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«On Whom the Toll Falls: A Model of Network Financing David Matthew Levinson DISSERTATION SERIES UCB-ITS-DS-1998-4 Spring 1998 ISSN 0192 4109 On Whom ...»

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Institute of Transportation Studies

University of California at Berkeley

On Whom the Toll Falls: A Model of Network Financing

David Matthew Levinson

DISSERTATION SERIES

UCB-ITS-DS-1998-4

Spring 1998

ISSN 0192 4109

On Whom the Toll Falls: A Model of Network Financing

by

David Matthew Levinson

B. (Georgia Institute of Technology) 1988

M. (University of Maryland) 1992

A dissertation submitted in partial satisfaction of the

requirements for the degree of Doctor of Philosophy in Engineering - Civil Engineering in the

GRADUATE DIVISION

of the

UNIVERSITY OF CALIFORNIA, BERKELEY

Committee in charge:

Professor Mark M. Hansen, Chair Professor David Gillen Professor Carlos Daganzo Professor Elizabeth Deakin Spring 1998

The dissertation of David Matthew Levinson is approved:

________________________________________________________________________

Chair Date ________________________________________________________________________

Date ________________________________________________________________________

Date ________________________________________________________________________

Date University of California, Berkeley Spring 1998 On Whom the Toll Falls: A Model of Network Financing Copyright 1998 by David Matthew Levinson

Abstract

On Whom the Toll Falls: A Model of Network Financing by David Matthew Levinson Doctor of Philosophy in Civil Engineering University of California, Berkeley Professor Mark M. Hansen, Chair This dissertation examines why and how jurisdictions choose to finance their roads.

The systematic causes of revenue choice are explored qualitatively by examining the history of turnpikes. The question is approached analytically by employing game theory to model revenue choice on a long road. The road is covered by a series of jurisdictions seeking to maximize local welfare. Jurisdictions are responsible for building and maintaining the local network. Complexity arises because local network users may not be local residents, and local residents may use non-local networks. Key factors posited to explain the choice of revenue mechanism include the length of trips using the road, the size of the governing jurisdiction, the degree of excludability, and the transaction costs of toll collection. These factors dictate the size and scope of the free rider problem. It is hypothesized that smaller jurisdictions and lower collection costs favor tolling policies over taxes.

The analytical model is operationalized by assuming jurisdictions have two decisions: the strategic decision to tax or toll, and the tactical decision of setting the rate of tax or toll. Models of user demand as a function of trip distance and monetary cost and of network costs as a function of traffic flow and the number of toll collections are specified.

The values of the constants and coefficients of the model are developed from recent cost literature and the estimation of a model of collection costs from California Toll Bridge data.

The model is applied to evaluate the dissertation’s hypotheses. The application evaluates the welfare implications of a jurisdiction and its neighbors imposing general tax, cordon toll, odometer tax, or perfect toll policies. Sensitivity tests of the model under alternative behavioral assumptions, and with varying model coefficients are conducted.

Finally, policy implications from the analysis are drawn. The general trends which bode well for road pricing (electronic toll collection (ETC), decentralization, advanced infrastructure, privatization, and federal rules) are established. Possible scenarios for three cases are presented: deploying ETC and building new toll roads, and converting free roads.

____________________________________________

Mark Hansen, Chair Dedication

–  –  –

whose blind faith have seen me through.

