Incentive subsidy scheme design with elastic transport demand

JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2014; 48:927 941 Publised online 10 October 2013 in Wiley Online Library (wileyonlinelibrary.com)..1253 Incentive subsidy sceme design wit elastic transport demand Wenqian Zou and Sosi Mizokami* Graduate Scool of Science and Tecnology, Kumamoto University, Kumamoto, Japan SUMMARY Huge public transport subsidies caused by deficits ave become a eavy financial burden on some local governments due to te decline of bus passenger numbers. It is essential to apply te performance-based contract to bus services considering maximization of social welfare. Tis paper constructs an incentive subsidy contract considering te decision-making powers of te service level and calculating te proper frequency elasticity aiming at two problems of performance-based contracts. Meanwile, we consider a role of bus operators ignored by most researcers. Under te sceme, te decision-making power of te service level is discussed based on five assumptions, and meanwile, bus operators are motivated to reduce cost and improve service level in te sceme. Te case of te bus service of Arao city indicates tat te optimal frequency equals to zero wen bus operators decide frequency. If bus operators determine efforts, te optimal effort also equals to zero wit te goal of maximizing te profit. Also, bus operators can play teir roles in lessening cost and improving service level to elp bus operators and te local government acieve a win-win situation, wic maximizes te social benefit in tis subsidy sceme wen all factors are decided by te government. Copyrigt 2013 Jon Wiley & Sons, Ltd. KEY WORDS: bus services; incentive subsidy sceme; Laffont-Tirole s model; frequency elasticity 1. INTRODUCTION External costs are incurred in urban areas tat experience substantial levels of traffic congestion due to te increasing number of private cars. Te existence of tese external costs is reflected in governments around te world seeking more sustainable means of meeting passenger transport requirements, including support for public transport because of its capacity to meet social obligations and to reduce te external costs of private car use. Terefore, transit subsidies are necessary, given substantial economies of scale, in order to permit services to be set at a level tat will result in reasonably efficient use of te public transport. Also, it is regarded as important to provide service for tose wo are unable to drive, in addition to elping cities find some relief from urban congestion and reducing fuel consumption. Altoug transit subsidies are necessary to lower te price of public transport and diminis discrimination, tey ave long been controversial. Pucer et al. [1] noted tat costs and subsidies are jointly determined, as iger costs elicit more subsidies, wic in turn induce iger costs. As a mecanism wit a major objective of containing te cost to government of service provision, competitive tendering (CT) was proposed and applied. Te CT contract attracted significant interest because of its attempt to apply responsibilities and incentives to contract operators to reduce cost. Te tree kinds of incentive contracts are gross-cost, net-cost, and cost-plus contracts. Te gross-cost contract introduced in London is payment to te operator of a specified sum of provision of te specifiedserviceforaspecified period, wit all revenue collected being for te account of te government [2]. Under te net-cost contract, instituted to Hong Kong bus companies, revenues must cover cost and guarantee profit. Worcman [3] concluded tat contract payments of *Correspondence to: Sosi Mizokami, Graduate Scool of Science and Tecnology, Kumamoto University, Kumamoto, Japan. E-mail: smizo@gpo.kumamoto-u.ac.jp Copyrigt 2013 Jon Wiley & Sons, Ltd.

928 W. ZOU AND S. MIZOKAMI Curitiba bus services are calculated from an analysis of eac operator s cost structure, and profit margins are set at 10% of turnover (cost-plus contract). Te success of te aforementioned CT regimes is measured by cost reduction. Te regimes are also used to force bus companies to improve service level. Gargett and Wallis [4] and Radbone [5] introduced te Adelaide competitive tendering and contracting tat was initiated by te government of Sout Australia in 1994. Under tis, a fixed sum, wic was te basis of te tender price bid and a patronage-related amount, wic was calculated according to te cange in patronage from te base year, comprised te contract payment. However, tere are some criticisms of competitive tendering. Henser and Stanley [6] pointed out weakness of competitive tendering. Altoug competitive tendering as lead to some noticeable gains in cost efficiency, te sizable financial gains are once-off, and subsequent retendering as delivered fewer financial benefits. Anoter reason is tat CT is focused on individual contracts wit no mecanism to ensure tat te incentive payment support sums to te optimal subsidy commitment across a broader geograpic area. Consequently, researcers ave looked for alternative ways for te appeal of active competition. Performance-based quality contracts align wit tis view troug incentive payments and bencmarked best practice costs. Henser and Stanley [6] consummated te concept of performance-based contracts (PBCs). Tey proposed tat te PBC framework takes into account te commercial angle of operators and te obligations of government to ensure tat subsidy support is spent in a way tat maximizes te net benefits of society. A PBC was proposed tat combines payment for delivering a minimum level of service and establised te optimum subsidy on te basis of te system-wide maximization of social surplus [7]. Te reward system can bot meet government community service obligations and realize an incentive regime tat rewards operators for passengers increases (above minimum level of service patronage levels). Gonzalez-Dıaz and Montoro-Sancez [8] concluded some lessons from incentive teory promoting quality in bus transport. Most performance-based contracts regulate te service level as te performance indicator; wen bus operators improved te service level, public transport demand may likely be influenced. Tere are two questions regarding performance-based contracts. Te first is wic part will determine te service level. In most contracts, te service level is usually determined by te bus operators. Te reason is tat a public transport operator usually as te best and most detailed knowledge of te market tey serve and also better knowledge of te cost structure of public transport services to assess te cost of increasing or decreasing frequencies and so fort. However, te objective of te bus operator is maximizing profit, and political considerations ave weiged eavily in te determination of a level barely sufficient to maintain a tolerable service, wit little attempt at a rational determination based on costs and benefits. Te second question is tat of elasticity between te service level and te demand. Bus service demand generally rises wen bus service quality acieves a viable and reasonable standard. Tere are many important aspects to be considered in increasing bus service demand, including te canges of bus service elements and caracteristics of ridersip factors. Suwardo et al. [9] concluded tat frequency cange is likely a more preferable recommendation tan cange in capacity because of te opportunity of raising load factor in te future. Also, in some of te researces of PBC, frequency was studied as an index of performance. However, tere is less incentive teory researc on ow to get te elasticity, wic tey employed in teir papers. Aiming tese two questions, te main purpose of tis paper is to propose an optimal performancebased incentive subsidy sceme, in wic te decision-making power regarding service level is discussed troug te proper frequency elasticity value. Under tis sceme, te bus operator is motivated not only to attract more passengers troug improving service level, but also to reduce deficits to obtain te premium, a point wic is ignored in existing performance-based contracts. Te structure of tis paper is organized as follows: Section 2 provides an incentive subsidy sceme based on Laffont-Tirole s model, and five solutions aiming at te decision-making power of te service level are proposed; Section 3 contains results and analysis of te situation of deficit and social welfare under te five solutions troug investigation of te public transport of Arao in Japan as te researc object; finally, Section 4 presents conclusions and te feasibility of introducing te incentive sceme.

