The Problematic Definition of Sprawl

The definition of urban sprawl is imprecise and varies. The Oxford Online Dictionary defines it as “the uncontrolled expansion of urban areas”; the Merriam-Webster Online Dictionary as “the spreading of urban developments (such as houses and shopping centers) on undeveloped land near a city”; the Encyclopedia Britannica as “the rapid expansion of the geographic extent of cities and towns, often characterized by low-density residential housing, single-use zoning, and increased reliance on the private automobile for transportation.” The same encyclopedia notes that “Urban sprawl has been correlated with increased energy use, pollution, and traffic congestion and a decline in community distinctiveness and cohesiveness.”

Wikipedia notes that “The term urban sprawl is highly politicized, and almost always has negative connotations. It [sprawl] is criticized for causing environmental degradation, and intensifying segregation and undermining the vitality of existing urban areas. Due to the pejorative meaning of the term, few openly support urban sprawl as such. The term has become a rallying cry for managing urban growth.” Rome (2001) argues that the environmentalist movement in the United States gained strength in the decades following World War II in reaction to growing suburban sprawl and explosive suburbanization.

Galster et al. (2001) have proposed a complex definition of urban sprawl based on eight metrics of land use: density, continuity, concentration, clustering, centrality, nuclearity, mixed uses, and proximity. According to them an urban land use pattern is sprawled when it scores low on at last one of these metrics. Adopting such a multitude of metrics and applying them loosely makes it clear that there can be many types of sprawl. Almost any urban area might be considered as being sprawled. Should each metric attain two possible values, high and low, there would be ${\displaystyle \sum _{k=1}^8\frac{8!}{k!\left(8-k\right)!}=255}$ types of sprawl in which a distinct combination of the metrics attained low values.

A taxonomy of the possible patterns of urban sprawl should be of limited interest to economists. Economists should ask the same key questions about urban sprawl that they ask about many other issues of resource allocation. The first is a question in positive economics: What market processes or government policies give rise to a particular type of sprawl? The second is a question in normative economics: Does the particular type of sprawl result from an efficient allocation of resources or from a misallocation caused by market failures? And if misallocation is the cause, then a third question arises: What policies, fiscal instruments, investments or plans can be utilized to correct the misallocation?

Sprawl on the Chessboard

Economic analysis has made meaningful contributions on a small number of sprawl types. I will illustrate these in a simple but easily comprehensible and quantifiable manner using the chessboard. Suppose that a black square on a chessboard represents urban land that is fully developed, covered with buildings and roads, and a white square represents open space, in an agricultural or natural state. Assume, temporarily, that black squares are identically developed, and at the same land use density. If each square were to be divided into 4 or 8 squares, we would have a modified “chessboard” of 256 or 512 squares and everything we are about to see could also be seen at that higher level of resolution. Panel (a) of Figure 1 shows a chessboard in which the 32 black squares are all gathered into a compact shape. Panel (b) shows the normal chessboard in which the black squares are always separated by white squares. In panel (c) the 32 developed squares are randomly allocated to positions on the chessboard. The three patterns have the same total developed area and density so they would be equally sprawled under the definition of total developed area or density of development.

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Figure 1. Alternative patterns of sprawl illustrated on a chessboard.

Urban economists have always been interested in the total land area occupied by urban development quite independent of sprawl becoming a popular social concern. Brueckner and Fansler (1983) and Brueckner (2000) and others have referred to urban sprawl in this particular sense. Another less widely used definition refers to the distribution of the total developed area in the sense of how exposed each unit developed area is to, or is mixed with, open space; or equivalently, how little it is surrounded by other developed land. This definition may be gleaned from the work of Burchfield, Overman, Puga, and Turner (2006), who have attempted to document sprawl using satellite-based observations and measurements of urban land use. They defined urban sprawl as the amount of undeveloped space that can be found on average within a one-kilometer radius of each 30 meter by 30 meter developed land area,¹ although they do not explain why such a definition may be important to adopt, especially by economists.

Under the second definition, we would need to measure each developed square’s exposure to (or contact with) open space. Suppose that we do so on the chessboard by counting the edges that a black square shares with white squares and adding up these numbers for the 32 black squares. The resulting index is 24 for pattern (a) in Figure 1. It is 112 for pattern (b) and 75 for the random pattern (c). So (a) would be the least sprawled pattern, followed by (c) and then by (b).

Some observers of sprawl favor a definition that leans toward haphazardness in land use. Pattern (a), whether the result of a plan or of markets, does not appear haphazard. The regular pattern (b) is more likely to be the result of a plan and does not appear haphazard. The random pattern (c) would be considered more sprawled under a definition based on haphazardness. Discontinuous development or leapfrogging can give an impression of haphazardness in the physical appearance of development, but economists have shown that such patterns can arise in perfect foresight models of land development without market failures in which developers rationally time the future date at which the land should be developed or redeveloped. Ohls and Pines (1975), Fujita (1976), and Moore and Wiggins (1990) have formulated and solved such models. While the economic behavior is rational and orderly, the land use outcome appears disorderly to an eye undisciplined by economic theory. For example, it can be economically efficient for a surface parking lot to exist side by side with a downtown tall building, or a farm in the suburbs to be surrounded by low density housing. The owner of the surface parking lot and the suburban farm could be expecting to make higher present value profits by developing at a later date. Keeping the land vacant until a future time can also be useful under uncertainty should conditions change and the land become valuable in an alternative use. In a different treatment of haphazardness, Irwin and Bockstael (2007) define urban sprawl as fragmentation in land development at the urban fringe caused by externalities among heterogeneous land uses.

