Emission Control under Private Port Operator Duopoly

Transcription

1 Emsson Control under Prvate Port Operator Duopoly Hyosoo (Kevn) Park a, Young-Tae Chang b, Bo Zou c a Robert H. Smth School of Busness, Unversty of Maryland, College Park, MD, USA b Graduate School of Logstcs, Inha Unversty, Incheon, Republc of Korea c Department of Cvl and Materals Engneerng, Unversty of Illnos at Chcago, Chcago, USA Abstract: Recent trends n regulatng martme vessel emssons have negatve effects on the compettveness of many ports as regulatons ncrease costs for shppng operators callng the ports. Ths paper develops analytcal models to examne the emsson standards set by governments for ports n ther jursdctons. Gven the emsson standards set by governments, whch affects fuel cost experenced by shppng operators, ports determne charges for shppng operators. Unlateral, blateral, and sngle-country regulaton cases are nvestgated. Specfcally, our analyss focuses on how ncrease n the maxmum reservaton prce of shppng operators, port capacty, and envronmental damage costs of ports affect optmal emsson standards. Keywords: Emsson standard, Duopoly, Envronmental damage cost, Port capacty, Landlord port, Port charge Introducton Ports are strategc nodes that facltate ntermodal freght transportaton, provde valueadded servces, and create jobs. Wth developments n global trade and martme nfrastructure, port competton has become ncreasngly ntense, especally between ports wth common/overlappng catchment areas. Port competton has been further fueled by grand-scale shppng operator allances, vessel sze ncreases, and advancements n ntermodal shppng networks (Song, 00; Song, 003; Cullnane et al., 005; Yap and Lam, 006; Chang et al., 008; Bae et al., 03). Shp emssons n and around ports have also attracted ncreasng attenton. Such emssons, ncludng SOx, NOx, and partculate matter (PM), lead to detrmental health effects for people n surroundng areas. PM emssons from shps, for example, s estmated to account for 60,000 cardopulmonary and lung cancer deaths each year globally (Corbett et al., 007). To mtgate the negatve envronmental mpacts, many ports have mplemented emsson controls. These emsson control measures may result from local laws and natonal regulatons such as n Sngapore and Chna. At the local level, port-cty muncpaltes pass legslaton to regulate shp emssons at and around ports such as n Antwerp and Rotterdam (Lam and Notteboom, 04), or establsh cty-wde ar polluton mtgaton plans wth ncluson of the port

2 sector as n Shangha and New York (Zheng et al., 07; Lee et al., 04). Port authortes, whch typcally assume publc roles, have also been ndependently adoptng emsson control measures (Tchavska and Tovar, 05; Wnnes et al., 05). Whle generatng envronmental benefts, port emsson control measures ncrease costs for shppng operators. Note that the term port emsson n ths paper refers to shp emssons at and around ports. Oceangong shppng costs can ncrease by 50-60% n swtchng from fuel contanng 4.5% sulfur (the current standard for non-emsson Control Area (ECA) ports) to fuel contanng 0.% sulfur (Notteboom, 0). Alternatvely, shps may nstall scrubbers to flter out sulfur content, but ths remans expensve (Brynolf et al., 04). To avod these addtonal costs, shppng operators may prefer callng ports wth lower or no emsson controls, whch dscourages emsson control at ports. A news artcle concernng the desgnaton of the Pearl Rver Delta n Chna as an ECA llustrates ths pont (Wang and Feng, 04): The fuel cost rse may gve a dsadvantage to ports wthn the Pearl Rver Delta and may also damage the compettveness of corporatons usng these ports. Industres may be lured to transfer to places outsde the ECA and thus damage the local employment. A thorough understandng of emsson control mpacts on port competton s thus needed, but s currently lackng. The exstng lterature has focused on the nterplay among port charges, shppng demand, and capacty expanson (Basso and Zhang, 007; De Borger and Van Dender; 006). The mplcatons of emsson regulatons for ports has attracted attenton only recently. A notable study by Homsombat et al. (03) found that f a port leves a hgher polluton tax, shppng demand at the port wll decrease. The lterature, however, has not consdered how to determne emsson standards and the senstvty of standards to maxmum reservaton prce, port charges, port capacty, port congeston, and the extent of envronmental damage. Nether has the lterature nvestgated the effects of competng ports settng dfferent emsson standards. As mentoned pror, ths s mportant for countres and port authortes to consder n regulatng shp emssons at and around ports. Ths paper develops analytcal models to nvestgate optmal port emsson standards n a duopoly port envronment. Emsson standards regulate the qualty of fuel used by shppng operators, n whch mproved fuel qualty (.e., less noxous gases emtted from fuel consumpton) ncreases fuel cost. Whle shppng operators can comply wth emsson regulatons through other polcy optons such as nstallng scrubbers or usng lquefed natural gas (Cullnane and Bergqvst, 04), we focus on fuel swtchng n ths paper. Ths s due to the fuel swtchng opton s readly avalable and the most wdely adopted measure by shppng operators. We consder cases n whch ports are located n both the same country and dfferent countres. Natonal governments set emsson standards for ports n order to maxmze socal welfare. Gven the emsson standards, proft-maxmzng prvate port operators set port charges. However, t should be noted that although we consder natonal governments beng responsble for settng emsson standards, the modelng framework s readly applcable to cases n whch emsson standard settng s establshed by muncpaltes or port authortes. Thus, the nsghts Throughout ths paper, we use emsson control and emsson regulaton nterchangeably.

