Properties of Pareto-Efficient Contracts and Regulations for Road Franchising Hai Yang Chair Professor Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology

Outline 1. Introduction of BOT schemes 2. Theoretical analysis of a BOT toll road project 3. Conclusions 4. Future research

What is a BOT scheme? BUILD OPERATE TRANSFER  Private firm constructs infrastructure facility  Toll  Concession period  Transfer to government BOT is a form of project financing To maximize total social welfare during the whole road life Aims of public sector: Aims of private sector: To maximize net profit during the concession period

Why do we need BOT schemes? Private sector:more efficient than the public sector, and therefore builds and operates facilities at less cost; Public sector:facing taxpayer resistance, unable to finance facilities; short of funding  Private sector willing and able to undertake for a profit  Users who find it worthwhile to patronize this new road and pay charges  Users who do not use these new roads benefit from reduced congestion on the old ones All may benefit whenever the charges cover all costs (including congestion and environmental costs)!

Aims of the research Private investors: Public sector: to identify how, and under what circumstances, a highway BOT project is feasible and profitable, to identify project risks, understanding how a proposed project will benefit the private investor, road users and the whole of society. Aim of research:to establish a BOT contract acceptable to both parties

Model Formulation City ACity B A single highway Three fundamental decision variables of a BOT project Total social welfare (whole road life ) Profit (concession period T ) BOT Contract Concession period: T Toll charge: p Road capacity: y Public sectorPrivate sector A highway project

The Demand-Supply Equilibrium Condition: Toll charge can be viewed as the function of travel demand q and road capacity y. Model Formulation Link travel time function Value-of-Time Inverse demand function Toll charge Homogeneous users with identical VOT;

The problem of the public sector: Total consumer surplus during concession period Total consumers’ surplus during post-concession period Construction cost Social welfare Model Formulation

The problem of the private sector: Total toll revenue during concession period Construction costProfit Model Formulation

Bi-objective programming for the BOT problem: where Note: Perfect information for both the public sector and the private sector Model Formulation

Definition (Pareto-Efficient Contract): is said to be a Pareto-efficient such that and with at least one strict inequality. A BOT triple contract if there is no other BOT triple Model Formulation

(a) and (b), and ; (c). Assumptions Assumption 1 Assumption 2 Assumption 3 is a strictly concave function; Homogeneous of degree zero link travel time function Constant return to scale in road construction (Elasticity of the investment cost in output capacity) (k: the unit capacity cost) or is volume-capacity ratio.

is a Pareto-efficient contract, then. Properties of Pareto-Efficient Contracts Proposition 1: Under Assumption 1, if a triple. Note: 1)Any BOT contract with concession period less than road life is wasteful, namely, renegotiating the contract can make at least one party better off. 2)This ‘‘lifetime concession period” result seems to be realistic because several BOT contracts around the world have been awarded for 99 years, including Highway 407 in Toronto, the Chicago Skyway and the Pocahontas Parkway (Virginia Route 495) in Richmond, Virginia.

Profit P ≥ 0

Properties of Pareto-Efficient Contracts Pareto-efficient contract,, solves Proposition 2: Under Assumptions 1- 3, the v/c ratio for any Thus, it is constant along the Pareto-optimal frontier and equals the socially optimal v/c ratio,.

Pareto Efficient Frontiers and Constant Volume/Capacity Ratio Monopoly Optimum Social Optimum Pareto optimal solution set Demand Capacity Social welfare Profit Pareto optimal frontier

Proposition 3: Under Assumptions 1, 2 and 3, for any Pareto-efficient contract, the average social cost per user is constant, namely, Properties of Pareto-Efficient Contracts per user per unit time or per trip during the concession period

Assumption 4 (Power construction cost function) decreasing returns to scale in road construction constant returns to scale in road construction increasing returns to scale in road construction Decreasing, constant and increasing returns to investment Properties of Pareto Efficient Contracts Effects of Returns to Scale in Road Construction

Properties of Pareto Efficient Contracts Social Optimum Monopoly optimum Pareto-optimal solution set Decreasing returns to scale in road construction Demand Capacity

Properties of Pareto Efficient Contracts Social optimum Monopoly optimum Increasing returns to scale in road construction Pareto optimal solution set Capacity Demand

Return to Investment and Profit Properties at Social Optimum Social optimum contract: Corresponding profit: Decreasing Increasing Constant

Return to Investment and Profit Properties at Pareto Efficient Solutions For increasing returns to scale in road construction Profit P < 0 for certain portion of the Pareto optimal frontier For constant or decreasing returns to scale in road construction, profit P ≥ 0 at any Pareto- efficient solution.

