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Evil deeds in urban economics

Berliant, Marcus and Fujita, Masahisa (2019): Evil deeds in urban economics.

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The purpose of this note is to update an ancient controversy over the comparison between discrete and continuous agent models of land use and agent location in urban economics. Berliant (1985) shows that that the following statement is self-contradictory: "There is a continuum of agents, each of whom owns or is endowed with a positive Lebesgue measure of land." A corollary follows: "As the number of agents tends to infinity, the set of agents who own a positive Lebesgue measure of land shrinks to zero." The basic question is this: Under what circumstances, if any, can we reconcile the two models?

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