TSINGHUA SCIENCE AND TECHNOLOGY ISSN 1007-0214 02/15 pp632-639 Volume 11, Number 6, December 2006

Applied Study of Price Discrimination Implemented on a Two-Path Route Expressway

SHI Jing (石 京)**

Institute of Transportation Engineering, Tsinghua University, Beijing 100084, China

Abstract: This study aims at implementing price discrimination to get maximum revenue on a two-path route expressway, focusing on the problems which occur in traffic forecasting when applying a “profit-maximizing” toll designed to maximize revenue for a certain toll road in Japan. A break-even discussion is inevitable in the process of planning a certain toll road. According to the theory of transportation economics, market segmentation price discrimination is supposed to be efficient in the transportation market to increase the revenue of fixed facilities. In the model, a bypass and an adjacent expressway form a two-path route section. Two different toll levels are implemented for the bypass: one is for through traffic, and the other is for inside- inside and inside-outside traffics. This two-path route plus two-toll-level system thus causes difficulty in traf- fic assignment that is based on the minimum route searching method. In the study, a rational approach of adjusting the through traffic is implemented to predict the traffic flow as well as revenue on two parallel routes with different toll levels. The approximate calculation method that fixes the split rate of the passing through traffic flow is applied to solve the two-path route plus two-toll-level problem since passing through traffic is price elastic. Market segmentation pricing, which gives two toll levels in a toll road, is proved to be practical for increasing revenue. The results are also verified to be rational by using the survey data of Meishin Expressway.

Key words: road planning; traffic forecast; two-toll-level problem; price discrimination

expressway systems, and it is not necessary to break- Introduction even for each expressway line. The certain toll roads, where tolls are charged separately for each road, are In Japan, the Japan Highway Public Corporation (JH) planned, constructed, and managed by JH itself, based is in charge of construction, operation, and manage- on a beneficiary and repayment principle[1]. Each cer- ment of both certain toll roads and the inter-city ex- tain toll road must satisfy two constraints, namely, pressway system throughout the country. The certain road users must obtain benefit from the road, and the toll roads and inter-city expressway systems are man- toll revenue should be used to pay off the loan over a aged as two different kinds of toll roads. The inter-city 40-year period. expressway system is part of the national freeway net- In recent years, toll roads have mostly been con- work, which uses a distance-based toll system with a structed in heavy traffic areas to ease traffic congestion. basic interchange charge all around the country. A toll The Kinki area, with a population of 23 million, is the pooling system is implemented for the inter-city second biggest economic block in Japan. Moreover, the Received: 2005-07-11; revised: 2005-09-15 population is concentrated in urban areas, such as the ﹡﹡ E-mail: [email protected]; Tel: 86-10-62772300 Kyoto-Osaka area. In the study area, i.e., the Kinki SHI Jing (石 京)：Applied Study of Price Discrimination Implemented on … 633 area, traffic congestion often occurs on both roadways the bypass of the Meishin Expressway, the expressway and expressways. A certain toll road, the Keiji Bypass, toll levels should be applied to through traffic; other- has been planned and constructed as a bypass of the wise, vehicles will avoid using the road. As a result, a Meishin Expressway. The bypass, which connects two-toll-level scheme is required. This causes difficul- Shiga Prefecture and Kyoto Prefecture, is expected to ties in using a minimum route searching based traffic ease the daily traffic congestion on the Meishin forecasting process. Expressway, as well as on the national arterial highway Many researchers have studied multi-toll-level prob- No. 1. When it is completely opened to traffic, a two- lems, or parallel routes problems, and many mathe- path expressway route will be formed between Setahi- matical models with simple assumed networks have gashi Junction and Oyamazaki Junction of the Meishin been proposed. However, in this study, traffic forecast Expressway (Fig. 1), which is also a part of the Kyoto and flow analyses have to be made on a more realistic city ring road. network level, and a practical model is, therefore, nec- essary. In this study, based on price elasticity of de- mand analysis, a rational approach is applied to fore- casting the traffic flows on a two-path-route with two toll levels. Furthermore, the predictions are verified by an analysis of survey data obtained from two separate parallel path segments with the same toll level on the Meishin Expressway. 1 Economics Literature