As noted, economists ought to analyze the efficiency of the resource allocation implied in a particular land use pattern. Suppose, for example, that in a very social chessboard city, people in the urban area residing in a black square make trips over a period of time visiting their friends who reside in all the black squares. Since travel depletes time and fuel and can cause congestion delays, pollution, accidents, and other externalities, an economist would try to evaluate alternative patterns by their travel-related resource consumption. In Figure 1, pattern (b) may involve longer travel times for social visits than pattern (a) because of the distances that separate the black squares. But travel in pattern (a), while it happens over shorter distances, may be a lot more congested because trips have a much higher density per unit distance traveled. Pattern (a) may require a subway system to relieve the high congestion, while pattern (b) may require extensive roads linking the dispersed squares. Without a detailed economic model, it becomes unclear which pattern is more economically efficient. Preferences play an important role: if people like traveling in private vehicles and driving along scenic routes, then pattern (b) could likely be more efficient, but if they enjoy using subways and walking to many places, then pattern (a) would be more efficient. But even if preferences favor pattern (b), pattern (a) may still be the most efficient due to resource constraints and prices. The cost of serving pattern (a) with a subway system may be lower than that of serving pattern (b) with a road system or vice versa.

It is easy to add additional complications. Recognize, for example, that the number of social visits and how far people live from their friends is endogenously, not exogenously, determined. Then, pattern (b) discourages social visits compared to pattern (a). Under pattern (a) urban dwellers may make more friends and consume fewer resources to visit each other. The preferences of the population and the technologies at work, together with the available resources, is what determines which pattern of sprawl is more efficient than another. There is no unique answer or one that is unequivocally determined by aesthetic, moral, or political considerations. Function, not form, is the key.

The degree of sprawl under any definition will also depend on the fiscal instruments and regulations in place and on whether such instruments have optimal values or are arbitrarily determined according to practical or political considerations. Suppose, for example, that traffic congestion is present under both patterns (a) and (b) of Figure 1, and that economic analysis finds that—under certain conditions—pattern (b) is more efficient than pattern (a). If traffic congestion is optimally priced, both patterns would be altered by such pricing. After such pricing, the more efficient pattern may now resemble pattern (a) more than pattern (b), which prevailed under unpriced congestion.

Sprawl as Low Density

Average low density or the prevalence of low-density areas relative to high-density areas is another way in which sprawl is often defined. On the chessboard we ignored variations in development density by assuming that all black squares have the same density. But if some squares are developed at higher densities, then fewer developed squares would be needed to accommodate the same total population. An extreme yearning for using density to minimize land use expansion appears in the science fiction book by Dantzig and Saaty (1973), two operations researchers. Ignoring costs, they speculated about the technological feasibility of an urban form that would accommodate a huge population in a cube with mile-long edges. They proposed this as a “livable city.” The fascination with compactness has also been expressed by asking wildly counterfactual questions such as: If the world’s 6.9 billion people lived in one city, how much land area would such a city require if it were developed at the density of the city of Paris (or Manhattan or some other high-density city)? The answer: only 331,356 square kilometers, which turns out to be the combined area of the states of Louisiana, Mississippi, and Arkansas or some similar area that is a stunningly low fraction of the world’s total land! Such utopian yearnings for compactness are fueled by the pastoralist fascination for land preservation.

Most discussions of urban sprawl bypass analysis and become inconclusive debates. There has been a polemically charged debate between urban planners and economists about the desirability of compact, high-density urban forms versus low-density sprawled urban forms. The economists Gordon and Richardson (1997) have defended low-density patterns created by the markets, arguing that either there is not much distortion caused by market failures in such patterns or, if some distortions do exist, then better pricing could take care of them. Ewing (1997), an urban planner, has argued in favor of compact patterns, defending the belief held by many planners that the sprawled low-density patterns entail significant market failures. The debate is inconclusive as it is not backed up on either side by models of economic behavior that can determine how efficiently markets are operating in allocating density.

Looking at the issue globally, it is undeniable that low-density urban development is associated with higher incomes and better transportation infrastructure in advanced countries, while high densities are associated with poverty and inadequate transport infrastructure in developing countries. The geographers Forstall, Greene, and Pick (2009) have studied data from circa 2003 on urban densities from less developed and advanced countries after making efforts to standardize the metropolitan area definitions across countries. They reported that the densest metropolitan areas were Karachi, Greater Cairo, Kolkata, Mumbai, Metro Manila, and Delhi, in that order, with average densities varying from 11,000 to 5,800 people per square kilometer. Los Angeles, Buenos Aires, London, and New York were the least dense, ranging from 1,400 to 1,100 people per square kilometer. Clearly, poorer populations demand a smaller amount of living space and poorer governments cannot provide adequate transport infrastructure. Both of these factors encourage populations to reside in high densities so that they can interact with each other by traveling on foot, by bicycle, or by other poorly motorized means. Their counterparts in richer countries demand more personal private spaces and make use of advanced transport infrastructure to interact over longer distances, residing in a sprawled, low-density pattern.

