1 VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO VIET HUNG INTEGRATING TRAVELERS’ PERCEIVED FACTORS IN MODELLING THE CEILING PRICE OF TOLL ROAD A CASE STUDY OF B O T PROJECTS IN VIET N[.]
VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO VIET HUNG INTEGRATING TRAVELERS’ PERCEIVED FACTORS IN MODELLING THE CEILING PRICE OF TOLL ROAD A CASE STUDY OF B.O.T PROJECTS IN VIET NAM MASTER’S THESIS Hanoi, 2019 VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO VIET HUNG INTEGRATING TRAVELERS’ PERCEIVED FACTORS IN MODELLING THE CEILING PRICE OF TOLL ROAD A CASE STUDY OF B.O.T PROJECTS IN VIET NAM MAJOR: INFRASTRUCTURE ENGINEERING CODE: PILOT RESEARCH SUPERVISOR: ANNEX LIST OF FORMS FOR MANAGEMENT Dr NGUYEN HOANG TUNG Hanoi, 2019 ACKNOWLEDGMENT During the period of studying to accomplish the topic of master’s thesis, there is not only self effort but also the enthusiastic guidance of teachers, as well as the encouragement of my family and friends First of all, I would like to express my gratitude sincerely to my supervisor, Lecturer Dr Nguyễn Hoàng Tùng who instructed directly me to conduct this research by making particular guidance I also would like to give special thanks to whole teachers at Vietnam Japan University, who have conveyed me the precious knowledge for the duration of my learning here Especially Professor Dr.Sci Nguyễn Đình Đức and Dr Phan Lê Bình who always have stimulated me to try my best and have inspired me a lot of motivations for studying as well as working in the life Besides that I am grateful to Professor Hironori Kato, the Co-Director of Master's Program in Infrastructure Engineering, for supporting me actively when I had a threemonth Internship Program in Japan Finally, I would like to thank my family and co-workers, who always are beside me during the implementing this master's thesis Although there have been lots of my attempts in the research process, due to limited ability and experience of self, this master's thesis still exist some unavoidable shortcomings So I am looking forward to hear sincere feedbacks from teachers and colleagues in order to supplement and complete more this research in the future Hà Nội, Jun 2019 Đỗ Việt Hùng i ABSTRACT The Build-Operate-Transfer (BOT) scheme is considered as an attractive means by the Vietnamese government to develop new infrastructure projects They were started to widely carried out from 2011 and it is predicted to continuously increase in the future The toll price of BOT road given by investor is set under the ceiling price that is regulated in Circular of Ministry of Transport It can be seen that most of BOT toll road projects have applied charge that are nearly equal to the given ceiling prices Nevertheless, the ceiling price at this Circular did not consider the scale of road, as well as did not take into account of travelers’ willingness to pay to toll price There has not ever researches of the topic to previous studies Therefore, this study focused on integrating “willingness to pay of travelers” to model of toll ceiling price in BOT road project by using a bi-level programming model to formulate for a simple two-road network to optimize toll price and propose ceiling pricing for BOT projects Some important findings of ceiling price include: (1) If government does not restrain toll price on BOT road, that leads to a negative social welfare; and (2) there must exist price which is maximum threshold of toll price for BOT road in order that social welfare becomes positive; and (3) ceiling price is set to be equal to minimum of “willingness to pay” and the threshold of toll price above ii TABLE OF CONTENTS ACKNOWLEDGMENT i ABSTRACT ii TABLE OF CONTENTS iii LIST OF FIGURES v LIST OF TABLES vi LIST OF ABBREVIATIONS vii CHAPTER INTRODUCTION CHAPTER LITERATURE REVIEW CHAPTER METHODOLOGY 3.1 The model setting 3.2 Solution procedure 11 3.2.1 Step 1: Determining route choice of travelers 11 3.2.2 Step 2: The operators determine the toll prices to maximize their own benefit respectively 13 3.2.2.1 BOT road 13 3.2.2.2 Existing road 14 3.2.3 Step 3: Evaluation social welfare 15 3.2.3.1 Case 1: All two roads get maximum their own benefit at the same time 15 3.2.3.2 Case 2: Only BOT road get maximum his own benefit under condition that it is positive social welfare 16 3.2.4 Step 4: Integrating the factor named "willingness to pay of travelers" to guarantee users' benefit 17 3.2.5 Step 