This is a preview of subscription content, log in via an institution to check access.
References
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).
“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.
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.
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.
Throughout I treat owner-occupants as producers of housing selling housing services to themselves as tenants.
The negative-exponential price-distance function is to my knowledge the simplest one for which price declines at a decreasing rate with distance. The logarithmically linear approximation is the simplest form of the production function with declining marginal physical productivities. It has been widely used in empirical work. I have found that either a linear or logarithmically-linear housing demand function is a workable approximation using national data; see my “The Demand for Non-Farm Housing,” inThe Demand For Durable Goads, ed. Arnold C. Harberger (Chicago: University of Chicago Press, 1960).
A proof of this assertion is given in the appendix.
See Clark,op. cit.
In each case I omitted tracts in the central business district and any tract with fewer than 100 residents from the population of tracts sampled on the grounds that in these land is devoted almost entirely to other than residential uses. Likewise, for uniformity the population sampled included only tracts in the central city, since the outlying parts of metropolitan areas are not tracted in all cases.
Central business district census tracts are listed in U.S. Bureau of the Census,1954 Census of Business, Central Business District Statistics, Summary Report (Washington, D.C.: U.S. Government Printing Office, 1958), pp. APP1-6.
U.S. Bureau of the Census,1950 Census of Population, Vol. III (Washington, D.C.: U.S. Government Printing Office, 1952), Table 1.
Ibid., Table 1. For two cities, Los Angeles and Cleveland, measurements were taken from larger tract maps obtained through the census tract key persons in those cities. In all cases, three measurements of area were made and averaged. If one of the three differed from the average of the other two by as much as one-third it was discarded and another measurement made. For three cities already available area measurements were used. For Boston these were taken from unpublished measurements supplied by the Research Division, United Community Services; for Chicago from Chicago Community Inventory, “Gross Land Area and Gross Population Density of Census Tracts and Community Areas for the City of Chicago, 1950,” (Unpublished, November, 1952); for Philadelphia from Philadelphia City Planning Commission, “Population Densities in 1940 and 1950 by Census Tracts-Philadelphia,” (Unpublished, August, 1954).
The median of theg's in Table I is about 0.35.
Since theg's are but estimates, part of the reason for differences among them is sampling variability. However, study of the estimated variances of the gradient estimates suggests that sampling variability accounts for only about 10 per cent of the variance of the estimated gradients among the several cities.
These measures cover only those local transit companies and public authorities which reported to the Association on their operations for 1950, and are available for only 37 of the 46 cities for which I computed density gradients. The compilations of the Association permit one to calculate passengers carried per vehicle mile operated as well for all but four of these cities. To avoid running too short of degrees of freedom, however, I did not include this variable.
The sources for all data used in this part of the analysis are given at the foot of Table VII.
The relation ofX 4 to density was first suggested to me by an unpublished manuscript of Lowdon Wingo.
Data on SMA retail sales were not available for one of the 37 cities for which I have data relating to local transit systems.
This is the log of the urbanized area population. Use of logs for this variable resulted in a more nearly linear scatter.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Muth, R.F. The spatial structure of the housing market. Papers of the Regional Science Association 7, 207–220 (1961). https://doi.org/10.1007/BF01969081
Issue Date:
DOI: https://doi.org/10.1007/BF01969081