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The 87th TRB Annual Meeting Jan. 13~17, 2008
Welfare and Financial Implications ofWelfare and Financial Implications of Unleashing Private Sector Investment
Resources on Transportation NetworksResources on Transportation Networks
Lei Zhang
Assistant ProfessorAssistant ProfessorDepartment of Civil and Environmental Engineering
University of Maryland
Road Network Ownership RegimesDecentralizationDecentralization
Competitive Market
Local/Municipal Government
U.S.
Nationalization Privatization
2008
Nationalization Privatization
Centralized Private
2Centralization
Centralized Government Monopoly
Private Sector Investment
Types of InvestmentLong term lease to operate existing facilitiesLong-term lease to operate existing facilities e.g. Chicago Skyway, Virginia Pocahontas Parkway,
Indiana Toll Road System
Capacity expansion and operation of existing facilities e.g. Texas’s I-635
Construction and operation of new facilities e.g. Dulles Greenway, California SR 125, Texas Hwy 130
3
Research Questions
To what extent can private sector investment resources help mitigate/solve existing transportation problems?
What are the societal benefits and costs of private-sector involvement in transportation financing?
How should we introduce and regulate private toll roads to maximize public welfare?
4
Two Stylized Small Networks
Link A a Parallel Network
Link B 1 2
a. Parallel NetworkOne OD pair and two roads
Link A Link B b. Serial Network
1 2 3 Three OD pairs and two roads
Users choose trip frequency, departure time, and route.
5
A Game Theoretical ModelPublic roads maximize welfare
∑∑∑ ∑∫ Δ+⎟⎞⎜⎛ aaaaaaqFSffFfCdqqPMaximize τ)()( ∑∑∑ ∑∫ Δ⋅−+⋅−⎟
⎠⎞⎜
⎝⎛
aab aFFSffFfCdqqPMaximize τ
τ),()(
0,
Private roads maximize profit
∑∑ −a
aa
a
aa
FFSfMaximize τ
τ ,
Subject to…Supply demand equilibrium conditions
6
Cost functions
Numerical Result – Parallel Network
Ownership Route A- Route B
Status quo
Socially Optimal
Private-Private
Free-Private
Public-Private Route B quo Optimal Private Private Private
Toll A ($/veh) 0 4.47 6.98 0 5.40 Toll B ($/veh) 0 4.47 6.98 5.475 5.62 Capacity A (veh/hr) 2624 2708 1316 1480 2320Capacity A (veh/hr) 2624 2708 1316 1480 2320Capacity B (veh/hr) 2624 2708 1316 1228 2175 VC Ratio A (no unit) 1.62 1.12 1.21 2.49 1.14 VC Ratio B (no unit) 1 62 1 12 1 21 1 12 1 09VC Ratio B (no unit) 1.62 1.12 1.21 1.12 1.09Rate of return A Rate of return B
– –
– –
69% 69%
– 22%
– 22%
Welfare Change ($) 0 8351 4131 3244 7801Welfare Change ($) 0 8351 4131 -3244 7801Efficiency 0 1 0.49 -0.39 0.93
7
Numerical Result – Serial Network
Ownership Route A- Route B
Status quo
Socially Optimal
Private-Private
Free-Private
Public-Private Route B quo Optimal Private Private Private
Toll A ($/veh) 0 4.47 8.41 0 2.67 Toll B ($/veh) 0 4.47 8.41 11.42 10.34 Capacity A (veh/hr) 19740 16250 7405 16220 14490Capacity A (veh/hr) 19740 16250 7405 16220 14490Capacity B (veh/hr) 19740 16250 7405 9349 8450 VC Ratio A (no unit) 1.42 1.12 1.02 1.22 1.12 VC Ratio B (no unit) 1 42 1 12 1 02 1 00 1 04VC Ratio B (no unit) 1.42 1.12 1.02 1.00 1.04Rate of return A Rate of return B
– –
– –
71% 71%
– 127%
– 116%
W lf Ch ($) 0 46310 8130 13110 21890Welfare Change ($) 0 46310 8130 13110 21890Efficiency 0 1 0.18 0.28 0.47
8
