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ZALEŻNOŚĆ RYZYKO-DOCHÓD WYBRANYCH SPÓŁEK ODPOWIEDZIALNYCH SPOŁECZNIE

100%
Fura B., Fura M.
Metody Ilościowe w Badaniach Ekonomicznych
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2016
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vol. 17
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issue 3
43-52
PL
Celem artykułu jest określenie relacji: ryzyko-dochód na przy¬kładzie spółek Indeksu RESPECT. Zależność tę przedstawiono na mapie ryzyko-dochód, czyli wykresie korelacyjnym stopy zwrotu i odchylenia standardowego. Punktem odniesienia dla badanej relacji jest Warszawski Indeks Giełdowy, indeks RESPECT i WIG-Poland. Dane empiryczne stanowią miesięczne kursy akcji 23. spółek notowanych na GPW w okresie od 19 listopada 2009 r. do 31 maja 2016 roku.
EN
The aim of this article is to determine the risk-return relationship on the example of RESPECT Index companies. This relationship is presented on the map risk-returs i.e. correlation graph of the rate of return and the standard deviation. The reference point for the study is Warsaw Stock Exchange Index, RESPECT index and WIG-Poland. Empirical data are monthly rates shares of 23 companies listed on the Warsaw Stock Exchange from 19th of November 2009 to 31st of May 2016.
2
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Optimization of consumer preferences – an example

100%
Fura B., Fura M.
Didactics of Mathematics
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2015
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issue 12(16)
61-68
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.
3
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Zasoby pracy w Polsce i Unii Europejskiej w świetle kryzysu demograficznego

100%
Fura M., Fura B.
Nierówności społeczne a wzrost gospodarczy
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2012
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vol. 24
306-315
PL
Artykuł prezentuje wyniki analizy liczby ludności, zasobów pracy, mierników aktywności ekonomicznej w kontekście procesy starzenia się populacji krajów rozwiniętych. Ponadto zwrócono uwagę na kluczowe elementy systemów emerytalnych obowiązujących w wybranych krajach Na tle międzynarodowym została ukazana sytuacja Polski. W konkluzji stwierdzono, że jednym z rozwiązań problemu malejących zasobów pracy wynikających z kryzysu demograficznego jest aktywność zawodowa osób w wieku emerytalnym.
EN
The article presents the analysis of number of the population, the workforce availability and measures of the economic activity in a context of the population aging process observed in developed countries. In the paper the attention was also paid to the key elements of the pensions systems which are valid in chosen European countries. The problems of Polish pension system were presented on the international background. It was affirmed in the conclusion that the professional activity after retirement is one of the solutions of the aging workforce resulting from the demographic crisis.
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