3 obtaned should be nterpreted as more generc than specfc to the context of natonal governments settng emsson standards. Utlzng the analytcal models, we seek to answer the followng questons: a) How wll natonal governments requre shppng operators to nternalze envronmental damage by settng port emsson standards when port operators seek maxmzng profts? b) How wll the maxmum reservaton prce of shppng operators, port capacty, and envronmental damage costs affect optmal port emsson standards? c) How wll dfferent emsson control cases affect establshng emsson standards and nteracton between port operators? Specfcally, three cases are nvestgated: ) unlateral regulaton n whch only one country actvely regulates port emssons; ) blateral regulaton n whch two port operators n two countres compete subject to emsson standards set by ther respectve natonal governments; 3) a sngle country n whch two ports are located. In answerng the questons above, ths paper makes three major contrbutons to the lterature. Frst, unlke exstng research concernng port competton (e.g., De Borger and Van Dender, 006; De Borger et al., 008; Luo et al., 0; Chen and Lu, 06), we consder port emsson standards as decsons made by natonal governments. Emsson standards affect the qualty of fuel used, and consequently, shppng cost. Second, we examne the effects of port capacty on optmal emsson standards. Port capacty s a major determnant n port selecton of shppng operators (Chang et al., 008). Yet t remans unknown how port capacty ncrease may change optmal emsson standards of the port and rvals. In fact, capacty consderaton s also lackng n non-martme emsson control research (e.g., Barrett, 994; Burguet and Sempere, 003; Greaker and Rosendahl, 008). Thrd, we nvestgate both symmetrc and asymmetrc cases, the latter featurng condtons n whch not all ports are subject to emsson controls (see Secton 4.3). Furthermore, we consder landlord ports n whch prvate port operators manage termnals and labor allocaton. The role of a port authorty s lmted to provdng basc nfrastructure and mandatory servces such as securty. Worldwde, the port sector has wtnessed a growng nvolvement of prvate operators as a means of mprovng admnstraton effcency and attractng addtonal captal (Cullnane and Song, 00). Gven that the prmary focus of a prvate port operator s maxmzng proft (De Mone, 996), the consderaton of prvate port operators wll promote understandng of publc-prvate nteracton n the context of port emsson controls; more specfcally, how governments should nternalze envronmental damage by settng emsson standards. The remander of ths paper s organzed as follows: Secton revews the exstng lterature regardng port competton and emsson regulatons. Secton 3 develops the theoretcal models of emsson regulaton for symmetrc prvate port operators and governments. Secton 4 examnes the case of asymmetrc port operators and governments under three emsson Emprcal evdence ponts to the growng port capactes n the world. For nstance, based on the estmated capacty developments up to 030, t seems there would already be suffcent capacty planned n most of the regons to accommodate the future traffc growth. Several regons [e.g., Southeast Asa and Chna] seem to have qute severe over-plannng of capacty ncreases (Mooney, 06). Gven ths trend, analyzng the effect of capacty expanson on emsson standard seems to be tmely. 3

4 regulaton cases. Numercal analyss s descrbed n Secton 4. Conclusons and drectons for future research are offered n Secton 5. Lterature revew Most exstng work on port competton assumed that ports compete based on capacty and prce. De Borger and Van Dender (006) proposed a two-stage model n whch competng ports ntally determne capactes and subsequently prces. The authors compared port congeston under dfferent market structures and found that duopoly facltes led to greater congeston compared wth cases of monopoly and welfare maxmzaton due to duopolstc ports delberately keep capactes low n order to reduce prce competton. Ther work was extended by Ish et al. (03) who ntroduced stochastc demand and multple plannng perods. They found that hgher port charges were mposed wth longer plannng perods. Anderson et al. (008) smulated competton between the ports of Shangha and Busan, and found that dfferent capacty expanson optons, such as addng a gantry crane and nvestng n new ports, can lead to dfferent outcomes. Entry deterrence games were consdered n Luo et al. (0) n whch an ncumbent port faces a new entrant provdng dfferentated servces. Preemptve prcng and capacty expanson were consdered as strateges that the ncumbent port can utlze to deter market entry of new port partcpants. The authors found that the effectveness of the ncumbent strategy depends on the prce elastcty of port servces and the dfference n port market shares. Recently, Chen and Lu (06) analyzed optmal port capacty, cargo volume, and servce prce n a duopoly wth uncertan demand. The authors found that ports would not nvest n condtons featurng hgh capacty costs, whle one or both ports may nvest f at least one port has low capacty costs. In addton, less capacty nvestment wll be made when ports are rsk-averse compared wth rsk-neutral. Port competton has also been nvestgated n conjuncton wth hnterland access. De Borger et al. (008) developed the frst port-nland network model n whch port compettveness s determned not only by port charges and capacty, but also by hnterland congeston and road tolls. The authors argued that addng hnterland access capacty would be more desrable than expandng port capacty. Wan and Zhang (03) assumed Cournot competton between ports based on prevous theoretcal and emprcal evdence wth endogenous tolls on access roads, and found that port capacty expanson under quantty competton ncreases profts as well as reduces rval profts. If tolls are dfferentated between commuters and trucks, polcy makers should charge trucks lower fees to mantan port compettveness. Álvarez-SanJame et al. (05) studed the effects of port and nland transport servce ntegraton on port profts and welfare. Such ntegraton was found advantageous to ports, but wth a correspondng potental welfare decrease whch negatvely affects shppers located closer to ports. An ntegrated servce provder should mpose only a fxed charge to attract shppers located n dstant regons. Prvatzaton s an emergng area n whch scholars analyze port competton usng analytcal models. Matsushma and Takauch (04) analyzed government ncentves to prvatze ports for countres nvolved n nternatonal trade. By developng a two-stage model n whch ports establsh charges and governments determne types of ownershp, the authors concluded that a government wth a larger domestc market s more lkely to natonalze ts port n order to protect ts domestc market from foregn frms. Czerny et al. (04) examned strategc welfare gans of prvatzaton when hub ports compete wth each other. In ther model, ports compete ) on 4

