The Optimal Design of Beijing Bus Fares of Transit System

Transcription

1 Research and Applications in Economics Volume 2, 2014 The Optimal Design of Beijing Bus Fares of Transit System Cong-ying QIU *1, Hai YAN 2, Na LI 3, Tao LI 4 Beijing Key Laboratory of Traffic Engineering, Beijing University of Technology, Beijing, China *1qiucongying20@gmail.com; 2 yhai@bjut.edu.cn; @qq.com; @qq.com Abstract I t s most urgent to curtail a large number of financial subsidies of ground transportation in Beijing, figure out the unbalanced problem of passengers flow and improve the service level of Beijing transit system. To solve these problems, on the basis of combination of current researches and investigation results, we use demand elasticity coefficient to design fares programme modes. In this paper, with a prerequisite for the guarantee of tiny decline in bus sharing rate, bus fares is raised to diminish financial subsidies. The paper proposes a solution that encourages the elderly to go out by avoiding peak hours and three bus fares solutions aiming at adults. The amount of subsidies is e valuate d by average re venue curve (AR curve ) and total revenue curve(tr curve) (YANG We n-ju, 2010). The combination of passenger effect and limit of subsidies, which are considered as evaluation index, will be applied to analyse pros and cons of each fares structure. Three major issues, including the bus fares structure, setting price, and comprehensive evaluation on transit system benefits programme, are discussed in this paper. It is significant for system optimization of the metropolitan bus transit. After discussion, scheme two that charges by pea k shifting and averting is selected for optimal bus fares solution. Demand (Daganzo Carlos F., 2012), pointed out that for the sake of maximizing social welfare, decision-making bodies should make the optimal pricing and design a public transport system based on the target level of demand and these two should be considered separately. FIG.1 S CALE FIGURE OF BUS S UBS IDIES ACCOUNTED FORTHE PROPORTION OF OVERALL EXPENDITURE Keywords Transportation Planning; Bus Fares; Optimal Decision; Demand Elasticity; Comprehensive Benefit Evaluation; Ground Transportation; Financial Subsidy; Passengers Flow Effect Introduction In 2012, the fiscal expenditure of public transit ranked second of all fields in Beijing. Relevant research shows that there is no significant inhibition on the rate of road occupied of private cars by reducing bus fares (MIN Jie, 2013). In addition, while financial subsidy of ground public transportation in Beijing is going up, its passenger capacity faces bottleneck, which is very difficult to promote. In 2012, Daganzo Ca rlos F., on the study of On the Design of Public Infrastructure Systems with Elastic FIG.2 RELATIONS HIP OFPASSENGERS FLOWAND FINANCIAL S UBS IDIES FROM 2008TO 2012 Similarly, there are a number of studies on bus fares pricing and benefit evaluation programs at present (Layard R., 2008; WANG Hai-yan, 2013; LI Jin-xia, 2013), such as the study Analysis of Bus Diversity Fares Vote System and Passengers flow Effect (JIN Jian, YANG De-ming, 2009). These studies, however, ignore the 72

2 Research and Applications in Economics Volume 2, impact of bus fares system structure on the travellers' choice. In this paper, the optimization problem is firstly formulated in its full complexity, where the investigation, the design of bus fares, the prices, the demand and the comprehensive benefit evaluation are to be determined. In the Economics, the concept of elastic coefficient (Yang H., 1997) reflects an existing functional relationship between two economic variables, and it is widely used in many fields (Vickrey W., 1945; XU Ya-hua, 2009). In this paper, demand elasticity coefficient model is to be determined on the basis of investigation. According to the specific situation in Beijing (Z HANG Wen-feng, 2010), the paper will consider the difference of various categories of traveller groups and discuss the pricing issue. Upon that, three programs of bus fares, which are tailored to Beijing, have been proposed. Finally, combining impact of revenue and passengers flow, the paper analyses the pros and cons of each scheme. Investigation and