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Yet just the reverse applies for neighborhood characteristics; the household chooses one from among many locations, each of which is characterized by a fixed set of attributes. The existence of fixed bundles of attributes at each location implies the household confronts significant constraints on the set of attributes it may consume. These constraints exist even when location is continuously variable, and are not to be confused with constraints which arise when the choice set with respect to location is discontinuous, as when a finite set of neighborhoods is available.

In the traditional monocentric model proximity to the center reduces commuting costs, hence land rents must decline with distance. , people may value distant sites more highly in spite of the longer commute. Let amenities at any distance u be represented by a scalar, a(u), which enters positively into the utility function. V(z, q, a(u)) [Polinsky-Shavell (1976)]. " Differentiating the indirect utility, V*(P(u),yy-T(u), a(u)), yields equilibrium rents such that households are indifferent to location.

Yinger (1976). Kern (1981)]. The stability of integrated or segregated residential outcomes in this class of models depends on preference functions and supplier behavior. Inferences regarding stability of residential patterns can be drawn by examining bid rent functions of both races. Bid rent gradients which make whites and blacks indifferent to location can be readily derived from the indirect utility function, with neighborhood racial composition one of the arguments. Whereas Yinger suggests that a segregated solution will be stable only if sustained by discriminatory actions by sellers, Kern (1981) shows that complete segregation can exist if both whites and blacks prefer white neighbors, but preferences of whites for white neighbors are stronger than the preference of blacks.