Unsuspected Perversities in the Theory of Location
On an infinitely-extensible plane (with uniform customer-density) the socially-optimal configuration of firms is a regular hexagonal lattice. Will the free market necessarily produce this configuration? We argue that the currently-accepted, affirmative answer has been erroneously derived from models in which equilibrium is undefined, and in which equilibrium conditions are asserted rather than being derived from behavioural postulates. We answer the question negatively, showing that, in a standard location model: (a) many configurations, including the hexagonal, satisfy the equilibrium conditions (and in no case is zero profits a necessary condition for equilibrium); and (b) if a hexagonal configuration is initially imposed, it is much less likely to persist through successive rounds of entry than is a square or a rectangular configuration.
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