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We calculate the optimal solutions of the fully heterogeneous Von Neumannexpansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$.This model provides an elementary description of the growth of a productioneconomy in the long run. The system turns from a contracting to an expandingphase as $N$ increases beyond $P$. The solution is characterized by a universalbehavior, independent of the parameters of the disorder statistics. Associatingtechnological innovation to an increase of $N$, we find that while such anincrease has a large positive impact on long term growth when $N\ll P$, itseffect on technologically advanced economies ($N\gg P$) is very weak.Comment: 8 pages, 1 figur

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