Quality and pricing of delivery services in the e-commerce sector 1

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1 Quality and icing of delivey sevices in te e-commece secto Claie Bosenbege 2, Helmut Ceme 3, Pilie De Donde 4 and Denis Joam 5 INTRODUCTION In most uoean counties, te national univesal ostal sevice ovides ave taditionally been te majo oeatos of acel ome delivey sevices. Fo e-etailes, an efficient and eliable delivey system is an essential inut. Wit te develoment of e-commece, e-customes ae inceasingly demanding faste tansotation and delivey of goods ucased online, and an eve inceasing sevice quality is exected. In tis context, ostal oeatos ae facing two majo callenges. Te fist one aises fom te inceasing cometition in te acel delivey maket, and secifically te develoment of oeatos offeing altenative modes of delivey. Tese altenative modes include fo instance delivey at a so called PaketSo in Gemany o delivey in elay oints as offeed by Kiala in Fance, Belgium and Luxemboug. We ave examined some of tese issues in an ealie ae (Bosenbege et al. 24), wic concentates on te icing oblem of te ostal oeato and te ossibility to set u its own elay netwok. Te second callenge is obably even moe fundamental. It concens te quality of te ome delivey sevice. Tis mode of delivey is cetainly te most convenient fo e-customes as long as tee is someone at ome to eceive te acel. But, in eality te obability of ome delivey failue is not negligible and many socio-economic factos lead to olonged sells of absence of all occuants. Tis esults in a elatively ig ootion of fist time delivey failue, causing ige oeating costs fo caies and lowe custome satisfaction. Tis oblem can be mitigated in vaious ways including e-aangement of delivey times (ossibly in te evening o on Sunday) o by imoving tack-and-tace sevice. Inceasing quality is costly and will equie bot investments and affect maginal costs. Cometitos in tun may of couse eact to tis by adjusting te quality of te altenative delivey modes. Tey may enance tacking sevices, incease te numbe of elay oints o invest in new tecnologies. xamles of te latte include Packstation and PaketKästen in Gemany o Cityssimo in Fance. Ou fomal model, esented in Section 2, is based on Bosenbege et al. (24). Tee ae two delivey tecnologies and taste diffeences fo tese ae eesented by a simle Hotelling model in wic consumes ae distibuted ove an inteval, wee location zeo coesonds to ome delivey wile one coesonds to delivey at a elay oint. Te majo innovation of tis ae is tat oeatos now coose te quality of tei delivey sevice. Imoving quality is costly and equies an investment wic may affect bot fixed and maginal cost. We assume tat te quality of bot delivey tecnologies can be imoved, but since te tecnologies ae diffeent te cost associated wit quality imovements will also diffe. Fom a uely metodological esective, ou model innovates in tat it combines oizontal oduct Tis ae as been esented at te 22nd CONFRNC ON POSTAL AND DLIVRY CONOMICS, June 4t 7t, 24, Fascati, Rome, Italy. We tank all te aticiants fo tei comments and questions. We ae aticulaly gateful to ou discussant Albeto Pimento and to Tim Bennan fo tei insigtful emaks and suggestions. 2 conomist, uoean and National Regulation Division, Le Goue La Poste. 3 Coesonding auto: Toulouse Scool of conomics (IDI, GRMAQ and IuF), elmut.ceme@tse-f.eu. 4 Toulouse Scool of conomics (IDI and GRMAQ-CNRS). 5 Cief economist, uoean and National Regulation Division, Le Goue La Poste.