Almost all observers are aware that average densities within a metropolitan area make a poor or partial measure of urban sprawl. Yet no one, to my knowledge, has attempted to map multiple metrics of sprawl into a single measure. A recent report by the OECD (2018) measures urban sprawl from 1975 on in 1,200 cities in 30 OECD countries using satellite data. The report defines urban sprawl as “an urban development pattern characterised by low population density that can be manifested in multiple ways. That is, an urban area may be sprawled because the population density is, on average, low. Furthermore, urban areas characterised by high average density can be considered sprawled if density varies widely across their footprint, leaving a substantial portion of urban land exposed to very low density levels. Urban sprawl can also be manifested in development that is discontinuous, strongly scattered and decentralised, where a large number of unconnected fragments are separated by large parts of non-artificial surfaces. (p. 29)

Economic Versus Geographic Sprawl

Anas and Rhee (2006) introduced the concept of economic sprawl as more appropriate than the traditional physically based concepts of geographic sprawl. They proposed, in the context of their specific model, that economic sprawl be measured as the average daily travel time experienced by a city’s population. An economic definition of sprawl is more useful because it defines sprawl in terms of a variable that directly matters to people and the economy. But there are many economic variables that can matter. Congestion, proximity to open space, population density, and job density are some of these variables. Sophisticated and complex economic models would be needed to analyze the causes and consequences of geographic and economic urban sprawl patterns. This need clashes with the economist’s inner need to walk before running, to understand things using simple theoretical models before more complex models can be developed. The economist’s responsibility is to provide rational analysis of how markets work and how they fail and how such failure affects the sprawl that we observe in the real world. Economists can also strive to provide the policy and regulatory tools that can be used to restore urban sprawl to its optimal extent. As we shall see, a lot can be learned from simple models.

We will examine what economists have concluded so far about how traffic congestion affects urban sprawl. We will see that much of the belief derived in the 1970s and 1980s about how traffic congestion creates too much sprawl has been revised drastically more recently. The reason is that in the 1970s and 1980s economists used a very narrow, simple model, the assumptions of which were not relaxed until recently. We will then see what urban economists have concluded about how property tax affects urban sprawl and how urban sprawl might be affected under property tax reform. We will also examine how travel times and sprawl change under urban growth, what the effect of consumer heterogeneity and income inequality on urban sprawl is, how segregation and large-lot zoning in the suburbs has contributed to urban sprawl, the relationship between agglomeration and urban sprawl, and how the emerging autonomous vehicle technology might affect urban sprawl in the future.

The Strotz-Alonso-Mills-Muth Monocentric Model

In urban economics, the simple model that has dominated since the 1960s is the model of the monocentric city, the SAMM model.² The model’s main focus is to understand, under static conditions, the trade-off between the rent paid on land and accessibility to a jobs center and the consequences of this trade-off on residential location and density at different distances from the center. The SAMM model, in its simplest form, assumes that each urban resident works in the same urban center, which is usually modeled as a massless point, dubbed the central business district (CBD). Residents are located in a circular apron spread all around the CBD and commute to the CBD by traveling on a radius. Each resident consumes a private amount of land (a proxy for house size) and a numeraire good that is a composite of all other goods.

The model is usually cast in terms of residents who are identical in income and in preferences. By assuming that relocation costs are zero, at an equilibrium there should be no motivation to change location, hence all residents must achieve the same equilibrium level of utility no matter where in the residential apron they are located. It is shown that the equilibrium rent on land declines at a rapidly decreasing rate with distance from the CBD until, by arbitrage in the land market, it becomes equal to the exogenous rural rent at the city’s endogenously determined edge, beyond which there is farming. As a result of the high rents, residents near the CBD who have low transport costs own small lots and reside at high densities. The density falls and the lot size rises with distance from the CBD as the transport cost to the CBD increases and rent decreases with distance from the CBD.

In the standard SAMM model, the radius of the circular city and hence its area are endogenously determined and there is no undeveloped land area within the city. Sprawl in such a situation has been defined as the total developed land area, the area of the residential circle around the CBD. If the market worked efficiently, there would be no reason to be concerned with the extent of sprawl since an efficient configuration is that which maximizes the welfare of the identical residents. But if the markets did not work efficiently, then there would be a difference between the market (laissez-faire) and the optimal amounts of sprawl. A central question is whether the total land area when the markets do not work efficiently is larger or smaller than the total land area when the markets work efficiently. In other words:

Under what conditions is excess sprawl positive, and under what conditions is it negative?

