Lectures_on_Urban_Economics_----_(2_Analyzing_Urban_Spatial_Structure)

2 Analyzing Urban Spatial Structure 2.1 Introduction Looking out the airplane window, an airline passenger landing in New York or Chicago would see the features of urban spatial structure rep- resented in a particularly dramatic fashion. In both of those cities, the urban center has a striking concentration of tall buildings, with build- ing heights gradually falling as distance from the center increases. The tallest buildings in both cities are office buildings and other commercial structures, but the central areas also contain many tall residential build- ings. Like the heights of the office buildings, the heights of these resi- dential structures decrease moving away from the center, dropping to three and two stories as distance increases. Single-story houses become common in the distant suburbs. Although it is less obvious from the airplane, an equally important spatial feature of cities involves the sizes of individual dwellings (apart- ments and houses). The dwellings within the tall residential buildings near the city center tend to be relatively small in terms of square footage, while suburban houses are much more spacious. Thus, although building heights fall moving away from the center, dwelling sizes increase. In walking around downtown residential neighborhoods in Chicago or New York, the traveler would notice another difference not clearly visible from the airplane. Relative to her suburban neighborhood at home, there would be many more people on the streets in these down- town neighborhoods, walking to restaurants, running errands, or heading to their workplaces. This difference is due to the high popula- tion density that prevails in central-city residential areas, which is also reflected in activities on the street. Population density falls moving away from the city center, reaching a much lower level in the suburbs. Brueckner, J. K. (2011). Lectures on urban economics. MIT Press. Created from utoronto on 2023-10-19 18:36:09. Copyright © 2011. MIT Press. All rights reserved.

24 Chapter 2 Other important regularities of urban spatial structure aren’t visible at all from an airplane or from the street. These features involve real- estate prices, and they require experience in real-estate transactions, or familiarity with urban data, to grasp. First, whereas vacant lots usually can be purchased for reasonable prices in the suburbs, vacant land near the city center (when it is available) is dramatically more expensive per acre. The same regularity applies to the price of housing floor space: the rental or purchase price per square foot of housing is much higher near the city center than in the suburbs. Consumers aren’t used to thinking about prices on a per square foot basis (focusing instead on the monthly rent or selling price for a dwelling), but any real-estate agent knows that residential prices per square foot fall moving away from the city center. Other regularities involve differences across cities rather than center- suburban differences within a single city. To appreciate these differ- ences, suppose that our traveler is from Omaha, Nebraska. When her plane lands there on her return trip, she will notice that buildings in central Omaha, though taller than those in Omaha’s suburbs, are much shorter than those in the big city she just visited. In addition, if the traveler had access to price data, she would see that a vacant lot in the center of Omaha would be cheaper than one in the center of New York. Economists have formulated a mathematical model of cities that attempts to capture all these regularities of urban spatial structure. This chapter develops and explains the model. But it does so without relying on mathematics, instead using an accessible diagrammatic approach. As will be seen, the urban model successfully predicts the regularities described above. Since the model thus gives an accurate picture of cities, it can be used reliably for predictive purposes in a policy context. For example, the model can predict how a city’s spatial structure would change if the gasoline tax were raised substantially, thereby raising the cost of driving. It can also be used to analyze how a variety of other policies would affect a city’s spatial structure. The model presented in this chapter originated in the works of William Alonso (1964), Richard Muth (1969), and Edwin Mills (1967). Systematic derivation of the model’s predictions was first done by William Wheaton (1974) and later elaborated by Jan Brueckner (1987). 1 1. For a comprehensive treatment of the economics of urban land use, see Fujita 1989. For a more recent book-length treatment, see Papageorgiou and Pines 1998. Glaeser 2008 also contains a chapter on this topic. For a useful overview paper, see Anas, Arnott, and Small 1998. Brueckner, J. K. (2011). Lectures on urban economics. MIT Press. Created from utoronto on 2023-10-19 18:36:09. Copyright © 2011. MIT Press. All rights reserved.

