The Organization of Cities

This chapter discusses how the state might organize an economy where there are advantages to teamwork. This chapter presents a way of thinking about the liberal state that starts from the notion of its antithesis: an all-encompassing state. In an all-encompassing state, every decision in daily life is made by the state: there is no specific protection; no decentralization of decision-making; no rule of law; no specific rights (e.g., civil, labor, or property); no markets or prices; no personal or real property; and little, if any, privacy. An all-encompassing state presumably is cumbersome in operation, slow in deliberation, and highly intrusive in the daily lives of its people. How might such a state become less cumbersome, more responsive, and less intrusive? The state can decentralize or entitle in several ways: establish professional, policing, and judicial systems with some autonomy; appoint committees and boards with specified discretion; empower local governments; foster and regulate (competitive) markets; enable corporations and other economic organizations; enable and enforce contracts among individuals and other legal entities; recognize and protect (through remedies) the rights of individuals, families, and other legal entities; fund entitlement programs. In this chapter, I explain how decentralization and entitlement enable an urban economy: e.g., in terms of realty, contracts, labor markets, and local government. The big question here is how humankind in its effort to make the state work effectively ends up with competitive markets as we increasingly see them today. In important respects, competitive markets serve the interests of actors in the state better than do cooperative or consensus-based approaches. Understanding the state and how it functions is therefore essential to understanding how competitive markets came to be as they are and how these markets in turn shape the urban economy.

Why did commercial cities begin to emerge in Western Europe as they did after 1100 CE? In this chapter, I review and synthesize important thinking about the evolution of commercial cities as a market economy took hold. After discussing ideas about the state in prehistory, I trace thinking about the economic functioning of communities in the ancient world, Roman World, early medieval Western Europe, and into the rise of commercial cities. I integrate the work of Abu-Lughod, Bairoch, Braudel, Cooley, Heaton, Hurd, Mann, Marshall, Power, Smith, Tawney, Tilly, and Weber. I am not so much interested in the historical accuracy of their thinking as I am in how these writers each conceptualized a process based on purposeful behavior. Of particular interest to me is the how the notion and practice of the state changed and how this affected the formation of cities. I build this review around seven themes. Continuing from Chap. 1, I see these as follows: the importance of the governance of a nation to the urban economy; occupational division of labor, command and control, and power; decentralization and entitlement within governance; the functioning of a community as settlement, trading city, or commercial city; the significance of transportation costs, the spatial division of labor, and trade; importance of networks, routes, and nodes in circuits of trade; and the conflicted role of the city.

My explanation starts from a notion of personal and real property broadly defined to include anything that an individual seeks to acquire, conserve, and protect. I see the acquisition of personal and real property as the expression of our self-actualization and the right to property therefore as an essential human freedom. It is widely thought that the emphasis in feudal society on rights and obligations in the village life gave way to market-centered behavior in city life. Markets, by their nature, would appear to be concerned only with the right to property and to impose great risk on the unwary: raising the question of a second essential freedom in the right to a decent life: that is, the notions of (1) a minimum quality of life for everyone and (2) opportunity for advancement in one’s condition. For an urban economy to grow and prosper, there need to be sufficient incentives for all individuals to play their part. The urban economy is powered by the presence of markets and nonmarket institutions that give rise to hope that offsets the fears and risks of market participation. My interpretive review leads to six main conclusions. (1) The growth of commercial cities is linked to opportunities for profit: not for efficiency in and of itself. (2) What drives profit is the elasticity of demand; market saturation leads to declining elasticity and necessitates creative destruction. (3) An essential freedom is the ability to express oneself through the acquisition and disposition of personal and real property. (4) The urban economy requires a confidence in market exchange and its fairness. (5) The promise of equality of opportunity turns the urban economy into a joint venture for all participants. (6) Market and nonmarket mechanisms are complementary in this.

Mills (1967)—a widely cited paper in its area—was among the first to present a model of an urban economy operating under perfect competition. Even by today’s standards, the model is bold in scope; it contains 4 industry sectors, 3 factors of production, and two geographic zones (CBD and suburb). In terms of the global economy, this is an open model; factors flow freely into or out of the city in response to market prices. My intention here is to simplify and clarify the model so that we can better understand its significant implications. Mills implicitly assumes that the state has already enabled competitive markets locally in commodities, housing, transportation, land, labor, and capital. The state has decentralized its authority by empowering property and labor rights and creating incentives for individuals to participate in markets fully enough for everyone in a given market to be a price taker (small player). In market equilibrium, the city reaches a size where the unit cost of production (including land rent, wages, and paid and imputed interest)—the same for each firm in the sector—is just equal to price. No firm is able to earn any profit. Workers who in-migrate to the city are implicitly no better off as a result than those who did not in-migrate. Each unit of capital that flows into the city earns the same rate of return: presumably the same as it could earn outside the city. Despite its elegance, the absence of an algebraic solution make the Mills model difficult to understand. Further, the lengthy set of assumptions made make it difficult to separate out the significance of any one assumption.