Excess Sprawl in the Congested Monocentric Model

The effect of unpriced traffic congestion on urban form was first studied by Strotz (1965), and then by many others in the 1970s and 1980s using the monocentric model. Imagine that all residents distributed in the residential apron arrive at the CBD at the same time, a stylization of the morning rush hour. In the evening they all leave the CBD at the same time, the evening rush hour. Simultaneous arrivals and departures are a crude approximation because congestion would become unbearable, but the approximation captures the crux of the traffic congestion problem. Indeed, the traffic flow per mile of radial road will be higher as we approach the CBD, since more and more cars join the traffic stream. A car traveling a unit distance delays other cars traveling the same unit distance since the road capacity is finite. This causes the social marginal cost (SMC) of traffic to exceed the private average cost (PAC). The gap between the SMC and the PAC increases for each mile of road closer to the CBD as the traffic volume increases. The unpriced gap makes travel cheaper than is socially efficient and causes excessive travel. In the monocentric city this means that the city becomes more sprawled than is socially efficient (excess sprawl is positive): the radius of the city with unpriced traffic is longer, and so excess sprawl caused by unpriced traffic congestion is positive.³ The first best remedy is to establish efficiency by levying a congestion toll on each mile of road so that the gap is fully closed. This causes the monocentric city’s circular residential apron to shrink, making the city more compact and increasing densities near the CBD. It is easy to understand this result intuitively. Faced with the congestion toll, each resident engages in toll avoidance. In the basic monocentric model there is only one margin for exercising such avoidance behavior. The resident must shorten her travel distance by choosing a residence location closer to the CBD. This behavior reduces distance traveled and cumulative congestion tolls paid. Thus the positive excess sprawl caused by unpriced congestion is eliminated by pricing the congestion.

While optimal congestion pricing is the first-best policy for achieving efficiency, some authors in the 1970s implicitly considered a land use control policy as a second-best policy that can be used when congestion pricing is not possible: an urban growth boundary (UGB) that restricts the radius of the monocentric city. Because the congestion toll is not available to make the monocentric city optimally compact, the compactness is achieved imperfectly by the UGB. The UGB reduces congestion toward its optimal value but at the expense of causing a distortion in the suburban land market, where land prices rise.

Three Departures From the Monocentric Model

Two Asymmetric Monocentric Cities

Cities do not exist in isolation but within a system of many cities of varying sizes and features. A straightforward extension of the monocentric city model that is much more general is a system of two monocentric cities. If the two cities were identical in every respect, then all of the results of monocentric analysis would apply to each city. But consider that the two cities differ in just one respect: a natural amenity. The natural amenity of each city enters the utility function of that city’s residents as a free public good but cannot be enjoyed by the residents of the other city. Changes or policy interventions can cause the identical residents to relocate between the two cities at the margin, and such moving between the two cities would continue until the utility levels obtained in each city are the same.

Anas and Pines (2008) analyzed such a system of two asymmetric cities. They assumed a given total population of identical consumers for the two cities, allowing each consumer to choose the city in which they will reside, and hence the amenity that they can freely enjoy, and the distance from its CBD where they will reside in their chosen city. They allowed costless relocation between and within the cities and the same income for each resident of the two cities, consisting of the earned income, which they assumed to be the same and exogenous, and the dividend income comprised of the combined aggregate profit from converting the rural land to urban use, plus the aggregate congestion toll revenue of the two cities, both being shared equally by the combined residents of the two cities. Traffic congestion occurs in each city in the same manner described for the solo monocentric city. Consistent with the solo case, sprawl is measured as the total developed land area occupied by both cities together. By arbitrage in the land market, the edge rent in each city is equal to a common agricultural rent that is exogenously given. In the equilibrium solution of the model when traffic congestion is not priced, the high-amenity city has a higher population, a longer radius, and higher rent and residential density profiles. More people must reach the CBD in the larger city, and the congestion externality is more onerous in the larger high-amenity city.

How does the above two-city system respond to congestion pricing? An intuitive explanation is easy to grasp. Suppose that first-best congestion pricing is introduced in both cities. As already noted, consumers will adjust to congestion pricing by means of intracity and intercity allocation changes. To understand the former, tentatively rule out intercity migration and note that, in that case, the response in each city will be as in the solo monocentric city. The consumers will adjust to the congestion pricing by moving closer to the CBD, and this will shorten the radius, raising land rents and densities in each of the two cities, reducing the aggregate sprawl of the two cities combined. But removing the restriction on intercity migration, there will be a second response whereby some consumers can react to the congestion by changing cities, moving from the city where utility is lower to the city where it is higher.

