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Maximal Paths in the von Neumann Model

In: Activity Analysis in the Theory of Growth and Planning

Author

Listed:
  • Lionel W. McKenzie

    (University of Rochester)

Abstract

I shall concern myself with the problem of optimal accumulation in the von Neumann model as it was initially posed by Dorfman, Samuelson, and Solow (1958) (DOSSO).2 In this problem the objective is to reach a point on a prescribed ray through the origin which is as far out as possible in a given number of periods. Let the prescribed ray be ( y ¯ ) $$ \left( {\bar y} \right) $$ . Then, if there is free disposal, and accumulation occurs over N periods from y 0 as a starting-point, it is equivalent to maximize the minimum of y i T y ¯ i $$ \frac{{y_i^T}}{{{{\bar y}_i}}} $$ over i such that y ¯ i > 0 $$ {\bar y_i} > 0 $$ . We may define ρ ( y ) = min y i y ¯ i f o r y ¯ i > 0 $$ \rho (y) = \min \frac{{{y_i}}}{{{{\bar y}_i}}}\,for\,{\bar y_i} > 0 $$ . Then ρ (y)is a utility function which is maximized.

Suggested Citation

  • Lionel W. McKenzie, 1967. "Maximal Paths in the von Neumann Model," International Economic Association Series, in: E. Malinvaud & M. O. L. Bacharach (ed.), Activity Analysis in the Theory of Growth and Planning, chapter 0, pages 43-63, Palgrave Macmillan.
  • Handle: RePEc:pal:intecp:978-1-349-08461-6_2
    DOI: 10.1007/978-1-349-08461-6_2
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    Cited by:

    1. Giorgio Giorgi & Cesare Zuccotti, 2016. "Equilibrium and Optimality in Gale-von Neumann Models," DEM Working Papers Series 119, University of Pavia, Department of Economics and Management.
    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).
    3. Kaganovich, Michael, 1998. "Sustained endogenous growth with decreasing returns and heterogeneous capital," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1575-1603, August.

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