What can a simpler model that envisages the urban economy as a producer of exports tell us about the organization of cities in competitive equilibrium? By equilibrium here, I mean first a condition whereby no firm or person has an incentive to change the way they participate in the urban economy. The model in this chapter imagines an urban economy taking into account competition in markets for labor and product that organizes the urban economy and structures its relationship with the outside world. The model imagines the urban economy consists of firms in a single industry that produce each the same good for export using constant returns to scale and this industry conforms to the economic notion of a perfectly competitive market. The model tells us about the determinants of city size and production in such an environment. First, the export price must be high enough for firms to profit from producing for export. Second, employment is proportional to output; as export demand increases, so too does employment. A constant unit cost of production means that both price and quantity in the export sector (P ₁ and Q ₁) must be exogenous to the model. The model envisages equilibrium in two markets: explicitly a single market for exports (wherein a given export bill is met where profitable) and implicitly a single market for labor inside and outside the urban economy. This model is analytically tractable (unlike the Mills model) in part because it is simple. This chapter is also a foil for models presented in subsequent chapters that are more interesting (but also more complex) because they make different assumptions. By contrasting model outcomes in the later chapters with the outcomes in this chapter, we will be able to see the significance of different assumptions.

Extending Chap. 5, the model in this chapter incorporates land to accommodate workers. With land for residences, the possibility arises that workers have to commute to their place of work. The presence of commuting costs in turn means that monopoly profit is possible even in an export industry that might otherwise be thought to consist of firms that are price takers and hence perfectly competitive. This is because the presence of commuting costs implies that the marginal cost curve for Industry 1 is upward sloped. I consider three cases here for the export industry: centralization of location with direct compensation for worker commuting cost, centralization with indirect compensation, and decentralization. While this model is competitive, it raises the question of whether firms in Industry 1 would collude, perhaps using local government, to recoup the excess profit that now flows to landlords. The organization of the urban economy reflects the fact that otherwise either firms earn different profits or workers earn different wages. In each of the three cases, the land market of the urban economy serves to equilibrate by offsetting any differences. The model in this chapter envisages equilibrium in four markets: explicitly a single market for exports and a single market for residential land within the urban economy, and implicitly a market for labor and a market for entrepreneurial talent inside and outside the urban economy. This model is better than the Mills model in that it predicts when an industry will centralize or decentralize.

In this chapter, I incorporate land for production in the export industry. There are two implications here from the fact that all firms must now be spread out in space. First, some firms will be closer to Point O and others further away. Second, some firms will be closer to workers’ residences and others further away. How are firms to reimburse workers for their cost of commuting? In addition to direct and indirect compensation, there is now a third possibility: hybrid compensation. Under hybrid compensation, firms indirectly compensate workers for the cost of commuting to the outer edge of the production area and directly compensate them for commuting costs within the production area. At any give location within the production area, firms therefore cover the costs of shipping to Point O and direct and indirect compensation of labor. Firms compete for more profitable locations until finally land rents in industrial areas generate zero excess profits everywhere. Workers similarly compete for residential land until finally there is no advantage for anyone to change location. The organization of the urban economy here is understood by focusing on the role of the marginal firm and the marginal worker under a notion of hybrid compensation. The model in this chapter envisages equilibrium in three markets: explicitly a single market for exports and a single market for land, and implicitly a single market for labor inside and outside the urban economy. This model is similar to the Mills model. However, because the Mills model does not consider compensation of commuting costs for workers, it does not ensure labor market equilibrium inside and outside the city.