INCENTIVE SUBSIDY SCHEME DESIGN 929 2. INCENTIVE SUBSIDY SCHEME MODEL In te present subsidy sceme in Japan, te government supplies enoug subsidies to make up for te gradually increasing deficit of bus operators, and tere is not any stimulation for bus operators to reduce deficit. Te local government as to pay te same amount of subsidies as te deficit stated by bus operators as sown on te left side of Figure 1. Zou and Mizokami [10] proposed a new incentive subsidy sceme as represented on te rigt side of Figure 1. In te sceme, te local government will give a premium to te bus operator if it successfully makes efforts to reduce deficit. Te result is tat bus operators get teir premium and te local government lessens subsidies, a win-win situation. Te goal of bus operators is maximizing profit U = t ψ(d), wereas te objective of te government is maximizing social welfare, tat is, maximizing te sum of passenger surplus benefit S (1 + λ)( β d + t) and te excess profit U = t ψ (d). Max t;d S ð1 þ λ Þ½β d þ ψðdþš λðt ψðdþþ s:t:t ψðdþ 0 (2:1) Were, S =passenger benefit; λ = sadow cost of public fund; ψ(d) = disutility of effort d; t = net monetary premium; β = deficit witout effort to reduce cost; and d = bus operator s effort. Under complete information, te government knows te deficit β and observes te bus operator s effort d. Te maximum social welfare is determined by te reduced cost d * and te excess profit U *. Wen te social welfare is maximized, U * =0. However, te service level was assumed to be te same as te current situation in Equation (2.1). Actually, one requirement of te incentive contract is improvement in te service level [11]. In order to analyze ow te cange in service level affects passengers and subsidies, tis article improves on te aforementioned model, introducing frequency as te service level variable, and builds an incentive subsidy model wit elastic transport demand. 2.1. Model description Te objective of te model is to maximize social welfare, tat is, to maximize of te sum of passenger surplus benefit and excess profit, as Equation (2.2) sown. Max SB ¼ ðu þ UB Þ (2:2) Were, SB = te social welfare; U = te excess profit of line ; and UB = te surplus benefit of passengers of line. Te excess profit U is te difference between te premium t and te disutility ψ(d, f ), as Equation (2.3) sown. Figure 1. Mecanism design of incentive subsidy sceme model.

930 W. ZOU AND S. MIZOKAMI U ¼ t ψðd ; f Þ (2:3) Were, t = te premium tat rewards bus operators for improving service level and reducing cost of line.ψ(d, f ) = te disutility of bus operators because of teir efforts to improve te service and reduce cost of line. Wen bus operators take efforts, disutility of efforts will occur. Te ψ(d, f ) is te increasing function of d, wic means te more is te disutility of efforts, te iger is te reduced cost. Meanwile, te bus operator is constrained by individual rationality. Te excess profit sould not be negative, as Equation (2.4) sown. U ¼ t ψðd ; f Þ 0 (2:4) Te subsidies and premium supplied to te bus operator are gatered from bot taxes and from passengers. Terefore, te surplus benefit UB is te difference between te benefit tat te public transport brings to passengers and te paid. Due to te existence of social cost coefficient, UB is expressed as Equation (2.5). UB ¼ Sf ð Þ ð1 þ λ ÞfCd ð ; f Þþt g (2:5) Were, S( f ) = te surplus of passengers of line ;λ = sadow cost of public fund; C(d, f ) = te deficit of line after efforts taken to reduce cost and improve service. Eventually, te social benefit SB can be written as Equation (2.6) sown. Max SB ¼ SB ¼ ðu þ UB Þ ¼ fsf ð Þ ð1 þ λþðcd ð ; f Þþt ÞþU g ¼ fsf ð Þ ð1 þ λ ÞðCd ð ; f Þþψðd ; f ÞÞ λu g (2:6) 2.2. Maximizing social benefit SB Tis study solves te social benefit maximization problem based on te Stackelberg model [12]. Te government is te leader wose object is maximizing te social welfare. Te bus operator is te follower wose object is maximizing profit. Te government must know ex ante tat te bus operator observes is actions. In te model, te premium t reduced cost d and te frequency f is variable. Te premium t, determined by te government, is supplied by te government to reward good performance of te operator. As we said before, tere is dispute about te decision-making power of te service level. In order to solve te problem, we make several assumptions about te decision-making power of d and f sown as Table I. According to assumptions, tere are five possible coices; we will respectively calculate te maximal social benefit of eac case to get te rigt decision of te service level. (1) Case 0 Under Case 0, te existing service level continues uncanged, wereas te reduced cost d and te premium t are determined by te government. Wen te social benefit is maximal, te excess profit equals to 0. t ¼ ψ n o d. And d fits ð1 þ λþ dc ð d Þ þ dψ ð d Þ ¼ 0. dd (2) Case 1 Under Case 1, t is determined by te government, wereas d and f are determined by bus operators. As we said, ψ(d, f ) is te decreasing function of d, but we do not know its relationsip wit f. Terefore, te model is solved based on two ypoteses. dd

