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.
Highlights
In the paper Panek (2018) three theorems about turnpikes4 in the non-stationary Gale economy with a technological limit are presented, where a single pro-E
Almost “very strong” multilane turnpike effect in a non-stationary Gale economy 67 duction turnpike was replaced with a bundle of turnpikes
In the first article a non-stationary economy with changing technology and increasing production efficiency over time is dealt with and in the second the proof of a “weak” multiline turnpike theorem in the Gale economy with changing technology and monotonically changing prices is presented
Summary
In the paper Panek (2018) three theorems about turnpikes in the non-stationary Gale economy with a technological limit are presented, where a single pro-. Production processes (x, y) ∈ Z(t)\{0} as well as inputs x and/or outputs y, on a multiline turnpike t in the Gale economy are well-defined up to structure (multiplication by a positive constant). The conclusion can be drawn that at each period the non-stationary Gale economy satisfying conditions (G1)-(G6) reaches its maximal (economic, technological) efficiency only on the turnpike t. { } Every sequence of production vectors {y(t)}t1 which satisfies conditions (9)‐(10) is called a (y0, t1) – feasible growth procet=s0s (production trajectory) in the non-stationary Gale economy with a multiline turnpike and varying technology. All those vectors belong to the turnpike N st This pt=atrticular, single turnpike which starts at period t and extends to the horizon T is called the peak turnpike (peak von Neumann ray) in the non-stationary Gale economy. The contradiction proves that pi(t) > 0. 17 Starting with the period until the end of horizon the prices do not change rapidly
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