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

1lei@umd.edu

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

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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?

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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.

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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

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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

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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

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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

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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

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25-year life-cycle for roads with a 10% discount rate

New Private Toll Roads 2006~2020

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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

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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

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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

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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

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Thank you!

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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

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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…

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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 .

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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

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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

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321 )()()( 1 σσσφ ia

ia

iaa

ia FFFlK −⋅⋅⋅= +

Length Capacity Capacity Change

Model Parameters

A complete set of parameters derived for the Twin Cities

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