5 transshpment traffc but have ther own hnterland demand, and ) on prce. Ther results suggest that smultaneous prvatzaton of both ports can ncrease the socal welfare of ther respectve countres, for prvatzng a port sgnals commtment to hgher prces to the competng port. In ths case, ports can reap sgnfcant profts from nternatonal transshppng. Wan et al. (06) analyzed capacty nvestment for accessblty at two competng ports and one nland regon, the latter of whch s the destnaton of cargo traffc. They found that under prvatzaton, capacty expanson n the nland regon ncreases port prce, whch ncreases overall welfare n port regons but decreases welfare n the nland regon. Ths leads to an undernvestment problem for both ports and nland regons. To facltate the coordnaton among the two ports and the nland regon, ports need to compensate the nland regon n order to ncrease ts nvestment. Lmted attenton, however, has been pad to addressng emsson controls n the context of port competton. As mentoned pror, we are only aware of Homsombat et al. (03) who examned emsson taxaton at ports. The authors showed that competng ports would levy a hgher emsson tax compared wth ports that coordnate emsson control efforts. Jont welfare maxmzaton between ports drve down emsson taxes below the Pgouvan tax rate due to the consderaton of promotng martme busness whch also benefts socety. Wang et al. (05) benchmarked the economc mplcatons of an open emsson tradng scheme and a martmeonly emsson tradng scheme for contaner shppng and dry bulk sectors. The emsson tradng schemes wll reduce vessel speed, shppng traffc, and shp fuel consumpton. Emsson permts wll be purchased by the contaner shppng sector from the dry-bulk sector. Sheng et al. (07) analyzed how unlateral or unform regulatons would affect shppng lnes and ports along two dfferent shppng routes. They found that total emssons ncrease under unlateral regulatons, but decrease under unform regulatons. Regardng non-martme transportaton research, Brueckner and Zhang (00) examned arlne responses to emsson charges. The authors found that arlnes would rase fares and decrease servce qualty. Ths analyss was extended by Czerny (05), who further consdered captal costs. He found that n the case that larger arcraft sze mproved fuel effcency, emsson charges generally ncreased arcraft sze. In the context of competton between hgh-speed ral (HSR) and avaton, the effect of competton on the envronment s nconclusve due to the opposng effects of mode substtuton and nduced demand (D Alfonso et al., 05; Socorro and Vecens, 03). In addton to the transportaton research, a stream of studes regardng emsson regulaton n the envronmental economcs lterature s worth notng. Most studes have focused on envronmental standards n nternatonal trade. Barrett (994) showed that when frms are nvolved n Cournot competton, natonal governments strategcally mpose weaker emsson standards to support domestc frms. However, n the case that frms feature prce competton, more strngent emsson standards are set. Burguet and Sempere (003) argued that governments do not necessarly set lower emsson standards under reduced tarffs even though they have ncentves to support domestc frms. Ths s because reduced tarffs can sgnfcantly deterorate the local envronment. Greaker and Rosendahl (008) examned upstream frms that sell polluton reducton technologes to downstream companes that pollute. They found that governments strengthen emsson standards n order to reduce polluton abatement costs by attractng more frms nto the upstream market. Davd and Snclar-Desgagné (005) explored the optmal level of polcy nstruments, such as taxes and emsson quotas, wth the eco-ndustry provdng abatement technology to pollutng frms. The authors concluded that governments 5

6 should mpose a hgher tax than the socal cost of emssons to prevent frms from abatng too lttle as the eco-ndustry exercses market power over polluters. The above revew has made clear four gaps n the lterature. Frst, almost no research has been conducted to jontly consder port competton and settng port emsson standards. Second, no studes have examned port emsson control and congeston smultaneously. Thrd, asymmetrc cases n whch not all ports are subject to emsson regulatons, whch can occur n the real world (Sheng et al., 07), have not been consdered. Lastly, no nvestgaton has been performed on the response of emsson standards to shppng demand, port capacty, and envronmental damage. Our research ntends to fll these gaps. It should be noted that congeston n ths study s consdered negatvely assocated wth port capacty. Worldwde, port capactes have been ncreasng to handle future cargo traffc (see footnote ), but often overnvestment n capacty rases concerns for governments. How emsson control should be algned wth capacty expanson? Our analyss wll provde useful nsght for ths queston. 3 Model: Symmetrc case In ths paper, we consder two-stage games. At the frst stage, natonal governments set emsson standards for ports wthn ther jursdcton whle antcpatng the prcng behavor of ports. The objectve of each government s to maxmze the socal welfare n ts jursdcton, whch consders port proft and envronmental damage caused by emssons. For the second stage, gven the emsson standards, each prvate port operator determnes charges to shppng operator n order to maxmze proft. In other words, the emsson standard s an endogenous varable from governments perspectve, and an exogenous varable from ports perspectve. Ths secton manly focuses on the stuaton that two competng ports n dfferent natons are subject to emsson control by ther respectve governments, though other modfed cases (.e., unlateral and sngle country regulaton) are consdered for asymmetrc ports and governments n Secton 4. The settng of emsson standards and determnaton of port charges depend on the shppng demand at each port, whch s a functon of the cost per unt cargo ncurred to shppng operators callng a port. For smplcty, we consder that a unt cargo s a twenty-foot equvalent unt (TEU) and the unt cost per TEU has three varable components n the context of port emsson controls: fuel cost whch s drectly affected by emsson standards, port charges, and port congeston costs. We use backward nducton to model prvate port operators decson frst and governments decson next. The resultng solutons of emsson standards that satsfy prvate port operators proft maxmzaton should be subgame-perfect Nash Equlbrum. In Secton 3., we examne the symmetrc case wth a general fuel cost functon. The shppng demand functon s specfed n Secton 3... We consder two stages of decsonmakng: emsson standard settng ( st stage) n Secton 3.. and port charge determnaton ( nd stage) n Secton In Secton 3., we analyze the more specfc case that the fuel cost functon s recprocal wth respect to emsson standard. Under the symmetry assumpton, the two governments wll set the same level of emsson standards n equlbrum. We specfy the model by assumng the same capacty and envronmental damage costs n both countres, n whch case the symmetrc emsson standards lead to symmetrc port charges. 6