2 diffeentiation à la Hotelling, 6 wit vetical diffeentiation à la Mussa and Rosen (978) and Saked and Sutton (983). Unlike most of te industial economics liteatue we ave continuous (individual) demand functions, ate tan just a zeo-one decision. A aticulaly inteesting featue of ou model is tat unde te esence of te two tyes of diffeentiation, a ue stategy equilibium tyically exists, even in a simultaneous ice and quality game. 7 We fist study te fist-best and te monooly solutions as efeence scenaios in Sections 3 and 4. Ten we tun to te duooly equilibium wic is te most inteesting case fom a actical esective in Section 5. Bot oeatos coose te quality of tei esective delivey sevice (ome o elay oint) and te ate and we caacteize te Nas equilibium of tis game. Wile we adot te simlest ossible model wic is consistent wit te main stylized featues of te undelying oblem, te analytical solutions ae often quite comlex. Tei inteetation is inteesting in itself, but to obtain sae conclusion we esot to numeical simulations in Section 6. Tese ae based on an emiical model in wic te cost stuctue and te distibution of tastes ae calibated to acieve maket saes wic ae consistent wit a stylized eesentation of te cuently obseved maket stuctue. We also integate easonable estimates about imact of quality on cost fo te two delivey modes. Section 7 concludes. 2 MODL Te model is based on Bosenbege et al. (24), enanced to account fo quality bot in consume s efeences and in te oeatos cost stuctue. To kee te ae self-contained we ecall te main featue of tis model wile concentating on te ole of quality. We study te maket of an e-commece oduct. Tee ae two delivey modes: at ome (index ) o in a elay (index ). Te maginal cost of tis oduct (excluding siing costs) is constant and denoted by k ; tee is no fixed cost. Tougout tis ae we assume tat te e-commece secto is efectly cometitive so tat ices equal maginal costs (siing included). Fomally we ave q k : 8 te consume ice (of te e-commece oduct) is equal to its maginal cost lus te fixed cost. In ote wods, tee is full ass-toug of siing costs to consumes. 9 Consumes ae distibuted ove a Hotelling line, z [ ], wit Gz ( ) denoting te distibution function and g( z ) te density. Consumes location eesents tei efeences ove ome vesus elay delivey. Home delivey is te efeed otion of consume, wile delivey in a elay is te most efeed otion of consume. Let q denote te consume ice fo te ome deliveed oduct set by te e-etaile, wile q eesents te consume ice fo te elay deliveed oduct. Utility of consume z wo buys x units of te good is given by 6 See Gabszewicz and Tisse (992) fo a suvey of te extensive liteatue. 7 Te industial economics liteatue as tyically concentated on sequential games, mainly because in te standad diffeentiation model tee te simultaneous game tyically as no ue stategy equilibium. 8 Imefect cometition in te e-commece secto would in most cases esult in a diffeent atten of ass-toug. Deending on te tye of cometition tee may be unde- o even ove-sifting of siing costs to te final custome. 9 Bosenbege (24) sows tat contaily to initial exectations, te develoment of te intenet as not led to efect cometition in te elevant makets. Still, it is sown tat even toug makets ae concentated and dominated by a few fims cometition intensity is so stong tat ofit magins ae small. As fa as ou oblem is concened tis yields fo all actical uoses te same esult as a efectly cometitive maket. In aticula, tee continues to be full ass-toug of siing costs. 2

3 2 ux ( ) qx tz if te good is deliveed at ome 2 ux ( ) qx t( z) if te good is deliveed in a elay () wee and ae aametes eesenting quality of delivey fo ome and elay delivey esectively. We can now oceed along te same lines as in Bosenbege et al. (24) to deive aggegate (maket) demand fo te two oducts wic ae given by X ( q q ) x( q ) G[ zˆ ( q q )] (4) X ( q q ) x( q )( G[ zˆ ( q q )]) (5) Wee zˆ( q q) is te maginal consume indiffeent between ome and elay delivey. Te cost functions of ome and elay delivey ae exessed by C( X) c( ) X F( ) (6) C ( X) c ( ) X F ( ) (7) wee te subscits and ae used to identify te maginal and fixed costs associated wit ome and elay delivey esectively. We assume fo i c c F F i i i i Wit tese assumtions te SOCs fo te coice of and ae moe likely to be satisfied. Howeve, tese ae not necessay conditions. 