Abstract: Paper No. 157

A Comparative Static Analysis of an Open Urban Model with a Full Labor Market and Suburban Employment

Stephen Ross and John Yinger

With few exceptions, mathematical models of urban spatial structure are based on restricted assumptions about the urban labor market. In particular, they assume that either or both wages and the demand for workers are fixed and that all employment is in the central business district (CBD). This paper provides a comparative static analysis of open urban models with more realistic labor markets, in which the demand for labor is derived from the production of an export good. The analysis, which employs general functional forms, is applied initially to an urban area with all employment in the CBD and then is extended to consider two models with suburban employment, one with a beltway and the other with a discrete suburb.

A few of the authors' comparative static results, such as the impact of agricultural rents on the physical size and population of an urban area, are the same as in the standard urban model with exogenous wages. However, adding a full labor market adds ambiguity to several other standard results, including the impact of a change in commuting costs on the characteristics of an urban area. Moreover, a full labor market requires the introduction of two new parameters, the price and shipping cost for the export good, and transforms wages from a parameter to a variable.

Many of the comparative static results for a monocentric model with a full labor market carry over to the models with suburban employment. For example, an increase in the export good, an increase in the exogenous utility level, an increase in the agricultural rental rate, or a decrease in shipping costs for the export good lead to an increase in wages in all cases. However, adding suburban employment enriches the model by accounting for interactions between labor markers and by allowing some parameters to change in one labor market but not the other. The authors show that, in almost all cases, wages in city and suburban labor markets move in the same direction in response to an exogenous shock. The only exception is that an increase in commuting costs in one market raises wages in that market but has an indeterminate impact on wages in the other market.

Finally, the authors show that the comparative static results are remarkably similar for the beltway and discrete-suburb models. In fact, only one result is different for the two models: movement of the residential boundary between city and suburban workers in response to a change in agricultural rents is negative (that is, toward the CBD) for the beltway model and ambiguous for the discrete-suburb model. Therefore, despite the lack of realism of the beltway model it may be a suitable vehicle for analyzing aspects of suburbanization other than the changes in the boundaries of suburban workers' residential zone.

The revised version of this paper was published in Regional Science and Urban Economics, October 1995, pp. 575-605. Those interested in this work should see that journal.