Progress in Urban Spatial Analysis: Existence, Sizes and Spatial Organization of Urban Areas

Abstract This article is a survey of the current state of urban spatial analysis; what has been learned in the past forty years and what interesting problems remain. Three topics are covered-reasons for the existence of urban areas, spatial organization of urban areas and their sizes. Introduction Urban areas have been the locus of most economic growth during the 200-300 years since there has been significant economic growth. Causation runs not only both ways but also between economic and urban growth as cause and effect of the most fundamental determinants of each. Of course, cities for defense and trade long predated the industrial revolution, not only in Europe but also in North Africa, West Asia, India, China and Central and South America. All great economists have speculated about urban areas, including not only Smith (1776), and others who were present at the creation, but also von Thunen (1866) and Marshall (1890) in the nineteenth century and a host of greats in the first half of the twentieth century, most notably Hoover (1948) and Losch (1954). Starting just after the mid twentieth century with Clark (1951), urban analysts began to multiply from backgrounds in geography and regional science, as well as economics. This paper is mostly about urban spatial analysis and the birth of that subject is arbitrarily placed with Alonso (1964). This paper is not intended to trace the development of urban spatial analysis. The best sources for that purpose, as well as for important original analysis, are: Fujita (1989), Fujita, Krugman and Venables (1999) and Fujita and Thisse (2002). These works have brought remarkable unity to the subject. Instead, this paper tries to describe the current state of urban spatial analysis: what has been learned during the last forty years and what interesting problems remain. The paper contains only scattered and inadequate references to the relevant literature. Specifically, this paper reviews three subjects: reasons for the existence of urban areas, their spatial organizations and their sizes. Why Urban Areas? This issue is about as well understood as any issue in urban economics. Abstract analysis starts with a featureless plain, any number of production sectors, all of which have constant returns production functions, and any number of households that supply labor and have well-behaved utility and demand functions. Households do not value proximity to other households, say for social reasons. Then if transportation of people and goods requires valuable inputs, there would be none in competitive equilibrium. Households would be uniformly distributed on the plain and each household's goods and services would be produced in a small area near the dwelling. There would be no transportation and no urban areas. This result was formalized in Starred. (1978), but was stated in Mills (1971), as a prelude to urban modeling. Of course, all economic activity is subject to scale (and or scope) economies at small, and in some cases large, rates of production. It follows that production takes place at substantial scale at discrete locations. Free entry leads to zero profit and production on the downward sloping part of the unit cost curve. The area within which each firm is a monopoly producer is either a hexagon or a hexagon with the corners shaved off, possibly a circle as a limiting case (see Mills and Lav, 1966). Employees' and customers' residences congregate near each production site in order to economize on transportation costs. Land values and rents peak at production sites and decrease linearly with distance from them if there is no capital-land substitution in housing production and with convex shape if substitution is possible [see Fujita and Thisse (2002), Chapters 3 and 4]. Firms that buy inputs from or sell outputs to firms with scale and scope economies also locate in adjacent areas even though they may have only minor such economics. …