INCENTIVE SUBSIDY SCHEME DESIGN 931 Table I. Decision-making power of variables and te optimal solution. Case 0 ð ψ d ; f f Case 1 Þ ð 0 ψ d ; f f Þ 0 Case 2 ð ψ d ; f f Case 3 Þ 0 ψðd ;f Þ f Case 4 t Government Government Government Government Government Government Government d t t t ¼ 0 t t t ¼ 0 t Government Operator Operator Operator Government Government Government f d d ¼ 0 d ¼ 0 d ¼ 0 d d ¼ 0 d Operator Operator Government Operator Operator Government f f ¼ 0 f f f ¼ 0 f 0 If ψ(d, f ) is te decreasing function of f,tefirst optimal order condition tat makes te excess profit maximum is d ¼ 0. Wen te optimal frequency f satisfies t ¼ ψ 0; f, te social benefit is maximal. If ψ(d,f ) is te increasing function of f, te first optimal order condition tat makes te excess profit maximum is d ¼ 0 f ¼ 0. Wen t ¼ ψð0; 0 Þ ¼ 0, te social benefit is maximal. dsð f Þ df f (3) Case 2 Under Case 2, t and f are determined by te government, wereas d is determined by te bus operator. Wen te first optimal order is d ¼ 0, te excess profit of te bus operator is maximal. Te optimal solution of social benefit is t ¼ ψ 0; f : And f satisfies ð1 þ λþ C ð 0; f Þ -1þ ð λþ ψ ð 0; f Þ f ¼ 0. (4) Case 3 Under Case 3, t and d are determined by te government, wereas f is determined by te bus operator. Because te relationsip between ψ(d, f ) and f is unknown, te model is solved based on te same ypoteses. If ψ(d,f ) is te decreasing function of f, te first order condition tat makes te excess profit maximum is f ¼ f ðd Þ. And wen t ¼ ψ d ; f, te social benefit is maximal. Te optimal frequency d satisfies n o dcðd ð1 þ λþ ;f ðd ÞÞ þ dψ ð d ; f ðd ÞÞ ¼ 0. dd dd If ψ(d, f ) is te increasing function of f, te first order condition tat makes te excess profit maximum is d ¼ 0 f ¼ 0. Wen t ¼ ψð0; 0 Þ ¼ 0, te social benefit is maximal. (5) Case 4 Under Case 4, t, d, and f are determined by te government. Te optimal first condition is t ¼ ψ d ; f, d ¼ df ð Þ. Te optimal frequency f n o satisfies dsðf Þ dcðdðf df ð1 þ λþ Þ;f Þ df þ dψ ð df ð Þ;f Þ df ¼ 0 From te aforementioned calculation, we can see tat wen f is determined by te bus operator under Case 1 and Case 3, te model is solved based on two situations because of te relationsip between ψ(d, f ) and f.wenψ(d, f ) is te increasing function of f, te bus service is terminated f ¼ 0. Tis means operators will stop te bus service. Wen ψ(d, f ) is te decreasing function of f, te optimal frequency f can be obtained troug te formulation. Wen d is determined by bus operators under Case 1 and Case 2, d ¼ 0. Tis means te best beavior of te bus operator is to take no efforts to reduce cost. 3. APPLICATION OF THE INCENTIVE SUBSIDY MODEL BASED ON ELASTIC DEMAND 3.1. Te bus services situation of Arao city Tis paper aims at te bus services in Arao city as te researc project. Arao is a city located in Kumamoto, Japan. As of 2011, te city as an estimated population of 56 144, wit te density of