5: Determining ceiling price of toll road under condition that optimal benefit of investor and the government, which taking into account "willingness to pay" of travelers 18 3.2.5.1 Case 1: If p1’ is less than WTP (i.e p1’ ≤ WTP) 19 3.2.5.2 Case 2: If p1’ is greater than WTP (i.e p1’ ≥ WTP) 19 iii 3.2.5.2.1 Recommendation 1: Downscale capacity of BOT road 19 3.2.5.2.2 Recommendation 2: Keep capacity of BOT road 20 CHAPTER CASE STUDY 22 4.1 Introduction for case study 22 4.2 Willingness to pay of travelers choosing this road to travel 23 4.3 Determining toll ceiling price of BOT road 25 4.3.1 Case 1: Toll ceiling price for vehicle has under 12 seats 25 4.3.1.1.1 Recommendation 1: Downscale capacity of BOT road 26 4.3.1.1.2 Recommendation 2: Keep capacity of BOT road 27 4.3.2 Case 2: Toll ceiling price for vehicle has under 30 seats 29 4.3.2.1.1 Recommendation 1: Downscale capacity of BOT road 30 4.3.2.1.2 Recommendation 2: Keep capacity of BOT road 31 4.4 Estimation WTP as regression function 32 4.4.1 Case 1: Estimation WTP function of travelers have car under 12 seats 33 4.4.2 Case 2: Estimation WTP function of travelers have vehicle under 30 seats 35 CHAPTER CONCLUSION 39 5.1 Conclusion 39 5.2 Limitation 39 REFERENCES 40 APPENDIX 41 iv LIST OF FIGURES Page Fig 1.1 Relationship between government, investor, travelers Fig 1.2 Number of BOT projects in Vietnam incl estimation Fig 1.3 Rank of Vietnam in the world about service and quality of road transport infrastructure Fig 1.4 Comparison of benefit between BOT road vs non-BOT road Fig 1.5 Toll price in BOT scheme in Vietnam Fig 1.6 GDP per capita and Toll price of some countries Fig 3.1 A network model 10 Fig 4.1 PV-CG Expressway and NH.1A 22 v LIST OF TABLES Page Table 1.1 Ceiling Prices in National Highway Table 1.2 Ceiling Prices in Expressway Table 4.1 Major parameters of two roads 23 Table 4.2 Characteristic of interviewees 24 Table 4.3 Descriptive statistic about WTP of travelers for toll price 25 Table 4.4 Regression Coefficient of WTP function 33 Table 4.5 Regression Coefficient of WTP function 35 Table 4.6 Regression Coefficient of WTP function 36 Table 4.7 Regression Coefficient of WTP function 37 vi LIST OF ABBREVIATIONS BOT Build – Operate - Transfer PPPs Public Private Partnerships PV-CG Expressway Pháp Vân – Cầu Giẽ Expressway NH.1A National Highway No.1A WTP Willingness to pay vii CHAPTER INTRODUCTION The more rapidly the economy grows, the more greater demand for infrastructure are In most countries, infrastructure was built from the state budget However, there are many items which need be spent by governmental budget and private capital is a good fund to complement these shortages Nowadays, more and more governments have encouraged private investor which take part in public investment projects Therefore, in order to support public infrastructure, Public Private Partnerships (PPPs) have become a major scheme (Hodge and Greve, 2007) and reduce public sector budget shortages (Kwak et al., 2009) PPPs are widely used to supply many infrastructure projects in the world Infrastructures invested by PPPs make economic efficiency increasing (Zhang, 2005) and facilitates the overall development of social infrastructure (Li et al., 2016b) In Vietnam, according to Decree No 63/2018/ND-CP: “PPP” is an investment form which is carried out on the basis of a contract between the State and an investor, in order to construction, renovation, operation, business, management of infrastructure works, provision of public services Build-Operate-Transfer (BOT) model is a form of PPP which has extensive applications in infrastructure projects The BOT scheme is gaining popularity and booming in public infrastructure around the world (Tan, 2012) It is adopted as an innovative way to sponsor for infrastructure construction in both developing and developed countries (Subprasom, 2004) In recent years, BOT arrangements have contributed to accelerating economic growth and improve quality service delivery and operation efficiency (Akintola et al., 2003) In Vietnam, the Build-Operate-Transfer (BOT) scheme is considered as an attractive means by the Vietnamese government to develop new infrastructure projects According to Decree No.63/2018/ND-CP, parties involving in this contract project include: the government, private investor and travelers 102 /134 102 /133 2008 2009 117/ /139 2010 120 /144 102 /148 123 /142 2011 2012 2013 