The optimum number of subcenters in the absence of road pricing but with
--ʌ--.
optimal road capacity nbo solves: dW (n) /dn =0or
no = μ + μw) N.
(46)
F
Note that, as a consequence no < nbo,where no is given by 22 .In the long run
and when the roads are optimised, the number of subcenters is larger with than
without congestion. Without congestion, the incentive to have more sub-centers
is to benefit from more product and more labour variety. With congestion,
there is an additional incentive to deconcentrate shopping and working place,
since more centers tend to decrease overall congestion levels. As extending road
capacity is costly, it remains optimal to have more subcenters in the case of
optimal road capacity. Note that if the government could decide the number
of subcenters given that firms will compete (in the goods and in the labour
market), it will again choose nb. In this case, the welfare level will be the same
as in the case where the firms are managed by a central authority subject to
the constraint that they have to break even.
7.3 Optimum number of subcenters and road capacities
in the presence of congestion charging
Before discussing the effect of charging instruments it is useful to remember that
we model congestion by using the bottleneck model. In the bottleneck model
the different road users reach an equilibrium distribution of their trips over time
when the sum of queueing and schedule delay costs are equal. When there is no
congestion charging, there is queueing and this is a pure inefficiency as a perfect
rearranging of users over time can eliminate all queueing costs.
We will discuss two congestion charging instruments.The first type of toll is
a fine toll that can be perfectly differentiated over the full period considered.
The second type of instrument is a one step toll. A one step toll means that
the relevant period can be subdivided into two periods: one period with a fixed
toll and one period without a toll. This is a much simpler but also a socially
less performant instrument than a fine toll. We could consider other charging
instruments (cordon tolls or parking levies that are not time differentiated) but
these can in our simple model be reduced to head taxes per consumer or to a
levy per firm. Fixed levies are not able to change the distribution over time of
trips and are therefore not efficient in reducing congestion. They can only affect
the total level of demand for the differentiated good but this is fixed.
With the bottleneck congestion model [4], the total variable travel cost per
individual (b) 2 П N can be reduced by a factor 2 when an optimal fine toll is used
and by a factor 4/3 when an optimal one step toll is used. With an optimal fine
toll, there are only schedule delay costs left as queueing is by definition inefficient
and therefore eliminated. The average congestion charge that corresponds to
the fine toll equilibrium will be equal to the average schedule delay cost. With
an optimal coarse toll, queueing is not completely eliminated.
21