932 W. ZOU AND S. MIZOKAMI 982.40 persons per km 2. At present, te public transport of Arao city is operated by Kyusu Sanko Bus Co., Ltd and Nisi-Nippon Railroad Co.,Ltd (NNR). Figure 2 sows te trend of te passengers and te subsidy from 2003 to 2009. Due to te growing popularity of private veicles, te operation situation as sarply deteriorated. In order to avoid te lessening of service levels bus operators and tus to avoid furter deficit te local government supplies sufficient subsidies. Tese subsidies reaced nearly 160m in 2003, causing a large financial burden on te government. In order to relieve te burden, transit privatization began in 2004. Savage [13] discussed te effects of privatization and reported tat operating costs and subsidization ad decreased after privatization. However, e mentioned tat demand ad declined as a result of service canges and tat services ad been concentrated to te most popular routes. Te transit privatization in Arao also faced tese problems, and it resulted tat te amount of subsidies fell from 154m to 55m and in passenger number by about 35% in te same year. Te object of te bus operator is to maximize profit troug controlling costs [14] and cutting bus lines wit large deficits. Bus service was considered by te bus operator as a business and not as a merit good, and te situation continued to deteriorate in 2005. Te government began to increase subsidies from 2006 in order to attract more passengers. However, te number of passengers continued to decrease. Tus, transit privatization in Arao reduced subsidies at te expense of a decrease in demand. Application of a subsidy mecanism considering passenger demand is tus crucial for bus services in Arao city. 3.2. Parameter calibration Te bus service is operated by two companies in Arao city. Kyusu Sanko Bus Co., Ltd owns 20 bus lines, wereas NNR as two bus lines. Te bus lines of Kyusu Sanko Bus Co., Ltd cover te wole city, wereas bus lines of NNR are running in te suburbs wit very low frequencies. Terefore, te paper takes bus lines of Kyusu Sanko Bus Co., Ltd as te researc object. First, we need to confirm C( f,d ),D ij ( f ), S( f )and ψ(d, f ) tat are needed to get te social welfare. 3.2.1. Te deficit C(f,d ) of line Te deficit of line is te difference among te cost of line before effort, te revenue of line and te reduced cost due to efforts. Te formulation is as Equation (3.1) sown. Cd ð ; f Þ ¼ Pðf Þ i; j ð d 3652f L (3:1) D ij f Þc ij ð Þ Were P( f ) = te cost of line before effort; D ij ( f ) = estimated demand between stop ij of line after effort; c (ij) = te ticket price between stop ij of line ; d = te reduced cost per mile of line ; f = te frequency per day of line ; and L = te lengt of line. P(f ) is related to te revenue kilometer of line. Regression analysis is carried out to calculate P( f ) troug using 20 bus lines data. Te result is sown in Table II. Te revenue kilometer is te function of f, and is expressed as 365 2 f L. Figure 2. Te current situation of bus services in Arao.

INCENTIVE SUBSIDY SCHEME DESIGN 933 Table II. Te calibration results. Variant Parameter t-value Constant 5.58 10 5 0.95 Revenue kilometer 191.4 13.6 Relevance 0.91 3.2.2. Passengers between stop i and stop j of line after effort D ij (f ) If te frequency canges, te demand of passengers must cange wit it. Te new demand is estimated based on te current passengers between stop i and stop j as Equation (3.2) sown. Te data of D B ij ð Þ is from te origin destination survey tat was carried out to passengers in 2010. D ij ð f Þ ¼ D B ij ð Þ þ ε! D B ij ð Þ f B f f B Were, D B ij ð Þ = passengers of line between stop ij; ε = frequency elasticity; f B ¼ te frequency before; and f =te frequency after canging te service level.. Tere as been muc researc on frequency elasticity. However, tere are fewer studies on ow to calculate te elasticity. Most of te elasticity value was obtained from data statistics [15]. Tis paper built a model to calculate frequency elasticity wile considering te trend of public transport and oter factors. Effective factors considered by tis paper include bus services, population level and number of private cars. Factors for bus services include frequency and te inerent trend of bus services. We also consider influences tat te adding or cancelling of lines may ave on demand. Te local government respectively reorganized te bus network in 2008 and 2009. Some bus lines were added and some canceled in eac reorganization of te network, and tese canged bus lines may affect demand in te subsequent year. Te factors of te previous year may influence te demand in te subsequent year, as Equation (3.3) sown. Te affecting factors are as presented in Equation (3.4). D t ¼ Ax t 1 ð Þ (3:2) Dðt 1Þ (3:3) Were, D t = te number of passengers of line in t year; A(x (t 1) ) = te index tat affecting number of passengers of line in t 1 year; N (t 1) = te number of passengers of line in t 1 year. ln Ax it 1 ð Þ ¼ μp ln x pt 1 ð Þ þ μ car ln x carðt 1Þ þ (3:4) μ bus þ η bus δ it 1 ð Þ þ ε bus f it 1 ð Þ ln N it 1 ð Þ Were, μ p = te influence coefficient of population; x p(t 1) = te population in t 1 year; μ car = te influence coefficient of car; x car(t 1) = te number of private cars in t 1 year; μ bus = te inerent influence coefficient of bus; η bus = te influence coefficient of cancelling or adding lines;δ (t 1) = passengers of line tat were influenced by cancelling or adding lines in t 1 year; ε bus = te elasticity of frequency; f (t 1) = te canged frequency of line in t 1 year. Utilizing te public transport data, te size of population, and te number of private cars from 2005 to 2010, te SPSS (IBM, Armonk City, NY, USA) was employed to calibrate parameters wit 95% confidence level. Results are sown in Table III. Te variant of population was excluded as a calibration parameter by te software, peraps because te population size as less influence on te demand because of low population growt rate. In 2005, te population of Arao was 56 420 and te growt rate 0.3%. Tere is scarcely population cange in Arao. Terefore, te parameter of size of population was excluded by te software. Te parameter of frequency is 0.349. Currie and Wallis [16] concluded tat te average elasticity is 0.35. Paulley et al. [17] calculated te frequency elasticity of bus demand as approximately 0.4 in te

