[NOTE: A slightly revised version of this paper appeared as "Nonoptimal Levels of Suburbanization" Environment and Planning A, Vol. 35, No. 2 (February, 2003), pp. 191-198.  Please use this citation when referring to this paper.]  

I. Introduction

Non-economists almost universally despise suburban sprawl, while economists generally are more ambivalent. The issue, as seen by the economist, is quite complex and hinges critically on the nature of externalities. If all externalities (crime, air and water pollution, congestion, noise, and so on) were properly internalized in each separate market, the economists' presumption would be that there would be no role for urban planners; they could only make things worse. Land would be allocated to the highest valued use, and the city's edge would just be where it turns out to be...but wherever that turns out to be would be optimal.

Clearly, externalities are not fully internalized in cities, and it might even seem unclear whether, on net, total externalities rise or fall when households relocate from the urban center to the suburban fringe. There will generally be longer commutes, with increasing levels of pollution and congestion in the suburb, and perhaps throughout the urban area. But it is also the case that significant population movement from the central city reduces population density there, with perhaps corresponding declines in external damages received by those who remain. I speculate that most economists would guess that, on the margin, suburbanization levels have costs greater than benefits. Yet, an apparently strong "revealed preference" argument (for many decades, massive population outflows from urban to suburban areas have occurred) must certainly carry some weight. Might not the private benefits of living in the suburbs exceed the full social costs of doing so, despite concomitant externalities?⁽¹⁾

The present paper represents an attempt to demonstrate that observed high levels of suburbanization represent a socially non-optimal urban pattern. Moreover, even if we had a Samuelsonian public goods optimum for every public good in the urban core, the extent of any remaining suburbanization would still be too large.

In Section II, I present a discussion of a flaw in the valuation of public goods, drawing heavily from more in-depth treatments (see Graves 2001 or Flores and Graves 2001, the latter representing the more formal treatment). In Section III, the results of Section II are applied to the case of suburbanization. It is seen here that suburbanization largely represents the purchase of a substitute for under-provided public goods in the urban core. Critically, this under-provision is not merely that we have failed to provide "Samuelson-optimal level" public goods, but rather that the Samuelson condition is, itself, theoretically flawed. The closing Section IV summarizes and discusses potential extensions.

II. An Input Market Failure and Its Implications for Optimal Public Goods Provision

In 1954 Samuelson argued that the proper amount of public goods would be forthcoming when the aggregated marginal willingness to pay of all households benefiting from the good was equated to the marginal cost of its production. Indeed, if one could tax each household at its marginal willingness to pay, the Pareto superior amount of both public and private goods would seem to be forthcoming. He was not optimistic about arriving at that optimal public good level, due to important problems of demand revelation leading to what is now called the "free rider" problem (for potential solutions to this problem, see Clarke 1971 and Ledyard and Groves 1977).

But, there is a problem with the Samuelson condition for social optimality that has gone unrecognized. The income level was taken as given in the argument leading up to the marginal conditions, and that turns out to be of critical importance. At the heart of economics is the presumption that we work to get the things we want, for (apart from philanthropy or theft) we can only acquire the things we want through the supply of our labor and other inputs into the production process. This works fine for ordinary private goods; we work up to the point where the marginal value of goods is equal to the marginal value of the foregone leisure associated with their acquisition.⁽²⁾

However, in the case of public goods, we have a very different situation. To the extent that we value public goods, we also realize that getting extra income to buy them will accomplish nothing. There is no market to which we can buy, say, reduced global CO₂ levels or endangered species preservation. We know that we will get whatever level of public goods that we collectively decide to have (ideally, or so it might at first seem, determined according to the conditions laid out by Samuelson), and we know that any one individual's desires will have a negligible effect on that. So, since the supply of labor to get the public good would be costly, yet would have no benefits to the supplier, the income that would have been generated if we could buy public goods like we can private goods does not get generated. In other words, even in a perfect demand revelation setting, we are in a 2^nd best world, because people are failing to optimally generate the income that would have gone toward public good purchases.

Indeed, and ironically, in a world of heterogeneous preferences, the more important public goods are, relative to private goods, in one's preferences, the lower will be the observed income.⁽³⁾ Consumers desiring private goods will want to generate the income to buy the many things they desire. Rational individuals who care a lot about the environment or any other public good will generate very little income because they can't get what they want, on the margin, regardless of income generated. Hence they will substitute toward leisure which they can affect, until the marginal value of leisure is equated to their (fairly low) marginal valuations of ordinary private goods.⁽⁴⁾

III. Urban Public Goods Provision and Suburbanization

The discussion of the preceding section ignores both the presence of complements and substitutes for public goods (implicitly assuming independence) and the fact that many public goods have a spatial component. Suburbanization, however, can be seen, in part, as a spatial reaction to the failure to produce optimal quantities of local public goods in the urban core.

