Tatonnement, Approach to Equilibrium and Excess Volatility in Firm Networks

Théo Dessertaine, José Moran, Michael Benzaquen, and Jean-Philippe Bouchaud

15 February, 2021

Abstract

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.

Keywords: Beyond GDP, inequality, empowerment, social cohesion, social inclusion, social solidarity, social sustainability, well-being