Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons

Mohajan, Devajit and Mohajan, Haradhan (2023): Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons. Published in: Journal of Economic Development, Environment, and People , Vol. 12, No. 1 (31 March 2023): pp. 25-40.

Abstract

In this study sensitivity analysis among Lagrange multipliers and commodity coupons is discussed with detailed mathematical analysis. In economics, utility maximization method is essential for increasing sustainable production and profit maximization. Two types of constraints, such as budget constraint, and coupon constraint are used to operate sensitivity analysis; consequently, two Lagrange multipliers are applied for the detailed mathematical analysis.

• Item Type: MPRA Paper
• Language: English
• Keywords: Lagrange multipliers, commodity coupon, 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 > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; 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; I - Health, Education, and Welfare > I3 - Welfare, Well-Being, and Poverty > I31 - General Welfare, Well-Being

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.

Blessing, L. T. M., Chakrabarti, A., & Wallace, K. M. (1998). An Overview of Descriptive Studies in Relation to a General Design Research Methodology. In E. Frankenberger, P. Badke-Schaub & H. Birkhofer (Eds.), Designers: The Key to Successful product Development. Berlin: Springer Verlag.

Castro, L. C., & Araujo, A. S. (2019). Marginal Utility & Its Diminishing Methods. International Journal of Tax Economics and Management, 2(6), 36-47.

Cobb, C. W., & Douglass, P. H. (1928). A Theory of Production. American Economics Review, 18(1), 139-165.

Das, S., & Mohajan, H. K. (2014a). Mock Theta Conjectures. Journal of Environmental Treatment Techniques, 2(1), 22-28.

Das, S., & Mohajan, H. K. (2014b). Generating Functions for X(n) and Y(n). American Review of Mathematics and Statistics, 2(1), 41-43.

Das, S., & Mohajan, H. K. (2014c). The Number of Vector Partitions of n (Counted According to the Weight) with Crank m. International Journal of Reciprocal Symmetry & Theoretical Physics, 1(2), 91–105.

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.

Fishburn, P. C. (1970). Utility Theory for Decision Making. Huntington, NY: Robert E. Krieger. Gauthier, D. (1975). Reason and Maximization. Canadian Journal of Philosophy, 4(3), 411-433.

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(2), 104-120.

Islam, J. N., Mohajan, H. K., & Datta, R. (2012a). Aspects of Microfinance System of Grameen Bank of Bangladesh. International Journal of Economics and Research, 3(4), 76-96.

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

Islam, J. N., Mohajan, H. K., & Moolio, P. (2012c). Borda Voting is Non-manipulable but Cloning Manipulation is Possible. International Journal of Development Research and Quantitative Techniques, 2(1), 28–37.

Juster, F. T. (1990). Rethinking Utility Theory. The Journal of Behavioral Economics, 19(2), 155-179.

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.

Legesse, B. (2014). Research Methods in Agribusiness and Value Chains. School of Agricultural Economics and Agribusiness, Haramaya University.

Marshall, A. (1920). Principles of Economics (8th Ed.). London: Macmillan.

Mohajan, D., & Mohajan, H. K. (2022a). Mathematical Analysis of SEIR Model to Prevent COVID-19 Pandemic. Journal of Economic Development, Environment and People, 11(4), 5-30.

Mohajan, D., & Mohajan, H. K. (2022b). Utility Maximization Analysis of an Emerging Firm: A Bordered Hessian Approach. Annals of Spiru Haret University. Economic Series, 22(4), 292-308.

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

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

Mohajan, D., & Mohajan, H. K. (2022e). Development of Grounded Theory in Social Sciences: A Qualitative Approach. Studies in Social Science & Humanities, 1(5), 13-24.

Mohajan, D., & Mohajan, H. K. (2022f). Exploration of Coding in Qualitative Data Analysis: Grounded Theory Perspective. Research and Advances in Education, 1(6), 50-60.

Mohajan, D., & Mohajan, H. K. (2022g). Memo Writing Procedures in Grounded Theory Research Methodology. Studies in Social Science & Humanities, 1(4), 10-18.