What can models that envisage the city as a producer of exports tell us about the organization of cities in equilibrium when more than one industry is present? In this chapter, I present a model that contains four industries (two that manufacture for export, one that produces an intermediate good, and one that retails to residents). In Industry 1 and Industry 2, the export price is given. In Industry 3 and Industry 4, the free entry of firms is seen to drive the price of a unit of output down to marginal cost. Industry 4 imports a good then sold to local consumers at a mark-up that means no excess profit. In this chapter, labor is the only factor of production and each industry has constant returns to scale. The models assume an open economy; the supply of labor locally is perfectly elastic. Profits and imports are treated as leakages from the city’s economy. In this chapter, no land is consumed: either to house workers or to accommodate production. In this chapter, the wages of all workers in the city are entirely expended on purchases from the retail sector (Industry 4). Export prices must be sufficiently high for firms to find it profitable to produce for export and therefore employ workers. If export demand were to increase, the aggregate quantity produced by Industry 2 or Industry 1 would increase as needed without affecting unit cost or unit profit. Industry 3 and Industry 4 would grow in step with the export industries. With four industries, the model in this chapter tells us something about how the city is organized sectorally: especially between production (Industries 1, 2, and 3) and retailing (Industry 4).

What does a model that sees the city as a producer of multiple goods tell us about the organization of cities in equilibrium when workers demand land for accommodation? The city is simple: a ribbon of land with Point O at one end. The city potentially has four industries: two that manufacture for export, one that produces an intermediate good, and one that retails to residents. All firms are price takers in all markets. In Industries 1 and 2, export price is given. In Industries 3 and 4, free entry of firms drives price down to marginal cost. Industry 4 imports a good then sold to local consumers at a mark-up. In each industry, labor is the only factor of production. The model assumes all four industries have constant returns to scale. The model assumes an open economy where the supply of labor locally is perfectly elastic. The model in this chapter assumes that firms in Industry 3 locate adjacent to firms in Industry 2 (who require the intermediate good). The model in this chapter assumes that firms in Industry 4 locate adjacent to other firms on the basis that workers shop near their place of work to save on trip costs. Profits, land rents, transportation costs, and imports are treated as leakages from the city’s economy. Export prices are exogenous, but quantities are endogenous. The model in this chapter envisages equilibrium in several markets: a market for exports in each industry, a market for retail goods in the city, a single market for residential land within the city, and a market for labor inside and outside the city. Because workers now occupy space, the model in this chapter must incorporate commuting costs and the tradeoffs between centralization and decentralization. Ignoring knife-edge and null solutions, there are 12 possible configurations of land use within the city.

In this chapter, land use for multi-industry production is considered. The diagrammatic solution from Chap. 9 is extended to incorporate land for production. In this chapter, I envisage equilibrium in up to six markets: a market for each of two export industries and an ancillary industry, a single market for retail goods within the city, a single market for residential and industrial land within the city, and a single market for labor inside and outside the city. In urban economics, there is a longstanding practice of imagining that industries each have a bid rent curve (bid rents that decline with distance from the city center) and that these bid rent curves then determine the allocation of land among commercial land uses. Industries there are seen to be decentralized simply because they have a relatively flat bid rent curve. Although this chapter is also based on bid rent curves, my approach is different in several respects. First, I distinguish between industries that export and industries that do not. Presumably, it is industries that export that put a high value on access to the geographic point of export (Point O). Second, to me, firms decentralize where the cost of commuting is high relative to the cost of shipping goods. Third, when firms centralize, they separate themselves geographically from their workers; when firms decentralize, they do not. Fourth, competition in the market for residential land ensures that only one export industry can be centralized. The central conclusion of this chapter is that we need to focus not on the bid rent curves of industries, but the bid rent curves of their workers. Without accommodation of their workers, there can be no production by the industry. This insight allows for an understanding of the outcomes of the model that would otherwise be daunting.

The Mills model emphasizes the importance of substitution in production by builders and exporters in the spatial organization of the urban economy. Firms are seen to alter their use of land, labor, and capital across the city in response to systematic variations in the price for land (market rent). Mills’ approach is similar to that of Muth (1969). The Mills and Muth models assume no substitution among goods by consumers. Regardless of how costly accommodation may become as we approach Point O, the consumer always consumes 1.0 unit of accommodation. In this chapter, I now introduce substitution by consumers. I begin with a classic formulation of the Alonso model in which the consumer substitutes between size of land parcel occupied and a composite “other good”. The consumer has a budget that gets expended on commuting cost, land rent, and the other good. In a competitive land market, the rent per unit land at every location adjusts until consumers are indifferent among sites at which they are the highest bidder. Where the price (market rent) for land is relatively high, the consumer consumes less land and possibly more of the other good. This outcome is different from the models in Chaps. 5–10 where the worker is assumed to always consume the same amount of land (and the same amount of the composite other good) regardless of location. This model is then extended to cover the case where the consumer expends both money and time in commuting. Finally, a variant of the model is presented in which the consumer values not the size of the parcel itself, but rather the distance from neighbors.

