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 ∞ 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.