Government Regulation for Achieving a Predetermined Pareto-Efficient Contract BOT contract Toll Rate of return on investment Return on output Several definitions on regulatory issue Markup charge The amount of profit earned from each unit of realized demand (each trip) during the concession period

Government Regulation for Achieving a Predetermined Pareto-Efficient Contract Regulatory mechanisms on highway projects Regulatory regimesimplementation Price-Cap Setting a maximum toll charge (price cap) ROR Setting a maximum rate of return on investment (“fair” rate ) Capacity Setting a minimum level of capacity (investment level) Demand Setting a minimum level of demand Markup Setting a maximum markup charge

Alternative Government Regulations Consider a target Pareto-efficient contract Regulation regimeOutcome BOT Contract Price-Cap ROR Capacity Demand Markup

Numerical Examples Link travel time function (BPR) Inverse demand function (negative exponential) The operating hours per year is assumed to be hours

Constant volume-capacity ratio: Average social cost per user: Socially optimum BOT contract: Monopoly optimum BOT contract: Case 1: Constant Returns to Scale in Road Construction

Social Welfare Profit (HK$) Constant Returns to Scale in Road Construction Regulation strategy Pareto optimal solution set SO MO

Volume-capacity ratio: Average social cost per user: Social optimum BOT contract: Monopoly optimum BOT contract: Case 2: Decreasing Returns to Scale in Road Construction

Social Welfare Profit (HK$) Pareto optimal solution set Regulation strategy SO MO 10 Descreasing Returns to Scale in Road Construction

Volume-capacity ratio: Average social cost per user: Social optimum BOT contract: Monopoly optimum BOT contract: Case 2: Increasing Returns to Scale in Road Construction

Social Welfare Profit (HK$) Zero-profit Pareto optimal contract: Years HK$ Veh/h Pareto optimal solution set Regulation strategy SO MO Increasing Returns to Scale in Road Construction

Outcomes of alternative government regulations

Regulations and Outcomes Target Pareto Efficient BOT contract Regulation regimeOutcome BOT Contract Price-Cap ROR Capacity Demand Markup

Conclusions  Introduced the definition of the Pareto efficient contract to the BOT problem  Investigated the properties of the set of Pareto efficient contracts  Examined the effectiveness of alternative government regulations

Relevant Research  Tan, Z.J., Yang, H. (2012) Flexible build-operate-transfer contracts for road franchising under demand uncertainty. Transportation Research 46B, No.10, 1419–  Tan, Z.J. and Yang, H. (2012) The Impact of user heterogeneity on road franchising. Transportation Research 48E, No.5, 958–975.  Wu, D., Yin, Y. and Yang, H. (2011) The independence of volume-capacity ratio of private toll roads in general networks. Transportation Research 45B, No.1, 96–101.  Tan, Z.J., Yang, H. and Guo, X.L. (2010) Properties of Pareto efficient contracts and regulations for road franchising. Transportation Research 44B, No.4,  Tan, Z.J., Yang, H. and Guo, X.L. (2009) Build-Operate-Transfer Schemes for Road Franchising with Road Deterioration and Maintenance Effects. Proceeding of the 18th International Symposium on Transportation and Traffic Theory (ISTTT18) (edited by Lam W.H.K., Wong, S.C. and Lo. H.K.), Springer, pp , Hong Kong, July  Guo, X.L. and Yang, H. (2009) Analysis of a build-operate-transfer scheme for road franchising. International Journal of Sustainable Transportation, Vol.3, No.5-6,