Almost “very strong” multilane turnpike effect in a non-stationary Gale economy with a temporary von Neumann equilibrium and price constraints

  • 1 University of Zielona Góra, Institute of Economics and Finance, ul. Podgórna 50, 65-246, Zielona Góra, Poland

Abstract

Mathematical models of economic dynamics and growth are usually expressed in terms of differential equations/inclusions (in the case of continuous time) or difference equations/inclusions (if discrete time is assumed).3 This class of models includes von Neumann-Leontief-Gale type dynamic input-output models to which the paper refers. The paper focuses on the turnpike stability of optimal growth processes in a Gale non-stationary economy with discrete time in the neighbourhood of von Neumann dynamic equilibrium states (so-called growth equilibrium). The paper refers to Panek (2019, 2020) and shows an intermediate result between the strong and very strong turnpike theorem in the non-stationary Gale economy with changing technology assuming that the prices of temporary equilibrium in such an economy (so-called von Neumann prices) do not change rapidly. The aim of the paper is to bring mathematical proof that the introduction of these assumptions making the model more realistic does not change its asymptotic (turnpike-like) properties.

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  • Acemoglu, D. (2009). Introduction to modern economic growth. Princeton and Oxford: Princeton University Press.

  • Deng, L., Fujio, M., & Khan, M. A. (2019). Optimal growth in the Robinson-Shinkai-Leontief model: The case of capital-intensive consumption goods. Studies in Nonlinear Dynamics and Econometrics, 23(4), 1-18.

  • Galor, O. (2010). Discrete dynamical systems. Heidelberg–Dortrecht–London–New York: Springer.

  • Guzowska, M. (2018). Local and global dynamics of Ramsey model. From continuous to discrete time. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(5), 1-29.

  • Makarov, V. L., & Rubinov, A. M. (1977). Mathematical theory of economic dynamic and equilibrium. New York–Heidelberg–Berlin: Springer-Verlag.

  • McKenzie, L. W. (2005). Optimal economic growth, turnpike theorems and comparative dynamics. In K. J. Arrow, M. D. Intriligator (Eds.), Handbook of mathematical economics (2nd ed., vol. 3, chapter 26, pp. 1281-1355). Elsevier.

  • Mitra, T., & Nishimura, K. (Eds.). (2009). Equilibrium, trade and growth. Selected papers of L. W. McKenzie. Cambridge, MA: MIT Press.

  • Nikaido, H. (1968). Convex structures and economic theory. New York: Academic Press.

  • Panek, E. (2003). Ekonomia matematyczna. Poznań: Wydawnictwo Akademii Ekonomicznej w Poznaniu.

  • Panek, E. (2014). O pewnej wersji twierdzenia o magistrali w gospodarce Gale’a ze zmienną technologią. Przegląd Statystyczny, 61(2), 105-114.

  • Panek, E. (2015a). Zakrzywiona magistrala w niestacjonarnej gospodarce Gale’a. Część I. Przegląd Statystyczny, 62(2), 149-163.

  • Panek, E. (2015b). Zakrzywiona magistrala w niestacjonarnej gospodarce Gale’a. Część II. Przegląd Statystyczny, 62(4), 349-360.

  • Panek, E. (2016). Gospodarka Gale’a z wieloma magistralami. „Słaby” efekt magistrali. Przegląd Statystyczny, 63(4), 355-374.

  • Panek, E. (2018). Niestacjonarna gospodarka Gale’a z graniczną technologią i wielopasmową magistralą. „Słaby”, „silny” i „bardzo silny” efekt magistrali. Przegląd Statystyczny, 65(4), 373-393.

  • Panek, E. (2019). Optimal growth processes in non-stationary Gale economy with multilane production turnpike. Economic and Business Review, 5(19), 3-23. doi:10.18559/ebr.2019.2.1.

  • Panek, E. (2020). A multiline turnpike in a non-stationary input-output economy with a temporary von Neumann equilibrium. Przegląd Statystyczny, 67(1) (in press).

  • Radner, R. (1961). Path of economic growth that are optimal with regard to final states: A turnpike theorem. Review of Economic Studies, 28(2), 98-104.

  • Takayama, A. (1985). Mathematical economics. Cambridge: Cambridge University Press.

  • Zalai, E. (2004). The von Neumann model and the early models of general equilibrium. Acta Oeconomica, 54(1), 3-38.

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