934 W. ZOU AND S. MIZOKAMI Table III. Te estimation results. Variant Parameter Significant values Constant 1.12 0.037 Influence coefficient of car 0.331 0.019 Inerent coefficient of bus 0.064 0.020 Coefficient of canged lines 7.50*10-6 0.001 Elasticity of frequency 0.349 0.001 sort run. Terefore, te frequency elasticity of Arao is reasonable. Te value of elasticity is positive, and tat means te passenger demand is te increase function of te frequency. 3.2.3. Te surplus S(f ) of passengers of line Te generalized cost borne by passengers is defined as te sum of ticket price and te cost of waiting and trip times. Wen bus operators increase frequency, passenger generalized cost will decrease from g B to g due to te reduction of te waiting time, as sown in Figure 3. As suc, te demand will increase from D B to D. Te area g B BAg tat is derived from a reduction in te generalized cost and te rise in demand is te passenger surplus measured as Equation (3.5). Sðf Þ ¼ 1 2 ij ¼ 1 2 ij n n D B ij D B ij ð Þ þ D ijð ð Þ þ D ijð f f o n o Þ g B ij ð Þ g ij ð Þ o Þ g B ij ð Þ c ij ð Þþ ωtime ij ð Þ þ ω 6013 2*f ð3:5þ Were, D B ij ð Þ ¼ te demand between stop ij of line before canging te frequency; D ij(f ) = te demand between stop ij of line after canging te frequency; g B ij ð Þ¼ te generalized cost between stop ij of line before; g (ij) = te generalized cost between stop ij of line after; c (ij) = te ticket price between stop ij of line ; ω = te time value of passengers (ω is set 24.94 (yen/min) based on te Japanese national standard); and Time (ij) = te trip time between stop ij of line. 3.2.4. Disutility of efforts ψ(d,f ) Wen te bus operator takes efforts to increase frequency or reduce cost, tese efforts would incur te cost ψ(d, f ). A reasonable subsidy mecanism applied to public transport operators in Kyusu, Japan is used to calculate te disutility. Te mecanism, wic acts as an incentive to promote bus operators Figure 3. Composite demand function.

INCENTIVE SUBSIDY SCHEME DESIGN 935 to improve te service level wile controlling cost, includes two conditions. One is te cost of te bus operator sould be below te average cost of bus operators in te area; te oter is te operating situation sould be improved compared wit te previous year by eiter reducing cost or increasing revenues. Wen bot conditions are satisfied, te bus operator can obtain te subsidies. A questionnaire survey was carried out to bus operators tat ad obtained te subsidy to gater data. Te content of te questionnaire is revealed as Table IV. Te data was used to calibrate te function of ψ(d, f )defined as Equation (3.6). ψðd ; f Þ ¼ expðα 0 þ α 1 gap þ α 2 d þ α 3 3652L f Þ (3:6) Were, gap= te difference between te average operating cost of all bus operators and te operating cost of one bus operator, tat is, a kind of yardstick cost. Table V presents te calibration results. Te parameter of te revenue kilometer is positive in Table V. Tat means ψ(d, f ) is te increasing function of f. Wen te bus operator decides f and ψ(d, f ) is te increasing function of f under Case 1 and Case 3, te optimal frequency f is zero. Tat means te bus operator stops supplying te bus service under tis situation, and tis is unreasonable. Terefore, te two situations will not be discussed during te following analysis. 3.3. Result analysis Tis paper takes te bus services of Arao city as an example to verify te incentive subsidy model on te basis of elastic demand. Results are sown as Table VI. Table IV. Te questionnaire survey content. Caracteristics of bus lines Operating situation Name of te bus line Starting/ terminal stop Lengt of te bus line Frequency (workday, day off) Revenue, cost Average operating cost in te area (yen/km) Te cange of te operating cost compared wit tat in last year (yen/km) Te cange of revenues compared wit tat in last year (yen/km) Te maintaining lines reasonable subsidies Table V. Te calibrating results. Variant Parameter t-value Constant 10.82538 73.19899 Difference 0.007861 12.40475 Reduced deficit 0.049383 6.718688 Revenue kilometer 8.71E-06 15.49588 Relevance 0.97 Table VI. Te calculating results f * (runs/day) D(f) (tousand persons/year) d * (million yen/year) C (million yen/year) t * (million yen/year) C + t * (million yen/year) S(f) (million yen/year) SB(f) (million yen/year) Current 62.5 382.3 0 72.6 0 72.6 0 0.0 Case 0 62.5 382.3 26.2 46.4 13.3 59.7 0 13.5 Case 2 143.9 505.8 0 176.4 3.2 179.6 1299.8 1111.1 Case 4 156.4 520.6 70.3 147.0 31.1 178.1 1484.0 1329.7