Toll Road Dynamics in the Real Worldif d d i h i ll
TIME
Y t 1Year t
Year t+1
Uniform Land Use and Economic Growths in All Zones
Year t-1 Year t+1USERS 1. Trip frequency, 2. Destination
Flow PUBLIC ROADS 1. Pricing choice
RevenueCosts
T /T ll3. Route choices
Network t CONSTRUCTOIN
2. Capacity choice
Network t+1
Toll/TaxTax/Toll
CONSTRUCTOINMAINTENANCE COSTS
PRIVATE ROADS 1. Pricing Choice 2. Capacity Choice
Costs
RevenueCosts
T ll
TIMEREGULATOR
3. LearningToll
Regulation on price, capacity, and market entry Market entry
Choice
9Private Sector Investment Resources
Choice
A Simulation-Based Approach
Demand SideFour-step travel demand model
Supply SideEmpirically estimated road construction and maintenance cost functions
Public RoadsWelfare-maximizing pricing and capacity choicesBudget-balancing choices
Private RoadsP fit i i i d i i k t t i iProfit-maximizing decision on market entry, pricing, and capacity
Regulator
10
RegulatorMinimum regulation on private roads
Test NetworkTwin Cities MinnesotaTwin Cities, Minnesota
7776 nodes, 20486 Links, ~ 6 million trips daily
Assumptions for the Test Network
Private roads estimate demand elasticities adaptively
Once a private road is built, the parallel public road will not be tolled, and will not be expanded for 10 years
Capacity expansion is discrete (1-lane, 2-lane, etc.)
When driving on public roads, drivers pay $0.056/kmg p , p y $
Multiple non-cooperative private-sector investors
25-year life-cycle for roads with a 10% discount rate
11
25-year life-cycle for roads with a 10% discount rate
New Private Toll Roads 2006~2020
12
Toll Road Growth and Toll Rate Dynamics
0 22
Average Private Toll ($/km)Lane-Km of Private Toll Roads
400
0 2
0.22Total private sector investment: $19.5 Billion
300
0 18
0.2
100
200
0 16
0.18
0
100
0.14
0.16
13
02006 2008 2010 2012 2014 2016 2018 2020
Year
0
Profitability of Private Sector Investment
1
Percentage of Private Roads Making Profits
0 8
0.9Average Annual Rate of Investment Return: 18.2%
0.7
0.8
0 5
0.6
0.4
0.5
2006 2008 2010 2012 2014 2016 2018 2020
14
2006 2008 2010 2012 2014 2016 2018 2020
Year
Welfare Impact of Private Investment
16000
Socially Optimal
No Private Investment
Net Social Benefit ($Million)
12000
14000 Free Entry of Private Roads
8000
10000
4000
6000
Total Welfare Increase: $6.7 Billion
0
2000User Benefit: $1.1 BillionPrivate Profit: $5.6 Billion
15
2006 2008 2010 2012 2014 2016 2018 2020Year
ConclusionsAnalytical methods for evaluating the welfare and financial impact of private toll roads are available and can be applied to real-world scenarios. ca be app ed to ea o d sce a os
Don’t expect private sector investment resources to eliminate congestion.
Private toll road projects profitable in the long run do not necessarily guarantee near-term profits.
If network effects are ignored, private investors tend to charge overly high tolls that work against profit
i i ti lmaximization goals.
Private investment improves social welfare, even when it is minimally regulated
16
it is minimally regulated.
Proper regulation distribute more benefits to users.
Future Research Directions
Multiple user classes and the distributional effects
Demand uncertainty and risk considerationsDemand uncertainty and risk considerations
Optimal regulationOptimal regulation
17
Thank you!
