A Simple Model of City Crowdedness

By Jordan Rappaport
December 2004 
RWP 04-12
Research Division 
Federal Reserve Bank of Kansas City 

Abstract

      Population density varies widely across U.S. cities. A calibrated general equilibrium model in which productivity and quality-of-life differ across locations can account for such variation. Individuals derive utility from consumption of a traded good, a nontraded good, leisure, and quality-of-life. The traded and nontraded goods are produced by combining mobile labor, mobile capital, and non-mobile land. An eight-fold increase in population density requires an approximate 50 percent productivity differential or an approximate 20 percent compensating differential. A thirty-two-fold increase in population density requires an approximate 95 percent productivity differential or a 33 percent compensating differential. Empirical evidence suggests productivity and quality-of-life differentials of this magnitude are plausible. The model implies that broad-based technological progress can induce substantial migration to localities with high quality-of-life.

Keywords: Population Density, Productivity, Quality-of-Life, Compensating Differentials, Economic Growth

JEL Codes: O400, O510, R110, R120

Jordan Rappaport  is a senior economist at the Federal Reserve Bank of Kansas City. Earlier versions of this paper were circulated with the title "Why Are Some Cities So Crowded?"  The author wishes to thank the following for for advice and feedback:  V.V. Chari, Steven Durlauf, Charles Engel, Vernon Henderson, Ruben Hernandez-Murillo, Peter Klenow, and Naryana Kocherlakota. Taisuke Nakata and Aarti Singh provided excellent research assistance. The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Kansas City or the Federal Reserve System.

Rappaport email:  jordan.m.rappaport@kc.frb.org

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