  We study the conditions under which input-output networks can dynamically
attain a competitive equilibrium, where markets clear and profits are zero. We
endow a classical firm network model with minimal dynamical rules that reduce
supply/demand imbalances and excess profits. We show that the time needed to
reach equilibrium diverges to infinity as the system approaches an instability
point beyond which the Hawkins-Simons condition is violated and competitive
equilibrium is no longer admissible. We argue that such slow dynamics is a
source of excess volatility, through accumulation and amplification of
exogenous shocks. Factoring in essential physical constraints absent in our
minimal model, such as causality or inventory management, we then propose a
dynamically consistent model that displays a rich variety of phenomena.
Competitive equilibrium can only be reached after some time and within some
restricted region of parameter space, outside of which one observes spontaneous
periodic and chaotic dynamics, reminiscent of real business cycles. This
suggests an alternative explanation of excess volatility in terms of purely
endogenous fluctuations. Diminishing return to scale and increased
perishability of goods are found to ease convergence towards equilibrium.