Consider individuals living in the urban core. The urban core typically has many problems (crime, pollution, congestion, noise, etc.) that are, at least partially, of a local public good nature. Non-optimally low levels of such public goods are provided in the urban core, with core residents under-generating income. Were we to get to the Samuelsonian optima for those goods, those levels would, per Section II, still be too low.

Were there perfect private good substitutes for all public goods, the correct amount of income would be generated and the, now larger, flow of private goods would be purchased with the larger incomes generated⁽⁵⁾ While not perfect, there is a spatial substitute for directly improving levels of urban crime, air quality, noise, and congestion, and so on-moving to the suburbs. As a consequence, many people will generate the income to acquire the higher levels of some local public goods in the suburban areas. But, suburbanization, with associated lengthy commutes and reduced goods consumption choices (restaurants, cultural amenities, etc.) is a poor substitute for direct increases in the provision of urban public goods. And, in the cases of some public goods (e.g. pollution in areas such as LA), suburbanization might fail to deliver much in improved consumption levels.

Hence, we observe non-optimal movements to the suburbs because of the failure to have the right amounts of public goods provided in the urban core-even if we had both perfect demand revelation and perfect information in applying the Samuelson aggregation rule.

More formally, define X₀, L₀, S₀, and Q₀ as the initial quantities of ordinary goods, leisure, lot-size, and the collectively determined public good.⁽⁶⁾ Assume initially that all economic agents are located in a homogeneous central city, effectively ignoring the spatial nature of cities. The representative agent will have failed to give up leisure to generate income to buy public goods, even if that agent has very high marginal benefits of the public good, because doing so will not enable any more of the good to be acquired. City residents will have adjusted leisure (and private goods), whose benefits they can capture by foregoing income, purchasing more of each than is optimal. That is,
 

(1) U₀ = U(X₀, L₀, S₀, Q₀) << U(X*, L*, S*, Q*) = U*
 

where, under independence, X₀ > X*, L₀ > L,* S₀ = S*, Q₀ < Q*, and the double inequality indicates that a large disparity exists between the constrained utility values (when the public good cannot be purchased with incremental income) and the unconstrained values⁽⁷⁾. Lot-size, S, is assumed the same in the initial case because there is a fixed number of people and suburbs do not yet exist.⁽⁸⁾

With suburbanization offering a (poor) substitute for in situ provision of public goods, we will observe a utility-enhancing (relative to U₀) increase in optimal levels of income generated to buy in private land markets the higher levels of local public goods available in the suburbs. In the traditional monocentric urban modeling context, the additional income will be buying not only higher (but not necessarily optimal) levels of local public goods, but will also be buying longer commute times, a joint bad. Additionally, suburban residents will be foregoing other desirable aspects of locating at the urban center (restaurant variety, cultural activities, and other density-dependent goods). Since rent compensation would result in equilibration of utility across the city-suburb location choice, we have:
 

(2) U(X₀, L₀, S₀, Q₀) < U(X_S, L_S, S_S, Q_S) = U(X_C, L_C, S_C, Q_C) << U(X*, L*, S*, Q*)
 

That is, the utility associated with moving to the suburbs will be greater than if that option were unavailable, but there is still a potentially large divergence between utility at either suburb or center vis-à-vis optimal in situ public goods provision. Rents in the suburbs will be bid up from initial agricultural levels, while those in the city will fall relatively, as people move to the suburbs. The lot-sizes will be larger in the suburbs than in the center, that is, S_S > S_C. Whether income generated and goods consumption in the suburbs will be greater than under the case of optimal in situ central public goods provision is ambiguous.⁽⁹⁾

The problem, at heart, is one of inability to disbundle locally provided public goods, including access in particular. To get higher levels of environmental or school quality by buying a suburban substitute location, one must accept lower levels of access to work and entertainment. Suburbanites are unable to buy exactly what they want, but only some of the things they want, by the very nature of space.

