Tâtonnement, Approach to Equilibrium and Excess Volatility in Firm Networks

We study the conditions under which input-output networks can dynamically
attain competitive equilibrium, where markets clear and profits are zero. We
endow a classical firm network model with simple dynamical rules that reduce
supply/demand imbalances and excess profits. We show that the time needed to
reach equilibrium diverges as the system approaches an instability point beyond
which the Hawkins-Simons condition is violated and competitive equilibrium is
no longer realisable. We argue that such slow dynamics is a source of excess
volatility, through accumulation and amplification of exogenous shocks.
Factoring in essential physical constraints, such as causality or inventory
management, we propose a dynamically consistent model that displays a rich
variety of phenomena. Competitive equilibrium can only be reached after some
time and within some region of parameter space, outside of which one observes
periodic and chaotic phases, reminiscent of real business cycles. This suggests
an alternative explanation of the excess volatility that is of purely
endogenous nature. Other regimes include deflationary equilibria and
intermittent crises characterised by bursts of inflation. Our model can be
calibrated using highly disaggregated data on individual firms and prices, and
may provide a powerful tool to describe out-of-equilibrium economies.