3 FIRST-BST SOLUTION In te absence of quality coice (exogenous s), te fist best is tivial; it simly involves maginal cost icing. Tis will also be te case ee, but te inteesting asect will be te otimal coice of s. Tis at is less tivial and it is useful to study tis fist best (FB) as a bencmak. Let and denote te esective linea siing ates fo ome and elay delivey aid by te e-etaile to te delivey oeato. Recall tat unde efect cometition in te e-commece secto, we ave q k and q k. Te FB oblem can be witten as follows 2 2 z max L [ v( q) tz] gzdz ( ) [ v( q) t( z) ] gzdz ( ) z [ X X c( ) X c( ) X F( ) F( )] (8) Obseve tat L eesents te total sulus: aggegate consume sulus lus ofits of te two oeatos. Te FOCs wit esect to ices yield c c Not suisingly ices ae equal to maginal cost. Te FOCs wit esect to quality, ten educe to 3

4 z ux ( ) ( ) gzdz Xc F (9) ux ( ) gzdz ( ) [ XcF] () z Te fist tem in tese exessions measues te maginal social benefit (aggegated ove all elevant consumes) of an incease in and esectively. Te second tem eflects te maginal total cost of a quality incease, accounting fo te incease in fixed and vaiable costs. Note tat since te benefits ae linea in, te second ode conditions equie tat te cost is sufficiently convex in quality (at least beyond some level). 4 RAMSY SOLUTION Wen we imose a beak-even constaint, wit some minimum ofit level, we obtain a Ramsey oblem. Te Lagangean exession associated wit tis oblem can be witten as follows 2 z 2 2 z L [( v q) tz]() gzdz [( v q) t( z)]() gzdz ( )[ X X c( ) X c( ) X F( ) F( )] () Diffeentiating wit esect to ices, eaanging and denoting te elasticity of aggegate demand of good i { } by i yields te following Ramsey tye exessions fo te otimal ices: c ( c) X q q q X q c ( c) X q q q X q (2) (3) Tese exessions ae not affected by te endogeneity of and. To be moe ecise, icing ules ae not affected but actual ice levels do cange. Te otimal level of s is now detemined by te following conditions L X X ( ) ( ) ( ) ( ) ( ) z 2 ux gzdz c c Xc F L 2 X X ux ( ) gzdz ( ) ( ) ( c) ( c) Xc F z Once again we can inteet tese conditions in tems of social costs and benefits. We can tink about te fist tem as te vaiation in consume sulus and te tem in backets as te vaiation We could ave secified utilities as ux ( ) wit to make maginal benefits of quality deceasing. Howeve, tis is simly a cange of vaiables; te unit in wic we measue quality is abitay and ou fomulation is just as geneal, even toug it imlies tat all te convexity is ut in te cost tem. 4

5 in oduce sulus o ofit. Te vaiation in ofit is now weigted by ( ). On te one and, ofits ae accounted fo in social welfae; tis exlains te weigt of. On to of tat an incease in ofits as te benefit of elaxing te beak-even constaint; tis exlains te exta weigt of, te Lagange multilie associated wit tis constaint. Obseve tat an inteio solution equies (wit obvious notation), i. i In ote wods quality as to incease u to a level wee its imact on ofit becomes negative. Tis suggests tat ofit maximization would yield a level of quality tat is too low. Howeve, we ave to be caeful because tis agument is valid fo given ices and ice will cange as i inceases. Still, te esult is inteesting because wit geneal demands and efeences, te quality coice of a ofit maximizing monooly may be too ig o too low, even fo given ices; see, e.g., Vaian (992, Section 4.4). Vaian s agument also sows wy we obtain an unambiguous esult in ou setting: wit efeences as defined by exession (), te net consume sulus is an inceasing function of. In addition, wit two quality aametes te agument needs exta egulaity conditions. 2 Keeing all tese qualifications in mind it emains tat tis conjectue is confimed by te numeical simulations below. 