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The minimal-time growth problem and turnpike effect in the stationary Gale economy

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  • Panek Emil

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

Abstract

In mathematical economics there is a number of so called “turnpike theorems” proved mainly on the basis of multiproduct models of economic dynamics. According to these theorems, all optimal paths of economic growth over a long period of time converge to a certain path (turnpike) in which the economy achieves the highest growth rate while remaining in a specific dynamic (von Neumann) equilibrium. The article refers to this trend and presents some properties of optimal growth processes in the Gale-type model of the stationary economy when the quality criterion of growth processes is not the utility of production—which is normally postulated in the turnpike theory—but the time needed by the economy to achieve the desired final state, e.g. the level of production or production value. According to the author’s knowledge, the idea of using time as a criterion for growth in turnpike theory (especially in Gale-type economy) is innovative.It has been proven that changing the growth criterion does not deprive the Gale economy of its asymptotic / turnpike properties.

Suggested Citation

  • Panek Emil, 2021. "The minimal-time growth problem and turnpike effect in the stationary Gale economy," Economics and Business Review, Sciendo, vol. 7(1), pages 7-25, March.
    • Handle: RePEc:vrs:ecobur:v:7:y:2021:i:1:p:7-25:n:3
    DOI: 10.18559/ebr.2021.1.2
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    References listed on IDEAS

    as
    1. Darong DAI & Kunrong SHEN, 2013. "A turnpike theorem involving a modified Golden Rule," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(11(588)), pages 25-40, November.
    2. repec:agr:journl:v:11(588):y:2013:i:11(588):p:25-40 is not listed on IDEAS
    3. Roy Radner, 1961. "Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 98-104.
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    More about this item

    Keywords

    stationary Gale economy; minimum-time growth problem; von Neumann equilibrium; production turnpike—von Neumann ray;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O49 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Other

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