iii

TABLE OF CONTENTS

1. CHAPTER ONE: INTRODUCTION

1.1 Introduction

1.2 Rationales for Road Pricing

1.2.1 Financing Infrastructure

1.2.2 Social Costs

1.2.3 Change in Tax Base with Alternative Fuels

1.2.4 Congestion Pricing

1.3 Research Overview

2. CHAPTER TWO: ROAD PRICING IN PRACTICE

2.1 Introduction

2.2 Tolls in the Ancient and Medieval World

2.3 Roads Before Modern Turnpikes

2.4 Turnpikes in Great Britain: 1656 - 1900

2.5 Turnpikes in America: 1785 - 1900

2.6 Turnpikes in America: 1900 - Present

2.7 Recent International Experience

2.8 Summary And Conclusions

3. CHAPTER THREE: THEORY

3.1 Introduction

3.2 Property Rights

3.3 Actions

3.4 Objectives

3.5 Profit

3.6 Consumers’ Surplus

3.7 Free Riders and Cross Subsidies

3.8 Game Theory

3.9 Summary and Conclusions

4. CHAPTER FOUR: A MODEL OF NETWORK FINANCING

4.1 Introduction

4.2 Network Geometry





4.3 User Classes

4.4 Jurisdiction Objectives

4.5 Consumption

4.5.1 Demand

iv 4.5.2 Consumers’ surplus

4.6 Production

4.6.1 Profit

4.6.2 Cost

4.6.3 Revenue

4.7 Policies

4.7.1 Environment

4.7.2 Jurisdiction Policies

4.8 Toll-Setting

4.8.1 Non-cooperative Toll-setting

4.8.2 Cooperative Toll-setting

4.9 Mathematical Solution

4.9.1 General Tax and Cordon Tolls

4.9.2 Odometer Tax

4.9.3 Perfect Toll

4.10 Summary and Conclusions

5. CHAPTER FIVE. EMPIRICAL JUSTIFICATION OF MODEL PARAMETERS....100

5.1 Introduction

5.2 Demand

5.2.1 Value of Time (VT)

5.2.2 Freeflow Speed (SF)

5.2.3 Private Vehicle Costs (!, ")

5.2.4 Sensitivity of Demand to Price an

5.2.5 Density of Trips Along Road (#)

5.3 Network Costs ($, %)

5.4 Collection Costs (&, ')

5.5 Conclusions and Summary

6. CHAPTER SIX. THE CHOICE OF REVENUE MECHANISM

6.1 Introduction

6.2 Revenue Choice: A Simple Game

6.3 Revenue Choice, Jurisdiction Size, and Collection Costs

6.3.1 Welfare and Jurisdiction Size

6.3.2 Policy Selection

6.3.3 Government Hierarchy

6.4 Technical Properties

6.4.1 Stability and Uniqueness of Tolls

v 6.4.2 Sensitivity to Model Coefficients

6.5 Jurisdiction Behaviors

6.5.1 Cooperative vs. Non-Cooperative Toll-Setting

6.5.2 Repeated Games

6.5.3 Alternative Objectives

6.6 Perfect Tolls and Odometer Taxes

6.7 Summary

7. CHAPTER SEVEN: SUMMARY AND CONCLUSIONS

7.1 Introduction

7.2 Summary of Research

7.2.1 History of Priced Roads

7.2.2 Theory and Model of Revenue Choice

7.2.3 Modeling Results

7.3 General Trends

7.3.1 Transaction Costs

7.3.2 Decentralization

7.3.3 Deployment of AdvancedHighway Infrastructure

7.3.4 Privatization

7.3.5 Federal Rules on Toll Roads

7.4 Speculations on the Deployment of Priced Roads

7.4.1 Electronic Toll Collection on Existing Toll Roads

7.4.2 New Toll Roads

7.4.3 Tolling Existing Unpriced Roads

7.5 Future Research

8. REFERENCES:

8.1 Chapter One

8.2 Chapter Two

8.3 Chapter Three

8.4 Chapter Four

8.5 Chapter Five

8.6 Chapter Six

8.7 Chapter Seven

9. END NOTES

vi

LIST OF FIGURES

Figure 1.1 Optimal Congestion Toll and Welfare Loss Without Toll

Figure 2.1 Turnpikes in Great Britain: 1650 - 1900

Figure 2.2 Toll Roads in the United States: 1940-91

Figure 4.1 One-Way, Long Road and Classes of Trips

Figure 4.2 Illustration of Alternative Regular Environments

Figure 4.3 Distance Decay and Tolls in All Cordon Toll Environment

Figure 5.1 Schematic of Road Loading Patterns

Figure 6.1 Welfare in J0 as a Function of J0 Toll in an All-Tax Environment

Figure 6.2 Welfare in J0 as a Function of J0 Toll in an All-Cordon Toll Environment.

.....127 Figure 6.3 Welfare in J0 at Welfare Maximizing Tolls as Jurisdiction Size Varies in an AllTax Environment

Figure 6.4 Welfare in J0 at Welfare Maximizing Tolls as Jurisdiction Size Varies in an AllCordon Toll Environment

Figure 6.5 Policy Choice as a Function of Fixed Collection Costs and Jurisdiction Size.

137 Figure 6.6 Policy Choice as a Function of Variable Collection Costs and Jurisdiction Size

Figure 6.7 Reaction Curves: Best J0 Toll as Tolls Vary in an All-Cordon Toll Environment

Figure 6.8 Uniqueness: Non-Cooperative Welfare Maximizing J0 Toll as Initial Toll for Other Jurisdictions Varies in All-Cordon Toll Environment

Figure 6.9 Comparison of Tolls Under Cooperative and Non-Cooperative Equilibria.