Source: World Economic Forum 104 /144 2014 93 /140 89 /138 92 /137 2015 2016 2017 Fig 1.3 Rank of Vietnam in the world about service and quality of road transport infrastructure When choosing to travel on BOT roads, although length of road between BOT road and non BOT road are equivalent and travelers have to pay a significant fee, so they obtain more benefit himself, such as get higher speed, reduce travel time, save fuel consumption, feel comfortably travel as well as restrain collisions can be happened Thence, it can be raised economic efficiency for businesses and individuals Besides that, we can obtain social benefit as decreasing congestion and emissions causing environmental pollution According to the statistics of the Ministry of Transport, Noi Bai - Lao Cai Expressway is estimated to reduce travel time by 50% and cost by 30%; Hanoi - Vinh National Highway is estimated to reduces about 30% of travel time and 20% of cost; Highway No.14 through Dak Nong province is Road invested by BOT project Emissions Fuel consumption Smooth traffic Charge price (VND / turn) Travel time (mins) Speed (Km/h) Length (Km) estimated to reduces about 30% of travel time and 6% of costs, Road invested by Non-BOT project Fig 1.4 Comparison of benefit between BOT road vs non-BOT road Many studies have investigated the properties of BOT contracts and their design process To design a BOT contract, three critical parameters need to be considered: the length of the concession period, the infrastructure’s capacity and the toll Three variables are essential to a BOT road project They determine the social welfare for the whole society during the whole life of the road and the profit of the private firm during the concession period In the concession period, the private sector receives the revenue of charged tolls (Tam, 1999) Generally, service charge and capacity decisions are critical in a typical BOT contracting process, and the private sector has the power to determine both of them in the concession period The private sector aims to maximize its own profit and may charge a high service fee, which eventually hurts the social welfare and not many road users want to patronize the BOT roads (Carpintero and Gomez, 2011) Therefore the optimal BOT contract depends on whether the optimum toll is profitable (Guo and Yang, 2009) And it is necessary for the government to set some restraints on BOT toll price to not lead to a negative social welfare (Jing et al., 2008) The carrying out of road toll in Vietnam goes through two stages, before and after the Decree No 18/2012/ND-CP about "fund of road maintenance and operation" took effect in January 2013 Before the Decree No 18/2012 / ND-CP took effect, we had systems of toll stations, in which one system are used to toll for project invested by state budget Another system is served for project invested by BOT contract After the Decree No.18/2012/ND-CP took effect, all of toll station of project invested by state budget were removed (by Document No 2250/TTg-KTN in December 2012) So, "the fund of road maintenance and operation" was born to get revenue for state budget in order to operate and maintain the projects invested by state budge Meanwhile, all toll stations of BOT project are keeping remain The toll price of BOT road given by investor is set under the ceiling price that is regulated in Circular No 35/2016/TT-BGTVT and No 60/2018/TT-BGTVT, namely “Regulations for ceiling price of toll road” The ceiling prices vary across types of vehicles and this for heavier vehicles tends to be higher Two tables of ceiling prices below are officially set for national highway and expressway and applied to any toll roads all over the nation Table 1.1 Ceiling Prices in National Highway Ceiling price N Type of vehicle VND/ticket/turn Vehicles has less than 12 seats, trucks under tons; Buses 52,000 Vehicles has 12 - 30 seats, trucks with capacity - tons 70,000 Vehicles has more 31 seats, trucks with capacity - 10 tons 87,000 Trucks with capacity 10 - 18 tons, 20 feet of container truck 140,000 Trucks with more capacity 18 tons, 40 feet of container truck 200,000 Table 1.2 Ceiling Prices in Expressway Ceiling price N Type of vehicle VND/per km Vehicles has less than 12 seats, trucks under tons; Buses 2,100 Vehicles has 12 - 30 seats, trucks with capacity - tons 3,000 Vehicles has more 31 seats, trucks with capacity - 10 tons 4,400 Trucks with capacity 10 - 18 