Private Nuisance, Zoning, and the Urban Economy

Abstract

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.