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## Didactics of Mathematics

2015 | nr 12 (16) | 61--68
Tytuł artykułu

### Optimization of Consumer Preferences - an Example

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the article we discuss a standard example of an optimization problem. In our problem we are optimizing the objective function, i.e. a consumer utility function with two variables representing quantities of two commodities denoted by x1 and x2. We consider the standard optimization problem in which we maximize the defined utility function subject to a budget constraint. More precisely, the problem is to choose quantities of two commodities 1st and 2nd, in order to maximize u(x1, x2) function subject to the budget constraint. The aim of the article is to present how we can exemplify and solve this kind of problems in a classroom. In the paper we suggest four methods of finding the solution. The first one is based on the graphical interpretation of the problem. Based on this we can get the approximate solution of the defined optimization problem. Then, we present an algebraic approach to find the optimum solution of the given problem. In the first method we use the budget constraint to transform the utility function of two variables into the function of one variable. The second algebraic method of achieving the solution is based on the second Goosen's law, which is known as the law of marginal utility theory. In the third algebraic method applied to find the maximum of the utility function, we use the Lagrange multipliers. The text emphasizes the educational aspect of the theory of consumer choice.(original abstract)
Słowa kluczowe
EN
PL
Czasopismo
Rocznik
Numer
Strony
61--68
Opis fizyczny
Twórcy
autor
• University of Rzeszów, Poland
autor
• Marshal Office of the Podkarpackie Region
Bibliografia
• Arfken G. (1985). Lagrange multipliers. In: Mathematical Methods for Physicists. 3ed edition. Academic Press. Orlando. Pp. 945-950.
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• Chiang A.C. (1984). Fundamental Methods of Mathematical Economics. 3ed edition. McGraw-Hill.
• Clavien C., Chapuisat M. (2015). The evolution of utility functions and psychological altruism. Studies in History and Philosophy of Biological and Biomedical Sciences. Pp. 1-8. http://dx.doi.org/10.1016/j.shpsc.2015.10.008 [in press].
• Dean M. (2009). Consumer theory. Lecture Notes for Fall 2009. Introductory Microeconomics. Brown University. Pp. 1-34.
• Fura B. (2012). Equilibrium in the Analysis of the Keynesian Model of National Income Using Active Teaching Methods. In: Didactics at Higher Education Institutions - efficiency of new methods of education. MITEL. Rzeszów. Pp. 117-135.
• Gossen H.H. (1983). The Laws of Human Relations and the Rules of Human Action Derived Therefrom. The MIT Press. London. Pp. 6, 53.
• Hagendorf K. (2010). A Critique of Gossen's Fundamental Theorem of the Theory of Pleasure. Université Paris Ouest - Nanterre. La Défense. Pp. 1-30. Available: http://ssrn.com/abstract=1615522 or http://dx.doi.org/10.2139/ssrn.1615522.
• Negishi T. (2014). History of Economic Theory. Elsevier Science. Publisher B.V., North Holland-Amsterdam-New York-Oxford-Tokyo.
• Rima I.H. (ed.) (2001). Development of Economic Analysis. 6th edition. Routledge. London. New York. Pp. 213-215.
• van Daal J. (2012). The Entwickelung according to Gossen. In: J.G. Backhaus (ed.). Handbook of the History of Economic Thought. Insights on the Founders of Modern Economics. Springer. Pp. 369-383.
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