In Japan, all freeways are toll roads and are con- structed beside existing highways. Travelers may choose between two adjacent roadways: one free but Fig. 1 Location of the certain toll road: Keiji Bypass slow or congested and the other with a fee but fast or This study was undertaken on the request of JH, the free-flowing, i.e., people are given the option to pay road administrator, who wishes to maximize revenue for a more highly valued service. This scheme is some- of the certain toll road. A profit maximizing criteria times called “value pricing”. Expressway planning should, therefore, be implemented to increase revenue needs a criterion to set the toll level. A value-pricing according to the repayment principle. program can be designed according to many criteria, As a matter of fact, it has been reported that traffic such as maximization of social welfare, control of flow flows surveyed on many certain toll roads are falling speed, or maximization of profit. far short of the predicted traffic flow for these roads[2]. One possible criterion is to apply the “second-best” Improving the precision of demand forecasts, including toll to the expressway, i.e., to maximize social welfare revenue prediction on the business level, is clearly an subject to a zero-toll constraint on the other roadway. important task. A break-even discussion and traffic According to the theory of transportation economics, flow analysis also should be conducted carefully on the marginal-cost pricing offers the best solution for opti- basis of a wide-area network, since consistency of mizing congested road traffic flows. However, several [4] forecast results is highly desirable. researchers, such as Yang et al. , have pointed out that In order to increase the revenue of the Keiji Bypass, if there are distortions in the economy, the first-best market segmentation pricing is assumed to take place, rules are in general no longer optimal. Recently in the [5-8] since the fixed facility is monopolistic[3]. The toll level literature , second-best tolls of road traffic conges- for the toll road of the Keiji Bypass should be high, tion in the presence of various technological and po- due to the high construction cost, and should ideally be litical impediments have been proposed. determined independently, depending on the forecasted Most recent research on value pricing has addressed traffic flow. However, since the certain toll road is also congestion pricing and road pricing, especially on “high occupancy/toll (HOT)” lanes. Road-pricing

634 Tsinghua Science and Technology, December 2006, 11(6): 632-639 concepts have moved to center stage in many transpor- parallel expressway routes besides zero-toll roadways, tation planning and policy-making venues. Recent re- and each may have different toll levels. It must be em- search, such as that by Braid[5], Verhoef et al.[6,7], and phasized that on a practical level, the traffic flow fore- Liu and McDonald[8], has uncovered a potential prob- cast and economical analysis must be implemented in a lem with current implementations of value pricing as a wide-area network. demonstration of road pricing. In this study, the revenue discussion includes two Another possible criterion is to set the toll just high parts. Firstly, we consider how to determine the enough to keep the traffic flowing at a minimum speci- amount of revenue that an operating corporation fied speed. However, this scheme is difficult to realize. should earn. Secondly, we consider how to distribute A third possible criterion is to apply a “profit- the revenue requirements among different categories of maximizing” toll which maximizes revenue, subject to users. the same zero-toll constraint. Market segmentation price discrimination is sup- This study focuses on the profit-maximizing version posed to be an efficient mechanism for increasing reve- of value pricing. The work of Kenneth et al.[9] is fo- nue. Charging different prices for the same product is cused on the profit-maximizing version of value pric- price discrimination. For most industrial products, ing, comparing its outcomes to those of the second- price discrimination is impractical due to the problem best version. Their study found that accounting for het- of resale. To make price discrimination successful, a erogeneity in the value of time is important in evaluat- seller must control its market. In the case of the trans- ing constrained policies using a model with two user portation field, transportation companies are in an es- groups, and improves the relative performance of poli- pecially good position to engage in price discrimina- cies that offer differential prices. They use a model to tion. It is generally possible to find a characteristic of explore the importance of heterogeneity in the value of customers that indicates their level of demand and, time for value-pricing demonstrations. since transportation services are not storable, they can Few papers have addressed user heterogeneity in a not be resold. In this case, production (road use) is in- two-route problem. Schmanske[10,11] and Arnott et al.[12] stantaneously consumed by those using the road. show that with heterogeneous users, differential tolls Market segmentation pricing should help to increase on separate roadways may be superior to a single toll. revenue if the market is monopolistic. If different cate- Bradford[13] shows that in a queue system with multi- gories of users have different price elasticity, market ple servers, a revenue-maximizing system administra- segmentation price discrimination should be functional. tor would charge higher tolls, hence offering lower Figure 2 depicts the concept of market segmentation congestion than socially optimal. price discrimination for a given toll road with two In this study, the criterion applied is a “profit- prices. Figure 2 shows that price can be decided ac- maximizing” toll, which maximizes revenue of the toll cording to the price elasticity of a user group. More road in question. However, a significant difference specifically, the price per trip will be higher if the price with common value pricing studies is that there are two elasticity of demand is low.

