Browsing by Author "Panek, Emil"
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Item Makroekonomiczne problemy sterowania optymalnego w matematycznej teorii wzrostu(Wydział Prawa i Administracji UAM, 1984) Panek, EmilThe work presents three tasks of optimum control of growth in a one-sector economy with a two-factor function of production of Cobb and Douglas, differing in assumptions on national income growth and consumption. Maximalization of consumption in a fixed period of time serves as a growth criterion in the first two tasks. In the third one the growth criterion being time necessary for the economy to reach a target level of consumption goods production. A certain group of conditions eliminating discontinuities („leaps") in the national income distribution revealed in the solutions of the preceding tasks was introduced here. On the marigin of the reached solutions, the author touches on certain general, as it seems, regularities, which are ruling optimum processes of growth in the long run.Item OPTYMALNA PROGRESJA PODATKOWA(Wydział Prawa i Administracji UAM, 2006) Panek, Emil; Kliber, PawełIn this paper we try to find the optimal income tax system. The government must collect a certain amount of tax. The society consists of people with different wealth. The problem is to find an appropriate tax rate for every level of wealth so that the total social utility (measured as the sum of the personal utilities) is maximised. We consider two different tax models - a static one and a dynamic one. It turns out that the best tax system is progressive. However, if we consider its dynamics, we find that such a system should offer large tax reliefs for investments.Item Optymalny podział inwestycji między dwa sektory — wyniki badań empirycznych(Wydział Prawa i Administracji UAM, 1987) Panek, EmilThe paper is composed of two parts. In the first, theoretical one, the author presents the Leontief dynamic model and investigates the variants of the solution of the problem of optimum distribution of investment between sectors in the two-sector version of that model. The solution is obtained by means of the Pontriagin maximum principle. In the second, empirical part, the author presents the results of calculations made on the basis of statistical data concerning Poland in the years 1965 - 1975. The author critically evaluates economically unrealistic variants of solution which postulat sudden "switches" in the distribution of investment between sectors. In the author's opinion, fully realistic processes taking place in real economies are characterized by "smooth" trajectories of investments and consumption. He shows that if the rules of investments distribution between sectors resulting from that solution had been applied in years 1965 -1975, a higher level of production of means of production and similar level of production of consumption goods would have been achieved. The author indicates that in view of the above solutions the leading plans of socio-economic development formulated on the highest level of authority should cover longer periods than the five-year-ones.