Since congestion is higher in the high-amenity and larger city, consumers in that city pay more in congestion tolls. In the margin, some of them relocate to the smaller and low-amenity city. By doing so, they realize several trade-offs. First, they sacrifice the enjoyment of the higher amenity in favor of the lower one; second, they experience a smaller negative income effect from the congestion tolls in the smaller city; and third, the lower average rents in the smaller city allow the renting of a bigger lot size on average. To establish a new equilibrium, the bigger city becomes smaller and the smaller city becomes larger in population. Suppose that the intracity effects dominate the intercity effect—then congestion pricing would cause both cities to shrink in radius and to densify at each distance from the CBD, decreasing aggregate sprawl measured as the combined land area. But if the intercity effect is dominant, then congestion pricing shrinks the land area of the bigger city, increasing the land area of the smaller city. But what happens to the combined total land area of the two cities, that is, what happens to aggregate sprawl? Unlike the case of the solo monocentric city, where congestion pricing unambiguously decreased urban sprawl, in the case of the two cities the result depends on model parameters in interesting ways. Figure 2 illustrates the findings of Anas and Pines (2008). Sprawl decreases in the bigger city, while the land area of the smaller city expands.

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Figure 2. The combined aggregate urban sprawl of a system of two asymmetric monocentric cities with traffic congestion (Anas & Pines, 2008).

Panel (a) of Figure 2 compares aggregate geographic and economic sprawl when the amenity differential of the two cities is made more consequential by increasing α‎, the elasticity of the amenity in the utility function (or the importance of the amenity). In the top graph of panel (a), we see that when α‎ is small then the two cities are close to identical, and geographic sprawl measured as the combined land area of the two cities is smaller in the optimal regime of congestion pricing than in the laissez-faire (or market) regime of unpriced traffic congestion (excess geographic sprawl is positive). But when the amenity is more important, then the result reverses and the combined land area of the two cities in the optimal allocation with priced congestion is larger than under the laissez-faire regime (excess geographic sprawl is negative).

Economic sprawl in the lower graph of panel (a) is measured as total commuting cost to the CBDs of the two cities. For all values of amenity importance, the optimal cities have lower economic sprawl than do the laissez-faire cities (excess economic sprawl is positive). The policy implications are clear. First, regardless of the amenity levels in the two cities, implementing first-best optimality will reduce commuting cost. But the consequences on geographic sprawl (combined total land area of the two cities) very much depends on the importance of the amenity. Only when the importance is low are economic and geographic sprawl both reduced by shrinking the total land area, which requires making each city smaller. Otherwise, if the amenity is important enough, then in the optimal configuration geographic sprawl, measured as land area, increases as economic sprawl, measured as travel time, decreases.

If UGBs are used as second-best optimal policy tools because congestion pricing is not available, then both optimal UGBs must be restrictive when the amenity differential is not important. When the amenity’s importance is high enough, then economic sprawl is reduced by increasing geographic sprawl: the combined land area of the optimally sprawled city system is larger than the combined area under laissez-faire. The optimum is achieved by population shifting, at the margin, from the larger high-amenity city to the smaller low-amenity city. As the marginal consumer relocates from the larger to the smaller city, her lot size increases. These changes cause the land area of the smaller city to expand and that of the larger city to shrink, with combined total area expanding. If one had to use the second-best UGB instruments in each city, then one should install a restrictive UGB in the larger city and an expansive UGB in the smaller one! While a restrictive UGB limits urban land use from encroaching on agriculture, an expansive UGB does the opposite, facilitating the expansion of urban land use at the expense of agriculture.

In panel (b) of Figure 2 the parameter that varies on the horizontal axis is the consumer’s elasticity of substitution between lot size and all other goods in the utility function. Both lot size and other goods are normal goods. A difference between panel (a) and panel (b) is that in the latter the vertical axes show the excess geographic and economic sprawl, whereas in panel (a) the absolute level of geographic and economic sprawl are shown in the upper and lower graphs, respectively. When the elasticity of substitution is small, composite good and lot size are nearly perfect complements. There are only very small substitution effects, and a consumer who responds to congestion tolls by moving from the large city to the small one is affected only by the income effect of the congestion pricing. The consumer who changes cities is experiencing a positive income effect because she avoids the higher tolls of the bigger city and pays the lower tolls of the smaller city. This positive income effect induces more land and composite good consumption since both goods are normal. Meanwhile, consumers who remain in the bigger city experience a negative income effect as they pay congestion tolls. This works out to a larger combined land area and more geographic sprawl (or negative excess sprawl), as shown in the upper graph of panel (b). At the same time, congestion pricing decreases aggregate economic sprawl (lower graph of panel (b)), measured as commuting cost. As the elasticity of substitution increases, the substitution effects become important as the marginal consumer responds to the tolls by changing location in the bigger city as well as by switching to the smaller city. The first is the same intracity allocative effect of the solo monocentric city, while the second is the intercity allocative effect. When the elasticity of substitution is small, then the intercity effect dominates, causing the small city to expand and the big city to shrink while the aggregate geographic sprawl (combined land area of the cities) increases and economic sprawl (total travel cost) decreases. When the elasticity of substitution is large enough, then both geographic and economic sprawl decrease. The implications for whether UGBs—if they are used in place of congestion tolling—should be expansive or restrictive follow (Figure 3).

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Figure 3. Effect of congestion pricing on urban sprawl (land area) in a system of two sufficiently asymmetric cities. Congestion pricing in both cities shrinks the larger city and expands the smaller city. When the elasticity of substitution between lot size and other goods is small, then aggregate urban sprawl measured as the combined area of both cities increases.

