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Analysis of Reciprocity and Substitution Theorems, and Slutsky Equation

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  • Mohajan, Haradhan

Abstract

The mathematical techniques are considered here to explain the economical problems. This article deals with the Substitution and Reciprocity Theorems for the various commodities. Finally, it also has considered the Slutsky Equation for the minimization of the prices and the budget constraints. The study has included analysis of some explicit examples to clarify the concepts of the results. The aim of this paper is to make the mathematical concepts interesting to the economists. An attempt has been taken here to discuss the problems in some detailed mathematical analysis in an elegant manner.

Suggested Citation

  • Mohajan, Haradhan, 2017. "Analysis of Reciprocity and Substitution Theorems, and Slutsky Equation," MPRA Paper 82938, University Library of Munich, Germany, revised 05 Feb 2017.
    • Handle: RePEc:pra:mprapa:82938
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    References listed on IDEAS

    as
    1. Falk, Armin & Fischbacher, Urs, 2006. "A theory of reciprocity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 293-315, February.
    2. 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.
    3. Stanca, Luca, 2009. "Measuring indirect reciprocity: Whose back do we scratch?," Journal of Economic Psychology, Elsevier, vol. 30(2), pages 190-202, April.
    4. Cassels,J. W. S., 1981. "Economics for Mathematicians," Cambridge Books, Cambridge University Press, number 9780521286145, September.
    5. John S. Chipman & Jean-Sébastien Lenfant, 2002. "Slutsky's 1915 Article: How It Came to Be Found and Interpreted," History of Political Economy, Duke University Press, vol. 34(3), pages 553-597, Fall.
    6. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Preference of Social Choice in Mathematical Economics," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 18-38, June.
    7. R. C. Geary, 1950. "A Note on "A Constant-Utility Index of the Cost of Living"," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 18(1), pages 65-66.
    8. Robert Sproule & Ambrose Leung, 2007. "Using the compensating and equivalent variations to define the Slutsky Equation under a discrete price change," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-9.
    9. Christian Weber, 2002. "Linearity, Slutsky symmetry, and a conjecture of Hicks," Economics Bulletin, AccessEcon, vol. 4(12), pages 1-5.
    10. repec:ebl:ecbull:v:4:y:2002:i:12:p:1-5 is not listed on IDEAS
    11. repec:ksb:journl:v:2:y:2009:i:1:p:42-66 is not listed on IDEAS
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor," MPRA Paper 117993, University Library of Munich, Germany, revised 07 May 2023.
    4. 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.
    5. 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.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation," MPRA Paper 117324, University Library of Munich, Germany, revised 27 Mar 2023.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model," MPRA Paper 117158, University Library of Munich, Germany, revised Feb 2023.
    12. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    13. 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.

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    More about this item

    Keywords

    Indifference Hypersurface; Lagrange Multiplier; Utility Function; Reciprocity and Substitution Theorems; Slutsky Equation.;
    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

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