Imperfect competition and congestion in the City

economy in the short run since the demand for the differentiated goods and
the differentiated labour supply are inelastic. We show below that the market
power of firms induces excessive entry in the long run.

If firms pay the total cost of the road infrastructure to their subcenter (S =
K), the equilibrium number of subcenters is larger than the optimum one (n^f >
no), where nf is given by (18), and n⁰ is given by (22): n^f = 1+ (μ^d + μ^w) FNK
and

n^f =1+n^o.                         (23)

[8] showed that monopolistic competition in a product market with a logit model
always generates an overentry of exactly one firm. We generalised this result
to a general equilibrium context. The intuition for this result is that the intro-
duction of an heterogeneous job market corresponds to an additional source of
heterogeneity. However, since the labour and product market are related, the
total degree of product heterogeneity stays about the same and the number of
firms is too large by exactly one unit as in the case where there is only product
differentiation.

Assume that 1 ≤ no, that is (F + K) /N ≤ (μ^d + μ^w¢.5 In this case, since
there is excessive entry, there exists a level of tax which can decentralize the
social optimum. The optimal tax is given by:

no K + F
(no — 1)

Therefore the firm should optimally be charged more than the price of the
infrastructures (since S>K). We have.

Proposition 3 In the absence of congestion, in a free-entry Nash equilibrium,
the first-best optimum can be decentralized by a levy per firm larger than the
infrastructure cost per subcenter. If the levy covers exactly the infrastructure
cost per subcenter,at equilibrium there is one subcenter too many.

6 Equilibrium with congestion

6.1 Model setting

We have assumed till now that the travel time on road i, ti , is constant. From
here on we drop this assumption so that the travel time cost on road i is an
increasing function of the number of users on this road. Each road is occupied
by the shoppers and by the commuters as well as by the trucks that deliver the

⁵ The minimum number of firm at the optimum is equal to one, since each consumer has
to buy a pro duct.

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