Equilibrium in Economy with Linear Production Sets

• Autorzy: Agnieszka Lipieta , Maria Sadko
• Języki publikacji: EN

Abstrakty

EN

Arrow and Debreu proved that, if in the mathematical model of the economy that they defined some conditions are satisfied, then there is a price system under which there is Walras equilibrium in this economy. We examine a procedure, defined on the basis of a continuous mapping, of transformation of production sets of the Arrow-Debreu economies in which at least one of the assumptions concerning the production sets is not satisfied. Finally, we get a class of Arrow- Debreu economies in which, after modification, there is Walras equilibrium. The research methods are based on the analysis of the linear mappings in real vector space of finite dimension, and the results have the form of mathematical theorems. (original abstract)

Słowa kluczowe

EN

Economic equilibrium; Arrow-Debreu model

PL

Równowaga gospodarcza; Model Arrowa-Debreu

• Czasopismo: Central European Journal of Economic Modelling and Econometrics (CEJEME)
• Rocznik: 2023
• Tom: 15
• Numer: nr 4
• Strony: 287--310

Twórcy

autor

Agnieszka Lipieta

• Cracow University of Economics, Poland

autor

Maria Sadko

• Cracow University of Economics, Poland

Bibliografia

• [1] Arrow K. J., Debreu G., (1954), Existence of an equilibrium for a competitive economy,Econometrica 22, 265-290.
• [2] Arrow K. J., Hurwicz L., (1958), On the stability of the competitive equilibrium I, Econometrica 26, 522-552.
• [3] Arrow K. J., Hurwicz L., (1959), On the stability of the competitive equilibrium II, Econometrica 27, 82-109.
• [4] Arrow K. J., Intriligator M. D., (1987), Handbook of Mathematical Economics Vol. 3, Amsterdam, North-Holland.
• [5] Aumann R. J. (1964), Market with a continuum of traders, Econometrica 32(1-2), 39-50.
• [6] Brouwer L. E. J., (1911), Über Abbildungen von Mannigfaltikeiten, Mathematische Annalen 71, 97-115.
• [7] Cheney E. W., (1966), Introduction to Approximation Theory, Mc Grow Hill, New York.
• [8] Debreu G., (1959), Theory of value, New York, Wiley.
• [9] Denkowska A., Lipieta A., (2022), Optimal demand-driven eco-mechanisms leading to equilibrium in competitive economy, Central European Journal of Economic Modelling and Econometrics 14(3), 225-302.
• [10] Goodwin R., Harris J. M., Nelson J. A., (2018), Microeconomics in Context (fourth edition), Taylor & Franics Ltd.
• [11] Hayek F. A., (1945), The Use of Knowledge in Society, American Economic Review 35(4), 519-530.
• [12] Hurwicz L., Reiter S., (2006), Designing Economic Mechanism, Cambridge University Press, New York.
• [13] Kakutani S., (1939), Some characterization of Euclidean Spaces, Japan J. Math. 16, 93-97.
• [14] Koopmans T. C., (1951), Activity analysis of production and allocation, Wiley, New York.
• [15] Lipieta A., (2010), The Debreu private ownership economy with complementary commodities and prices, Economic Modelling 27, 22-27.
• [16] Lipieta A., (2015), Producers' Adjustment Trajectories Resulting in Equilibrium in the Economy with Linear Consumption Sets, Central European Journal of Economic Modelling and Econometrics 7, 187-204.
• [17] Lipieta A., (2018), The Role of Imitative Mechanisms Within the Economic Evolution, Economics and Business Review 4(4), 64-82.
• [18] Lipieta A., Lipieta A., (2023a), The role of destructive mechanism within economic evolution, Panoeconomicus 70(2), 279-301.
• [19] Lipieta A., Lipieta A., (2023b), Long-run equilibrium in the context of COVID-19 pandemic, Journal of Economic Studies 50(3), 385-406.
• [20] Lipieta A., Malawski A., (2021), Eco-mechanisms within economic evolution: Schumpeterian approach, Journal of Economic Structures 10:4.
• [21] Maćkowiak P., (2010), The existence of equilibrium without fixed-point arguments, Journal of Mathematical Economics 46, 1194-1199.
• [22] Magill M., Quinzii M., (2002), Theory of Incomplete Markets, MIT Press, Cambridge.
• [23] Malawski A., (1999), Metoda aksjomatyczna w ekonomii, Ossolineum, Wrocław.
• [24] Marschak T. A., (1968), Computation In Organizations: Comparison Of Price Mechanisms And Other Adjustment Processes, [in:] Risk and Uncertainty, Proceedings of A Conference held by the International Economic Association Series, [eds.:] K. Borch, J. Mossin, The Macmillan Press LTD, 311-356.
• [25] Mas-Colell A., Whinston M. D., Green J. R., (1995), Microeconomic Theory, Oxford University Press, New York.
• [26] McKenzie L. W., (1959), On the Existence of General Equilibrium for a Competitive Economy, Econometrica 27(1), 54-71.
• [27] Moore J., (2007), General Equilibrium and Welfare Economics, Springer Berlin-Heidelberg-New York.
• [28] Musielak J., (1989), Wstęp do analizy funkcjonalnej, PWN, Warszawa.
• [29] Panek E., (1993), Elementy ekonomii matematycznej - równowaga i wzrost, Wydawnictwo Naukowe PWN, Warszawa.
• [30] Panek E., (1997), Elementy ekonomii matematycznej - statyka, Wydawnictwo Naukowe PWN, Warszawa.
• [31] Sonnenschein H., (1972), Market excess-demand functions, Econometrica 40(3), 549-563
• [32] Sonnenschein H., (1973), Do Walras' identity and continuity characterize the class of community excess-demand functions?, Journal of Economic Theory 6(4), 345-354.
• [33] Tao Y., (2016), Spontaneous economic order, Journal of Evolutionary Economics 26, 467-500.
• [34] Ulman M., (2021), Ekonomia z liniowymi zbiorami produkcji, Master thesis, Krakow University of Economics.
• [35] Walras L., (1874), Éléments d'économie politique pure ou théorie de la richesse sociale, Lausanne: L Corbaz & Cie, Paris: Guillaumin & Cie, Basel: H. Georg, 1874-77.

Identyfikatory

DOI

10.24425/cejeme.2023.149070