7 3. Symmetrc case wth general fuel cost functon 3.. Shppng demand at ports In ths paper, we consder a system consstng of two adjacent ports whch provde perfectly substtutable servces. Ths assumpton s a smplfcaton of the realty as the two ports can offer dfferentated servces. For example, some part of a port s hnterland can be exclusve to the port (Notteboom, 009; Homsombat et al., 06, Wan et al., 06). In addton, complementary servces could also exst for cargo movng between the two ports through a feeder lne. Consderng mperfect substtutablty could lead to somewhat dfferent results. However, t s unlkely to change the nsghts fundamentally, though more analytcal complexty would be added as noted n De Borger et al. (008). In addton, our model can have realstc mplcatons for ports competng over transshpment cargo, as shppng operators would behave ndfferently toward routes featurng the same operatng costs. The model developed n ths paper can appeal to Asan ports partcularly as transshpment competton s most severe among the Asan ports, and the emsson control dlemma s more pronounced than ports n Europe and North Amerca. For ths reason, the focus of the paper s on transshpment cargo. Shppng operators select one of the two ports based on the unt cost per TEU. Followng De Borger and Van Dender (006) and De Borger et al. (008), we assume that total shppng demand at two ports s gven by the nverse demand functon p( Q Q). More specfcally, p( Q Q) s the generalzed port prce that shppng operators charge to shppers usng a port. Under equlbrum, total demand s dstrbuted at the two ports so that the generalzed port prces usng the two ports are the same. Ths leads to: p( Q Q ) P D( Q, K) f ( e ) () p( Q Q ) P D( Q, K) f ( e ) () where P (=,) and K are port charges per TEU at port and handlng capacty at each port, respectvely; D( Q, K) s the port congeston cost whch s a functon of port demand Q and handlng capacty K. Although we assume that the ports consdered compete on contaner cargo, the analyss could be extended to ncludng other types of cargo, and even cruse passengers. Varable e denotes the maxmum amount of pollutants per unt cargo (TEU) permtted by the emsson standard at port. f( e ) s the resultng addtonal fuel cost per TEU. A hgher e nfers a lower emsson standard and consequently lower f( e ). For the fuel cost functon, we only mpose ts characterstcs: f( e ) 0. For smplcty, we also use more concse notatons later f f ( e ) and f f ( e ). The fuel cost here should be nterpreted as a normalzed cost. The orgnal form of fuel cost can be expressed as f( e ), where s constant and the second term denotes addtonal cost burden (or complance cost, or fuel cost premum) resultng from emsson regulatons. For 7

8 example, one can consder as the prce of the most noxous marne ol, and f( e ) as the addtonal cost of refnng fuel to reduce noxous gas content. We normalze to zero for smplcty, and dong so does not affect the man nsghts obtaned n the paper. Thus, n what follows, we mean addtonal fuel cost burdens due to emsson regulaton by fuel cost. In ths paper, we consder the followng functonal forms for p( Q Q) and D( Q, K ): p( Q Q ) b a( Q Q ) (3) Q D( Q, K) =, (4) K Eq. (3) specfes a lnear form of the nverse demand functon wth parameters ab, 0. Parameter b s the shppng operators maxmum reservaton prce, whch depends on external forces that nfluence shppng operators wllngness to pay. If we assume that ports provde dfferentated servces (Dxt, 979), Eq.(3) would be expressed as p ( Q, Q) b aq a jqj, where, j,, j, and a a 0. Introducng the dfferentaton parameters would not j change the man results of ths paper. Thus, we work wth the smpler specfcaton n (3). Eq. (4) defnes port congeston cost as a lnear functon of port demand capacty rato, wth parameter 0 beng the factor convertng the rato nto congeston cost. The specfcaton suggests that congeston cost ncreases wth port demand, but decreases wth hourly capacty. Ths specfcaton was used n prevous studes (e.g., Basso and Zhang, 007; De Borger and Van Dender, 006) and has the advantage of beng smple and amenable to drvng analytcal nsghts. On the other hand, as ths specfcaton does not restrct demand to be less than port capacty, smulatons were performed later wth an alternatve form of the congeston cost Q functon (Basso, 008; Zhang and Zhang, 997). Under ths alternatve form, K( K Q ) congeston cost approaches nfnty as Q K, and the restrcton that demand not exceedng capacty s automatcally satsfed. Results of the smulatons are summarzed n Appendx N. Replacng the relevant terms n Eqs. () and () by ther expressons n Eqs. (3) and (4), demand at each port can be derved as follows: Q ( g a ) b( g a) gp ap gf af (5) Q ( g a ) b( g a) ap gp af gf (6) where g a K 0. Holdng e and e constant, we take dervatves of Eq. (5) wth respect to P and P, whch yelds: 8

9 Q g P g a Q a P g a 0 0 (7) (8) Smlar expressons can be derved for Q. Eqs. (7) and (8) are ntutve: shppng demand at a port decreases when ts own port charge s ncreased, and ncreases when the other port ncreases ts charge. 3.. Port charge settng stage Ths secton analyzes how ports determne charges for maxmzng profts n response to establshed emsson standards. In what follows, backward nducton s used to nvestgate the optmalty condtons and comparatve statcs. Proft maxmzaton for each port can be expressed as: max PQ, =, (9) p Eq. (9) mplctly assumes that the margnal cost of a port s constant and normalzed to zero. In practce, the full cost structure of prvate port operators can dffer consderably by port (Goss, 990b), so generalzng costs of operators s dffcult. Here we consder the most obvous and common cost component for prvate port operators: the fxed rent pad to the landlord port authortes that s proportonal to cargo volumes (Goss, 990a). Ths leads to the objectve functon ( P c) Q, =,. The constant margnal cost c s normalzed to zero followng Basso and Zhang (007), as dong so does not affect the man results below. For Port, the frst-order condton (FOC) s gven by: Q Q P 0 P P (0) Substtutng Eq. (7) for Q P nto Eq. (0) results n: 9

10 a P a Q D( Q, K) g () The frst term on the rght-hand sde (RHS) ndcates that Port accounts for ts market power when determnng charge. Recallng that g a K 0, ths term wll be reduced as port capacty ncreases. The second term on the RHS s the port congeston cost. The response functon of ports regardng compettors s upward-slopng. To see ths, we use Eqs. (5)-(7), and Eq. (0) and obtan: b( g a) ap gf af P g b( g a) ap af gf P g P a The above equatons mply that 0 P g j for j. Hence, a port wll rase ts charge n response to an ncrease n the charge of ts compettor. Fgure llustrates the best response functons of ports. Fgure. Best response functons of ports where, 0