Analysis In this paper, bus travellers are divided into three categories, the elderly whose age are not less than 65 (hereinafter referred to as the elderly ), the adult whose age are from 18 to 64 years old (hereinafter referred to as adult ) and students who have student advantage discount cards (hereinafter referred to as student ). At present the elderly enjoy preferential policies which they don't need to pay for the bus, and their travel demand has greater elasticity. Therefore we conduct a preference survey mainly aimed at the appropriate price adjustment, and a scheme of travelling by peak shifting and averting. Adults are the major component of public transportation and also the main target of pricing issue. It is assumed that their travel behaviours are accounted for two parts, commuting and non-commuting travel. As for students, they are the low-income group and have relatively stable travel demand, which make them have minor significance to the study. Thus, the student is not in consideration. Due to the difference of design purposes, we design two sets of investigation questionnaires both for the elderly and adults respectively. There are 277 valid questionnaires in total: 49 of the elderly and 228 of adults (136 of commuters and 92 of non-commuters). Bus Travel Features and Analysis of the Elderly We investigate the travel purposes, travel reasons, average monthly number of trips and travel distance of the elderly. The results are shown in Table1: TABLE 1 SURVEY RESULT OF THE ELDERLY BUS TRAVEL The Average Monthly Number of Travel (unit: captia) <10 Times 10~30 Times 30~60 Times >60 Times Number of People of Average Monthly Bus-travelling Distance (unit: captia) <5 stations 5~10 stations 10~15 stations >15 stations Travel P urpose (unit: captia) Shopping P ick Up the Child Exercises Others Reason for Choosing Bus Travel (unit: captia) Low P rice Others 49 4 Statistics show that the proportion of the elderly whose average monthly number of trips are less than 30 times is 77.6%. Additionally, it has a large proportion of non-rigid travel demand and short travel distance, which are less than 15 stations (about 4 km). Low price is the major reason of this group, where the proportion accounts for 92.5%. Therefore, it is feasible to induce the bus travel behaviours of the elderly by means of adjusting fares. The scheme proposed in the questionnaire is welcomed among the elderly, where they will be charged if their bus travels are during peak hours on workdays, while free during flat hours. In the 49 respondents, it is of 71.4% support rate: 35 people support this scheme, 9 against, and 2 to maintain their neutrality. This scheme is aimed at alleviating the pressure of passengers flow in peak hours, and encouraging the elderly to travel in flat hours. Furthermore, it appropriately retains their rights of the special cares from government and to some extent alleviates the financial pressure. Analysis of Bus Travel Elasticity of Adults The investigation results of adults travel purpose, frequency and etc. are as following: TABLE 2 BUSTRAVEL PURPOSEANDFREQUENCY OF ADULTS Travel P urpose Average Monthly Number of Trips (unit of schemes: time) Schemes People Distribut ion (unit: captia) Frequency Distribut ion commuting % Non-commuting % < % 15~ % 30~ % 60~ % > % 73

3 Research and Applications in Economics Volume 2, 2014 In the meantime, we have investigated their psychological acceptable fares. Psychological acceptable fare is the highest fare that a passenger can accept psychologically, and once actual fare is higher than it, the passenger will change his/her mind to choose other travel modes. Number of trips n is the cumulative sum, of which psychological acceptable fares are less than or equal to bus fare p yuan. Therefore, there are n times bus travels when the bus fare is p yuan. Without considering the effects of time distribution, once bus travel can be accounted for one unit of passengers flow, that is, number of trips = passengers flow. Thus the relationship between bus fares and travel willingness ratio is obtained as Fig.3: The demand elasticity coefficient that each bus fare corresponds to is obtained from (1). Considering the difference of elastic coefficient in a certain