Properties of Pareto-Efficient Contracts and Regulations for Road Franchising

1. 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

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

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

4. 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)!

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

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

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

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

9. Model Formulation The problem of the private sector: Profit Construction cost Total toll revenue during concession period

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

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

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

13. Properties of Pareto-Efficient Contracts Proposition 1:Under Assumption 1, if a triple is a Pareto-efficient contract, then . • Note: • 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. .

14. Profit P≥ 0

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

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

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

18. Properties of Pareto Efficient Contracts Effects of Returns to Scale in Road Construction 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

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

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

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

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

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

24. Government Regulation for Achieving a Predetermined Pareto-Efficient Contract Regulatory mechanisms on highway projects

25. Alternative Government Regulations Consider a target Pareto-efficient contract

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

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

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

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

30. 10 SO Regulation strategy Pareto optimal solution set MO Descreasing Returns to Scale in Road Construction Social Welfare Profit (HK$)

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

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

33. Outcomes of alternative government regulations

34. Regulations and Outcomes Target Pareto Efficient BOT contract

35. 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

36. Relevant Research • Tan, Z.J., Yang, H. (2012) Flexible build-operate-transfer contracts for road franchising under demand uncertainty. Transportation Research 46B, No.10, 1419–1439. • 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, 415-433. • 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.241-261, Hong Kong, 16-18 July 2009. • 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, 312-338.