How great is the empirical relevance of the point made here likely to be in the "real world?" The importance of the argument here is apparent from the hedonic compensation that yields the middle equality in Equation (2). With fully informed people and no exhaustion of people-types on the margin, the rents or property values at the suburban fringe will leave identically-situated households with the same utility in the suburbs as those at the urban center. But, those in the center are continuing to consume the sub-optimal amounts of the many urban public goods that the suburbanites are receiving; the only reason they are better off is that the movement to the suburbs will have lowered their rents somewhat.⁽¹⁰⁾

Hence, commuting costs and losses of other urban public goods largely offset the gains in utility from higher levels of public goods associated with moving to the suburbs. People will have generated more income to enable them to move to the suburbs to get the local public goods they so desperately want, but they don't really make themselves much better off. Rather, while greatly changing their behavior in terms of what they buy, people move along a utility surface that is only slightly shifted outward by movement to the suburbs. Hedonic compensation, if full, guarantees that; there will, of course, be sorting with perhaps entire groups exhausted at the center, hence there could be a non-negligible utility gain to some suburban movers. Provision of the proper amounts of public goods at the center is, however, clearly preferred to observed patterns of suburbanization.

But history is what it is. How do we decide, now that suburbanization has proceeded at non-optimally high rates for many decades, where to supply marginal increments in local public goods? We can improve street lighting or crime rates in the city or in the suburbs-where should the public goods be supplied? The spatially optimal distribution (of a much larger than the Samuelson optimal total amount) of public goods will favor the central urban area, because for any given marginal cost, any provision there has more marginal benefits because of greater population density.⁽¹¹⁾

Pondering the longer-run implications of providing the urban core public goods in situ rather than requiring the purchase of poor substitutes at the suburban fringe offers further insight into the advantages of properly valuing public goods. Were clean air, noise abatement, quality schools, reduced congestion and the like provided directly in the right amounts in the central core, the net associated cost increases (and income generation increases) might not be as large as one might initially surmise. As mentioned earlier, people are already generating much income to buy poor suburban substitutes for urban public goods. For example, providing quality urban public schools would eliminate both the expenses associated with sending children to private schools currently (for many occupying the urban centers), and would allow those who moved to the suburbs for better schools to return to the center, saving commuting and other costs.

The enhanced values of central locations would raise rents and property values in the center relative to the suburban fringe. This would have the long-run effect of encouraging greater density as capital is substituted for the relatively more expensive land at the center. This, in turn, would facilitate the spread of viable mass transit, including just walking, as opposed to the current situation that tends to increasingly discourage alternative transport modes over time. The greater population density would allow many (or perhaps all⁽¹²⁾) cities to enjoy the kinds of cultural and restaurant amenities now taken for granted in only a few urban areas. Indeed, if the correct amounts of public goods were provided in central locations, the principle determinant of suburbanization would be the income elasticity of demand for lot-size relative to the income elasticity of commuting costs, independent of the local suburban public goods that are at present positively correlated with lot-size.

IV. Summary and Generalizations

An input market free-riding flaw will inevitably accompany the output market failure resulting from the nature of public goods. The output market flaw has long been recognized; it is unprofitable to produce goods whose consumption cannot be excluded. And, zero marginal social costs of usage imply that any positive marginal charges would, in any event, non-optimally discourage individual consumption. But, even governmental provision in what would seem to be the right relative amounts (comparing the vertically summed demands with marginal cost, at a given income) yields the wrong amount of the public good. This is because households will generate the wrong amount of income when generating that income doesn't allow increments in the public goods they care about. We work to buy the things we want-when we cannot get those things by working, rational people will not work.

In the case of suburbanization, however, people will generate the income that will allow them to buy higher levels of local public goods in the suburbs, but this is a poor substitute for in situ provision of those public goods on efficiency grounds.

The failure to get the right amount of the public good has more general non-spatial implications for the optimal quantities of private goods provided. The suburbanization result generalizes to private goods lacking a spatial nature that are substitutes and complements for public goods. Any private good which is a substitute for a public good will be over-produced relative to its optimal production, were public goods provided in the right (larger) relative amounts. For example, private personal protection goods and services (locks, burglar alarms, protective weapons, costly altered behavior, etc.) are over-consumed when the provision of police public good protection is under-provided.

Similarly, though not stressed here, private goods that are complements with public goods will be under-produced when the public goods are not produced in their larger optimal quantities. As the classic example, consider the lighthouse that fails to get built because the benefits, even with a perfect demand revelation Samuelson rule, fall a bit short of the costs. Because those benefits are calculated without the income that would have been generated to buy such goods were they available for purchase, it is quite possible that the lighthouse should have been built. But, if the lighthouse were built, the demand for boats (which is, after all, a demand for a stream of safe boating experiences) would have been higher. Thus, there will be an under-provision of private goods that are complementary with public goods in the current milieu of free riding in input markets.