tons, 20 feet of container truck 8,000 Trucks with more capacity 18 tons, 40 feet of container truck 12,000 At this time of December 2018, there were 46 road projects invested in BOT scheme are going on toll charge (Department Public Private Partnership - Ministry of Transport, 2018) Observed Prices of BOT Toll Roads, it can be seen that most of BOT toll road projects have applied charge that are nearly equal to the given ceiling prices Toll pricing observed in 46 BOT projects is presented in table as below: Ceiling price 32 Number of projects (4) - Trucks with capacity 10 - 18 tons, 20 feet of container truck Ceiling price 140 120 115 21 110 Number 100 90 of 85 projects 80 75 70 60 40 Charge price (thousand VND) 33 Number of projects 70 50 45 40 35 30 23 22 15 Charge price (thousand VND) 52 35 30 26 25 20 15 10 Ceiling price (2) - Vehicles has 12 - 30 seats, trucks with capacity - tons Charge price (thousand VND) Charge price (thousand VND) Charge price (thousand VND) (1) - Vehicles has less than 12 seats, trucks with capacity under tons; Buses (3) - Vehicles has more 31 seats, trucks with capacity - 10 tons Ceiling price 87 75 65 30 60 Number 55 of 44 projects 40 33 22 (5) - Trucks with more capacity 18 tons, 40 feet of container truck Ceiling price 200 180 175 23 170 Number 160 of projects 140 135 120 80 Fig 1.5 Toll price in BOT scheme in Vietnam For BOT project, the balance of benefit between: the government, private investor and travelers is most important However, the ceiling price at this Circular has some problem That is, (1) the scale of project has not been considered Projects with different initial investment, different capacity of road are all applied at this ceiling price This is not reasonable (2) The Willingness to pay of travelers and ability to pay depending on the income of travelers have not taken into account in this ceiling price The charge price for BOT projects in Vietnam is equivalent to others countries while GDP per capita is less than (World Bank) That means, if it is absolute comparison, the charge price in Vietnam is more expensive 8,827 $ ((Source: Word Bank) 6,594 $ 3,400 China 3,000 2,343 $ 2,000 Thailand Vietnam GDP per capita, 2017 (unit: USD) 1,940 $ 1,400 India Charge price (unit: VND/km) Fig 1.6 GDP per capita and Toll price of some countries In practice, a BOT road usually co-exists with existing road managed by government, which can compose a simple two-road network The BOT project represents a major capital investment for which project conducts So, it is necessary to evaluate the financial viability and feasibility of the BOT project By viewing a toll price of BOT contracts on perspectives from three parties, including: (1) the government, whose objective is to maximize social welfare; (2) the private investors, who desire to gain maximum profit; both are expressed by criteria of financial evaluation, containing: Net present value (NPV), the internal rate of return (IRR), and the breakeven year; and (3) the travelers, whose objective is to minimize the travel cost described by "willingness to pay" Being aware of these issues, this study will focus on the effects of "Willingness to pay" to ceiling price of a BOT project in the context of a simple two-road network From that, we will integrate “willingness to pay of travelers” to model of toll ceiling price in BOT road project CHAPTER LITERATURE REVIEW Our research is closely related to the literature about toll and benefit under BOT contracts which attract a lot of attention A study discussed that a toll road getting benefit to private investor can make welfare falling for the whole highway network system (Mill, 1995) A simultaneous combination of concession period, road capability and toll price as a three variables occurred in BOT contract allows to optimize BOT contract in order to obtain maximum social welfare and gain an acceptable profit for private investor (Guo and Yang, 2009) In highway transportation network, the considering toll pricing under optimal combination of demand and capability of BOT road by bi-level programing formulas (Yang and Meng, 2000, 2002) Likewise, this model analyzed the influence of toll pricing to route choice of travelers and measured investor profit or social welfare of government (Chen and Subprasom, 2007) The toll level determined by the bi-level model was formulated to maximize social welfare while taking into account choice behavior