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.