11 b( g a) ap gf af g, (4 g a ) b( g ag a ) agf ( g a ) f b( g a) ap af gf 3 g 4 (4 g a ) b( g ag a ) ( g a ) f agf We can establsh the stablty condton at the prcng stage by summng the own- and crossprce effects. Q Q 0 P P g a As the own-prce effect domnates the cross-prce effect, the soluton of Eq. (0) should lead to a unque stable equlbrum (Dxt, 986; Basso and Zhang, 007). Usng Eqs. (5)-(7) and solvng for Eq. (0), port charges can be expressed as: P (4 g a ) b( g ag a ) ( g a ) f agf () P (4 g a ) b( g ag a ) agf ( g a ) f (3) Wth Eqs. () and (3), we now nvestgate how port charges wll be affected by the emsson standards for Port. Takng the frst-order dervatves of P and P wth respect to e results n: P ( g a ) f 0 e (4 g a ) P agf 0 e (4 g a ) (4) (5)

12 where f 0 by assumpton. Eq. (4) shows that charge at Port wll ncrease f Government lowers ts emsson standard (larger e ). Ths can be explaned as follows. A lower emsson standard contrbutes to reduced unt cost per TEU, whch ncreases demand at Port. Referrng back to Eq. (), Port would levy a hgher charge n response to the ncreased demand. Consderng Eq. (5), when Government lowers the emsson standard, addtonal fuel cost and consequently the generalzed port prce at Port wll be reduced, whch mposes more compettve pressure on Port. To reman compettve, Port wll respond by decreasng ts charge Emsson standard settng stage Ths secton nvestgates how natonal governments set emsson standards to maxmze socal welfare n ts jursdcton. We abstract away shppng operators welfare, whch n lne wth De Borger et al. (008) and Wan and Zhang (03), as n practce, shppng operators and shppers callng at a port are comprsed of numerous natonaltes. Another smplfcaton made here s the omsson of shppers welfare for hnterland access. Ths s because, as mentoned n Secton 3.., the focus of the paper s on transshpment cargo. However, addng hnterland demand or capacty would not change the key results of ths paper. 3 As a result, the socal welfare maxmzaton by each natonal government can be expressed as maxmzng the port proft mnus the envronmental damage caused by port emssons: max W ( P e ) Q (6) e where s the envronmental damage cost per unt pollutant for each country. Eq. (6) assumes that the envronmental damage cost s lnear for the noxous gas content emtted per TEU. Alternatvely, the damage cost may be specfed as quadratc (Kopp et al., 0), n whch case Eq. (6) would become W ( P e ) Q. Whle we dd not derve analytcal property for such a quadratc damage cost functon, our numercal analyss suggests that the nsghts obtaned (.e., the effect of the maxmum reservaton prce, port capacty, and envronmental damage cost on the optmal emsson standard) reman under a quadratc damage functon. The FOC of Eq. (6) s: W P ( ) Q P Q P Q Q P e Q 0 e e P e P e e 3 We thank one revewer for rasng these ponts.

13 Q P P Q Q e P Q P Q Q P e e P e P e e (7) The second equalty above s obtaned usng the envelop theorem (Eq. (0)). The astersk denotes t s the value at optmum. From the second equalty, t can be seen that the FOC equates the margnal proft (the left-hand sde (LHS)) to the margnal envronmental damage cost (the RHS) resultng from one unt ncrease n e. The margnal envronmental damage cost conssts of two terms: the change n envronmental damage cost assocated wth the change n shppng demand, and the change n envronment damage cost due to the unt ncrease n e. To further nterpret Eq. (7), we nvestgate the effect of emsson standards on port demand at ( e ). Usng Eqs. (5), (7), (8), (4), and (5), and mposng symmetry, we can express dq e de ( ) as: dq ( e, e ) Q P Q P Q g( g a ) f 0 ( )(4 ) de P e P e e g a g a (8) Hence, ports wll attract addtonal demand when the optmal emsson standard becomes lower. The postvty of Eq. (8) means that the bracketed term on the RHS of Eq. (7) s postve at e e e, and therefore, the bracketed term on the LHS of Eq. (7) s also postve. We now use Eq. (8) to examne whether relevng the emsson standard decreases own generalzed port prce. Ths s mportant to understand the strategc use of emsson standards, whch helps to explan key results of ths paper very ncely. Eqs. () and (3) mply b a( Q Q ) P D( Q, K) f ( e ) Totally dfferentatng both sdes wth respect to e, we have dq dq dp dd( Q, K) df ( e ) a de de de de de The RHS s the effect of the emsson standard on own generalzed port prce (wthout loss of generalty, we consder Port here). To see the effect, we nvestgate the sgn of LHS as t s easer to work wth. Usng Eqs. (6), (7), (8), (4), and (5), we have 3

14 dq ( e, e ) ag f ( )(4 ) de g a g a Combnng the above equaton wth Eq. (8), we obtan dp dd( Q, K) df ( e ) de de de dq dq a de de agf ( g a)( g a) 0 That s, reducng the emsson standard at a port decreases own generalzed port prce. Ths s crtcal to understandng the strategc use of emsson standards to soften competton and manpulate equlbrum prces. By settng the optmal emsson standard, a natural queston that may arse s: how does the addtonal fuel cost compare wth Pgouvan tax? 4 Under Pgouvan tax, a regulator leves an amount equal to the envronmental damage cost from the pollutng frm (Pgou, 93). In our analyss, the addtonal fuel cost per TEU, whch s f f f (by symmetry), can be vewed as performng a smlar role as an emsson tax. If the natonal governments followed Pgou s rule, then the emsson tax would equal the envronmental damage cost per TEU,.e., f e. On the other hand, we show below that under the optmal emsson standard the addtonal fuel cost wll exceed the unt envronmental damage cost per TEU,.e., f e. That s, the emsson standard wll mpose a greater cost burden than a Pgouvan tax. Ths s formalzed n Proposton. Proposton. When governments and ports are symmetrc, the addtonal fuel cost (due to regulaton) ncurred per TEU wll be greater than the unt envronmental damage cost at ports,.e., f e. Proof: See Appendx A. 4 The general defnton of Pgouvan tax covers taxaton on any negatve externaltes, ncludng the correctve tax for congeston as well as emsson. In ths manuscrpt, we focus our attenton on tax leved on emsson. 4