Suburbanization has been occurring for many decades. This suburbanization has been widely vilified, but with arguments that were largely unconvincing to economists. The present paper provides an argument suburbanization has proceeded, and continues to proceed, at too rapid a rate. The high post-WWII growth in income and population (combined with the input market failures emphasized here) would suggest that far higher levels of local goods should have been, and should be, provided in our large urban areas. Producing those local public goods at optimal levels would result in far less suburbanization than has been observed over the past half-century.
 
 

Clarke, E.H. (1971). "Multipart Pricing of Public Goods." Public Choice. 11: 17-37.

Groves, T and J.O. Ledyard (1977). "Optimal Allocations of Public Goods: A Solution to the "Free Rider" Problem." Econometrica.45 (4): 783-809.

Flores, N. and P.E. Graves (2001). "The Valuation of Public Goods: Why We Work." manuscript.

Graves, P.E. (2001). "Valuing Public Goods." manuscript

Samuelson, P.A. (1954). "The Pure Theory of Public Expenditures." Review of Economics and Statistics. 36: 387-389.

Tiebout, C. (1956). "A Pure Theory of Local Expenditures," Journal of Political Economy. 64: 416-24.

1. Many years ago an author (who I will let remain anonymous) of a book that represented a stinging criticism of suburbanization in the Chicago context, sheepishly admitted in a Chicago Tribune interview that, yes, he lived in the suburbs. He justified this by saying he wished he could afford to live in the city, but it was too expensive.

2.  Indeed, the point is more general. In any decision involving additional income (e.g. schooling or training) the marginal benefits of expected future goods gained are compared to the costs of the training. The focus here, for simplicity, is only on short-run work-leisure decisions.

3.  Marginal willingness to pay, in situations involving real money, typically looks small, relative to stated willingness to pay in hypothetical situations. Traditionally, this is viewed as "hypothetical bias" in the contingent valuation literature. The argument here suggests that it is the real-world payments that may be "wrong," because the wrong income is being generated. The big "hypothetical" numbers might be paired with respondent increases in work effort to get the necessary income (for people generally realize that they have to pay for the things they want). The number recorded by the researcher as current income, in stated preference studies, may not be appropriate. Hence, the stated preference numbers could be more valid than generally presumed--in the proper conceptual experiment.

4.  They may also pursue less remunerative occupations (e.g. working with environmental groups and the like) that offer an alternative means of impacting provision of public goods.

5.  Perfect private market substitutes effectively eliminate the public goods problem; income generated would be optimal, the proper amounts of all goods would be produced, and there would be no problems of either demand revelation or input market failure. Note that the prospect of a perfect Tiebout 1956 world is even more dubious in the present urban-suburban spatial context. The bundling of both non-governmental (e.g. access to the center) and governmental location-specific public goods results in an internal contradiction--to get the range of local goods required to have efficient provision would require so many jurisdictions that cross-jurisdictional spillovers would defeat that efficiency.

6.  Vector notation for both ordinary goods and for public goods is suppressed for simplicity, as is potential capitalization of local public goods in labor markets in addition to land markets.

7.   Note that the disparity might have been relatively small when we first began providing public goods collectively. For example, when environmental programs were first promulgated, as the environment quality freely available from nature came to be viewed as inappropriately low, the spread between optimal and actual utility might have been small. But, as income and population have grown over time, the marginal values of public goods relative to those of the ever-increasing quantities of private goods has doubtless risen sharply.

8.   It is possible that the portion of private goods that are housing-related might imply larger lot-sizes before optimal public goods provision, though this is not critical to the argument. When suburbs begin to exist, equilibrium lot-sizes will become larger at the edge for the usual monocentric reasons.

9.   It would seem clear, however, that issues of what is a "good" versus a "necessary bad" that appear in discussions of national income accounting would become quite relevant in this setting. Moreover, the same type of consideration would apply to leisure activities. Consider, for example, increased commuting that draws equi-marginally from work and other leisure activities. The increased commuting would both raise GDP and increase official measurements of "leisure," but would hardly be seen as a good thing by typical agents.

10.   Indeed, suburban flight may cause added losses in some urban amenities, off-setting rent reductions.

11.  Current population densities, of course, bear no relation to what they would be if urban public goods had been optimally supplied over time. One might speculate that Tokyo would be considered not very densely settled if urban public goods had always been provided optimally, but policy approaches for some public goods (noise pollution, for example) might also involve less-dense living schemes, as could income effects on lot-size. The net impact on average urban density would seem to be clear, however.

12.  Some smaller cities might reasonably be expected to disappear when larger urban areas are as desirable as they would be under a longer-term scenario.