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

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with N processes and P goods in the limit N --> infinity. 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 behaviour, independent of the parameters of the disorder statistics. Associating technological innovation with an increase of N, we find that while such an increase has a large positive impact on long term growth when N << P, its effect on technologically advanced economies (N >> P) is very weak.