5 DUOPOLY WITH SINGL TCHNOLOGY OPRATORS Let us now assume tat tee ae two oeatos. One of tem, labeled P is te incumbent ostal oeato wo only delives at ome. Te cometing oeato (entant),, only delives to elays. Its cost function as te same stuctue as (7), wit a constant maginal cost of c( ) and a fixed cost F( ). We caacteize te Nas equilibium of tis game, wee oeato P sets q and wile oeato (simultaneously) sets q and. In equilibium eac oeato s ice must be te best-esonse to te ote oeato s stategy. To detemine te best-esonse functions we now study te otimization oblem of eac of te oeatos. Te objective function of oeato P is now to maximize social welfae subject to a beak-even constaint and is eesented by te following Lagangean exession wee z 2 2 D2 z ( )[ X c( ) X F( )] L [( v q) tz]() gzdz [( v q) t( z)]() gzdz (4) [ c ( )] X F ( ) (5) is oeato s ofit. Tis exession diffes fom its counteat in te monooly case, (8), in tat ofits associated wit te elay tecnology,, ae not multilied by ( ) ; tis is nomal because tey now go to te ote oeato and no longe contibute to te budget balancing of oeato P. Te FOC wit esect to and imlicitly define te best Tis is because te invese demand function wic is given by q u ( x) becomes steee as teta inceases. 2 ven if we neglect ice vaiations te oety tat L 2 and L 2 olds at te ofit maximizing, does not necessaily imly tat social otimum is acieved fo ige levels of and. 5

6 esonse functions of oeato P, yielding and as functions of te ote oeato s stategic vaiables, namely and. Diffeentiating yields te FOCs fo oeato. Tese exessions in tun define te best-esonse functions of oeato. Te Nas equilibium levels of ( ) ae ten detemined as te solution to te system of equations consisting of te FOCs. As fa as ices ae concened, we obtain te taditional Ramsey exession. c( ) c( ) X q (6) q ( ) q X q Te otimality condition fo as a simila inteetation as in te evious sections. It is given by z X X ux ( ) gzdz ( ) ( ) ( c) Xc F ( c) Once again it eesents te net social benefit of a vaiation in. Consume sulus and s ofit eceive a weigt of, wile P s ofit as a weigt of ( ). Obseve tat since X xg()( z P u x) 2t, we no longe know te sign of. Put diffeently, we can no longe say fo sue tat a ofit maximizing oeato cooses a quality level tat is too low even fo a given ice. Intuitively, tis is not suising. A ofit maximizing oeato neglects te imact of quality on net consume sulus, wic ee is ositive; see Section 4. Tis exlains te undeovision of quality in te monooly case. Howeve, in duooly, an incease in also deceases oeato s ofit. Tis tem is neglected too wen oeato P is ofit maximizing and tis goes in te oosite diection (towads an oveovision of quality). Note tat a solution wit is ossible, even wen. Tis is because a ofit maximizing oeato will always set its ice above maginal cost. To mitigate distotions in te maginal consume oeato P ten also as an incentive to set a ice above maginal cost and tis may imly a maku wic oves to be sufficient to cove te fixed costs. In te simle case wee oeato P is ofit maximizing te FOCs become c( ) q (7) X [ c( )] Xc F (8) Te FOCs of oeato can be eaanged in a simila way to yield c( ) (9) q Te comaative statics oeties of te best-esonse functions ae quite comlicated, even 6 X [ c( )] Xc F (2)

7 fo te case wee bot oeatos maximize ofits, wee tey ae imlicitly defined by equations (7) (2). Picing beavio is simle only wen demand elasticities ae constant. In tat case, an oeato s ice is indeendent of te ote oeato s ice. In ote wods, tee is no stategic inteaction in ices and oeato s icing olicies ae tat of two indeendent monoolies. Howeve, tee is stategic inteaction via te quality levels. Futemoe, equations (7) and (9) ten imly constant makus. Consequently, te incease in maginal costs due to an imovement in quality will be moe tan fully sifted to te consumes, wile te incease in fixed costs does not affect ices. Tis is efectly in lines wit standad monooly icing esults. Toug wot mentioning, tis oety is of limited actical elevance in ou setting, because te assumtion of constant elasticity aeas to be vey estictive ee. To see tis, obseve tat elasticities in (7) and (9) ae tose of maket demand and not of individual demands. ven wen individual demands ave a constant elasticity, maket demand deends also on te distibution G, and on te location of te maginal consume wic in tun deends on bot oeatos ices. Wit all tese effects at lay it would take ate stingent assumtions to obtain a constant elasticity aggegate demand. Since tee