Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-02-02
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages
Scientific paper
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method. When technologies are strictly inefficient, a phase transition occurs upon increasing $n$. For low $n$, the system is in an expanding phase characterized by the existence of many profitable opportunities for new technologies. For high $n$, technologies roughly saturate the possible productions and the economy becomes strongly selective with respect to innovations. The phase transition and other significant features of the model are discussed in detail. When the inefficiency assumption is relaxed, the economy becomes unstable at high $n$.
Castillo Perez I.
Marsili Margherita
Martino Alessandro de
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