936 W. ZOU AND S. MIZOKAMI 3.3.1. Te optimal frequncy f Figure 4 sows te optimal frequency of te bus network under different cases. Te frequency stays constant and is 62.5 runs/day under Case 0, wereas te optimal frequency under Case 2 and Case 4 is sarply increased. Te number of runs is 143.9 per day under Case 2, 2.3 times tat of te current frequency; te number is 156.4 per day under Case 4, 2.5 times. Te frequency under te Case 4 is iger tan tat under Case 2. 3.3.2. Reduced deficit d At present, te average operating cost per kilometer in Arao city is 187. Te average operating cost is reduced by 32/km under Case 0, wereas it is reduced by 43/km under Case 4. Te situation of reduced cost of bus lines under Case 0 and Case 4 is presented as Figure 5. Te fluctuant range of reduced cost of eac bus line is 13 48 under Case 0, wereas te fluctuant range under Case 4 is 28 50. Te reduced cost is relevant wit te revenue kilometer. Taking te Case 0 as an example, it is seen tat te reduced cost is more wen te revenue kilometer is iger. Figure 6 sows te relationsip between te frequency and te reduced cost. As stated earlier, te frequency under Case 4 is iger tan tat under Case 2. Troug Figure 6, it is seen te frequency of te line under Case 4 is iger tan te frequency of same line under Case 2 wen te reduced cost of te bus line is larger. Tat means te bus operator would prefer to improve te service of te bus line wit larger cost reduction. In suc a case, te bus operator can obtain a iger premium wit less cost. 3.3.3. Te premium t Te premium under different cases is presented in Table VI. Te premium under Case 0 is 13.3m per year due to te reduced cost of 26.2 million. Under Case 2, te bus operator gets 3.2m because of te increase of frequency; te premium under Case 4 is 31.1m, wic is 2.3 times te premium under Case 0. Te reason is tat te frequency under Case 4 as a sarp augment, reacing 156.4 runs a day, and meanwile te bus operator takes efforts to reduce costs to 70.3m. In conclusion, wen Figure 4. Te frequency under cases. Figure 5. Optimal reduced cost of eac bus line.

INCENTIVE SUBSIDY SCHEME DESIGN 937 Figure 6. Relationsip between te frequency and te reduced cost. te bus operator takes more efforts to increase te frequency and reduce cost, it will obtain a iger premium from te government as a reward. 3.3.4. Te deficit C and total subsidies Figure 7 sows a comparison of deficit and subsidies. Total deficit of bus services in Arao city is 72.6m. Wen te bus operator takes efforts to reduce deficit to 46.4m under Case 0, te total amount of subsidies declines to 59.7m, wic is 12.9m lower compared wit te current total subsidies. Te bus operator increases frequency to attract more passengers and get more revenues under Case 2 and Case 4, but it pays more cost. Terefore, deficit and total subsidies ave a significant increase under te two situations. Te deficits rise to 176.4m, and te total subsidies are 179.6m under Case 2. Because te bus operator not only increases te frequency but also takes efforts to reduce cost under Case 4, te bus operator supplies more service wit fewer deficit compared wit tat under Case 2. Te deficit is 147m, and te total subsidies are 178.1m under Case 4. 3.3.5. Te passenger surplus S(f ) Under Case 0, te bus operator keeps te frequency constant, and tere is no passenger surplus. Te passenger surplus benefit increases to 1299.8m under Case 2 due to te augment of te frequency, wereas te increase of passenger surplus benefit is 1484.0m under Case 4. Te surplus under Case 4 is larger tan Case 2 because of te iger frequency and less subsidies. 3.3.6. Te social welfare SB Te social welfare under Case 0 is 13.5m because te bus operator takes efforts to reduce deficit, so te amount of subsidies eventually decreased. Under Case 2, te social welfare reaces 1111.1m because te bus operator takes measures to increase frequency to about 2.3 times tat under te current situation. Improving frequency increases te number of passengers, and subsidies tus increase. It is found tat te effect to passengers caused by increasing frequency is more significant compared wit te effect on subsidies; as suc, social welfare as a positive relationsip wit frequency. Figure 7. Deficit and total subsidies under different cases.

938 W. ZOU AND S. MIZOKAMI Social welfare under Case 4 is te igest because of te bus operator not only taking efforts to reduce cost but also taking measures to increase frequency. 3.3.7. fvsd(f) and fvsb Figure 8 sows te relationsip between te frequency and te demand under Case 4. Te current frequency is 62.5 runs/day, wereas te frequency under Case 4 is 156.4 runs/way. Tis paper takes 10 frequency points between 62.5 runs/day and 200 runs/day to do te sensitivity analysis. It is seen tat te demand increases as te frequency rising. Te increasing range gets smaller wen te frequency exceeds te optimal frequency 156.4 runs/day. Te reason is tat te demand may be saturated as te frequency increases. Figure 9 sows te relationsip between te frequency and te social welfare under Case 4 troug taking 10 frequency points. Te frequency of te first point is te current level, and te social welfare is caused by te reduced subsidies. Te social welfare of te oter 9 points is caused by te improved service frequency and te reduced subsidies. Tere is a positive relationsip between te frequency and te social welfare. However, it is seen tat te social welfare of points 9 and 10 increases very slow wen te frequency is iger tan te optimal frequency 156.4 runs/day. Te reason is tat te demand of te two points increases fewer sown as Figure 8 wile tere is still significant growt of subsidies due to te increasing frequency. Above all, te relationsip between te frequency and te demand and te relationsip between te frequency and te social welfare are positive. However, te increase trend of te demand and te social welfare of points 9 and 10 is not significant wen te frequency is iger tan te optimal frequency 156.4 runs/day. Tis means te larger frequency is not better, and it sould be considered wit te local public transport demand. Figure 8. Te relationsip between frequency and demand. Figure 9. Te relationsip between frequency and social welfare.

