Resilient-to-Fragile Transition and Excess Volatility in Supply Chain Networks

Abstract

We study a production network in which firms use non-substitutable (Leontief) inputs, hold precautionary inventories and face idiosyncratic productivity shocks, with adjustment occurring through quantities rather than prices. We show analytically and numerically that a critical boundary exists in the space of shock volatility and inventory holdings: above this threshold, the economy absorbs shocks and fluctuates mildly while below it, cascading shortages make system-wide crises inevitable. Close to the threshold, aggregate output volatility diverges through network-mediated amplification of purely idiosyncratic shocks, providing a concrete mechanism for the ``small shocks, large business cycles'' puzzle. Because inventories are costly, competitive pressure drives firms toward the fragility boundary: a resilience-efficiency trade-off emerges, putting the gains from lean supply chains at risk. Finally, we show that supplier diversification shifts the threshold and, depending on its abundance, can eliminate the fragile regime entirely.

55 pages, 4 figures