1. For a summary of the evidence relating to the spread of population within urban areas see Philip M. Hauser, “The Changing Population Pattern of the Modern City,” inCities and Society, 2nd ed., eds. Paul K. Hatt and Albert J. Reiss, Jr. (Glencoe, Illinois: The Free Press, 1957), pp. 157–74. The most complete study of urban population distribution I have seen is Donald J. Bogue and Dorothy L. Harris,Comparative Population and Urban Research via Multiple Regression and Convariance Analysis. (Oxford, Ohio: Scripps Foundation, 1954).
2. “Urban Population Densities,”Journal of the Royal Statistical Society, Series A, CXIV (Part IV, 1951), 490–96. The essentials of my analysis were worked out before I became aware of Clark's empirical observations. Hence, I am more confident of the predictive power of this analysis than I would have been had it been constructed for the expressed purpose of yielding a negative-exponential density decline.
3. Throughout this paper, when I speak of housing I mean the bundle of consumer services supplied both by structures and by the land on which they are located.
4. Likewise, for the equilibrium location of a household to be at a finite distance, the savings in housing costs must not increase more rapidly than transportation costs as distance increases.
5. Throughout I treat owner-occupants as producers of housing selling housing services to themselves as tenants.