Typical properties of optimal growth in the Von Neumann expanding model for large random economies

Details Typical properties of optimal growth in the Von Neumann expanding model for large random economies Typical properties of optimal growth in the Von Neumann expanding model for large random economies

2005-07-05

arxiv.org/abs/physics/0507032v1

JSTAT (2005) L09003

Physics

Physics and Society

8 pages, 1 figure

Scientific paper

10.1088/1742-5468/2005/09/L09003

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak.

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