Will a large economy be stable? Building on Robert May's original argument
for large ecosystems, we conjecture that evolutionary and behavioural forces
conspire to drive the economy towards marginal stability. We study networks of
firms in which inputs for production are not easily substitutable, as in
several real-world supply chains. Relying on results from Random Matrix Theory,
we argue that such networks generically become dysfunctional when their size
increases, when the heterogeneity between firms becomes too strong or when
substitutability of their production inputs is reduced. At marginal stability
and for large heterogeneities, we find that the distribution of firm sizes
develops a power-law tail, as observed empirically. Crises can be triggered by
small idiosyncratic shocks, which lead to "avalanches" of defaults
characterized by a power-law distribution of total output losses. This scenario
would naturally explain the well-known "small shocks, large business cycles"
puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford
