A simple model of city crowdedness

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.