congestion pricing. In this table, we report results as real numbers (even if the
number of firms can also be treated as integer). In the absence of congestion, we
have 3.7 subcenters in the free entry equilibrium. We report the gross margin
p - w and not p and w separatly since w can be chosen freely. This margin will be
higher when the benefits of variety (for products and for workplaces) gets larger.
If there is no congestion, the optimal number of subcenters equals the free entry
equilibrium number minus one (2.7) and the welfare loss per individual due to
the excessive number of subcentres is small: it equals 0.023 to be compared
with an expenditure on differentiated goods of 1.62 and a total welfare level of
10.565. With congestion, we see that the gross margin increases and the free
entry number of firms increases from 3.7 to 5.014.The introduction of congestion
results in a lower welfare level: (- 0.330). One can use three policies to improve
the free entry equilibrium with congestion. The first is to limit the number of
subcenters. Using fixed fees on firms that exceed the public infrastructure costs,
this policy would result in a lower number of firms: 4.35 rather than 5.014. The
welfare gain of this type of policy is also very small: 0.004. A second policy that
can be used is to combine a different number of firms and a different road size
(by appropriate taxes). The optimal policy would, in this case, result in slightly
more subcenters (5.333) but smaller roads. (94% of the road size in the free
entry equilibrium). Recall that the road size in the free entry equilibrium with
congestion was by assumption optimal for this equilibrium number of firms.
The welfare gain of being able to adjust the number of subcenters becomes
much larger when the road size can also be adjusted: the welfare gain compared
to the free entry equilibrium is 0.124. A third policy, that can be used is to
introduce road pricing. This will again decrease the number of subcenters: in
the free entry equilibrium only 4.407 firms can survive leading to a welfare gain
of 0.149. We can combine the three policies in different ways. When we add to
road pricing, the possibility of controlling the number of subcenters, we have a
smaller number of subcenters: 3.78 and this means a slightly higher welfare gain
than road pricing only: 0157 instead of 0.149. When we add on top of these two
policies the optimisation of the road size, it is again optimal to have a larger
number of subcenters (5.333) and the optimal road size is now only 67% of what
is was in the free entry equilibrium. Combining the three policies generates the
highest welfare gain: 0.272.
INSERT TABLE 2 about here
Many sensitivity studies are possible. We chose to increase the benefit of
variety parameters μd and μw from 0.2 to 0.6. Table 3 reports all the results for
this case. We see in the equilibria a much higher number of firms (9 rather than
3.7 in the absence of congestion) and a much smaller increase in the equilibrium
number of firms when we introduce congestion (again calibrated such as to add
50% to the travel time). The number of firms increases from 9 to 10.523(a 17%
increase) while for the smaller μ values reported in the base case, the equilib-
rium number of firms increases by 77% when we introduced congestion. The
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