2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210104We 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.19 pages, 5 figuresStatistical MechanicsGeneral Financetext