INCENTIVE SUBSIDY SCHEME DESIGN 939 4. CONCLUSION Public transport subsidies caused by deficit ave become a uge financial burden of te local governments in Japan. Most governments support te loss-making subsidy sceme. Meanwile, passengers are decreasing year by year because of te popularity of private cars and decline of population. Tere is no motivation to encourage bus operators to improve te service level to attract more passengers under te present subsidy sceme. Terefore, many researcers propose reformation of public transport contracts. During te development process of te contract, competitive tendering contracts and performance-based contracts are respectively put forward. Te performance-based contract suggested tat te subsidy mecanism sould be related to te service level of bus operators. However, all te mecanisms ignore te role of bus operators in lessening subsidies. Terefore, it is essential to design a new kind of subsidy sceme, wic will motivate bus operators not only to improve service level to attract more passengers, but also to take efforts to reduce cost. Te reward of efforts is te premium based on te improved service level and te reduced costs supplied by te government. Referring Zou and Mizokami [10], tis paper proposed an incentive subsidy model based on elastic demand. Under te sceme, two questions of te PBC are considered. One is te decision-making power of te service level; te oter is ow to measure te elasticity of te service level. Referring Suwardo et al. [9], tis paper uses frequency as te index of service level and calculates its elasticity wile considering intrinsic trends of public transport and oter factors. Meanwile, decision-making power is respectively assumed to yield te maximizing social welfare based on elastic demand. It is proved tat te model can elp local governments and bus operators reac a win-win solution by taking public transport in Arao as te researc object. Te paper gives five cases based on different powers of decisions of te service level. Premium and effort are determined by te government wit frequency invariant under Case 0. Te premium is determined by te government, wereas te effort to reduced cost and te frequency are determined by bus operators under Case 1. In Case 2, te premium and te frequency are determined by te government, wereas te effort is determined by bus operators. In te Case 3, besides te frequency, oter two factors are determined by te government. All factors are determined by te government under Case 4. Case 1 and Case 3 are eliminated because of inconsistent wit te actual troug taking public transport in Arao as researc object to calculate. Te current deficit is 72.6m. Under Case 0, te bus operator takes efforts to reduce costs 26.2m. Te government not only makes up deficit of 46.4m, but also supplies a premium of 13.3m. Total subsidies are 59.7m, 12.9m less tan te current subsidies. Te number of passengers does not cange because of frequency invariant. Te social welfare increases 13.5m. Te optimal condition under Case 2 is d ¼ 0, meaning te bus operator would make no efforts to reduce cost. Te optimal frequency is 143.9 runs/day, 2.3 times of te current frequency. Due to te increasing frequency, deficit of te bus operator sarply increases to 176.4m. Te bus operator also gets 3.2m premium because of te improved service. Te total subsidy supplied by te government is 179.6m, an increase of 107m from current deficit. Te number of passengers also rises 1.3 times, and te passenger surplus is 1299.8m. Te social welfare is 1111.1m. Te optimal frequency is 156.4 runs/day, 2.5 times te current frequency under Case 4. Te bus operator takes efforts to reduce cost by 70.3m, and te deficit after efforts is 147.0m. Te degree of efforts is positively related to te revenue kilometer. Te government supplies subsidies to make up te deficit, and pays a 31.1m premium at te same time. Total expenses reac 178.1m, a 105.5m increase from current subsidies. Te number of passengers also rises more tan 1.5 times, and te passenger surplus is 1484.0m. Te social welfare is 1329.7m. It is seen tat te passenger surplus and te social welfare are bot greatly improved under Cases 2 and 4, wen te frequency is determined by te government. In Case 2, te bus operator determines te effort, and te optimal coice for it is taking no effort to reduce cost. Terefore, te total subsidy under Case 4 is lower tan tat under Case 2, wereas te frequency is iger under Case 4 compared wit tat under Case 2. Te reason is tat all parameters are determined by te government under Case 4. As stated earlier, te government will make decisions considering maximization of social welfare. Terefore, te social welfare is maximizing under Case 4. Under tis sceme, te bus operator is encouraged to take efforts to reduce cost and improve service level. Meanwile, social welfare can be maximized.

