Imperfect competition and congestion in the City



Introducing congestion pricing via a fine toll, will affect the mark-ups in two
ways. First via the cost of intermediate deliveries and second via the margin on
consumers as this depends on congestion too. The trucks delivering intermediate
goods to firms will now pay, on average, a congestion charge but they will on
average also experience less congestion. The net effect is zero in the case of
the fine toll, so optimal congestion charges do not affect the cost to the firm of
intermediate deliveries. The second effect is clearly negative: congestion pricing
decreases the mark-up of firms since the congestion protection of the market
is largely eliminated: where as decreasing the price attracts new customers
and thus more congestion but this congestion is taken care of by the fine toll.
Alltogether, the profit margins are smaller with fine tolls than without tolling.
Using the same arguments as for Proposition 4, we have:

Proposition 7 Assuming fixed road capacity and optimal congestion pricing,
there exists a unique symmetric Nash equilibrium in prices and wages where the
producer price and wage is given by:

pCp = c +     + wep + (μd + μw }    + + ʒ b2          (47)

cp n cp             n - 1   2n s

and the average consumer price including toll is:

Pecp + αd δ~ N α                        (48)

cp      2n s

while the average net wage after deduction of the toll is:

w - αw δ~                     (49)

ep      2n s

In this analysis, it is assumed that the firms anticipate the change in the
toll level when they decide to change their price. This rational behavior may be
questioned. Alternatively, one can assume that the toll level is not changed in
reaction to price changes.

Proposition 7 implies that, for any given road capacity and any given number
of firms, profit margins will be lower with road pricing. As a consequence the
number of subcenters that will exist in the long run will be lower with road
pricing than without road pricing.

Assume the government can also determine the size of the roads and price
them optimally. Maximising welfare with respect to road capacity s, taking into
account that travel costs are reduced by a factor 2 with an optimal fine toll, we
obtain:

o -ON δi
sep(n)    nξ V 2.

So that in the optimum, the total construction cost per individual is independent
of the number of subcenters and is equal to:

22



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