The Minimal-Time Growth Problem and 'Very Strong' Turnpike Theorem

• Autorzy: Emil Panek
• Języki publikacji: EN

Abstrakty

EN

This paper refers to the author's previous work, in which the 'weak' turnpike theorem in the stationary Gale economy was proved. This theorem states that each optimal growth process {y*(t)}t*1t=0 that leads the economy in the shortest possible time t*1 from the (initial) state of y0 to the set of target/postulated states Y1 almost always runs in the neighbourhood of the production turnpike, where the economy remains in a specific dynamic equilibrium (peak growth equilibrium). This paper presents a proof of the 'very strong' turnpike theorem in the stationary Gale economy, which states that if the optimal process (the solution to the minimaltime growth problem) reaches a turnpike in a certain period of time tˇ < t*1 - 1, then it stays on it everywhere else, except for, at most, final period t*1. The obtained result confirms the wellknown Samuelson hypothesis about the specific turnpike stability of optimal growth paths in multiproduct/multisectoral von Neumann-Leontief-Gale-type models, also in the case where the growth criterion is not the (normally assumed) utility of production but the time needed by the economy to achieve the postulated target level or volume of production. (original abstract)

Słowa kluczowe

PL

Gospodarka; Równowaga gospodarcza; Analiza ścieżkowa; Model wzrostu gospodarczego; Funkcja produkcji; Ekonomia matematyczna; Matematyczne modele ekonomiczne

EN

Economy; Economic equilibrium; Path analysis; Economic growth model; Production function; Mathematical economics; Mathematical economic models

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2021
• Tom: 68
• Numer: z. 4
• Strony: 45-58

Twórcy

autor

Emil Panek

• University of Zielona Góra, Poland

Bibliografia

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Identyfikatory

DOI

10.5604/01.3001.0015.7799