intermediate input from the center to the subcenters. The total usage on road
i, expressed in car equivalent, is:
ρi = N [(καh + αd) Pd + αwpw] . (25)
where κ represents the car equivalent of a truck carrying the homogenous good.
The α0 s can also to some extent take into account the difference in timing of
the three types of road use.
We assume that the relation between travel cost, ti , and total activity on
the road i, ρi , is given by:
ti = t + δρi
s
(26)
where s is the capacity of the road measured in car equivalent (for the time
period considered in the model), and δ is a coefficient that translates waiting
time and schedule delay costs in equivalent queueing time. The first term rep-
resents the transport time in the absence of any congestion. The second term
in (26) represents the variable travel cost. This expression is the reduced form
of the bottleneck model [4] where road users decide on their trip timing (with
no congestion pricing).
Recall the market clearing condition (13): Pid = Piw . Equation (26) reduces
to:
NN
ti = t + δ—αPid = t + δ—αPw,
(27)
where α ≡ καh + αd + αw . In the symmetric case, Piw = Pid =1/n and the
travel cost, denoted by te , is the same on all routes:
te = t + δ N α.
(28)
ns
6.2 Demand for goods and supply of labour
With congestion, the indirect utility of a consumer working at i and consuming
at k is Uik = Ωik + wi — pk + μwεi + μdεk, where:
⅛k = ( —αwtk - β) + θ (1 - β) + h - αdti + (1 /N ) X X πl - T.
i=1...n
Using the same notation as in the non-congested case, this expression can we
written as:
Uik = Ω — Λw Pw — ΛdPd + Wi — Pk + μw εi + μdεfc, (29)
where Ω is given by equation (9), Λw = αwδNα and Λd = αdδNα.
14
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