15 Why s the result dfferent from the desrable regulaton that Pgou suggested? Ths may be because governments do not drectly nteract wth shppng operators (whch produce emssons), but wth ports whch do not correct negatve externaltes. Snce ports compensate shppng operators fuel cost through lowerng port charge (Eq. (4)) wthout correctng for ther negatve socal mpacts, governments have greater ncentves to tghten regulatons. More nterestng nsght can be drawn f we connect Proposton wth the generalzed port prce: governments rase the emsson standards at a suffcently hgh level to soften the competton between ports on generalzed port prce. As shown just above, a hgher emsson standard ncreases ts own generalzed port prce, whch can counteract the effect of port charge reducton on competton (see Eq. (4)). Softenng generalzed port prce competton s ratonal from governments perspectve. Ferce prce competton between ports make ther natons worse-off because ports collect lower revenue and port traffc ncreases. Both effects decrease the average socal welfare per TEU. As governments cannot manpulate port charge drectly, they decrease envronmental damage cost nstead by ncreasng emsson standard. Ths argument echoes prevous studes (e.g., Basso and Zhang, 007; De Borger and Van Dender, 006; Czerny et al., 07), whch showed that port capacty should be set at a low level to soften port charge competton. The dfference here s that we consder rasng emsson standards nstead of lowerng the capacty to soften the competton on generalzed port prce. Proposton provdes an nterestng mplcaton for practce. Chang et al. (08) found that ncreased fuel cost from emsson controls reduces port traffc n Europe substantally. Whle ths concerns polcy makers n Europe for losng compettveness of ther ports (also concerns polcy makers n Asa), our results suggest that more strngent emsson controls are desrable for socety. After all, socal welfare s the combnaton of port profts and envronmental costs of port operatons. However, t remans to be seen whether ths result s generalzable to regulatng publc port operators, whch we leave for future studes. 3. Symmetrc case wth a recprocal fuel cost functon Ths subsecton analyzes the symmetrc case n whch the fuel cost functon form s known. Specfcally, the followng recprocal fuel cost functon form s consdered: f ( e ), =, (9) e Eq. (9) assumes that the addtonal fuel cost ncreases wth hgher emsson standards, and the rate of cost ncreases wth the emsson standard. Ths recprocal functonal form has a sold emprcal groundng that removng pollutants becomes ncreasngly costly wth cleaner fuels. For nstance, marne desel ol costs ncrease by 0-30% f the sulfur content n fuel decreases from.5% to 0.5%, but ncreases by 50-60% f the sulfur content n fuel decreases from 0.5% to 0.% (Notteboom, 0). Wth ths explct functonal form for fuel cost, one can obtan defntve effects of the maxmum reservaton prce, port capacty, and envronmental damage on emssons standards. 5

16 One can obtan port demand and the optmal prcng of ports by substtutng f ( e ) e nto Eqs. (5), (6), (), and (3). For brevty, we do not detal them here. In addton, new nformaton about the equlbrum condtons can be derved. Dfferentatng Eq. (6) wth respect to e twce and mposng symmetry results n: W g( g a ) ( g a ) 3 P e e ( g a )(4 g a ) e (4 g a ) The above second-order condton (SOC) requres that P ( g a ) e (4 g a ) (0) In the specal case that a approxmated by P 4e 4 g,.e., ( ak ) K 0, nequalty (0) can be f,.e., port charge should be set hgher than a quarter of the addtonal fuel cost per TEU. In the subsequent analyss, the SOC s assumed to hold. In the followng propostons, the effects of a few key exogenous varables are examned. Proposton. If ports and governments are symmetrc and the fuel cost has a recprocal functon form, then governments wll lower port emsson standards when shppng operators maxmum reservaton prce ncreases,.e., e b 0. Proof: See Appendx B. An ncrease n the maxmum reservaton prce drves up the overall demand, whch ncreases congeston n equlbrum gven the capacty. Ths softens the competton on generalzed port prce, whch reduces governments need to further soften the competton by tghtenng the emsson standards. Instead, governments decrease emsson standards to encourage port busness that has become more lucratve (due to greater demand) than before. Proposton 3. If ports and governments are symmetrc and the fuel cost functon s recprocal, then governments wll rase emsson standards when ports expand capacty,.e., e K 0. Proof: See Appendx C. 6

17 One may nterpret Proposton 3 agan through generalzed port prce competton. An ncrease n port capacty reduces congeston when the demand functon s gven. Ths strengthens the generalzed port prce competton f emsson standards reman unchanged. Thus, a need arses for governments to soften the competton by strengthenng emsson standards. Heavy capacty expanson s frequently observed n the real world, partcularly n northeast Asa where ports compete for hub status. Proposton 3 ndcates that natonal governments seekng socal welfare maxmzaton should consder strcter emsson controls. Proposton 4. If ports and governments are symmetrc and the fuel cost functon s recprocal, then governments wll rase emsson standards at ports n whch the envronmental damage cost per unt pollutant at ports ncreases,.e., e 0. Proof: See Appendx D. Ths proposton can be ntutvely understood. When becomes larger, negatve externaltes from port emssons wll ncrease. To reduce the envronmental damage, governments wll naturally respond by rasng emsson standards. Proposton 4 may be used to explan why port emsson controls have become more strngent lately around the world. Record hgh port traffc has deterorated atmospherc condtons n many port areas, causng sgnfcant publc health problems. The growng publc awareness of ths ssue has ncreased percepton and valuaton of envronmental damage, resultng n governments adoptng more strngent emsson controls, especally n Europe and North Amerca. 4 Model: Asymmetrc case Ths secton relaxes the symmetry assumpton. Secton 4. specfes demand at ports. Secton 4. presents the proft-maxmzaton problem of prvate port operators. We then analyze how governments set emsson standards n cases where regulaton s unlateral and blateral n Sectons 4.3 and 4.4, respectvely. Lastly, n Secton 4.5, we derve emsson standards n whch the government has both ports n ts jursdcton. 4. Shppng demand at ports When the two competng ports dffer n ther characterstcs, port demand equlbrum n Eqs. () and () s modfed as: p( Q Q ) P D( Q, K ) f ( e ) () p( Q Q ) P D( Q, K ) f ( e ) () 7