How does consideration of an asset market for realty help us better understand the operation of the urban economy? On the one hand, the asset market for realty bridges the gap between the short run (current demand) and the longer run (the economic life of a building). We distinguish here between realty as an asset (over that longer run) and the role of realty in the provision by landlords of a service (e.g., accommodation) to users in the short run. In this chapter, I present and interpret a four-quadrant model of the realty market that originates with DiPasquale and Wheaton (1996). In that model, a sufficiently high asset price (for floor space) gradually attracts investment which builds up stock (net of depreciation) and thus reduces market rent and asset price until finally there is no further incentive to add to the stock. To make that model easier to understand, I first begin with a two-quadrant version. Here, new stock is added instantly in the amount needed to bring market rent and hence asset price down to where the latter is just equal to the cost of construction. The two-quadrant model is in market equilibrium. However, the four-quadrant model is only a slow approximation to capital market equilibrium. To me, the slow approximation reflects the risks of investment. Spanning from the two-quadrant model to the four-quadrant model forces us to think about risk and its incorporation into the functioning of the urban economy. That sets up the following chapter.

The Mills model treats capital as malleable; it assumes that, at the end of each time period, invested capital is recovered and then fully available for re-investment in some other best use the next time period. When we come to real estate and other fixed capital formation however, such malleability may not be present. If there is a resulting potential for loss should investors want or need to re-sell structures, fixtures, and other equipment at a future date, this risk presumably is incorporated into their decisions about the investment. In investment, there can be either upside risks (capital gains and other revenue) or downside risks (capital losses or other costs) and these may not be symmetric. In this chapter, I present a model of an export firm in a situation similar to that in Chap. 5. I assume that the firm must make a capital investment in advance (say for a building) but is uncertain as to the amount of labor that will be forthcoming to it. If the amount of labor forthcoming is low, the firm incurs the opportunity cost of the capital sitting unused. If the amount of labor forthcoming is high, the firm has the regret of not being able to earn still more profit. The model then predicts how much capital the firm commits as a function of the level of uncertainty about how much labor will be forthcoming. In general, the greater the uncertainty, the more the firm builds excess capacity. In turn, this implies “underused” fixed capital might foster new industries that cannot afford to invest capital on their own.

When asked to explain the spatial arrangement of a city today, economists typically start from the location-theoretic Alonso-Mills-Muth paradigm wherein competitive bidding for land leads to concentric rings of land uses around a city center or sub-center. With the publication of Principles of City Land Values in 1903, Richard Hurd became prominent at the time in thinking about the growth and development of modern commercial cities. Often cited and yet rarely interpreted, Hurd offers a different, but complementary, perspective on the economy of the city that emphasizes the role of real estate and the internalization of externalities through districting. Hurd wrote at a time when land use planning was largely private, not public. However, many of the tools that are used in land-use planning today (e.g., plans of subdivision, restrictions on land use, and neighborhood amenities) originated in private planning as practiced in the late 19th century. In this chapter, I re-interpret Hurd in the context of modern real estate thought and consider how a real estate perspective helps us better understand spatial arrangement in a city. In an important sense, this chapter bridges between the focus on real estate investment in Chaps. 12 and 13 and the focus on land use planning and transportation in Chap. 15 through Chap. 20. Perhaps as well as any chapter in this book, this chapter exemplifies the importance of self-actualization: homeowners using their autonomy (freedom) to make choices in the marketplace that realize a life important to them.

How does municipal land use planning affect the organization of cities? The mantra of planning is that planners fix problems created by the private market; many of these problems are characterized in general as “sprawl“. This chapter considers a linear program model—a simplified version of Schlager (1965)—in which planners allocate uses (demand for land fixed in quantity for each use) to zones (land supply fixed in each zone) within a city to be efficient. Schlager then imagines the planner’s problem as allocating, by types of land use, the amount of each land use in each zone. Presumably, a zone is an area within which the unit cost of developing land for a particular use is everywhere the same. The planner’s problem is to find a design that minimizes this total cost subject to two sets of constraints. First, the land use allocation for any zone must not exceed the amount of available land there. Second, the aggregate amount of land needed for each use must be supplied. Each constraint generates a shadow price: the opportunity cost of supplying the marginal unit of land use demanded or of the last unit of land supplied in a zone. The dual to this model tells us that planners allocate uses to zones in a way that mimics the operation of a competitive market for land and therefore gives us a baseline (foil) for thinking about the impact of other planning actions. In this model, I show the equivalence between a planned city and a city in which all land use allocation is through a competitive market in land.

