reason is that the influence of congestion on the profit margins becomes much
smaller compared to the benefit of variety. The relative contribution of the three
policy instruments is different than in the base case. The control of the number
of subcenters is an ineffective policy instrument with very small welfare gains:
ranging from 0.004 in the case with congestion to 0.009 in the case without con-
gestion. The introduction of road pricing again generates an important welfare
gain: 0.140. In this case, the most important policy instrument is the control
of the size of the roads combined with the control of the number of subcenters.
This policy that induces many more subcenters (16 rather than 10) and much
narrower roads (46.5% of the base case) leads to the most efficient equilibrium.
We have studied so far the symmetric model which allows us to derive ana-
lytical results. It is straightforward to write down the non-symmetrical version
where costs, quality and transport costs are different for the different subcen-
ters. In this case it is necessary to use numerical approaches based on variational
inequalities to analyse the properties of the solutions.
INSERT TABLE 3 about here
References
[1] Anas, A., Arnott R and Small K., (1998) , “Urban spatial structure”, Journal
of Economic Literature, September, p 1426-1464.
[2] Anderson, S., A. de Palma and Y. Nesterov, (1995), ”Oligopolistic competi-
tion and the optimal provision of products”, Econometrica 63, , p 1281-1301.
[3] Ginsburgh V. and M. Keyzer, (1997), ”The structure of applied general
equilibrium models”, MIT Press, Cambridge, 1997.
[4] Arnott R., A. de Palma and R. Lindsey, ”A structural model of peak pe-
riod congestion: a traffic bottleneck model with elastic demand”, American
Economic Review, 1993, 83(1), p 161-179.
[5] Fujita M. and J.-F. Thisse,”Economics of Agglomeration”, Cambridge Uni-
versity Press, Cambridge 2002.
[6] Van Dender K., ”Nash-Bertrand Competition in a duopoly with congestion”,
Discussion Paper, Irvine.
[7] Edelson N. M. ”Congestion tolls under monopoly”, American Economic Re-
view, 1971, p 873-882.
[8] Anderson S., A. de Palma and J.-F. Thisse, ”Discrete Choice Theory of
Product Differentiation”, MIT Press, Cambridge, 1992.
26
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