Many Identical Replicable Monocentric Cities

Consider now Anas and Pines (2013), who investigated a different relaxation of the solo SAMM model. In this case the monocentric cities are many and identical to each other and the cities are replicable (the number of cities is endogenously determined) to accommodate a given total population of consumers. To create each city, a fixed investment is needed. Each city has the same amount of inelastic supply of core land surrounding the CBD. The suburban land surrounds the core land, and its supply is infinitely elastic. The market price of the suburban land is the exogenous agricultural land rent, and the amount of suburban land to accommodate the suburban residents is endogenous. Traffic congestion impacts only suburban residents who must cross from the suburban land into the core by using a bridge of limited capacity. Transport cost within the core area is assumed to be costless for simplicity. Such a city yields profits from converting the land in the core area from farms to urban use and has revenue from various instruments that may be used to improve utility. These revenues are used to finance the fixed investment.

The instruments include a congestion toll that is levied on the suburban residents crossing the bridge into the core. Other instruments are an excise tax on suburban land and a head tax paid by all consumers residing in the core area or in the suburbs. A central issue examined with the model is the combination of fiscal instruments and the profits from land development in the core (a Henry George tax on land values) that should be used to pay for the fixed investment. It is proved that when all instruments are available to the planner, then the Henry George theorem applies in modified form: the profits from land development in the core plus the congestion toll revenue must be used to pay for the fixed public good investment, while the head tax and the excise tax on suburban land should not be used. The optimality of using these two sources of revenue follows intuitively from the fact that the taxation of profits from land development in the core is non-distortionary because the supply of land in the core is inelastic and that a toll that corrects a negative externality eliminates an existing distortion. The other two instruments, the excise tax on suburban land and the head tax, are distortionary and should be avoided if the non-distortionary instruments are available.

Lower-best regimes are optimal when congestion pricing is not available, and, hence, the distortionary instruments must be used to improve utility by indirectly reducing congestion, but in each lower-best regime all of the profits from land development are always used. It is always better to use the suburban excise tax on land and the head tax together if they are both available, and this is unambiguously the second-best fiscal regime. The third-best and fourth-best regimes are achieved by using either the excise tax on suburban land or the head tax, depending on which one is available. Which of these regimes achieves higher utility depends on the strength of the income and substitution effects. If substitution effects are strong enough, then the excise tax on land is the third-best regime, but if income effects are strong enough, then the head tax regime is the third best regime. The fifth- and lowest-best regime is to use only the profits from land development in the core to fund the fixed public investment.

How do the fiscal instruments mitigate congestion in this general equilibrium system of identical cities while helping to finance the city-level public investment? The solo monocentric city model with congestion but no public investment shows core densities and core rents increasing and total land area decreasing if the congestion toll or the excise tax on land is used. But in a system of identical cities with endogenous city formation, quite the opposite happens. To improve utility by reducing congestion, under all combination of instruments described above, more and smaller and less sprawled cities emerge at long-run equilibrium with lower densities and lower rents in the core. If lot size and other goods are sufficiently complementary in consumption (have low elasticity of substitution), then it is optimal that the aggregate land area of the city system increases by the creation of more cities even as congestion tolls or the excise tax on land decrease the total area of each city and congestion in each city (Figure 4). Planners should increase aggregate geographic sprawl across all cities by investing in the creation of more cities in order to improve utility by mitigating the economic sprawl of high congestion. The regime in which the excise tax on suburban land is used is equivalent to having restrictive growth boundaries in each city. The population that is squeezed out of each city, whether by the congestion toll or by the excise tax on suburban land (or restrictive UGB), is accommodated by the creation of more cities.

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Figure 4. Effect of congestion pricing on aggregate urban sprawl: (a) when congestion is not priced there are three identical cities accommodating a given total population and each is large in land area; (b) when congestion is priced there are seven cities accommodating the same total population as in (a) and each city is smaller in land area. When the consumer’s elasticity of substitution between lot size and all other goods is sufficiently small, then the aggregate sprawl (land area) of the seven smaller cities in pattern (b) is larger than the aggregate sprawl (land area) of the three larger cities in pattern (a).

The Effect of Sprawl on Travel Times

Many observers of sprawl, including economists, recognize that highway-building programs since the invention of the automobile have contributed to urban expansion and sprawl. So conclude Downs (2004), Dunphy (1997), Glaeser and Kahn (2004), and Baum-Snow (2007). Nechyba and Walsh (2004) express this as follows: “It is difficult to imagine large increases in suburbanization without this rise of the automobile, even if other causes have contributed to the sprawling of cities in the presence of the automobile” (p. 182). The highway lobby pre–World War II resulted in urban suburban road building (Barrett, 1983) and contributed to making central city public transit uneconomical and subsidized. The lack of marginal cost pricing in urban transportation presumably made road travel too cheap (Vickrey, 1963; Walters, 1961), and the cost–benefit rules used by transportation planners may have promoted too much highway building (Krauss, Mohring, & Pinfold, 1976; Wheaton, 1978), causing too much urban expansion into suburban areas where land was initially cheap.