940 W. ZOU AND S. MIZOKAMI Altoug te subsidy sarply increases in Case 4, te total subsidy is almost te same as te subsidy in 2003, as Figure 2 sows. However, te number of passengers is less tan te number under Case 4, and te passenger surplus and social benefit are also greatly improved. Figure 8 and Figure 9 present tat te optimal frequency 156.4 runs/day is reasonable, and we consider Case 4 to be feasible for use in real public transport. However, tere are two questions needed to be discussed. Te first question is tat te total subsidies are still not decreased a lot under te optimal Case 4, altoug te number of passengers increases compared wit te current situation. It is wital ig to te local government. Te reason is tat te aforementioned model is a teoretical model, and te final result is te optimum solution witout te constraint of subsidy cap. Wen te incentive model is applied into te public transport, te subsidy cap is suggested to be considered by te government. Anoter question is te wole model assumes complete information to obtain optimal frequency. Tat is a very strong assumption especially in te presence of a private operator. Zou and Mizokami [10] analyzed te subsidy situation under incomplete information, and te service level is assumed te same as te current in te sceme. It is found tat bus operators take fewer efforts to reduce deficits wen te information is more nontransparent. More researc is required on ow te incentive sceme under a situation of incomplete information affects bus service level and subsidy amount. REFERENCES 1. Pucer J, Markstede A, Hirscman I. Impacts of subsidies on te costs of urban public transport. Journal of Transport economics and policy 1983; 17(2):155 176. 2. Mattews B, Bristow A, Nas C. Competitive tendering and deregulation in te Britis Bus market - a comparison of impacts on costs and demand in London and te Britis metropolitan areas. Te 7t International Conference on Competition and Ownersip in Land Passenger Transport, Molde, Norway, 2001. 3. Worcman N. Trends: boom and bus. Tecnology Review 1993; 96(8):12 17. 4. Gargett A, Wallis I. Quasi-commercial Bus service contracts in sout Australia. Fourt International Conference on Competition & Ownersip in Land Passenger Transport, 1995. 5. Radbone I. Te competitive tendering of public transport in Adelaide. Fift International Conference on Competition & Ownersip in Land Passenger Transport, 1997. 6. Henser DA, Stanley J. Performance-based quality contracts in bus service provision. Transportation Researc Part A: Policy and Practice 2002; 37(6):519 538. 7. Henser DA, Stanley J. Transacting under a Performance-based Contract: Te Role of Negotiation and Competitive Tendering. Transportation Researc Part A: Policy and Practice 2008; 42(9):1143 1151. 8. Gonzalez-Dıaz M, Montoro-Sancez A. Some lessons from incentive teory: promoting quality in Bus transport. Transport Policy 2011; 18(2):299 306. 9. Suwardo, Napia M, Kamaruddin I. Ridersip factors cange and Bus service demand sensitivity assessment of te fixed-route bus service for sort-term action plan. Journal of Civil & Environmental Engineering 2010; 10(2):1 10. 10. Zou W, Mizokami S. Mecanism design for Bus transport incentive subsidy sceme. 11t International Congress Asian Planning Scools Association, Tokyo, Japan, 2011. 11. Cruz N, Marques R. Te rocky road of urban transportation contracts. Journal of Management in Engineering 2013, in press. DOI: 10.1061/(ASCE)ME.1943-5479.0000224. 12. Stackelberg H. Marketform and Gleicgewict. Julius Springer: Vienna, 1934. 13. Savage I. Deregulation and privatization of Britain s local bus industry. Journal of Regulatory Economics 1993; 5(2):143 158. 14. Simões P, Cruz N, Marques R. Te performance of private partners in te waste sector. Journal of Cleaner Production 2012; 29(30):214 221. 15. Ceung YHF, Krose EP, Jansen JAL. Te effect of frequency canges in regional Bus services on patronage in te Neterlands. PTRC Summer Annual Meeting, University of Sussex, England, 1985; 97 105. 16. Currie G, Wallis I. Effective ways to grow urban Bus markets a syntesis of evidence. Journal of Transport Geograpy 2008; 16(6):419 429. 17. Paulley N, Mackett R, Preston J, Wardman M, Titeridge H, Wite P. Factors affecting te demand for public transport. Proceedings of te European Transport Conference, Strasburg, Germany, 2004. 18. Laffont J-J, Tirole J. A Teory of Incentives in Procurement and Regulation. Te MIT Press 1993; 53 124.

INCENTIVE SUBSIDY SCHEME DESIGN 941 APPENDIX Tese data U and UB are needed to calculate te social welfare SB sown as Equation (2.2). Equation (2.3) sows ψ(d, f )andt are used to get U,wileS( f ),C( f,d )andt are used to get UB sown as Equation (2.5). Te parameter notation table explains te parameters wic are used to calculate te aforementioned data. Parameter notation Parameter Description Unit SB Te social welfare yen U Te excess profit of line yen UB Te surplus benefit of passengers of line yen ψ(d,f ) Te disutility of bus operators due to teir efforts to improve yen te service and reduce cost of line S(f ) Te surplus of passengers of line yen C(d,f ) Te deficit of line after efforts taken to reduce cost and improve service yen t Te premium rewarding bus operators for improving service yen level and reducing cost of line λ Sadow cost of public fund Te value is assumed 5% in te paper referring Laffont and Tirole [18]. d Te reduced cost line yen/km P(f ) Te cost of line before effort yen D ij (f ) Estimated demand between stop ij of line after effort person D B ij ð Þ Passengers of line between stop ijte data is got from te person origin destination survey done in 2010. f Te frequency after runs/day f B Te frequency before runs/day c (ij) Te ticket price between stop ij of line yen Time (ij) Te waiting time and trip time between stop ij of line min ω Te time value of passengers (set 24.94 (yen/min) based on yen/min te Japanese national standard) g (ij) Te generalized cost between stop ij of line after yen g B ij ð Þ Te generalized cost between stop ij of line before it is yen comprised by ticket price, waiting time and trip time between stop ij of line L Te lengt of line kilometer ε Frequency elasticity D t Te demand of passengers of line in t year person A(x (t 1) ) Te index tat affecting demand of passengers of line in t 1 year N (t 1) Te demand of passengers of line in t 1 year person μ p Te influence coefficient of population x p(t 1) Te population in t 1 year person μ car Te influence coefficient of car x car(t 1) Te number of private cars in t 1 year veicle μ bus Te inerent influence coefficient of bus η bus Te influence coefficient of cancelling or adding lines δ (t 1) Passengers of line tat were influenced by cancelling or person adding lines in t 1 year f (t 1) Te canged frequency of line in t 1 year runs/day gap Te difference between te average operating cost of all bus yen/km operators and te operating cost of one bus operator te data is got troug survey α 0 Te constant of te disutility α 1 Te parameter of te gap α 2 Te parameter of efforts α 3 Te parameter of te revenue kilometer