of travelers (Yang and Zhang, 2003) A heterogeneous choice of travelers influents private profit and social welfare under various combinations of toll price and road capacity (Yang et al., 2002) In addition, the competition about toll and capacity occurred among roads (Xiao et al., 2007) The price is assumed to be a function of the travelling demand (Tan et al., 2010), considering on a simple two-road network, an equilibrium of traveling demand happened among travelers, leads to they will choose the road had minimum travel cost (Yates, 1992) Meanwhile National Highways Authority of India (NHAI) has set a formula for calculation of toll fee based on wholesale price index which is “the price of a representative basket of wholesale goods” (Government of India report, 2009) Following those previous literatures, researchers have developed different models and almost studies focused on optimization of toll charge to balance private profit and social welfare However, the existing models have not determine: (1) toll ceiling price model for each BOT project, and (2) impact of "willingness to pay" of travelers to target of perspectives mentioned above CHAPTER METHODOLOGY 3.1 The model setting As mentioned in Chapter 1, by the financial evaluation (i.e., NPV, IRR, breakeven year) and “Willingness to pay” of travelers, the project performances including private profit, social welfare and travelers’ benefit are considered in the decision process of BOT contract Particularly, (1) Private investor's benefit is remaining profit after deducting initial construction expense from their revenue that obtain from toll charge in concession period interval, minus initial construction expense (2) Government's benefit is welfare due to BOT road brings for society in concession period as well as until end of economic life of road (3) Traveler's benefit is "willingness to pay" level to use BOT road Subject to constraint conditions about benefit of private investor and the government, the optimal price will be found out Comparison this price with "willingness to pay" of travelers, the ceiling price of toll road will be set up for this BOT project The above explanations can be conveyed by the multi-equation as follows: Investor’s benefit = function of price = f1 (price) Government’s benefit = function of price = f1 (price) Travelers’ benefit = Willingness to pay Subject to: Constraint of investor’s benefit and government’s benefit The model is set up with a two-road network providing the transportation supply between two places Assume that, the government built a road links two places and they have been operating its In the future, in order to decrease the heavy traffic on the current road, the government plans to build a new road paralleling the existed road by a BOT scheme That is, the government will invite a private investor to build a BOT road by own investor cost Then they will operate this road and get revenue from road toll within concession period The private sector sets up the price of toll road for BOT road according to the market competition between two this roads The BOT road is denote by and the existing road is labeled by The two-road network is illustrated as Figure, and some notation is give as follows: y1 : the BOT road capacity p1 : the toll charge of BOT road Q1 : the flow volume on BOT road I (y1) : Total investment of BOT road y2 : the existing road capacity Fig 3.1 A network model p2 : the toll price of existing road Q2 : the flow volume on existing road M (Qi) : unit of maintenance and operation cost, assume that it is fixed Q0 : total travel demand between two places Ti (Qi, yi), i =1, 2: the generalized price (including travel cost and travel time) of each road A bi-level programming model is formulated for a two-road network containing BOT road There are five steps with various issues to optimize toll charge and propose toll ceiling pricing for BOT project Step 1: The lower-level program occurs between two road operators relating route choice behavior of travelers according to their travel cost Users' response depend on to each toll price which is set up by operators respectively 10 Step 2: The upper-level program represents the objective of decision makers In particular, operators determine the toll prices to maximize their own benefit respectively Step 3: Evaluation social welfare through criteria named total travel cost difference under the scenario that