18 where all notatons drectly follow Eqs. () and () except that K (=,), the handlng capacty at port, s now dfferent for ports. The functonal forms for p( Q Q), D( Q, K ), and f( e ) are assumed to be the same as Eqs. (3), (4) and (9), respectvely. 5 Smlar to the symmetrc case, we can derve the expressons for the two ports: Q ( g g a ) b( g a) g P ap g e a e (3) Q ( g g a ) b( g a) ap g P a e g e (4) where g a K ( =,). Note that gg a > 0. Holdng the dervatve of Eq. (3) wth respect to P and P, whch leads to: e and e constant, we take Q g P g g a Q a P g g a 0 0 (5) (6) whch can be smlarly nterpreted as Eqs. (7) and (8). 4. Port charge settng stage Proft maxmzaton of each port can be expressed as: max PQ, =, (7) p The FOC s gven by: Q 5 Alternatvely, one could generalze the congeston functon as D ( Q, K ) =,, where each K country has dfferent tme costs. Ths, however, does not change the man results that would follow, as s contaned n the expresson g a K ( =,). We thank a revewer for pontng ths out. 8

19 Q Q P 0 P P (8) Substtutng Eq. (5) for Q P n Eq. (8) results n the followng prcng rule: a P a Q D( Q, K) g (9) Ths s analogous to the prcng rule n the symmetrc case (Eq. ()). However, now the capactes at the two ports are not equal. A hgher capacty at Port, whch s assocated wth a lower g, wll decrease the relatve market power of Port (the frst term on the RHS of Eq. (9)), leadng to decreased port charge. Usng Eqs. (3)-(4) and solvng Eq. (9) for both ports, port charges can be expressed as: P (4 g g a ) b( g g ag a ) ( g g a ) e ag e (30) P (4 g g a ) b( g g ag a ) ag e ( g g a ) e (3) Takng the frst-order dervatves wth respect to e, we obtan: P g g a e e g g a ( ) (4 ) 0 P ag 0 e e (4 g g a ) (3) (33) whch can be smlarly nterpreted as Eqs. (4) and (5). 4.3 Unlateral regulaton case Ths secton analyzes the case n whch only one of two countres regulates port emssons. For the other country, ts government only consders port revenue maxmzaton. We use subscrpts and to denote the country/port wth and wthout emsson regulaton. We further assume that Country should stll comply wth a mnmum emsson standard whch s assocated wth the drtest fuel used n martme shppng. For example, the Internatonal 9

20 Martme Organzaton stpulates that sulfur content n fuel should not exceed 3.5% for all shps as of 05. We agan consder a leader-follower game structure. The stage of settng port charges s the same as n Secton 3. and thus not repeated here. At the stage of settng the emsson standards, the two governments face the followng problems: max W ( P e ) Q e max e s.t. w e u u P Q e (34) u u where superscrpt u n W and w denotes unlateral ; e and e are the emsson standards at ports and respectvely; and e denotes the mnmum emsson standard for Country. For Port, the FOC s: u W u P u u Q P Q P Q u Q ( P e ) Q 0 e e P e P e e P Q P Q e Q P Q P Q Q u u u P e e P e P e e (35) The second equalty s obtaned usng Eq. (8). The astersk denotes values at optmum. Eq. (35) s almost smlar to Eq. (7), except that the envronmental damage cost per unt pollutant has subscrpt ( ). Next, we consder the effects of the emsson standards on port demand at Eqs. (3), (5), (6), (3), and (33), we can express u dq( e, e) de as: ( e, e ). Usng dq ( e, e) Q P Q P Q g ( g g a ) 0 ( )(4 ) u de P e P e e e gg a gg a (36) whch has a smlar form as Eq. (8). Eq. (35) cannot be solved explctly, but can be rearranged to gan nsghts. After some algebra (see Appendx E), Eq. (35) leads to the followng mplct form for the optmal emsson standard: 0

21 u ( gg a ) gg a e ( )(4 ) (37) where ( dq de )( e Q ). Eq. (3) mples that holdng constant, a government wll lower ts emsson standard f ncreases. One possble cause for a larger s hgher crude ol prce. On the contrary, holdng constant, the emsson standard wll be set hgher when the unt envronmental damage cost per pollutant ( ) ncreases. These nterpretatons, however, are only tentatve because depends on and. For Port, t s conceptually vald that e wll be set at e to mnmze fuel cost. In fact, t u can be shown that w decreases wth e : u w u P u Q P Q P Q u Q P Q Q P P 0 e e P e P e e P e e where the nequalty holds due to Eqs. (4), (6), (3) and (33). Thus the choce of Country s ndependent of the emsson standard of Country. e u e by We also examne the second-order condton (SOC) of Eq. (34) for Port. Dfferentatng b W e wth respect to e results n: u W g( gg a ) ( gg a ) 3 P e e ( gg a )(4 gg a ) e (4 gg a ) The SOC requres, whch yelds: u W e 0 P ( gg a ) e (4 gg a ) (38) If a g g,.e., ( a( K K) ) KK 0, nequalty (38) suggests that f( e ) ;.e., port charge should be set hgher than a quarter of the addtonal fuel u u u 4e 4 P

