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ECN 190/TTP 215 Lecture 16

Transportation Economics:

Highway Congestion

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Highway Travel: Congestion

Let V=volume (number of vehicles passing agiven point per hour)

D=density (number of vehicles per unitdistance)

S=speed. Then these three variables mustsatisfy the relation:

V = DS But they are inter-related! Draw this as:

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Congestion graphs:

Maximum volume Vm, density D

m, speed S

0

left (upper) branch is congestion

right (lower)branch is hyper-congestion

S0

S

S0

S

D Dm

a. Flow vs. Density

Vm

V

D Dm

b. Speed vs. Density

V Vm

c. Speed vs. Flow

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Time spent on each trip:

The time spent on each trip is inverselyproportional to speed, or 1/S.

We will focus on the congestion portion ofthe speed vs. flow graph, so that 1/S isincreasingin the flow V

Suppose there is a (fixed) consumer cost oftime, and then evaluate the average costs oftime per trip, c(V)

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Average costs of time spent, E.g. 1:

with VK=capacity. Total costs are:

marginal costs are:

decreasing returns for k>0;

kK20K20K )V/V(cc)V/V(fcc)V;V(c +=+=

])V/V(cc[V)V;V(C kK20K +=

kK20K )V/V(c)1k(cV/)V;V(CMC ++==

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Costs of time:

This gives us cost curves:

Cost per vehicle

kc2

c2

MC

AC

C0

VK Volume

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Average costs of time spent, E.g. 2:

Average costs,

marginal costs are,

>+

=

.1V/Vif)1V/V(cc

1V/Vifc)V;V(c

KK20

K0

K

>+=

.1V/Vif)1V/V2(cc

1V/Vifcmc

KK20

K0

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Cost of time:

This gives us cost curves:

VK Volume

c0

Cost per vehicle

MC

ACc0+c2

Slope=c2/Vk

Slope=2c2/Vk

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Social costs of automobile travel

Type of cost Cost ($ per vehicle-mile in

1989 US prices)

Costs borne mainly by Highway users in aggregate:

(1) Running costs 0.068

(2) Vehicle capital 0.188(3) Time 0.120(4) Schedule delay 0.066

Costs borne partially by non-users:

(5) Accidents 0.179

(6) Parking (CBD fringe) 0.136Total:

Without parking 0.621With parking 0.757

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Social Optimum

Social Benefits,

Social costs are,

Net social benefits, choose V and VKto

=V

0

Vd)V(PB

)V(K)V/V(VcC kk +=

)V(K)V/V(VcVd)V(PNSB KK

V

0

=

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Average costs of time spent, E.g. 1:

Toll is:

Toll is increasing in traffic volume;

Toll is decreasing in capacity.

kK20K )V/V(cc)V;V(c +=

ACMC

)V/V(k'c)V/V(Toll kKK

=

==

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Illustrate toll:

Cost per vehicle

TollMC

AC

C0

V1 V0 Volume

D

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Average costs of time spent, E.g. 2:

Average costs,

marginal costs are,

>+

=

.1V/Vif)1V/V(cc

1V/Vifc)V;V(c

KK20

K0

K

>+=

.1V/Vif)1V/V2(cc

1V/Vifcmc

KK20

K0

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Average costs of time spent, E.g. 2:

toll is,

Results: toll is zero at less than capacity, and increasing inV at more than capacity

(takes range of values < c2 at capacity)

>=