How an Economy Shrinks in Space: Concavity-on-jobs and upward consolidation under demographic decline

When a country's population declines, the aggregate economy appears to contract on the intensive margin: industrial diversity intact, every industry a little smaller. At the regional level, contraction is uneven and takes the extensive form: entire industries disappear, one after another. The relevant unit is the city: industries are nested by size—the hierarchy property of industrial location—each viable only above a minimum population. Necessity industries' thresholds bunch at the low end, so a city's industry count—and its jobs—is sharply concave in size (concavity on jobs). A modest loss pushes a small city below many thresholds at once; a large core sheds a few specialized industries, one at a time. Lost industries consolidate upward to the next city large enough to host them; for the worker it means a step down to a lower-paid local job. To recover that income, workers move up to the apex—the only city hosting the full industry range. Studying Japan—two decades ahead of the OECD, Tokyo at its apex—with worker-level panel data on the young workers who carry the migration, a wage regression in real, housing-inclusive wages identifies a Tokyo-bound migration incentive that varies by origin, following concavity on jobs.