable Input and Output Models under the Scientific Visualization. Computational Intelligence and Neuroscience. Article ID 6269358.