Resilience vs. Fragility: Global Properties of Economies with Endogenous Production Networks

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We provide a global analysis of the canonical single-factor production network model with arbitrary constant returns to scale production technologies. We show that Leontief production functions with endogenous weights are sufficient to replicate outcomes in any such economy. Our main result leverages this to provide a primitive formula for the unique equilibrium prices in all such economies: the equilibrium log-price vector is a ``min-max' over pairs of input-output networks of a primitive affine function of log-productivity shocks. We call the economy resilient (fragile) if increases in microeconomic productivity risk at the sector level increase (decrease) equilibrium GDP. We show that the ``min' and ``max' correspond economically to the competing forces of resilience and fragility: if all sectors are resilient (fragile), then only the min (max) remains. Finally, we use these results to generalize Hulten's theorem to economies with endogenous production networks and apply this result to provide robust upper and lower bounds on the variance of GDP that can result from microeconomic productivity shocks.