Fig. 2 Market segmentation price discrimination in case of certain toll road (in the case of keeping the revenue equivalent)

SHI Jing (石 京)：Applied Study of Price Discrimination Implemented on … 635

the traffic passing through the Keiji Bypass. Hence, a 2 Two-Path Route Plus Two-Toll- two-toll-level system concerning a two-path route, as Level Problem shown in Fig. 3, occurs on the bypass as a result of market segmentation price discrimination. The two- When the Keiji Bypass opens to traffic, a two-path toll-level system would be practical if users with freeway route will be formed. The toll for the Meishin different categories of price elasticity exist. The prob- Expressway is 24.6 Yen/km; the toll for the Keiji By- lem requires a novel approach since it is impossible to pass for inside-outside traffic should be higher than predict the through traffic flow by using a normal that of expressway because of the high construction minimum route searching based traffic assignment cost. To ease traffic congestion on the Meishin Ex- method. pressway, the toll level of the Expressway is applied to

Fig. 3 Two-toll-level problem concerning a two-path route

the annual working time, and the numbers in the work 3 Framework of the Model System force (Table 1).

In the road planning process, it is generally necessary Table 1 Calibrated time value to first do an ex-post forecast to judge the validity of Year Time value (Yen/min) the model system. Ex-post prediction is the most im- 1994 91 portant step for improving prediction precision in the 1999 95 [14] forecasting process , and ideally should be conducted 2008 113 using a real road network, since all the census survey 2020 139 points can then be checked. Traffic analysis is an inevitable step to judge the rationality of the forecasted Figure 4 depicts a flowchart of the forecasting proc- results. Financial analysis and economical analysis ess. In the flowchart, vkm denotes the distance in vehi- should be conducted to judge whether the proposed cle kilometers. Ex-post prediction was conducted be- road plan possesses efficiency and benefit. All these fore future demand forecasting. Four toll levels were analyses require a forecast system that can form a route set for the Keiji Bypass for the financial analysis. table of the assignment results. The OD matrix is estimated according to the OD In this study, a traffic demand forecast is conducted census and future control totals forecast by the by using a four-step forecast method based on the government. The basic information used for the Road Traffic Censes Survey data in 1999. A practical forecast is given below. incremental assignment method is preferentially used (1) Incremental portion is 0.3:0.2:0.2:0.2:0.1. in the traffic flow prediction due to its practicability[15] (2) Generalized time is used for the minimum route to assign four kinds of vehicle origin-destination (OD) searching process according to matrixes onto a network. A diversion curve made by TLVRC= 60 /+ / (1) JH is used to calculate the traffic flow for toll roads. To where L is the link length, R is the toll charge (Yen), V avoid the over-estimation of traffic flow of toll roads, is the link velocity, and C is the time value (Yen/min). generalized time is used for the minimum route- (3) A flow-speed (Q-V) curve is used to calculate the searching step. The time value is derived from the GDP, link time.

