  We study the competitive equilibrium of large random economies with linear
activities using methods of statistical mechanics. We focus on economies with
$C$ commodities, $N$ firms, each running a randomly drawn linear technology,
and one consumer. We derive, in the limit $N,C\to\infty$ with $n=N/C$ fixed, a
complete description of the statistical properties of typical equilibria. We
find two regimes, which in the limit of efficient technologies are separated by
a phase transition, and argue that endogenous technological change drives the
economy close to the critical point.
