Imperfect competition and congestion in the City



1 Introduction

This paper presents a model to study imperfect competition with congestion.
We use this model to study the price and wage setting as well as the equilibrium
number of differentiated shopping and workplace subcentres. Urban residents
live and work in the center, while they also work and buy differentiated goods
in subcenters. The shopping centers hire workers with differentiated disutilities
of work and import intermediate goods from the center. Shoppers, workers
and trucks share the same congested road infrastructure from the center to
each of the shopping centers. There is only one producer per subcentre and
he maximizes profit. He makes decisions on the price of his differentiated good
variety and on the wage he needs to offer to attract workers. Lowering his price
attracts more customers but also generates many more effects in this model.
More customers means more congestion by shoppers, forces the firm to hire more
workers and this requires higher wages. In addition, more workers also create
more congestion and more customers also require more deliveries by trucks that
have also become more expensive because of congestion.

We analyse the non-cooperative equilibrium in prices for this type of economy
using a general equilibrium setting and a logit representation for the differen-
tiated goods. The existence and welfare effects of equilibria with and without
congestion are analysed. The effect of congestion and infrastructure charging
policies on the price and wage setting and on the equilibrium number of sub-
centers is studied too.

Our model can be compared to three strands of the literature: the imperfect
competition literature, the literature on congestion pricing with imperfect com-
petition and the literature on the endogenous location of shopping centers. Our
model uses the logit model to represent differentiated goods. Compared to the
traditional models of imperfect competition (surveyed in [8]), our model offers
two additional features. First, it examines imperfect competition in a general
equilibrium framework as the labour market and the delivery of intermediate
goods are explicitly modelled. Second, our model introduces congestion. Both
elements will be shown to have an important effect on the imperfect equilibrium
outcome. Introducing a general equilibrium framework and a differentiated job
market offers much more complexity as firms compete on two markets rather
than one. The equilibrium mark-up and the equilibrium number of firms are
shown to be increasing in the product and job heterogeneity parameters. Con-
gestion adds another component to the equilibrium mark-up because conges-
tion acts as a disincentive to cut prices. The welfare economics of the number
of firms also changes as we now have two market imperfections that interact.
Congestion (and market power) can be relieved by having congestion pricing,
by having more subcentres but also by having larger road infrastructure. The
three strategies are to some extent substitutes.

The interplay between congestion and imperfect competition has already
been covered in the case of homogenous goods for a monopoly by [7], and for
a duopoly by [6].They show that the optimal congestion charge is smaller than
the Pigouvian charge and that the homogenous good case can lead to multiple



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