fares stage is very slight, we divide the bus fares into three price intervals, which low, middle and high price are respectively correspond to 0.6~2.0yuan, 2.0~5.0yuan, 5.0~10.0yuan. The elasticity coefficient is obtained by the weighted average method: Commuters Non-commuters TABLE 3 ELASTICITY COEFFICIENTOF ADULTS P rice Intervals Elasticity Coefficient Low Middle High Low Middle High It is assumed that the variation of passengers flow in interval is as following: In above equation: QQ ii = ββ ii QQ ii x bus fare after adjusted, yuan; xx αα PP ii (2) α original fare, yuan. The present original fare in Beijing is 1.0 yuan, so α=1.0 in this paper; FIG.3 RELATIONS HIP OF BUS FARES AND TRAVEL WILLINGNESS RATIO As Fig.1 shows, bus passenger flow and fares are negatively correlated. Hereinafter the paper will discuss their corresponding relationship, of which the specific variations of bus passenger flow when bus fares change. ΔQi, Qi, βi, Pi respectively stand for the variation of passenger flow,, the demand elasticity coefficient and fares of interval i. Total variations of passenger flow are as following: Structure of Bus Fares QQ tttttttttt = ii =1 QQ ii (3) TABLE 4 INTRODUCTION OF FARES STRUCTURE Modes of Bus Fares Introduction of Methods It is assumed that elastic coefficient indicates the sensitivity of the bus passenger flow to fares, that is, the specific variations of bus passenger flow when the bus fare changes in unit. The equation is as following: ββ = / PP = ( QQ/QQ)/( PP/PP) (1 ) In above equation: β demand elastic coefficient of fare Q bus passengers flow, captia P bus fare, yuan ΔQ variation of passengers flow, captia ΔP variation of bus fares, yuan Schemes Scheme1 Scheme2 Scheme3 Characteristics S tructure: S ingle fare Advantages: Simple fare structure and e asy to implement Disadvantage: Single fare causes irrationality and unfairness when the bus travel is too long S truc ture: Charge by peak shifting and averting Advantages: Transfer part of passengers flow in peak hours into flat hours, which balances the passengers flow Disadvantage: Increase the economic burden of commuters S truc ture: According to the c umulative number of swiping card, charge in stages Advantages: Charge in stages according to different travel needs, which ensures commuters basic travel and decreases non-commuters travel times effec tively Disadvantage: The difference of travel costs between commuters and non-commuters leads to unbalanc ed passengers flow 74

4 Research and Applications in Economics Volume 2, On the basis of domestic (LIU Ping-chang, 2008) (YAN Hai, 2004) and foreign (WANG Jing, 2008) research status quo, we propose three specific bus fare structure schemes which are respectively aimed at different purposes (Daganzo Carlos F., 2010). 1) Ideas of Adjusting Fares As Fig.1 shows, when bus fare raises, the passenger flow will drop accordingly. Revenues and costs are influenced by the interaction of fares and passengers flow. Therefore, it s necessary, when meets the pricing issue, to control the change volume of passenger flow in a certain stage, in order to ensure the passenger capacity of ground transportation. In consequence, it is assumed that, when establishing pricing schemes, we will take no account of the increase of passengers flow, which is the result of the population growth, but will take a constraint condition of fares change, that not less than 95% of original passenger flow. Maximize social welfare by means of reducing the financial subsidy of ground transportation. Meanwhile, all of the bus fare models in this paper will be based on travel willingness and demand characteristics that are reflected on the investigation. 