# Maximal Paths in the von Neumann Model

## 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

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### References

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