ae no easonable simlifying assumtions tat would make te analytical model moe tactable, we now tun to a simulation execise to study te oeties of te diffeent solutions we ave just defined. Figue : Fixed cost of quality fo elay ( F ( ), in ed) and fo ome delivey ( F ( ), in blue) 6 NUMRICAL SIMULATIONS Ou calibation is based on te one esented in Bosenbege et al. (24), wic is a secial case of ou cuent model fo. Moe ecisely, we ave used te same value of te tansotation cost t associated wit te Hotelling model, te same quadatic utility functions ux, ( ) and tus te same linea demand functions x( q), te same maginal cost k fo te oduct wic is deliveed, and te same constant maginal costs of delivey fo te two tecnologies, wit ome delivey being 5% moe exensive at c 5 tan elay delivey at c. In ote wods we ave assumed tat te maginal delivey cost does not deend on quality. Some of ou assumtions, oweve, diffe fom Bosenbege et al. (24). Fo comutational easons, we assume ee a unifom distibution of consumes ove te Hotelling line. Wit tis distibution, te maket sae of ome delivey is 3% wen bot delivey 7

8 metods ave te same unit quality ( ) and wen tey ae eac iced at maginal cost ( q k c 5 and q kc ), and of 68% wen te elay delivey ice is inceased to 2 (keeing and q 5 ). We assume a fixed cost of delivey tat vaies wit quality fo bot delivey metods i.e., F( ) and F( ) and tat te two tecnologies ave te following caacteistics: (i) te fixed cost of ome delivey is lage tan te fixed cost of elays wen bot ave te same unitay quality (te scenaio studied in Bosenbege et al (24)): F () wile F () 5, (ii) bot costs ae convex in quality, as it quickly becomes moe exensive to incease quality at te magin, and (iii) te fixed cost of quality becomes lage fo elays tan fo ome delivey wen te quality of bot is inceased by moe tan 7% above tei stating level of. Tis latte assumtion eflects te difficulty to scale u significantly te elay tecnology witout incuing significant costs. Figue illustates te fixed costs of quality fo bot tecnologies. We fist study te situation wee a monooly oeates bot tecnologies, befoe moving to te case of a duooly wit eac fim oeating its own delivey tecnology. Monooly oeato wit two tecnologies We stat fom te fist best allocation (fist numeical ow in Table ) wee ices ae of couse equal to maginal costs, and tus ige fo ome delivey tan fo elays ( c 5 c ), and wee te otimal quality is lage fo ome delivey tan fo elays ( 4 ). Quality is lowe fo elays tan fo ome delivey fo two easons. Fist, nealy two tids of consumes efe to be deliveed at ome, so tat te aggegate maginal benefit of a lage quality is muc ige fo tan fo ; ecall tat te cost of quality is a fixed cost. Second, even toug F( ) 99 F( ) 324 at te fist best, te fixed cost of quality inceases faste in elays tan fo ome delivey wen. Obseve tat te lage maket sae of ome delivey is entiely due to te diffeences in te sae of fixed costs of quality between te two tecnologies, ate tan to any intinsic efeence of consumes fo one ate tan te ote (since we assume a unifom taste distibution). In te fist-best allocation, te fixed costs of quality ae not coveed, so tat te monooly oeato makes a loss. Te next ows in Table coesond to te Ramsey equilibia as te minimum ofit equiement is inceased (see last column). As inceases, te monooly inceases bot its ices above maginal costs. It also deceases te elay quality to save on costs. Sae CS Welfae % % % % % % % Table : quilibium allocation unde monooly Inteestingly, te otimal value of ome delivey quality is not monotone in ; it fist 8

9 inceases wit, and ten deceases once a tesold is cossed. At te same time, bot te maket sae of ome delivey and its contibution to oveall ofit incease monotonically wit. Te contibution of elays to te bottom line is non monotone, fist inceasing wit and ten deceasing. Bot consume sulus and aggegate welfae decease wit. Finally, as becomes vey lage, becomes lage tan. An allocation of aticula inteest is te one coesonding to i.e., te second best Ramsey allocation. Home delivey quality is sligtly lage tan its fist best level, wile elay quality is lowe. Pices ae significantly lage tan at tei fist best level, wit elay ceae tan ome