2) Detailing of Schemes (1) Scheme One Fare calculation thought is as follows: The total variations of passenger flow are equal to the sum of commuters and of non-commuters, and is also less than 5% of original passenger flow. Therefore, the following inequality is obtained: ii =1 QQ cccccc,ii + ii =1 QQ nnnnnn,ii = 0.05 QQ tttttttttt (4 ) ΔQcom,i and ΔQnon,i respectively stand for the variation of commuters passenger flow and that of non-commuters. Combining (2), obtain that x=1.07yuan. (2) Scheme Two The travel in peak hours is approximately regarded as rigid travel of commuters. Therefore, passenger flow in peak hours is regarded as that of commuters and passenger flow in flat hours as that of non-commuters. Fare calculation thought is as follows: Because the total variations of passenger flow are equal to the sum of commuters and of non-commuters. Besides, it is also less than 5% of original passenger flow. Therefore, the following inequality is obtained: ii =1 QQ ffffffff,ii + ii =1 QQ pppppppp,ii < 0.05 QQ tttttttttt (5) ΔQflat,i and ΔQpeak,i respectively stand for the term i variation of passenger flow in flat hours and in peak hours. Combining (2), obtain different combination values of x1, x2. According to the different combination values and passenger flow, calculate the travel cost of per person per time, and then multiply the total passenger flow to obtain revenue value. The functional relationship of fares and revenue is showed as Fig.4: FIG.4 FARES -REV ENUE RELATIONS HIP OF SCHEME2 Take the fare combination that has maximum revenue value as the optimal one. After calculation, obtain the fare in peak hours x1=1.07 yuan, the fare in flat hours x2=1.09 yuan. (3) Scheme Three The detailing structure of Scheme 3 is: When a passenger uses the same bus card in a month, if he/she takes a bus less than 15 times, the relatively high fare will be implemented; if in the stage of between 15 to 60 times, the relatively low fare will be implemented; if in the part which is more than 60 times, the relatively high fare will be performed. The investigation shows that, the proportion of 136 commuters whose bus travel times are less than 60 times is 85%. This 60 times bus travel are regarded as the basic amount of bus travel of each commuter. That is why we divide travel times into three stages: Stage 1 is 0~15 times, stage 2 is 15~60 times and stage 3 is over 60 times. Regard the stage 1 and the part which is more than 60 times of stage 3 as non-commuting travel. Regard stage 2 and within 60 times of stage 3 as commuting travel. After calculation, elastic coefficient of commuting 75

5 Research and Applications in Economics Volume 2, 2014 travel β1= , and of non-commuting travel β2= It is approximately assumed that: commuting travel (60-15)/2 d+60 e non-commuting travel 15/2 f+(100-60)/2 e d, e, f respectively stand for the passengers flow of the stage 2, stage 3 and stage 1. In order to reduce the cost of commuters, we will calculate the travel cost of per person per time in various stages in this fare system, and control commuters travel cost each time lower than of non-commuter. It is assumed that the stage fare of 0 to 15 times d1 = ex yuan; stage fare of 15 to 60 times d2 = x yuan; the fare of more than 60 times d3 = ex yuan. x is the basic fare, b>1, a multiple based on the basic fare. values of b vary. TABLE 5 COSTOF REVENUEIN THE INCOME STATEMENT UNDER DIFFERENT B VALUES b Each Travel Revenue Cost P rofit Cost (yuan) (yuan) (yuan) (yuan) According to data above, the relations function between b and profit is obtained: Next we will discuss that when the values of bvary, how the bus fares and passengers flow will be: Assume b=1.5, then: As for a person of stage 1, each travel cost for him/her is x1=1.5x As for a person of stage 2, each travel cost for him/her is xx 2 = xx + ( )xx = 1.2xx 37.5 As for a person of stage 3, each travel cost for him/her is xx 3 = xx + (60 15)xx + (80 60)1.5xx 80 obtain xx 3 = 1.2xx ββ 2 (1.5xx aa) = ΔΔQQ 1 aa QQ 1 ββ 1 (xx aa) = ΔQQ 2 aa QQ 2 ββ 2 (1.5xx aa) = ΔQQ 3 aa QQ 3 ββ 2 (1.5xx aa) = ΔQQ 1 aa QQ 1 ΔQQ 1+ ΔQQ 2+ ΔQQ (QQ 1 + QQ 2 + QQ 3 ) Based on the simultaneous equations above, the bus fares of three stages are obtained when b=1.5. Analogously, specific fares are obtained when the FIG.5 RELATIONS FUNCTION OF b VALUE AND PROFIT The relationship between b and revenue is a quadratic function. We select the largest profit combination. According to calculation, when b=2.3, the corresponding combination of fare is the optimal plan, and then obtain x1=x3=1.97 yuan, x2=0.84yuan. In this case, in the stage of 0 ~ 15 times, every travel cost of per person is 1.97 yuan; in the stage of 15 ~ 60 times, the cost is 1.30 yuan; in the part of more than 60 times, the cost is 1.34 yuan. In consequence, the cost of commuters is less than that of non-commuters. It accords with the expected design of cost-sequence. Evaluation of Schemes According to the calculation principles in 3.2.1, w here the passenger effect and profit after raising fares, evaluate three schemes (LIU Chuang, 2009). Profit Profit p = revenue i cost c. As for cost c, according to the data from 2008 to 2012, every travel cost of per person at present is 2.53 yuan, and then multiplies passengers flow to obtain the total 76

