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On the Existence of a Stationary Optimal Stock for a Multi-sector Economy with Nonconvex Technology

In: Equilibrium and Dynamics

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  • Tapan Mitra

Abstract

In 1967, David Gale’s seminal paper, ‘On Optimal Development in a Multi-Sector Economy’, presented a general result on the existence of optimal programmes over an infinite horizon, when future utilities are not discounted. This paper changed, in a very substantive manner, the way in which economists approached the problems of optimal allocation of resources over time. The question with which the paper concerned itself was, of course, a very challenging one: it had engaged the attention of economists like Ramsey, Samuelson and Solow, Koopmans and Weizsacker, among others, over roughly a forty-year period. But the enduring importance of the paper lies less in the specific ‘answer’ obtained, and more on the techniques used to obtain it. In effect, David Gale showed that the main propositions of optimal growth theory could be established by reasoning, both elegant and compelling, with a few simple results from the theory of convex analysis.

Suggested Citation

  • Tapan Mitra, 1992. "On the Existence of a Stationary Optimal Stock for a Multi-sector Economy with Nonconvex Technology," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 10, pages 214-240, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-349-11696-6_10
    DOI: 10.1007/978-1-349-11696-6_10
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    Cited by:

    1. Joshi, Sumit, 1997. "Existence in undiscounted non-stationary non-convex multisector environments," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 111-126, August.

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