18
Research Design
Evaluating a Mixed-Ownership PolicyFree entrance of private toll roads on a public road network
Comparing Pricing, Welfare, and Financial Consequences between Mixed-Ownership andConsequences between Mixed-Ownership and
Status quo (Gas tax, general taxes, public ownership only)
C l l k i d hCompletely market-oriented approach
Socially optimal
Methodological focusQuantitative modeling
19
Quantitative modeling
Equilibrium (point) and evolutionary (process) analyses
Solution Method – Capacity
Pure Strategy Nash Equilibrium FOC + Equilibrium ConstraintsqSystem of 24 non-linear equations for the parallel-serial networkSolve for all stationary pointsEvaluate objectives at all stationary pointsNot applicable to large networks
A Numerical Example…A Numerical Example…
20
Solution Method – TollA di t fi t d ti lit ditiAccording to first-order necessary optimality conditionsOwnership Parallel Network Serial Network Private-Private B cU B
1 ABAB fcUfcc 632 )( ++
...+= Af
AA A
Ufτ ABf
f fcU
cU
B
B
1+ B
f
f
B
B
Uccc
fcUfcc543 )(
)(
++
++
Private-Public Free += AAUfτ A
Bf f
cU B1 AB
fA
B fcUfcc 632 )( ++...+= fA A
Ufτ 0=Bτ
Bf
fcU B
1+ Bf BUccc 543 )( ++
Public-Private A-B ( )B
fBB
B BUfU
c−τ1
1
( )BBBUfc τ−⎥⎤
⎢⎡ 3
A B ...+= A
fA
A AUfτ
...+= Bf
BB BUfτ
( )fB
f B
fcU + 1
BBf
Bf f
cU
cU
B
B
1
1
+
( )fB
f
B
B
UfUccc
τ⎥⎥⎦⎢
⎢⎣ ++ 543 )(
A
BAf
BA
Uccc
fcUfcc532
643
)(
)(
++
++
ff AUccc )( ++
fPc ≡1 ; 13122
qq PPc ≡ ; 23123qq PPc ≡ ; 23134
qq PPc ≡ ; ∑≡b
bqPc5 ; ∏≡
b
bqPc6 .
21
Parallel network has been studied by:de Palma and Lindsey 2000, Verhoef 2002 among others
Numerical Result – Parallel-Serial Network
Ownership Status Quo Socially O i l
Competition S i 1
Competition S i 2Optimal Scenario 1 Scenario 2
Toll A ($/veh/link) 0 4.47 5.70 5.79 Toll B ($/veh/link) 0 4.47 5.70 5.47 Toll C ($/veh/link) 0 4 47 8 40 8 36Toll C ($/veh/link) 0 4.47 8.40 8.36Capacity A (veh/hr) 9870 8125 6753 (Fix.)8125 Capacity B (veh/hr) 9870 8125 3784 3372 Capacity C (veh/hr) 19740 16250 8125 (Fix )8125Capacity C (veh/hr) 19740 16250 8125 (Fix.)8125Rate of return 1 Rate of return 2
– –
– –
60% 28%
55% 22%
? Welfare ($) 0 46310 24560 26080? We a e ($) 0 63 0 560 6080Efficiency 0 1 0.53 0.56
22
Revenue and cost functions
RRevenueA notion of link revenue is convenient in describing various policiesRevenue Toll • Flow
)( ia
ia
ia fE ⋅⋅= ψτ
CostOnly a portion of maintenance cost is volume dependent (PatersonOnly a portion of maintenance cost is volume-dependent (Paterson
and Archondo-Callo 1991) link maintenance cost (M) function for all links:
Length Capacity Flow
E i i l t di t (K l ti d L i 2003) li k
Length Capacity Flow321 )()()( αααμ i
ai
aaia fFlM ⋅=
Empirical studies suggest (Karamalaputi and Levinson 2003) link expansion cost depends on link length, capacity and capacity changeLink expansion cost (K) function:
Length Capacity Capacity Change
23
321 )()()( 1 σσσφ ia
ia
iaa
ia FFFlK −⋅⋅⋅= +
Length Capacity Capacity Change
Model Parameters
A complete set of parameters derived for the Twin Cities
24