In Chap. 15, I simplified Schlager by ignoring what he labels “design standards”. In this chapter, I incorporate design standards into a full version of the Schlager model. To Schlager, a design standard is an assertion about the relationship of one kind of land use to another kind of land use nearby. Schlager’s design standards take the form of either a minimum or a maximum. We might put a lower limit on a land use in a zone when that land use is complementary to other uses: e.g., having it in the zone reduces the amount of travel for persons who would otherwise have to go elsewhere to find that use. In this sense, complementarity standards are seen to reduce urban sprawl. Expressed differently, the planner might want to ensure a minimum ratio of L use to H use in any zone. An alternative here would be to use a quadratic restriction of the form X _nL X _nH  = 0 which has the effect of ensuring that the two land uses do not occur in the same zone n. We can think of Schlager’s linear approach (that is, using X _nL  < a _LH X _nH ) as also forcing X _nL to be near zero when a _LH is set close to zero. In practice, linear models are easier to work with than quadratic models. In this sense, Schlager’s approach to design standards is a neat trick operationally. As an example, one might want a public school nearby to accommodate children living in the vicinity. The design standard here would be the minimum number of hectares to be set aside for school use per hectare of land assigned to a particular kind of residential use (e.g., a single detached house). Alternatively, we might put an upper limit on the amount of a land use in a zone when that land use is a private nuisance as regards other land uses nearby. In the case of a maximum, we would then be able to limit the amount of land use of one kind where another kind is present. Here, the planner seeks to keep the nuisance land use small relative to the other use.

In this chapter, I introduce transportation costs into the model from Chap. 15. My purpose here is to lay out a way of thinking about municipal land use planning that allows us to understand how it might organize a city. The model in this chapter then shows us how a planner might alternatively address the organization of a city to take into account issues of sprawl. The model introduces transportation costs formulated as quadratic programming problem wherein the benefits of land use complementarity can be directly assessed and shadow prices (Lagrangeans) can be interpreted. I draw an important conclusion from this analysis. The planned organization of a city under this model can look quite different from the planned organization under the design standards of Chap. 16. Put differently, if planners expect design standards to get at issues of sprawl and congestion, they will be disappointed. The significance of this argument is that it refocuses urban development policy away from land use and toward the notion of prices and marginal cost.

Herbert and Stevens (1960) present an early application of Linear Programming. However, their approach is different from that used in Chaps. 15 and 16. In this chapter, groups of households (users) are assigned to districts of a city on the basis of their ability to pay the most rent (as opposed to least cost). Underlying the Herbert-Stevens model is the idea that each group has a bid rent for each type of real estate. In this chapter, I use the Herbert-Stevens model to help us better understand how a competitive market allocates land (districts) to users (groups). As with any linear program (primal), there is a corresponding dual linear program that solves for the shadow prices on constraints in the primal. In the Herbert-Stevens model, there is one shadow price for each district in the city and one shadow price for each type of user. I here follow Wheaton’s approach of assuming that the bid rent of a household is itself a function of the household’s well being: the higher the bid rent, the less well-off the household (because they have less income left over to buy other things). In equilibrium, the Herbert-Stevens model ensures that every unit of real estate is occupied by the highest bidder, every household get allocated something, and no one can be made better off by altering (reducing) their rent. I then contrast this model with the linear programs models developed in Chaps. 15 through 17 and the Alonso model in Chap. 11.

In the final model in this book, I present a simplified version of Ripper and Varaiya (1974) which uses Linear Programming to plan efficient urban development in the presence of multiple industries. The Ripper-Varaiya model assumes an infinitely elastic supply of each factor at a given factor price. As in the Mills model, it incorporates local transportation as one of its industries. The Ripper-Varaiya model uses input-output to represent the production of commodities: similar to Chap. 10. What makes the Ripper-Varaiya model different is that the city can use whatever bill of imports is most efficient. This allows for the possibility that the city is merely a transshipment point (with no production locally) if it is less costly to supply export demands from elsewhere. With a novel twist, the Ripper-Varaiya model is also able to incorporate congestion. The model determines the efficient allocation of land use within the city. While the Ripper-Varaiya model can be solved only numerically, I show how its solution conforms to findings in earlier chapter and at the same time helps us better understand the organization of the urban economy.

In Part A of this book, I began by delineating the concept of purposeful individuals who seek to realize the good life through decisions about their ordinary lives (in terms of production and family). My main argument is that this initiative shapes the economy, the political life that enables or restrains it, and the emergence of cities. In Parts B through F, I re-interpreted classic models of the urban economy in terms of this argument. In this concluding chapter, I draw together some overall thoughts about how the urban economy has advanced as an intellectual project and where future scholarship might best be focused.