Although there is not much debate that travel technology reliant on cars and roads causes suburban expansion and that suburban expansion, in turn, reinforces the tendency to drive because low densities become locked in because public transit is lacking and distances are unwalkable, the role of the automobile in urban sprawl is largely misunderstood. Consider the views of a vocal proponent of anti-sprawl measures and policies, the Sierra Club. On its website, it claims that sprawl greatly increases travel times by car: “Sprawl spreads development out over large amounts of land; puts long distances between homes, stores, and job centers; and makes people more and more dependent on driving in their daily lives” and “Sprawl lengthens trips and forces us to drive everywhere. The average American driver currently spends the equivalent of 55 eight-hour workdays behind the wheel every year.” This clearly refers to an average total travel time by car of 440 hours per year, or 1.20 hours (72 minutes) per day, or 36 minutes per day one-way. Assuming 250 work days per year and the fact that non-work trips in the United States are about four times as numerous as work trips (Nelson & Niles, 2000), we are dealing with 1,250 round trips over a year (about 3.4 trips per day), or 21.2 minutes per round trip (work plus non-work trips). The Sierra Club treats such a number as being excessive. As we discussed earlier in this article, the part of travel delays caused by unpriced traffic congestion can be considered as wasteful or excessive, but not all of the 21.2 minutes per day. Nor does the Sierra Club consider that in a high-density urban environment there would be considerable travel time spent waiting at stations and moving in public transit vehicles, which are, on average, slower. Additionally, as urban economists know well, land and floor prices in very high-density cities would be higher, causing any gains in travel times to be offset by higher housing prices and lower levels of housing consumption.

The more interesting assertion in the Sierra Club’s claim, however, is that sprawl greatly lengthens travel times. By that reasoning average travel times should increase greatly with metropolitan population size since larger metropolitan areas are more sprawled in terms of total land area than are smaller ones. The log-log regression equation presented in Figure 5 dispels this notion. The slope of the regression line is an estimate of the spot elasticity of commute time with respect to metropolitan population size. This spot elasticity is about 0.1 whether the regression is run with 1990 or 2000 US Transportation Census data and commute time is across all travel modes. As explained in Anas (2015), the regression implies (keeping metropolitan public transit share constant)

an interval elasticity such that a doubling of workers across MSAs is predicted to cause a 7.77 percent increase in commute times, on average. In the year 2000 workers in Louisville were just under half a million and their average one-way commute was 22.7 minutes. In Pittsburgh with twice the workers, the commute was 25.5 minutes, and in Houston with twice again, 28.8 minutes. Chicago, with twice as many workers as Houston had 30.5 minutes, and New York with more than twice as many workers as Chicago, 34 minutes. (p. 232)

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Figure 5. The logarithm of the average one-way commuting time per day as a function of the logarithm of metropolitan population (measured by workers) for the top 49 metropolitan areas (Anas, 2015).

These cross-sectional increases in commuting times are very moderate indeed and suggest that urban sprawl does not greatly lengthen average times as apparently implied by the Sierra Club’s public statement. To further explore the issue, in Anas (2015), a microeconomic structural computable general equilibrium model calibrated to the Chicago MSA with year 2000 Census data was used. The model predicted how much travel times would increase should the population of the Chicago metropolitan area increase by 24% from the year 2000 to the year 2030 as projected by the planners. If no new road capacity is added, then congestion per mile increases. The urbanized land area expands 19%, less than the 24% population increase, but indicating that considerable sprawl will occur. However, the vehicle miles traveled per car trip actually decrease by 1.31% and the miles per car trip to work by 2.78%. Even with fewer miles per trip, the higher congestion per mile that comes from the population increase causes travel time by car to increase by 6.25% and commuting time by 4.54%, from about 30.3 minutes in 2000 to about 31.7 minutes in 2030. A number of behavioral adjustments to the increased congestion across several margins keep travel times stable, while there is a much greater increase in urban sprawl. These adjustments are: (1) switching, at the margin, of some population to locations well served by public transit; (2) responding to the higher congestion per mile by making fewer and shorter non-work trips; and (3) locating residences and workplaces closer to each other as jobs and residences suburbanize apace. Job sprawl then plays an important and useful role in keeping travel times from increasing too much in the presence of increasing urban expansion,⁴ an instance of more geographic sprawl helping to keep economic sprawl in check.

Heterogeneity and Sprawl

Studies of urban sprawl using the monocentric model and the three departures from the monocentric model that we discussed all assume that the modeled population of consumers are identical in preferences. How might the results become modified if we were to model heterogeneity among consumers? There are two important questions in this context: the first is whether heterogeneity causes more sprawl; the second, how the treatment of heterogeneity might affect the efficiency of urban sprawl. For the first question we have answers in the extant literature from two different treatments of heterogeneity in a monocentric city. Anas (1990) adds a white noise term to consumer preferences and represents consumer choices by the multinomial logit model of choice among discrete locations (rings of the monocentric city). Results are like those of the SAMM model, but increasing the white noise heterogeneity in tastes flattens the rent and population density gradients, causing the monocentric city to become more sprawled. This pattern is also shown to be the efficient solution. In Anas and Kim (1992), a SAMM model is empirically tested for Baltimore, Denver, Milwaukee, Philadelphia, Rochester, and Toledo by disaggregating the consumer population into groups by income as opposed to the standard practice of using average metropolitan income as in Mills (1972). The disaggregation causes a much more sprawled equilibrium land use pattern as compared to the aggregated approach.

