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Dynamic Programming of Economic Growth

In: Activity Analysis in the Theory of Growth and Planning

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  • Roy Radner

    (University of California)

Abstract

In the present paper a class of problems of optimal economic growth is formulated in terms of the ‘functional equation’ approach of dynamic programming (Bellman, 1957).2 A study is made of the continuity and concavity properties of the state valuation function, i.e. the function indicating the maximum total discounted welfare (utility) that can be achieved starting from a given initial state of the economy. Under suitable conditions this function is characterized by a certain functional equation. Both the cases of a finite and an infinite planning horizon are treated, the latter case being discussed under the assumption of constant technology and tastes. Here iteration of a certain transformation associated with the functional equation is shown to provide convergence to the state valuation function. Exact solutions are given for the case of linear-logarithmic production and welfare functions.

Suggested Citation

  • Roy Radner, 1967. "Dynamic Programming of Economic Growth," International Economic Association Series, in: E. Malinvaud & M. O. L. Bacharach (ed.), Activity Analysis in the Theory of Growth and Planning, chapter 0, pages 111-141, Palgrave Macmillan.
    • Handle: RePEc:pal:intecp:978-1-349-08461-6_4
    DOI: 10.1007/978-1-349-08461-6_4
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    Cited by:

    1. Roger Guesnerie & Pierre Malgrange, 1972. "Formalisation des objectifs à moyen terme. Application au VIe Plan," Revue Économique, Programme National Persée, vol. 23(3), pages 442-492.
    2. McKenzie, L., 1999. "The First Conferences on the Theory of Economic Growth," RCER Working Papers 459, University of Rochester - Center for Economic Research (RCER).

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