Mohajan, D., & Mohajan, H. K. (2022h). Constructivist Grounded Theory: A New Research Approach in Social Science. Research and Advances in Education, 1(4), 8-16.

Mohajan, D., & Mohajan, H. K. (2022i). Feminism and Feminist Grounded Theory: A Comprehensive Research Analysis. Journal of Economic Development, Environment and People, 11(3), 49-61.

Mohajan, D., & Mohajan, H. K. (2022j). Profit Maximization Strategy in an Industry: A Sustainable Procedure. Law and Economy, 1(3), 17-43.

Mohajan, D., & Mohajan, H. K. (2023a). Sensitivity Analysis among Commodities and Prices: Utility Maximization Perceptions. Law and Economy, 2(2), 1-16.

Mohajan, D., & Mohajan, H. K. (2023b). Straussian Grounded Theory: An Evolved Variant in Qualitative Research. Studies in Social Science & Humanities, 2(2), 33-40.

Mohajan, D., & Mohajan, H. K. (2023c). Sensitivity Analysis between Lagrange Multipliers and Consumer Coupon: Utility Maximization Perspective. Frontiers in Management Science, 2(1), 14-25.

Mohajan, D., & Mohajan, H. K. (2023d). Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure. Law and Economy, 2(1), 1-15.

Mohajan, D., & Mohajan, H. K. (2023e). Classic Grounded Theory: A Qualitative Research on Human Behavior. Studies in Social Science & Humanities, 2(1), 1-7.

Mohajan, D., & Mohajan, H. K. (2023f). Sensitivity Analysis between Commodity and Budget: Utility Maximization Case. Law and Economy, 2(3), 10-21.

Mohajan, D., & Mohajan, H. K. (2023g). Sensitivity Analysis for Profit Maximization with Respect to Per Unit Cost of Subsidiary Raw Materials. Frontiers in Management Science, 2(2), 13-27.

Mohajan, D., & Mohajan, H. K. (2023h). Families of Grounded Theory: A Theoretical Structure for Novel Researchers. Studies in Social Science & Humanities, 2(1), 56-65.

Mohajan, D., & Mohajan, H. K. (2023i). Broca Index: A Simple Tool to Measure Ideal Body Weight. Innovation in Science and Technology, 2(2), 21–24.

Mohajan, D., & Mohajan, H. K. (2023j). Obesity and Its Related Diseases: A New Escalating Alarming in Global Health. Journal of Innovations in Medical Research, 2(3), 12–23.

Mohajan, D., & Mohajan, H. K. (2023k). Body Mass Index (BMI) is a Popular Anthropometric Tool to Measure Obesity among Adults. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023l). A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023m). Ponderal Index: An Important Anthropometric Indicator for Physical Growth. Unpublished Manuscript.

Mohajan, D., & Mohajan, H. K. (2023n). Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness. Innovation in Science and Technology, 2(2), 38-43.

Mohajan, D., & Mohajan, H. K. (2023o). Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case. Annals of Spiru Haret University. Economic Series, 23(1), 167-185.

Mohajan, D., & Mohajan, H. K. (2023p). Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science. Journal of Economic Development, Environment and People, 12(1), 72-81.

Mohajan, D., & Mohajan, H. K. (2023q). Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint. Studies in Social Science & Humanities, 2(4), 40-64.

Mohajan, D., & Mohajan, H. K. (2023r). Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration. Law and Economy, 2(4), 32-48.

Mohajan, D., & Mohajan, H. K. (2023s). Sensitivity Analysis for Profit Maximization with Respect to Per Unit Cost of Subsidiary Raw Materials. Frontiers in Management Science, 2(2), 13–27.

Mohajan, H. K. (2011a). Greenhouse Gas Emissions Increase Global Warming. International Journal of Economic and Political Integration, 1(2), 21-34.

Mohajan, H. K. (2011b). The NNP and Sustainability in Open Economy: Highlights on Recent World Economy and on Open Economy of Bangladesh. KASBIT Business Journal, 4(2), 32–47.

Mohajan, H. K. (2011c). Optimal Environmental Taxes Due to Health Effect. KASBIT Business Journal, 4(1), 1–19.