As to the effects of heterogeneity on the efficiency of urban sprawl, the issue has not been investigated in the literature. It is well known that with several consumer types there can be multiple efficient allocations and that a social planner can influence which of these efficient allocations will occur by engaging in income redistribution among the consumer types. One general question, therefore, would be to identify what kinds of income redistribution would result in more sprawl. Anas and Kim (1992) showed that increasing the income of a consumer group flattens its rent profile with distance from the CBD. From this result we can conjecture, with some confidence, that making incomes more equal would decrease the sprawl of urban land use.

Sprawl, Segregation, and Spatial Mismatch

An important question is whether a sprawled metropolitan area is the consequence of race-prejudiced or income-prejudiced preferences that encourage segregation. In the 20th century, prejudice is believed to have caused white flight to American suburbs, and large lot zoning ordinances in suburban communities are often blamed for keeping poorer Americans from locating in the suburbs because they cannot afford the larger houses. There is also an alternative theory of suburban large lot zoning that claims the cause to be of fiscal origin, related to the fact that public schools in the United States are supported by ad valorem property taxes from real estate (chiefly housing) located in a school district (see, e.g., Mills & Hamilton, 1989). A richer household owns a larger house on more land than does a poorer household. Assuming the same number of kids per household, the poorer households send more kids to school per acre of land while generating proportionally lower property tax revenue per kid. This reduces school expenditures per pupil, causing lower education quality. According to this theory, large lot zoning in the suburbs is explained as an action by the richer households of a community to pre-emptively protect school quality.

Large lot zoning can cause aggregate suburban land use to increase, hence causing more sprawl. But should large lot zoning be prohibited, some of the lower-income populations currently confined to central cities would flock to the suburbs, adding to suburban land use, albeit at higher densities. Also, if policy makes segregation in the suburbs difficult, then the reduced gains from suburbanization for the higher-income groups might cause a return to the central city by some of them, which would increase gentrification and integration in neighborhoods and schools. The net effect of these countervailing tendencies on urban sprawl is unclear.

The jobs–housing mismatch problem (Kain, 1992) can be reasonably seen as a consequence of urban sprawl and large lot zoning, and indeed the mismatch should cause higher travel times for the poorer central city residents who hold suburban jobs but are excluded from suburban residences. Recent work, however, claims paradoxically that as poor and minority residents in US cities continued to relocate to the suburbs in the 2000s, proximity to jobs decreased for all residents but more so for the poor and minority households (Kneebone & Holmes, 2015).

Sprawl and Agglomeration Economies

Many urban economists claim or believe that the productivity of firms in an urban setting is driven in part by positive Marshallian externalities (Marshall, 1920) that stem from the proximity of jobs to each other and the idea exchanges and information flows that result from such proximity. Ciccone and Hall (1996) and many others have provided various estimates of the Marshallian effect that seem to support the idea. If so, then would job sprawl significantly reduce the force of such agglomeration effects by reducing the proximity among jobs? Consider, for example, a firm located downtown in the CBD. As we saw, when this firm moves to a suburban location, it can benefit from paying lower rents on land and lower wages to workers and it can charge higher prices to customers who avoid congestion when they travel to the firm. Should the suburban location have fewer neighboring firms, the firm loses any agglomeration-driven productivity externalities that it was gaining from other CBD firms when it was producing in the CBD, and the location of the firm is less beneficial to other firms in the suburbs than in the CBD. There is, however, a benefit that comes from the substitution of land for labor at the suburban location where land is cheaper. It is once again difficult to see how these countervailing influences net out. Does urban sprawl increase the productivity of firms because the substitution of land for labor makes each labor unit more productive, making up for the loss in the external productivity from the weakened agglomeration effect? The issue needs to be studied both theoretically and empirically.

The Future of Sprawl: More Sprawl or Less?

What is the future of urban sprawl? Will metropolitan areas be more sprawled or less sprawled 30, 40, or 50 years from now? Potentially important changes lurk on the horizon as an emerging autonomous car technology promises to change the economics of driving. This new technology promises to greatly reduce the value of time of the driver, since the driver would be able to utilize time in the car doing many other things: eating, reading, communicating, sleeping, etc. The value of time is by far the most important travel cost. It would be greatly reduced, making it possible to travel and commute over much longer distances than is tolerable with conventional driving. A plausible prediction is that there will be more travel and longer trips and more urban sprawl. This could also result in more congestion unless there are increases in highway capacity or new ways to use the existing capacity more intensively without worsening congestion. At the same time, deliveries of all sorts of goods and services to homes and offices are increasing too and causing more congestion. Economists should think of sprawl in a new setting of cities driven by these new technologies in order to figure out the future of sprawl and what, if anything, to do about it.