...distances dwelling costs. Residents benefit if, as is likely, they prefer lower densities than in competitive equilibrium. But there is a limit to the extra commuting and housing costs that nevertheless make residents better off. Theoretical and numerical analyses are presented to show that likely parameter values almost certainly result in reductions in residents' welfare.

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Virtually all the myriad residential land use controls that pervade U.S. metropolitan areas are intended to limit densities in one way or another: minimum lot size controls, setback requirements, height limitations, subdivision regulations, rationing of municipal services, etc. (see Fischel 1985). States have sovereign control of land use within their borders, but for most practical purposes, states have assigned control over land use to incorporated municipalities within metropolitan areas. (1)

Density controls are popularly associated with suburbs, but many central cities have a panoply of controls. (2) The highest income parts of Chicago, stretching along the lakefront from the loop Central Business District (CBD) northward to the Evanston border, have had permitted densities reduced by about a third during the last 30 years or so (see Mills 2000).

This article concerns residential development and density controls. However, qualitatively similar controls are imposed on businesses, and similar analysis could be applied to them.

Scholarly papers that study density controls appear every year. Many papers contain estimates of effects of a set of density controls at some time and place. Recent high-quality analyses are Fu and Somerville (2001), Glaeser, Gyourko and Saks (2003) and Thorsnes (2000). Other papers present theoretical analyses of density controls; see Pasha (1996) and Crone (1983). Most theoretical papers, however, simply refer to possible externalities from high-density residential settlements. Fujita (1989) has done a sophisticated analysis of density controls. However, he takes no account of the effects of controls on commuting distances. The focus of this article is whether markets optimize urban density.

An idea that underlies most thinking and writing about density controls, including mine, is that they may be intended to exclude low-income and/or minority people from high-income suburbs. That notion can hardly apply to central cities as a whole but could well apply to parts of cities that have stringent density controls. A sequence of extraordinary papers by Epple and others (Epple and Platt (1998) and the references therein) shows that, with reasonable assumptions, local fiscal actions may lead to voluntary segregation even in the absence of land use controls.

Economic Analysis of Density Controls

Start with the simplest monocentric urban model, which I believe captures the essence of the issue. Similar analysis could be applied to the area around a suburban center. Assume realistically that land, structural capital and housing markets within a metropolitan area are competitive. Housing is produced with land and structural capital. The best estimates (see Thorsnes 1997) of the elasticity of substitution in housing production place it close to one, but the precise value is not important in this article. The rental rate on structural capital is exogenous to the metropolitan area, but the metropolitan area rental rates on land and housing are in competitive equilibrium so that dwelling owners, whether occupiers or landlords, receive competitive returns on their equity.

There is an unmodeled transportation system that moves workers between their dwellings and centrally located jobs at constant money and time cost per mile of travel. It has long been known that the long-run, competitive equilibrium density-distance function is as shown by [D.sub.M](t) in Figure 1. Here M refers to the competitive market and t to the miles from the employment center (CBD). [bar.t.sub.M] is the distance from the CBD to the edge of the metropolitan area, the farthest distance at which urban landowners can outbid rural landowners (perhaps farmers) for land. D(t) refers to housing density; D(t) = K(t)/L(t), where K(t) is structural capital and L(t) is land, both at t. L(t) is exogenous, but increasing in t, determined by the topography of the metropolitan area. H(t) = F(K(t), L(t)) is the total housing at t and H(t) = (POP(t))h(t), where POP(t) is population resident at t and h(t) is housing per capita at t. Asymmetrically, L(t) is exogenous, but land rent is endogenous, whereas K(t) is endogenous but structural capital rent is exogenous.

[FIGURE 1 OMITTED]

Residents have conventional convex indifference curves between housing and other consumer goods and services. Utility increases in housing per capita h(t) and decreases in t, other things being equal because of time and money costs of commuting.

It has long been known that the basic model holds even if residents have different incomes. Residents self-segregate, so that those in a given distance interval have similar incomes. Under known conditions, high-income residents self-segregate in suburbs. The same holds for density preferences. Residents with strong preferences for low density, segregate themselves where density satisfies their preferences, presumably in distant suburbs.

Density controls relate directly or indirectly to K(t)/L(t). Height limitations and setback requirements relate directly to K(t)/L(t), but restrictions to single-family housing relate in part to K(t)/L(t) and in part to POP(t)/L(t). As a close approximation, I assume that density controls relate to K(t)/L(t).

I assume that density controls are uniformly binding throughout the metropolitan area. That is contrary to the fact that controls are more typically binding in high-income than in low-income communities and neighborhoods. If controls are uniformly binding, then the density function is [D.sub.Z](t), where Z refers to "zoned," a euphemism for controls. If controls are binding, then [D.sub.Z](t) must be below [D.sub.M](t) for all t. [bar.t.sub.Z] is...

NOTE: All illustrations and photos have been removed from this article.



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