Mohajan, H. K. (2012a). 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. (2012b). Aspects of Green Marketing: A Prospect for Bangladesh. International Journal of Economics and Research, 3(3), 1-11.

Mohajan, H. K. (2012c). Importance of Green Marketing at Present and Future. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2012d). Greenhouse Gas Emissions of the USA. Indus Journal of Management & Social Sciences, 6(2), 132-148.

Mohajan, H. K. (2012e). Relation between Lease Finance and Purchase. International Journal of Economics and Research, 3(3), 146–158.

Mohajan, H. K. (2012f). Air Pollution Causes Health Effects and Net National Product of a Country Decreases: A Theoretical Framework. International Journal of Development Research and Quantitative Techniques, 2(2), 3–10.

Mohajan, H. K. (2013a). Economic Development of Bangladesh. Journal of Business Management and Administration, 1(4), 41-48.

Mohajan, H. K. (2013b). Ethiopia: A Socio-economic Study. Journal of Business Management and Administration, 1(5), 59-74.

Mohajan, H. K. (2013c). Friedmann, Robertson-Walker (FRW) Models in Cosmology. Journal of Environmental Treatment Techniques, 1(3), 158-164.

Mohajan, H. K. (2013d). Global Greenhouse Gas Emissions and Climate Change. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2013e). Poverty and Economic Development of Kenya. International Journal of Information Technology and Business Management, 18(1), 72-82.

Mohajan, H. K. (2013f). Global Food Price Hike is a Burden to the Poor. International Journal of Information Technology and Business Management, 19(1), 1–15.

Mohajan, H. K. (2013g). Food, Agriculture and Economic Situation of Bangladesh. MPRA Paper No. 54240. https://mpra.ub.uni-muenchen.de/54240/

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

Mohajan, H. K. (2014b). Chinese Sulphur Dioxide Emissions and Local Environment Pollution. International Journal of Scientific Research in Knowledge, 2(6), 265-276.

Mohajan, H. K. (2014c). The Most Fatal 2014 Outbreak of Ebolavirus Disease in Western Africa. American Journal of Epidemiology and Infectious Disease, 2(4), 101-108.

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

Mohajan, H. K. (2014e). Food and Nutrition of Bangladesh. Peak Journal of Food Science and Technology, 2(1), 1-17.

Mohajan, H. K. (2014f). Gravitational Collapse of a Massive Star and Black Hole Formation. International Journal of Reciprocal Symmetry & Theoretical Physics, 1(2), 125–140.

Mohajan, H. K. (2014g). General Upper Limit of the Age of the Universe. ARPN Journal of Science and Technology, 4(1), 4–12.

Mohajan, H. K. (2015a). Sustainable Development Policy of Global Economy. American Journal of Environmental Protection, 3(1), 12-29.

Mohajan, H. K. (2015b). Present and Future of Nestlé Bangladesh Limited. American Journal of Food and Nutrition, 3(2), 34-43.

Mohajan, H. K. (2015c). Basic Concepts of Differential Geometry and Fibre Bundles. ABC Journal of Advanced Research, 4(1), 57-73.

Mohajan, H. K. (2015d). Tuberculosis is a Fatal Disease among Some Developing Countries of the World. American Journal of Infectious Diseases and Microbiology, 3(1), 18-31.

Mohajan, H. K. (2015e). Generalization of Euler and Ramanujan’s Partition Function. Asian Journal of Applied Science and Engineering, 4(3), 167–190.

Mohajan, H. K. (2016a). An Analysis of Knowledge Management for the Development of Global Health. American Journal of Social Sciences, 4(4), 38-57.

Mohajan, H. K. (2016b). Global Hyperbolicity in Space-time Manifold. International Journal of Professional Studies, 1(1), 14–30.

Mohajan, H. K. (2016c). Singularities in Global Hyperbolic Space-time Manifold. Asian Journal of Applied Science and Engineering, 5(1), 41–58.

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

Mohajan, H. K. (2017d). A Brief Analysis of de Sitter Universe in Relativistic Cosmology. Journal of Scientific Achievements, 2(11), 1–17.