636 Tsinghua Science and Technology, December 2006, 11(6): 632-639

(5) There are 10 706 links and 6931 nodes in the na- tional-wide network, and the study area consists of 7 prefectures, such as Kyoto and Osaka. The average origin and destination traffic per zone is about 40 000 vehicle trips/24 h. 4 Demand Elasticity Analysis

To analyze whether market segmentation price dis- crimination is practical for the toll road under question, it is necessary to do a demand price elasticity analysis. The price elasticity of demand measures how much the quantity demanded responds to a change in price. De- mand for service and/or goods is said to be elastic when the quantity demanded responds substantially to changes in the price. Demand is inelastic when the quantity demanded responds only slightly to changes in the price. Usually, if the absolute value of price elas- ticity is greater than 1.0, it is elastic; otherwise, it is inelastic[16]. Several toll levels for the Keiji Bypass are used as preset values to do the traffic prediction. Toll level I, the 800 Yen level, is the same as that for the Meishin Expressway. Vehicle trips of different user categories, as shown in Tables 2 and 3, are summed from the route table of traffic assignment results. In Tables 2 and 3, toll

Fig. 4 Flowchart of forecasting process level I is the expressway toll level (24.6 Yen/km) and toll level II is 37.3 Yen/km; the through traffic pays the (4) A diversion curve is used to predict traffic flow same toll as the local (inside-inside, outside) traffic. for the toll road according to Table 2 Predicted vehicle trips of the Keiji Bypass in ⎧ 1 ,0;T ≥ different toll levels without discrimination ⎪ βδ+ ⎪ ⎡⎤X λ Toll level of Total Traffic flow P = ⎨1+ α ⎢⎥ iT ⎣⎦S the Keiji price ⎪ Inside- Inside- ⎪ 0, T < 0 (2) Bypass (Yen) Through Total ⎩ inside outside where P is the diversion rate, and T is the time differ- I 800 9012 36 053 16 938 62 003 ence between roadway and toll road (min). X is the II 900 9494 32 606 5791 47 891 toll charge (Yen/min), S is the shift rate, and III 1000 9012 30 942 5488 45 442 α, β, λ, δ are parameters. δ is used only when the IV 1100 8937 29 936 4529 43 402 toll road distance is less than 20 km.

Table 3 Predicted vehicle trips of the through traffic in different toll levels without discrimination Toll level of the Keiji Total price Meishin through Bypass through Total flow Bypass (Yen) Traffic flow Split rate (%) Traffic flow Split rate (%) I 800 35 800 68.0 16 938 32.0 52 738 II 900 47 437 89.1 5791 10.9 53 228 III 1000 47 839 89.7 5488 10.3 53 327 IV 1100 48 819 91.5 4529 8.5 53 348

SHI Jing (石 京)：Applied Study of Price Discrimination Implemented on … 637

The price elasticity of different categories of users is outside flow. The elasticity of income (Table 5) also analyzed as shown in Table 4. The assignment results shows the same results. The results also suggest that show that inside-inside and inside-outside flow are ine- for solving the two-toll-level problem, it may be ra- lastic, while through traffic is elastic, i.e., it varies due tional to fix split rates for through traffic, since through to the toll level. The results indicate that it is possible traffic is price elastic. to increase the toll level for inside-inside and inside-

Table 4 Price elasticity of traffic demand (dp, the difference percentage between Toll level I and Toll level II, is 12.50%) Traffic flow Ratio Elasticity Toll level I Toll level II Difference (d=c/a) (%) (e=d/dp) (a) (b) (c=b−a) Inside-inside 9012 9494 482 5.35 0.43 (Inelastic) Inside-outside 36 053 32 606 −3447 −9.56 − 0.76 (Inelastic) Through 16 938 5791 −11 147 −65.81 −5.26 (Elastic) Total 62 003 47 891 −14 112 −22.76 −1.82 (Elastic)