6 Research and Applications in Economics Volume 2, cost. (Data Source: Beijing Municipal Bureau of Finance) Beijing Public Transport Holdings, Ltd is the main provider of ground public transportation in Beijing. Therefore, it has the features of imperfectly competitive market. The market demand curve is a monopoly supplier whom should meet. As for revenue i, it can be obtained by the demand curve and the AR curve, which are fully consistent (YANG Wen-ju, 2010). The demand curve is shown as Fig.1, and its function is y = x , which indicates that decision-making bodies can control bus fares by means of changing passengers flow and that bus passengers flow changes in the opposite direction to market price. Revenue function TR, y = x 0.318, is the derivative function of AR. The relationship among unit price of bus fares, total revenue i and passengers flows is showed as Fig.6: FIG.6 THE AR CURVE AND THE TR CURVE GRAPH The relationship among each travel cost of per person, passengers flow and total revenue is obtained by AR and TR curve. The calculation thought of each travel cost of per person is showed as follows: Select the optimal fare combination from three schemes to multiply the passenger flow of commuters and non-commuters, then to be divided by the total passengers flow. Upon that, every travel cost of per person of 3 schemes is respectively obtained. Substitute those values into AR function to obtain Q, which corresponds to the adjusting fares associated with status that is based on each scheme. Then, substitute Q into TR function, so that the total revenue of each scheme, total cost c and profit pare obtained. Magnify p, in accordance with the proportional relationship, and substitute it into the financial subsides. Finally, the savings are obtained respectively. The calculation results are shown as Table 6: TABLE 6 THE EARNING SITUATION IMPACT ON THREE SCHEMES Schemes Scheme 1 Scheme 2 Scheme 3 Each Travel Cost Total Revenue i1 Total Cost c1 P rofit p1 Reduce Expenses Each Travel Cost Total Revenue i2 Total Cost c2 P rofit p2 Reduce Expenses Each Travel Cost Total Revenue i3 Total Cost c3 P rofit p3 Reduce Expenses 1.07yuan 6872yuan 8533yuan -4920yuan 358million yuan 1.07yuan 6532yuan 8533yuan -4920yuan 358million yuan 1.33yuan 5792yuan 6223yuan -2959yuan 468million yuan In the table above, each travel cost is the ratio of total cost and total passengers flow. Substitute those values into AR and TR curves, others are obtained. However, each travel cost of commuters and non-commuters needs to be considered separately. Even though the benefits of Scheme 1 and 2 are consistent, each travel cost of commuters and non-commuters is different. In the end of (3) of 3.2.2, each travel cost is listed specifically. The lowest each travel cost of commuters is Scheme 3. On the basis of equation profit p = revenue i cost c, we can draw a conclusion that although the revenue of Scheme 3 is less than 1 and 2, on account of significantly reducing the total cost, its profit is the highest. Scheme 3 is the optimal benefit selection among the three. Analysis of Passengers Flow Effect The calculation thoughts of three schemes are to take a constraint condition of fares change, where the variation is not less than 5% of original passengers flow. Therefore, their total passenger flows are the same. Due to the different pertinence of three schemes, the effect of passenger flowof non-commuters and commuters varies. In order to analyse the specific passengers flow, we select the optimal profit of fare combinations from each scheme. Then, we obtain the specific variation in passenger flow of non-commuters and commuters, and compare that with original passenger flow of commuter, non-commuter, obtaining the variation range. The results are shown as Table 7: 77

