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1

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

100%

Panek E.

Economics and Business Review

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2020

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vol. 6(20)

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issue 2

66-80

EN

Mathematical models of economic dynamics and growth are usually expressed in terms of diefrential equations/inclusions (in the case of continuous time) or diefrence equations/inclusions (if discrete time is assumed). 3 hTis class of models includes von Neumann-Leontief-Gale type dynamic input-output models to which the paper refers. eTh 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). eTh 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. eTh 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.

2

Gale Economy with Investments and Limit Technology

75%

Panek E.

Central European Journal of Economic Modelling and Econometrics

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2022

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issue 1

3

Gospodarka Gale'a z wieloma magistralami. „Słaby” efekt magistrali

63%

Panek E.

Przegląd Statystyczny

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2016

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vol. 63

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issue 4

355-374

EN

In the vast literature on turnpike theory it is generally assumed that the model path – called the turnpike – to which in a long time period all the optimal processes are convergent, is uniquely determined. Its geometric image in the Gale’s model (in its stationary version) is a ray in the space of all states of the economy. We call it von Neumann’s ray. In this paper we evade the assumption of the uniqueness of this turnpike (von Neumann’s ray) and study the behaviour of the stationary Gale’s economy with the compact turnpikes’ bundle. We call it multilane turnpike. We present proofs for several variants of the “weak” multilane turnpike theorem in the stationary Gales’ economy.

PL

W bogatej literaturze z teorii magistral zazwyczaj zakłada się, że wzorcowa ścieżka – zwana magistralą – do której w długich okresach czasu zbieżne są wszystkie optymalne procesy wzrostu, jest określona jednoznacznie. W modelu Gale’a (w wersji stacjonarnej) jej obrazem geometrycznym jest półprosta w przestrzeni stanów gospodarki, zwana promieniem von Neumanna. W artykule uchylamy założenie jednoznaczności magistrali (promienia von Neumanna) i badamy zachowanie stacjonarnej gospodarki typu Gale’a ze zwartą wiązką magistral, którą umownie nazywamy magistralą wielopasmową. Prezentujemy dowód kilku wariantów „słabego” twierdzenia o wielopasmowej magistrali w stacjonarnej gospodarce Gale’a.

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1 Central European Journal of Economic Modelling and Econometrics

1 Economics and Business Review

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3 Panek E.

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

Gale Economy with Investments and Limit Technology

Gospodarka Gale'a z wieloma magistralami. „Słaby” efekt magistrali