equilibria in the case of a duopoly. We generalise this literature in three ways.
First we use a general equilibrium framework with shopping, commuting and
delivery trafffic where the three types of traffic are influenced by the strategy
of the monopsonist firm. Second we study the case of differentiated rather than
homogenous goods and finally we allow for any number of competitors on the
market.
Fujita and Thisse ([5] p. 221) survey shopping center models. These models
study the endogenous location of shops and employment centers as well as con-
sumers in a linear or homogenous space. Shopping centres may exist because of
search costs or when they offer sufficiently differentiated products. Our model
has a different focus: the location of consumers is given (they reside in the city
center), the possible locations of subcenters are given ex-ante and every subcen-
ter has only one producer that offers a given variety of the good. This means
that we do not aim to study the origin, location or composition of subcenters,
instead we limit ourselves to the study of the properties of the competition
between different subcenters.
In the model interpretation we follow in this paper, we have residents that
live in the city center but shop at and commute to subcenters. This is not neces-
sarily the most common urban structure (see [1]). Our generic model allows an
alternative interpretation. In this alternative interpretation, households choose
a subcenter to reside in (they ”shop” for a residence) and they work in the city
and in another subcenter.
In sections 2 and 3 we develop the model structure. In sections 4 and 5 we
study the equilibrium and the optimum without congestion. In sections 6 and
7, we deal with the equilibrium and optimum with congestion. In section 7 we
discuss the potential and interaction of three types of policies: road congestion
charging, limiting the number of subcenters by a levy per subcenter and ex-
tending the capacity of the roads. Section 8 concludes with a simple numerical
illustration.
2 The model setting
We consider a center, and n subcenters. Residents are located in the center and
consume a differentiated good and a homogeneous good. They supply differen-
tiated labor as well as homogeneous labor. Each resident is active and provides
the same amount of work. The homogeneous good is produced competitively
in the center using homogeneous labor and requires no transport costs. We
focus our attention on the production and the consumption of the differentiated
good. There are n differentiated goods with subcenter i producing the quantity
Di.such that D = i=1...n Di In each subcenter, one producer offers one variety
of the good (e.g. due to increasing returns to scale), hires heterogeneous labor,
uses the homogeneous good as intermediary input and sells his product at the
factory gates. We denote by ti the travel time between the center and subcenter
i (distance divided by speed) per trip. Households commute to subcenter i to
supply labour with a travel time of αwti , where αw denotes the number of trips