Analyzing Urban Spatial Structure 25 The presentation in this chapter is basically a nonmathematical version of Brueckner’s approach. 2.2 Basic Assumptions As is true of all economic models, the urban model is based on strategi- cally chosen simplifications, which facilitate a simple analysis. These simplifications are chosen to capture the essential features of cities, leaving out details that may be less important. Once the model is ana- lyzed and its predictions are derived, greater realism can be added, often with little effect on the main conclusions. The first assumption is that all the city’s jobs are in the center, in an area called the “central business district” (CBD). In reality, many job sites are outside city centers, scattered in various locations or else con- centrated in remote employment subcenters. Thus, although job decen- tralization (the movement of jobs out of the CBD) is a hallmark of modern cities, this process is initially ignored in developing the model. It therefore applies best to cities of the early to mid twentieth century, in which jobs were more centralized than they are now. However, once the model has been analyzed, it can be realistically modified to include the formation of employment subcenters. As will be seen, many of its lessons are unaffected. Since the goal is to analyze residential (as opposed to business) land use, the CBD is collapsed to a single point at the city center, so that it takes up no space. The model could easily be modified to allow the CBD to have a positive land area, in which case the nature of land use within the business area would become a focus in addition to residen- tial land use outside the CBD. The second major assumption is that the city has a dense network of radial roads. With such a network, a resident living some distance from the CBD can travel to work in a radial direction, straight into the center, as illustrated in figure 2.1. In reality, cities are criss-crossed by freeways, which are often used in combination with surface streets to access the CBD, thus leading to non-radial automobile commute paths for many residents. As will be seen below, freeways can be added to the model without changing its essential lessons. The third major assumption is that the city contains identical house- holds. Each household has the same preferences over consumption goods, and each earns the same income from work at the CBD. For simplicity, household size is normalized to one, so that the city consists Brueckner, J. K. (2011). Lectures on urban economics. MIT Press. Created from utoronto on 2023-10-19 18:36:09. Copyright © 2011. MIT Press. All rights reserved.

26 Chapter 2 entirely of single-person households. The identical-household assump- tion is relaxed below by allowing the city to have two different income groups: rich and poor. The fourth major assumption is that the city’s residents consume only two goods: housing and a composite good that consists of every- thing other than housing. Since the model is about cities, it naturally focuses on housing. Simplicity requires that all other consumption be lumped together into a single composite commodity, which will be called “bread.” 2.3 Commuting Cost Let x denote radial distance from a consumer’s residence to the CBD. The cost of commuting to work at the CBD is higher the larger is x , and this cost generally has two components. The first is a “money” (or “out-of-pocket”) cost. For an automobile user, the money cost consists of the cost of gasoline and insurance as well as depreciation on the automobile. For a public-transit user, the money cost is simply the transit fare. The second component of commuting cost is time cost, which captures the “opportunity cost” of the time spent commuting— time that is mostly unavailable for other productive or enjoyable activities. Because a proper consideration of time cost makes the analysis more complicated, this component of commuting cost is ignored in developing the basic model. However, time cost is needed in analyzing a city that contains different income groups, so it will be re-introduced below. Residence Residence CBD Figure 2.1 Radial commuting. Brueckner, J. K. (2011). Lectures on urban economics. MIT Press. Created from utoronto on 2023-10-19 18:36:09. Copyright © 2011. MIT Press. All rights reserved.

Analyzing Urban Spatial Structure 27 The parameter t represents the per-mile cost of commuting. For a resident living x miles from the CBD, total commuting cost per period is then tx , or commuting cost per mile times distance. For an automo- bile commuter, t would be computed as follows: Suppose that operat- ing the automobile costs $0.45 per mile, a number close to the value allowed by the Internal Revenue Service in deducting expenses for business use of an auto. Then, a one-way trip to the CBD from a residence at distance x costs 0.45 x , and a round trip costs 0.90 x . A resident working 50 weeks per year will make 250 round trips to the CBD. Multiplying the previous expression by this number yields (250)0.90 x = 225 x as the commuting cost per year from distance x . Thus, under these assumptions t would equal 225. 2 The fact that the same commuting-cost parameter ( t ) applies to all residents reflects another implicit assumption of the model: all resi- dents use the same transport mode to get to work. Urban models with competing transport modes (and thus different possible mode choices) have been developed, but they involve additional complexity. Let the income earned per period at the CBD by each resident be denoted by y . Then disposable income, net of commuting cost, for a resident living at distance x is equal to y – tx. This expression shows that disposable income decreases as x increases, a consequence of a longer and more costly commute. This fact is crucial in generating the model’s predictions about urban spatial structure. 2.4 Consumer Analysis As was mentioned earlier, city residents consume two goods: housing and “bread.” Bread consumption is denoted by c , and since the price per unit is normalized to $1, c gives dollars spent on bread (all goods other than housing). Housing consumption is denoted by q , but the physical units corresponding to q must be chosen. The problem is that housing is a complicated good, with a variety of characteristics that consumers value. The characteristics of housing include square footage of floor space in the dwelling, yard size, construction quality, age, and amenities (views, for example). Although a dwelling is then best 2. Note that the model focuses entirely on commuting cost, ignoring the cost of trips carried out for other purposes (such as shopping). These trips might be viewed as occur- ring close to home at a cost that is negligible relative to the cost of commuting. Alterna- tively, the consumer could be assumed to shop on the way home from work at no extra cost, a behavior that appears to be common. Brueckner, J. K. (2011). Lectures on urban economics. MIT Press. Created from utoronto on 2023-10-19 18:36:09. Copyright © 2011. MIT Press. All rights reserved.