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On application of Newton’s Method to solve optimization problems in the consumer theory. Expansion’s Paths and Engel Curves

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Strasburger A., Zembrzuski A.
Metody Ilościowe w Badaniach Ekonomicznych
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2011
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vol. 12
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issue 1
135-146
EN
The paper continues investigations concerned with numerical modeling of the neoclassical theory of consumption begun in our previous paper [Strasburger et al. (2009)] This time we are interested in expansion’s paths and Engel curves for separable utility functions.. The used numerical procedure is based on Newton’s approximation method, implemented in the MATLAB environment. Based on the prior determination of the approximate solutions of the optimum problem we determine in this paper the expansion paths and Engel curves and compare them with their standard form studied in econometrics.
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WHO WANTS TO WORK LONGER?

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Strasburger A., Zajkowska O.
Metody Ilościowe w Badaniach Ekonomicznych
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2013
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vol. 14
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issue 2
220-228
EN
The observed collapse of demographic pyramid increases the tension on the social security systems, especially pensions. It implies a requirement to extend the retirement age. On the basis of Eurobarometer 65.1 we calculate difference between expected and preferred retirement age in Poland. Then we show the determinants of individual differences. Particular attention is paid to the problem of non-random missing observations.
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Teoretyczne podstawy metody Newtona przybliżonego rozwiązywania równań nieliniowych

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Strasburger A., Tempczyk W.
Metody Ilościowe w Badaniach Ekonomicznych
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2011
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vol. 12
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issue 2
357-364
PL
Artykuł przedstawia podstawowe pojęcia teoretyczne i sformułowania leżące u podstaw wielowymiarowej metody Newtona konstruowania przybliżonych rozwiązań układu równań nieliniowych, a użytej w pracach [Strasburger i inni (2009), Strasburger i inni (2011)] dla modelowania pewnych aspektów teorii konsumpcji. Metoda ta korzysta ze stosunkowo prostych pojęć matematycznych i stanowi bardzo elastyczne narzędzie zarówno do rozważań teoretycznych jak i obliczeń numerycznych. Metoda ta z pewnością zasługuje na to, by być lepiej znaną w społeczności ekonomistów matematycznych.
EN
The paper surveys basic theoretical concepts and formulations underlying the multidimensional Newton’s method of constructing approximate solutions to systems of nonlinear equations., which was used in the papers [Strasburger et al. (2009), Strasburger et al. (2011)] for modeling certain aspects of consumer’s theory. This method is based on relatively simple mathematical concepts and is a very flexible tool for both theoretical arguments as well as for numerical computations. It certainly deserves to be better known in the community of mathematical economists.
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