Mohajan, H. K. (2017e). Development of Einstein’s Static Cosmological Model of the Universe. Journal of Scientific Achievements, 2(7), 18-30.

Mohajan, H. K. (2017f). Analysis of Reciprocity and Substitution Theorems, and Slutsky Equation. Noble International Journal of Economics and Financial Research, 2(3), 54–75.

Mohajan, H. K. (2018a). Qualitative Research Methodology in Social Sciences and Related Subjects. Journal of Economic Development, Environment and People, 2(1), 19-46.

Mohajan, H. K. (2018b). Aspects of Mathematical Economics, Social Choice and Game Theory. PhD Dissertation, Jamal Nazrul Islam Research Centre for Mathematical and Physical Sciences (JNIRCMPS), University of Chittagong, Chittagong, Bangladesh.

Mohajan, H. K. (2018c). The Rohingya Muslims in Myanmar are Victim of Genocide! ABC Journal of Advanced Research, 7(1), 59-72.

Mohajan, H. K. (2018d). Medical Errors Must be Reduced for the Welfare of the Global Health Sector. International Journal of Public Health and Health Systems, 3(5), 91-101.

Mohajan, H. K. (2018e). Analysis of Food Production and Poverty Reduction of Bangladesh. Annals of Spiru Haret University Economic Series, 18(1), 191–205.

Mohajan, H. K. (2020a). Quantitative Research: A Successful Investigation in Natural and Social Sciences. Journal of Economic Development, Environment and People, 9(4), 50–79.

Mohajan, H. K. (2020b). COVID-19–The Most Fatal Pandemic Outbreak: An Analysis of Economic Consequences. Annals of Spiru Haret University Economic Series, 20(2), 127-146.

Mohajan, H. K. (2020c). The COVID-19 in Italy: Remedies to Reduce the Infections and Deaths. Malaysian Journal of Medical and Biological Research, 7(2), 59-66.

Mohajan, H. K. (2020d). Most Fatal Pandemic COVID-19 Outbreak: An Analysis of Economic Consequences. Annals of Spiru Haret University Economic Series, 20(2), 127-146.

Mohajan, H. K. (2020e). Circular Economy can Provide a Sustainable Global Society. Journal of Economic Development, Environment and People, 9(3), 38-62.

Mohajan, H. K. (2021a). Aspects of Global COVID-19 Pandemic. Lambert Academic Publishing, Germany.

Mohajan, H. K. (2021b). Global COVID-19 Pandemic: Prevention and Protection Techniques. Journal of Economic Development, Environment and People, 10(1), 51-72.

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. (2021d). 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. (2021e). Third Industrial Revolution Brings Global Development. Journal of Social Sciences and Humanities, 7(4), 239-251.

Mohajan, H. K. (2022a). Four Waves of Feminism: A Blessing for Global Humanity. Studies in Social Science & Humanities, 1(2), 1-8.

Mohajan, H. K. (2022b). An Overview on the Feminism and Its Categories. Research and Advances in Education, 1(3), 11-26.

Mohajan, H. K. (2022c). Cost Minimization Analysis of a Running Firm with Economic Policy. Annals of Spiru Haret University. Economic Series, 22(3), 317-337.

Mohajan, H. K. (2022d). Mathematical Analysis of SIR Model for COVID-19 Transmission. Journal of Innovations in Medical Research, 1(2), 1-18.

Mohajan, H. K., Datta, R., & Das, A. K. (2012). Emerging Equity Market and Economic Development: Bangladesh Perspective. International Journal of Economics and Research, 3(3), 128-145.

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.

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

Polit, D. F., & Hungler, B. P. (2013). Essentials of Nursing Research: Methods, Appraisal, and Utilization (8th Ed.). Philadelphia: Wolters Kluwer/Lippincott Williams and Wilkins.

Rahman, M. M., & Mohajan, H. K. (2019). Rohingya-The Stateless Community Becoming the Lost Generation. Journal of Economic Development, Environment and People, 8(2), 24-36.

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.