there is BOT road and there is non BOT road Step 4: Integrating the factor named "willingness to pay of travelers" to guarantee users' benefit Step 5: Determining ceiling price of toll road under condition that optimal benefit of investor and the government, which taking into account "willingness to pay" of travelers 3.2 Solution procedure 3.2.1 Step 1: Determining route choice of travelers The route choice of travelers when facing to each price set up by operators depends on their objective is that minimize own travel cost Assume that the toll charge p1 is chosen by private investor and p2 is chosen by government The user travel cost function can be expressed as the Bureau of Public Roads (BPR) travel time function which was chosen because it is so widely used: Q Ti Qi ,yi =λ.t0 (1+α i yi β ) + pi (1) Where: Ti (Qi, yi) is generalized price including travel cost and travel time λ is a parameter that transfers time to fare t0 is the free flow travel time α, β are parameters Without less of generalization, taking: α = β = 11 So, we have travel cost function, T1 for users choosing the BOT road: T1 Q1 ,y1 =λ.t0 (1+ Q1 ) + p1 y1 (1a) Likewise, travel cost function, T2 for users choosing the existing road: T2 Q2 ,y2 =λ.t0 (1+ Q2 ) + p2 y2 (1b) The objective function of travelers’ road choice for a given toll price is modelled as a standard user demand equilibrium according to the minimum travel cost, and can be expressed as follows: , T1 ( ) T2 ( ) + Subject to: Q0 = Q1 + Q2 (2) (3) The first term in Eq.(2) is total travel cost of users choosing BOT road to travel and the second term is total travel cost of users choosing existing road to travel The Lagrange function for the problem Eq.(2) and Eq.(3) is as follows: L(T1 , T2 , µ) = T1 ( ) + T2 ( ) − µ (Q0 − Q1 − Q2 ) (4) Where, μ is Lagrange multiplier corresponding with flow volume condition in Eq.(3) The optimal condition of Eq.(2) and (3) is derivative of the Lagrange function with T1 and T2 being nil respectively, can be described as follows: ∂L = T (Q ) + µ = ∂T (5a) ∂L = T (Q ) + µ = ∂T (5b) Combined Eq.(5a), (5b) with (1a), (1b) we have: 12 λ.t0 (1+ Q1 Q ) + p1 = λ.t0 (1+ ) + p2 y1 y2 Q =Q +Q Solve it, we can obtain: Q1 = y1 y2 Q0 + (p2 − p1 ) y1 +y y2 λ.t0 (6a) y1 y2 Q0 − (p2 − p1 ) y1 +y y1 λ.t0 (6b) Q2 = We can see from Eq.(6a) and (6b) that the flow volume of roads are concern with toll price and capacity of roads in a road network 3.2.2 Step 2: The operators determine the toll prices to maximize their own benefit respectively Based on the choice behavior of travelers, operators make decision for toll price to maximize their own benefit respectively 3.2.2.1 BOT road The benefit of BOT road is generated from toll revenue obtaining by toll charge of BOT road, and minus amount of initial construction cost and cost of maintenance and operation So, the operator will set up toll price level to maximize their own benefit It can be presented as below: max(Q p − I(y ) − Q M) (7) The first term in Eq.(7) is the revenue from toll price, the second term is initial investment expense, and the third term is cost of maintenance and operation Substitute Q1 from Eq (6a) into function of Eq.(7), we have: y1 y y1 +y y y Q Q0 1 + (p2 − p1 ) p1 − I y1 − + p2 − p1 y2 λ.t0 y1 +y y2 λ.t0 13 M (8) The optimal condition of Eq.(7) is derivative of the function in Eq.(8) with p1 being nil, can be described as follows: y y Q y y ∂ 1 = 0+ p2 − 2p1 ) + M = ∂ y1 +y y2 λ.t0 λ.t0 y1 +y λ.t0 2 Thus, λ.t0 Q0 p1 = + p2 + M y2 (9) So, p1 in Eq.(9) is the value of toll price so that the operator of BOT road get maximum his own benefit 3.2.2.2 Existing road Likewise, the benefit of existing road is generated from toll revenue obtaining by toll charge of BOT road, and only minus cost of maintenance and operation It can be presented as below: max(Q p − Q M) (10) The first term in Eq.(10) is the revenue from toll price, the second term is cost of maintenance and operation Substitute Q2 from Eq (6b) into function of Eq.(10), we have: y1 y2 Q0 y y Q 1 − (p2 − p1 ) p2 − − p2 − p1 y1 +y y1 λ.t0 y1 +y y1 λ.t0 M (11) The optimal condition of Eq.(10) is derivative of the function in Eq.(11) with p2 being nil, can be described as follows: y y Q y y ∂ 1 = 0− 2p2 + p1 + M = ∂ y1 +y y1 λ.t0 λ.t0 y1 +y λ.t0 2 Thus, 14 λ t Q p = +p +M y (12) So, p2 in Eq.