22 cost per TEU, whch s the same as the symmetrc case (see dscussons below nequalty (0)). In our analyss, we assume that the SOC holds. Also smlar to the symmetrc case s that the emsson standard at Port wll mpose a greater cost burden to shppng operators than a Pgouvan tax. We formalze ths as Proposton 5 below. Proposton 5. Under unlateral regulaton, the addtonal fuel cost per TEU due to the mposton of emsson control wll be greater than the unt envronmental damage cost at Port, u u.e., e e. Proof: See Appendx F. Proposton 5 can be nterpreted n a smlar way as Proposton : Government mposes strcter emsson regulatons than would be under Pgouvan taxaton, expectng that Port wll compensate shppng operators fuel cost by reducng port charges (Eq. (3)). Moreover, tghtenng of the emsson standards wll releve the competton on generalzed port prce competton. We further examne the effects of shppng operators maxmum reservaton prce (b), port capactes (K and K), and the envronmental damage cost per unt pollutant ( ) on the optmal u emsson standard at Port ( e ). The fndngs are formalzed n Propostons 6-8. Proposton 6. Government wll lower the emsson standard at Port when the maxmum u reservaton prce of shppng operators ncreases,.e., e b. Proof: See Appendx G. 0 Proposton 6 can be nterpreted n a smlar way as Proposton. Because a hgher maxmum reservaton prce releves the competton on generalzed port prce, Government does not need to further soften competton. Instead, Government wll support port busness by weakenng ts emsson standard. Proposton 7. Government wll rase the emsson standard at Port when ether port expands u u capacty,.e., e K and e K. 0 Proof: See Appendx H. 0 Capacty expanson at ether port results n more ntense competton on generalzed port prce, as congeston s reduced and both ports wll respond by lowerng port charges. To releve competton, Government wll mpose a more strngent emsson standard.

23 For the effects of the envronmental damage cost per unt pollutant, only s consdered. does not appear n (34) and thus has no effects on the optmal emsson standards at Port. Proposton 8. Government wll rase the emsson standard at Port when the envronmental u damage cost per unt pollutant at Port ncreases,.e., e. Proof: See Appendx I. 0 Ths proposton can be ntutvely understood as n the symmetrc case (Proposton 4). Government rases the emsson standard at Port n order to mtgate the ncreased negatve externaltes from emssons from Port. 4.4 Blateral regulaton case Ths secton nvestgates the case n whch the two natonal governments both consder the envronmental costs of ther respectve port operatons. The problem faced by each government s: b max W ( P e ) Q, =, (39) e The FOC of Eq. (39) has the same expressons as Eq. (35). The optmal emsson standards for both governments follow a smlar form as Eq. (37): e b ( gg a ) gg a,, ( )(4 ) As the structure of the FOC s the same for both governments, t can be easly seen that Proposton 5 now apples to both countres. In the remander of ths secton, we nvestgate the effects of shppng operators maxmum reservaton prce (b), port capactes (K and K), and the envronmental damage cost per unt of b b noxous content ( and ) on the optmal emsson standards e and e. For the effect of b b, a concluson cannot be drawn analytcally by takng the dervatve of e ( =,) wth b respect to b. However, f port charges are held constant at the equlbrum values ( P and P b ), the followng proposton can be obtaned: 3

24 b b Proposton 9. Under the blateral regulaton, f port charges are fxed at P and P, then each government wll set a hgher emsson standard as the maxmum reservaton prce ncreases, b.e., e b b b ( =,). 0 P, P Proof: See Appendx J. At frst sght, Proposton 9 seems to contradct Propostons and 6. However, the result s b b condtonal on fxng port charges at P and P, whch dampens the change n the generalzed prce competton. In ths case, the governments would focus more on the envronmental damage. Because an ncrease n the maxmum reservaton prce attracts more demand resultng n greater envronmental damage, the governments set hgher emsson standards to mtgate the damage. The effect of port capactes on held constant at P and b b e can only be analytcally derved when port charges are b P, as descrbed n Proposton 0. Proposton 0. Under the blateral regulaton, f port charges are fxed at the equlbrum values b b ( P and P ), then each government wll set a hgher emsson standard as the capacty of ts port s expanded, but wll lower ts emsson standard f the capacty of the other port s expanded, b.e., e K b b and e K (, j =,, j ). 0 P, P Proof: See Appendx K. j 0 P, P b b Smlar to the reasonng for Proposton 9, fxng port charges at P and P and ncreasng capacty at Port, Government wll manly focus on mtgatng the envronmental damage due to ncreased demand. The emsson standard wll be strengthened at Port. On the other hand, f Port ncreases capacty, the competton on generalzed port prce wll favor Port. To stay compettve, Government wll respond by lowerng ts emsson standard. In realty, port charges wll also respond to port capacty change. To see ths, we dfferentate P (Eq. (30)) wth respect to K and K whle holdng emsson standards constant: P a g ( ) ( ) K g g a K e e g b a b (4, ) e e (4 gg a ) K a( P D( Q, K)) 0 a g a( g a)( Q Q ) g ( P D( Q, K )) (40) 4

25 P ag g a( b ) g ( b ) K g g a K e e (4 ) e, e ag g = (4 g g a ) K 0 a( g a)( Q Q ) a( P D( Q, K )) g( P D( Q, K)) (4) The second equalty n (40) s obtaned usng Eqs. ()-(4) and (9). The last nequalty n (40) derves from the fact that 4g g a 0, g K 0, and a( g a)( Q Q ) g( P D( Q, K)) a( P D( Q, K)) 0. Smlarly, for expresson (4), the full effects of port capacty on emsson standards wthout fxng port charges wll be nvestgated n the numercal analyss (Secton 4). Fnally, we can draw analytcal conclusons on the effects of and when port charge s suffcently large. Ths does not requre fxng port charges. Proposton. If port charge b P s suffcently large such that b b b b a gg ( gg a ) 4, P e gg a P e gg a where ( =,), (4 gg a ) 4gg a 4gg a each government wll rase ts emsson standard facng a hgher envronmental damage cost per unt pollutant n the country, but wll lower ts emsson standard when the envronmental b damage cost per unt pollutant n the other country ncreases,.e., e 0 and e 0 (,, j ). b j Proof: See Appendx L. Note that 0 ( =,) always holds because the frst bracketed term on the RHS of the expresson s postve as we assume the SOC (Eq. (38)) holds. b b The senstvty of e and e to and s straghtforward. When ncreases, the envronmental damage cost at Port wll ncrease. To mtgate ths, Government wll respond by rasng ts emsson standard. When ncreases, the unt cost per TEU at Port wll ncrease, whch negatvely affects the compettveness of Port. In response, Government wll lower ts emsson standard to gan further compettve advantage. 4.5 Sngle country case Ths secton examnes the case that two competng ports are located n the same country. The government sets emsson standards at both ports to maxmze overall socal welfare: 5