delivey. Total welfae is not muc (2%) lowe tan at its fist best level, but its comosition is vey diffeent, wit muc lowe (25%) consume sulus. Te ositive contibution of elays to ofit is comensated by te negative contibution of ome delivey. Te last ow in Table eots te ofit-maximizing equilibium. Te monooly kees a vey small elay maket caacteized bot by a vey lage ice (lage tan ome delivey s) and a low quality. Te monooly ten extacts a maximum of sulus fom te consumes located close to te elay end of te Hotelling line. Te ome delivey quality is sligtly below its fist-best level, and te ice is muc ige. Pofit (geneated quasi exclusively by ome delivey) is lage tan consume sulus, and total welfae is vey muc lowe (36%) tan at its fist-best level. Duooly wit distinct tecnologies We now tun to te duooly equilibium wee eac fim oeates a distinct tecnology, and wee te entant sets te elay delivey caacteistics in ode to maximize its ofit. Te fist ow of Table 2 eots te equilibium wee te ostal oeato sets ome delivey ice and quality to maximize total welfae witout any beak-even constaint. Not suisingly, te ofit-maximizing entant osts a ice ige tan maginal cost and also degades elay quality comaed to its fist best level. Te ostal oeato also inceases its ice above maginal cost, to mitigate distotions in te maginal consumes (see Bosenbege et al. (24) wee quality level ae exogenous) and inceases te quality of ome delivey above te fist-best level. Te ome delivey maket sae is ten significantly ige tan in te fist best. Bot oeatos make a loss in tis equilibium. Consequently, wit a welfae maximizing ome delivey oeato wo is not subject to a beak-even constaint enty is not sustainable. Te ome delivey oeato s loss is lowe tan at te fist best allocation, but bot consume sulus and welfae ae also lowe. Sae CS Welfae % % % % % Table 2: quilibium allocation unde duooly As we incease te minimum ofit equiement of te ostal oeato, (moving down in Table 2), te ostal oeato inceases its ice and deceases its quality, wile te elay entant inceases bot its ice and its quality. Te elay s maket sae inceases wit. All tis is in stak contast (excet fo te inceases in ices) wit wat aens as we incease in te monooly scenaio. Te entant even cooses a quality level tat is above te fist best level fo te elay wen is lage enoug. Te ostal oeato eacts to tis vey ig quality level fo 9

10 te elay by setting a lowe-tan-fist-best-otimal quality level fo ome delivey. Te elay s maket sae is ten lage tan its fist-best level. Bot te entant s and te incumbent s ofits incease wit. Te entant s ofit is always lage tan te incumbent s. Te elay ice emains smalle tan te ome delivey ice wateve te value of. Comaing te allocations wee te ostal oeato beaks even ( ) in Tables and 2, we see tat te intoduction of cometition in te elay maket deceases bot consume sulus and aggegate welfae. Obseve tat tis is effectively a geneal esult, wic does not deend on te calibation, as long as. Tis is because wit, te duooly equilibium is also an otion available to te Ramsey monoolist. Consequently, it is lain tat te Ramsey solution can only yield a ige welfae. Te last ow of Table 2 eots te equilibium wee bot oeatos simultaneously maximize tei own ofit. Te ofit-maximizing scenaio is bette fo consumes but wose fo te fims tan unde a monooly. Pices ae significantly lowe, elay quality is lage but ome delivey quality is smalle. Te elay maket sae is muc lage unde a duooly tan a monooly. Finally, as an illustation of te ossible imact of quality egulation in tis setting, we ave comuted te ofit-maximizing equilibium wee te ostal oeato faces a minimum quality level wic is set at te fist-best level. In ote wods, only is egulated. Fo te est, te ostal oeato sets its ofit-maximizing ice wen is exogenously set at., wile te elay entant sets bot ice and quality to maximize its ofit. Results ae eoted in Table 3. P max S. CS W ; % W ; % W ; % Table 3: Minimum quality standads in Pofit-maximizing and mixed duooly. We obtain tat total welfae is lowe tan witout te constaint on (last ow of Table 2), sowing tat it is bette not to egulate te ostal oeato in tis cicumstance. In ote wods, no egulation is bette tan a atial and asymmetic