(12) is the value of toll price so that the operator of existing road get maximum his own benefit 3.2.3 Step 3: Evaluation social welfare We are carrying out to evaluate social welfare by the criteria named total travel cost difference under the scenario that there is BOT road and there is non BOT road The total travel cost difference is defined that offsets of travel cost when there is only existing road for users travel, with travel cost when there are two road for user choose a road to travel Let D(p1, p2) be a total travel cost difference, can be described as follows: D(p , p ) = T Q0 ,y2 Q − [T Q1 ,y1 Q + T Q2 ,y Q ] (13) Subject to Q0 = Q1 + Q2 Tải FULL (51 trang): https://bit.ly/3qJvTQ2 Dự phòng: fb.com/TaiHo123doc.net Where: T Q0 ,y2 =λ.t0 (1+ Q0 ) y2 (14) The first item in Eq.(13) is travel cost of users when whole travelers use existing road, the second and third item are travel cost when users choose a route for their travel We determine two scenarios: case 1st is evaluation social welfare when all two roads get maximum their own benefit at the same time And case 2nd is evaluation social welfare when there is only one of two road getting maximum his benefit – it is operator of BOT road 3.2.3.1 Case 1: All two roads get maximum their own benefit at the same time That means, Eq.(9) and Eq.(12) simultaneously occur We have multi-equation: 15 λ t Q +p +M y ⎨p = λ t Q + p + M ⎩ y ⎧p = Solve it, we obtain the value of p1 and p2 are p1* and p2* respectively p∗ = λ t Q 2y + y y y +M (15) p∗ = λ t Q y + 2y y y +M (16) Substitute V1, V2, p1*, p2*, T (Q0, y2), T1 (Q1, y1) and T2 (Q2, y2) in Eq.(6a), (6b), (15), (16), (14), (1a) and (1b) respectively into D (p1, p2) in Eq.(13), we can get the total travel cost difference in this case calculated in Appendix, and presented result as below: D(p∗ , p∗ ) = Tải FULL (51 trang): https://bit.ly/3qJvTQ2 Dự phòng: fb.com/TaiHo123doc.net ( −2 −2 ) − M (17) ( + ) Generally, the new road capacity is greater than that existing road, namely y1 ≥ y2 Consequently, D(p1*, p2*) ≤ 0, that mean the free competition leads to a negative social welfare 3.2.3.2 Case 2: Only BOT road get maximum his own benefit under condition that it is positive social welfare That means, there is only Eq.(9) occur Substitute V1, V2, p1, T (Q0, y2), T1 (Q1, y1) and T2 (Q2, y2) in Eq.(6a), (6b), (9), (14), (1a) and (1b) respectively into D (p1, p2) in Eq.(13), we can get the total travel cost difference in this case calculated in Appendix, and presented result as below: D(p , p ) = − +2 2( + ) p + ( + ) 16 − 2( + ) (18) Social welfare is positive when total travel cost difference in Eq.(18) is greater than zero That means, − +2 2( + ) p + ( + ) − 2( + ) ≥0 Thus, p ≤ =− − ( +2 ) (19) Substitute p2 in Eq.(19) into Eq.(9), we get the p1 can be expressed as follows: p ≤ = + ( +2 ) + +2 (20) The price, p1’ is the maximum value threshold of toll price for BOT road so that social welfare become positive 3.2.4 Step 4: Integrating the factor named "willingness to pay of travelers" to guarantee users' benefit To guarantee benefit of travelers, the condition named “Willingness to pay” of travelers is set additionally and is compared with p1’ In order to estimate the “Willingness to pay” of travelers for toll price in BOT road, this study is conducted by steps of Contingent Valuation Method according to survey questionnaire In which, open questions are used to interviewees so that they gave their own “willingness to pay” pricing Then a series of bid question was given in order to determine amplitude of “willingness to pay” of travelers Using Descriptive Statistic tool in Excel software in order to be statistic and calculate value of WTP Using Regression tool in Excel software in order to analyze independent variables affecting WTP of travelers for toll price Variables in regression function include: Age, Gender, Education level, Marital status, Career Status, Income, Travel 17 6790888 ...VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO VIET HUNG INTEGRATING TRAVELERS’ PERCEIVED FACTORS IN MODELLING THE CEILING PRICE OF TOLL ROAD A CASE STUDY OF B.O.T PROJECTS IN VIET... 1.3 Rank of Vietnam in the world about service and quality of road transport infrastructure When choosing to travel on BOT roads, although length of road between BOT road and non BOT road are... welfare under various combinations of toll price and road capacity (Yang et al., 2002) In addition, the competition about toll and capacity occurred among roads (Xiao et al., 2007) The price is assumed