Will a large economy be stable? In this talk, I will present a model for a network economy where firms' productions are interdependent, and study the conditions under which such input-output networks admit a competitive economic equilibrium, where markets clear and profits are zero. Insights from random matrix theory allow to understand some of the emergent properties of this equilibrium and to provide a classification for the different types of crises it can be subject to. After this, I will endow the model with dynamics, and present results with strong links to generalised Lotka-Volterra models in theoretical ecology, where inter-species interactions are modelled with random matrices and where the system naturally self-organises into a critical state. In both cases, the stationary points must consist of positive species populations/prices/outputs. Building on these ideas, I will show the key concepts behind an economic agent-based model that can exhibit convergence to equilibrium, limit cycles and chaotic dynamics, as well as a phase of spontaneous crises whose origin can be understood using "semi-linear" dynamics.
