Maximal Paths in the von Neumann Model

  • Lionel W. McKenzie
Part of the International Economic Association Series book series (IEA)

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 \( \left( {\bar y} \right) \). 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 \( \frac{{y_i^T}}{{{{\bar y}_i}}} \) over i such that \( {\bar y_i} > 0 \). We may define \( \rho (y) = \min \frac{{{y_i}}}{{{{\bar y}_i}}}\,for\,{\bar y_i} > 0 \). Then ρ (y)is a utility function which is maximized.

Keywords

Dition Rium Guaran 

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References

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Copyright information

© International Economic Association 1967

Authors and Affiliations

  • Lionel W. McKenzie
    • 1
  1. 1.University of RochesterRochesterUSA

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