Table 5 Price elasticity of income demand (dp is 12.50%) Traffic flow Ratio Elasticity Toll level I Toll level II Difference (d=c/a) (%) (e=d/dp) (a) (b) (c=b−a) Inside-inside 4169 4329 160 3.84 0.31 (Inelastic) Inside-outside 20 828 20 774 −54 −0.26 − 0.02 (Inelastic) Through 23 699 8903 −14 796 −62.43 −4.99 (Elastic) Total 48 696 34 006 −14 690 −30.17 −2.41 (Elastic)

parallel routes. 5 Reasonable Approach and Step 2 Toll levels II, III, and IV for the bypass are Predicted Flow applied to the assignment of inside-inside and inside- outside traffic flow on the Keiji Bypass. An approximate calculation method that fixes the split Step 3 The through traffic flow according to the rates of the through traffic flow is applied to solve the split rate obtained in Step 1 is adjusted. Traffic flow for two-toll-level problem since it is difficult to predict the Keiji Bypass is obtained from the combination of through traffic flow using a normal predicting method inside-inside traffic, inside-outside traffic, and the based on a minimum route searching approach. First, through traffic. toll level I for the inter-city expressway is applied to Step 4 A financial analysis is conducted to deter- the Keiji Bypass to obtain the split rate for through mine the best toll level for the Keiji Bypass. Toll level traffic flow. In this case, the Keiji Bypass has the same II was found to be the best toll level according to the toll level as the Meishin Expressway. Next, the other revenue maximum criterion. toll levels are applied to obtain the break-even price for According to the above computing steps, the results the Keiji Bypass. However, the through traffic should of each toll level are estimated and shown in Table 6. be revised due to the presence of the split rates. The re- As the total price increases, the total number of vehicle sults are verified by using the left-right path survey trips decreases. Through traffic vehicle trips almost do data of the Meishin Expressway. not vary since the toll levels are the same. The problem is solved through the following steps. Since the predicting approach is approximate, it is Step 1 Toll level I for the inter-city expressway is necessary to show that the predicted traffic flow should applied to through traffic on the Keiji Bypass to obtain be within a tolerable range. Three traffic volumes the route split rate for through traffic flow for the two which form a tolerable range are shown in Fig. 5.

638 Tsinghua Science and Technology, December 2006, 11(6): 632-639

Therefore, maximum value is applied to the environ- available, most users may still keep using their current mental assessment, minimum value is applied to the fi- route as usual. Therefore, it is suggested that an infor- nancial analysis, and intermediate value is used for fa- mation system, such as electrical displayboard, which cility design. As a result, the financial analysis shows provides the travel time, congestion situation, should toll level II to give the best break-even result. The ve- be used. Furthermore, the discrete choice model is hicle trips in Fig. 5 are combined according to the fol- supposed to be appropriate if it is necessary to analyze lowing equations, in which F indicates traffic volume, further the split rate of through traffic flow. and subscripts pth, in+in, and in+out indicate through traffic, inside-inside traffic, and inside-outside traffic, 6 Conclusions and I and II represent toll levels I and II. Transportation economics provides the basic principles For the breakeven discussion, for increasing revenue of a fixed transport facility. In F =min{F , F }+min{F , F }+ b pth-I pth-II in+out-I in+out-II this study, market segmentation pricing, which gives min{F , F } (3) in+in-I in+in-II two toll levels for a certain toll road, is shown to be For the environmental assessment, practical for increasing revenue, but also causes diffi- FE=max{Fpth-800, Fpth-900}+max{Fin+out-800, Fin+out-900}+ culties in the traffic forecasting process. An approxi- max{Fin+in-800, Fin+in-900} (4) mate calculation method that fixes the split rate of the For the facility design, through traffic flow is applied to solving the two-path