7 Research and Applications in Economics Volume 2, 2014 TABLE 7 TRAFFIC CONDITIONS IMPACT ON THREE SCHEMES Variation of P assengers Change Rate of flow (unit: captia) Passengers flow Schemes Non-commu Non-comm Commuter Commuter ter uter One % -4.86% Two % -6.26% Three % % Among these bus fare models, to enhance bus fares must bring about decline in passengers flow inevitably. Due to the different pertinence of three schemes, the effect of adjusting on passenger varies. In Scheme 1, the overall passengers flow is balanced. The change rate of commuters is consistent with non-commuters. Besides, its small margin can help market achieve a smooth transition. In Scheme 2, inhibition of non-commuters is more significant than commuters. However, on account of the larger cardinal number of commuters passengers flow, it has better performance on achieving a smooth transition than Scheme 1. Moreover, passengers flow in peak hours will be significantly inhibited, which can balance the passenger flow uneven distribution of time. It is conducive to enhancing the service of bus. In order to reach the maximum of benefit, Scheme 3 is the best choice. In Scheme 3, the effect on passenger flow of commuter and non-commuter, which is the optimal fare combination, is unreasonable. Due to the large fare differences between commuting and non-commuting, commuters passenger flow increase and non-commuters passenger flow decrease by a large decline. Although this scheme seems to be considerable and has a satisfactory profit, there are some obvious defects in balancing passenger flow, which makes a substantial increase in commuting travel, irrational use of resources, and m ore serious traffic congestion problems. Furthermore, it increases social costs in other areas. Therefore Scheme 3 should not be considered. Conclusions This paper mainly discusses three fundamental issues, bus-fares structure, setting price and comprehensive benefits evaluations. On basis of specified regional study, three bus-fares structures are proposed for the status quo of Beijing. By using principle of the Economics, the paper evaluates the passenger volume effect and profit condition. The results show that the Scheme 3 has considerable economic benefits and the Scheme 2has most balanced passenger volume effect, which lessening peak-hour volume. This paper focuses on establishment of bus-fares structure, which has a little consideration on the transfer with other modes of transportation. The bus-fares structure with optimal comprehensive benefits can be put forward further, by expanding sample size and considering the correlation with other modes of transportation. REFERENCES Daganzo Carlos F. On the Design of Public Infrastructure Systems with Elastic Demand. Transportation Research Part B: Methodological, 2012, 46(9): Daganzo Carlos F. Public Transportation Systems: Basic Principles of System Design, Operations Planning and Real-Time Control JIN Jian, YANG De-ming. Analysis of Bus Diversity Fares Vote System and Passenger Flow Effect. Journal of Traffic and Transportation Engineering, 2009, 10(3): Layard R., Mayraz G., Nickell S. The Marginal Utility of Income. Journal of Public Economics, 2008, 92(8): LI Jin-xia, ZHOU Ai-lian, He Rong-rong. Synthesize d Evaluation Method of Public Transport Fares. Technology & Economy in Areas of Communications, 2013, 15(1): LIU Chuang, LU Wei, WU Wan-jiang. The Optimization Method Research of Public Traffic Fares Establishment. Traffic & Transportation, 2009 (z1). LIU Ping-chang, GUO J i-fu, CHEN Jin-chuan. Beijing Urban Transit Model: Development and Application. Urban Transport of China, 2008, 6(1): MIN Jie, ZHANG Yi-han, TAN Ke-hu. Based On Elasticity Demand for Bus Transit Fares to Analyze the Subsidies Effect of Beijing. Contemporary Economics, 2013 (13): Vickrey W. Measuring Marginal Utility by Reactions to Risk. Econometrica: Journal of the Econometric Society, 1945: WANG Hai-yan, YU Rong, WANG Guo-xiang. Calculating Me thod of Urban Public Transport Finance Subsidy. Journal of Transportation Systems Engineering and Information Technology, 2013, 13(6): WANG Jing. Theories and Methods of Pricing and 78

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