structure of an economy. Krugman (1998) also discusses the formation of urban areas in a dynamic
context. By drawing on economic base theory and potential analysis the concentration of production
is argued to be self-reinforcing.
In the model to be presented the only known characteristic of the geography is the location of the
city center (CBD). The spatial distribution of population is not specified, and we do not model the
level of local sector activities in specific locations. What we model is the propensity that households
do their shopping locally rather than in the city center. This propensity is represented by the fraction
of local sector employment relative to population in specific locations; E/L. Hence, this fraction
reflects the spatial shopping behavior of households. The spatial distribution of E/L can be explained
through the same kind of mechanisms that are relevant when the center structure in an area is to be
explained. For this purpose Krugman (1995) distinguishes between two general sorts of
interdependence of business activities. First, the “centrifugal” forces reflect the competition for
customers, workers and land. This competition promotes a spatial dispersion of business. Second,
the “centripetal” forces reflect positive external scale effects of a cluster of stores that offer a variety
of goods and services. Such forces attract customers to an area, and promote agglomerations of
business activities.
In this paper we consider E/L as the net result of centrifugal and centripetal forces. The centripetal
forces explain why a city center in general offers a larger variety of consumer goods, and different
kind of scale economies explain why a positive relationship can be expected between city size and
productivity, see Quigley (1998). For the same reason it can be argued that stores in the city center
in general will offer goods and services at lower prices than more peripherally located stores. Such a
tendency can also result from a game theoretical approach to spatial price competition. In de Palma
et al. (1994) findings suggest that prices tend to be lower at centrally located stores, which face the
most competition.
In this paper the centripetal forces will be represented by price reductions, while transportation costs
of potential customers represent the centrifugal forces. We start out with a situation where there is
only one type of good. Hence, we first ignore the possibility of multipurpose shopping in a setting
with a diversity of goods. We also ignore the possibility of congestion. Providing the consumers with
this service, a number of E1 employees is needed pr 1000 customers. This in turn defines the ratio
E/L=E1/1000 (which we conveniently measure in terms of employees pr 1000 workers). As long as
the traveling cost remains below the price reduction, nobody wants to do their shopping in local
firms. Hence E/L=0 in this case. At some particular distance, however, the traveling cost will begin
to exceed the price reduction. At this point we assume that local stores will take over the whole
market, and correspondingly E/L=E1/1000 from this point on. This situation is illustrated in Figure 2.