.....146 Figure 6.10 Comparison of Welfare Under Cooperative and Non-Cooperative Equilibria

Figure 6.11 Illustration of Infinitely Long Road Covered Completely by Two Jurisdictions

Figure 6.12 Comparison of Tolls by Objective, Toll-Setting Equilibrium

Figure 6.13 Comparison of Per Capita Welfare by Objective, Toll-Setting Equilibrium.

..157 Figure 6.14 Comparison of Per Capita Profit by Objective, Toll-Setting Equilibrium.......158 Figure 6.15 Tolls under Perfect Tolls and Odometer Taxes as Tollbooth Spacing Varies.

Figure 6.16 Welfare under Perfect Tolls and Odometer Taxes as Tollbooth Spacing Varies

vii

LIST OF TABLES

Table 1.1 U.

S. Highway & Local Street Revenues & Expenditures: 1995

Table 1.2 Air Pollution and Global Change Costs of Highway Travel

Table 2.1 Turnpike Incorporation in the United States, 1792-1845

Table 2.2 Miles of Toll Highways in Operation in 1963

Table 3.1 Revenue Instruments

Table 3.2 Types of Riders

Table 3.3 Incidence of Costs by User Group and Revenue Mechanism

Table 4.1 General Trip Classification

Table 4.2 Objective Functions

Table 4.3 Total Transportation Revenue (RT) to Jurisdiction by Policy

Table 4.4 Decomposition of Price of Infrastructure (PI)

Table 4.5 Policies Examined in this Dissertation

Table 4.6 Model Components: General Tax and Cordon Toll

Table 4.7 Estimation of Mathematical Solution Associated with User Class (gG) for General Tax and Cordon Toll Policies in J0 and Environment

Table 4.8 Rate of Toll Under Various Policies

Table 5.1 Car Price Model Estimation

Table 5.2 Average Unit and Incremental Cost of Car Ownership

Table 5.3 Long Run Total Expenditures Results

Table 5.4 Long Run Marginal Infrastructure Costs and Scale Economies

Table 5.5 Interchange Spacing on Free and Closed-Toll Highways

Table 5.6 Data from California Toll Bridges

Table 5.7 Regression on Collection Costs from California Bridges

Table 5.8 Empirical Coefficients on Demand and Cost Models

Table 6.1 Normal Form of Revenue Mechanism Game

Table 6.2 Payoffs of Revenue Mechanism Game: J0 vs.

Representative Jurisdiction........126 Table 6.3 Baseline Scenario: Empirical Values of Model Coefficients

Table 6.4 Comparison of Tolls and Welfare for Different Jurisdiction Sizes

Table 6.5 Elasticity About Mean

Table 6.6 Welfare of Boundary Crossing Trips on Infinite Road Covered by Two Jurisdictions

Table 6.7 Conditions for Supergame Strategies to be Equilibria

Table 6.8 Conditions for Supergame Strategies, and Results from Equations Above.

.......152 Table 6.9 Equations for Two Jurisdiction System

viii

ACKNOWLEDGMENTS

I gratefully acknowledge the support given by many persons and organizations who have directly and indirectly contributed to this research.

Professor Mark Hansen has carefully read several drafts of the dissertation, challenged many assumptions and therefore ensured a higher quality product. Professor David Gillen strongly encouraged my research and provided economic insight and focus.

Professor Betty Deakin, by asking “So?” has helped bring some policy relevance to an otherwise technical enterprise. Professor Carlos Daganzo challenged any ambiguity or lack of clarity in the theory and analytical model, insisting upon precision in communication.

This research was funded in part by a Dissertation Fellowship from the University of California Transportation Center. It was also partially funded by Memorandum of Understanding 275 between the California Department of Transportation and the University of California at Berkeley’s PATH program. Professor Adib Kanafani helped arrange Institute of Transportation Studies funding in my first few years at Berkeley, and thereby facilitated the initial thinking that were the seeds of this research.

Previous version of portions of this research were presented at the North American Meeting of the Regional Science Association International, in Arlington, VA (Nov. 1996), at the Transportation Research Board Conference in Washington DC (Jan. 1998), at the Western Regional Science Association Conference in Monterey CA (Feb. 1998), at seminars at George Mason University (Nov. 1996), the Massachusetts Institute of Technology (April 1997), the University of California at Berkeley, Purdue Univeristy, and the University of Iowa (all in April 1998). The attendees are thanked for their comments.



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