Ff= (Fb +FE)/2 (5) route plus two-toll-level problem since through traffic is shown to be price elastic. The results are verified ra- Table 6 Revised vehicle trips for Keiji Bypass tionally by using the Meishin Expressway survey data. Toll level of Total Traffic flow the Keiji price References Inside- Inside- Bypass (Yen) Through Total inside outside [1] Society of Road Administration. Road Administration I 800 9012 36 053 16 938 62 003 2003. Japan: Council of National Road Users, 2003: 179- II 900 9494 32 606 17 091 59 191 181. III 1000 9012 30 942 17 188 57 142 [2] Japan Highway. Income and expenses of certain toll roads. IV 1100 8937 29 936 17 129 56 002 http://www.jhnet.go.jp/press/rel/2002/08/30a/betten3.html. Note: In the case of toll level II, III, IV, the through flows have the [3] Kenneth D B. Principles of Transportation Economics. same fixed toll as that of the Meishin Expressway. USA: Addison Wesley Longman, Inc., 1997: 20-24. [4] Yang Hai, Huang Hai-jun. Carpooling and congestion pric- ing in a multilane highway with high-occupancy-vehicle lanes. Transportation Research Part A, 1999, 33: 130-155. [5] Braid R M. Peak-load pricing of a transportation route with an unpriced substitute. Journal of Urban Economics, 1996, 40: 170-197. [6] Verhoef E T, Nijkamp P, Rietveld P. Second-best conges- tion pricing: The case of an untolled alternative. Journal of Urban Economics, 1996, 40: 170-197. [7] Verhoef E T, Small K A. Product differentiation on roads: Second-best congestion pricing with heterogeneity under public and private ownership. Irvine Economics Paper, University of California at Irvine, 1999, 99-00-01. Fig. 5 Combined vehicle trips [8] Liu L N, McDonald J F. Economic efficiency of second- However, this split rate depends on whether or not best congestion pricing schemes in urban highway systems. users can obtain information about the bypass roads. If Transportation Research, 1999, 33B: 157-188. information about the toll level or travel time is not [9] Small A K, Yan Jia. The value of “value pricing” of roads:

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Second-best pricing and product differentiation. Journal of [14] Shi Jing. An efficient approach to improving precision of Urban Economics, 2001, 49: 310-336. ex-post prediction with balancing factors in traffic [10] Shmanske S. Price discrimination and congestion. Na- assignment. In: Proceeding of 8th AATT. Beijing: China tional Tax Journal, 1991, 44: 529-532. Communications Press, 2004: 822-825. (in Chinese) [11] Shmanske S. A simulation of price discriminating tolls. [15] Matsui H, Fujita M. Development of a user equilibrium as- Journal of Transport Economics and Policy, 1993, 27: signment model for an urban road network including ex- 225-235. pressways. Review of JSCE, 2000, 653 (IV-48): 85-94. [12] Arnott R, de Palma A, Lindsey C R. Route choice with (in Japanese) heterogeneous drivers and group-specific congestion costs. [16] Mankiw N G. Principles of Economics (2nd Edition). USA: Regional Science and Urban Economics, 1992, 22: 71-102. Harcoute College Publishers, 2001: 93-114. [13] Bradford R M. Pricing, routing, and incentive compatibil- ity in multiserver queues. European Journal of Opera- tional Research, 1996, 89: 226-236.

2006 International RFID Technologies Summit Forum Held in Tsinghua School of Economics and Management

The International Radio Frequency Identification (RFID) Technologies Summit Forum, organized jointly by the Research Center for Contemporary Management, Tsinghua School of Economics and Management (SEM) and the Asia Pacific RFID Technology Association, was held from August 21 to 23, 2006 in Tsinghua’s SEM international auditorium. During the three-day summit, experts showed manufacturers and users the latest research which drives the con- version of products. All RFID software and hardware manufactures and vendors were provided with information on the most advanced research and technology. The close contact and exchange of ideas among specialists and manu- facturers have greatly facilitated national and international cooperation and exchange. The summit touched upon such RFID technologies and applications as tag and reader, communicating interface and frequency, data structure, safety and primacy, applied systems integrations, RFID standards, knowledge prop- erty rights, industry platform, library applications, defense-forging and defense-stealing, SCM management, animal identification management, mine management, traffic management, military logistics, sports entertainment, indus- trial applications, medical treatment applications, post applications, and janitor management. The 2006 International RFID Technologies Summit Forum was generously supported by the Ministry of Infor- mation Industry, Ministry of Communications, Ministry of Railways, the Office for Information Technology, and various academic journals, governmental bodies, and the media. According to the organizing committee, the Inter- national RFID Technologies Summit Forum will be held once a year at Tsinghua to continue to promote the devel- opment in China of RFID technologies.

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