egulation. Te ostal quality constaint induces te entant to decease bot its ice and te quality of its elays, and te incumbent eacts by inceasing its ice fo ome delivey. Bot oeatos ofit deceases afte te intoduction of te quality constaint on ome delivey. Similaly, intoducing a minimum quality standad (even lowe tan te fist-best level) in a mixed oligooly lowes welfae. Bot total welfae and consume sulus ae educed comaed to te case witout quality egulation, wit only a beak-even constaint. Tis is because of te ice inceases induced by te ige quality levels. Te unique winne of te quality egulation in tis case is te entant wo makes ige ofits. 7 CONCLUSION Tis ae as studied a stylized delivey maket fo e-commece oducts. Tee ae two delivey tecnologies, ome delivey and delivey to a elay oint. Taste diffeences fo tese ae eesented by a simle Hotelling model in wic consumes ae distibuted ove an inteval. Oeatos also coose te quality of tei delivey sevice. Imoving quality is costly and equies an investment wic may affect bot fixed and maginal cost. We ave fist studied a setting in wic a single oeato uses bot tecnologies and ten consideed a

11 duooly wit two single tecnology oeatos. Te ome delivey oeato may o may not be egulated wile te elay oeato is not subject to egulation and maximizes its ofit. Te following main lessons ave emeged. Fist, if te ostal oeato is egulated so tat it maximizes welfae witout beak-even constaint, ten enty by a ofit-maximizing etail oeato is not ofitable. Second, te intoduction of cometition on a egulated maket (wee te incumbent beaks-even) deceases welfae and consume sulus. Tid, if te maket is not egulated, enty is socially beneficial (comaed to a maximizing ofit monooly situation). Consume sulus is ige, tanks to lowe ices and to a lage elay quality. Fout, quality egulation (imosing to te ome delivey oeato to eac te fist best quality level) may ave an advese effect on welfae. Total welfae is lowe tan witout te constaint on (last ow of Table 2). Consequently no egulation is te sueio olicy unde tese cicumstances. Tis advese effect in te welfae is due to te decease in te ostal oeatos ofits wic is so lage tat it is not countebalanced by te consume sulus incease. Note tat te ome delivey oeato now makes losses. Imosing a fist-best quality level fo ome delivey in a cometitive maket uts te oeato in an unsustainable economic situation. ven unde a beak-even constaint couled wit a minimum quality-level constaint (lowe tan te fist-best level), bot total welfae and consume sulus ae educed comaed to te case witout quality egulation (wit only a beak-even constaint) because of te ice inceases induced by a ige quality. Te unique winne of te quality egulation in tis case is te entant wo makes ige ofits. Ou numeical esults do of couse deend on te oeties of te cost functions. In aticula te discussion of te vaious scenaios as sown tat te degee of convexity of te fixed cost associated wit te elay tecnology wit esect to quality lays a cucial ole. To kee te esentation concise, we ave concentated on a single secification, namely te one eesented in Figue. Wile tis secification eflects te stylized oeties of te two tecnologies, te ecise degee of convexity is of couse subject to debate and te lack of available data ecludes at tis oint a fully-fledged estimation of tese functions. To assess te obustness of ou esults, we ave teefoe efomed a seies of additional simulations bot wit a lage and wit a smalle degee of convexity of te cost function of elay delivey. 3 Wile tis canges of couse all te numeical esults, it is quite stiking tat all of ou qualitative conclusions emain unaffected. RFRNCS Bosenbege Claie (24), Te concentation enomenon in e-commece, mimeo. Bosenbege Claie, Helmut Ceme, Pilie De Donde, Denis Joam and Sébastien Lécou (24), Picing of delivey sevices in te e-commece secto, in M.A. Cew and T.J. Bennan eds, Te Role of te Postal and Delivey Secto in a Digital Age, Celtenam, UK and Notamton, MA, USA: dwad lga, Mussa, Micael and Sewin Rosen (978), Monooly and oduct quality, Jounal of conomic Teoy, 8, Saked, Avne and Jon Sutton (982), Relaxing ice cometition toug oduct diffeentiation, Review of conomics Studies, 49, 3 4. Vaian, Hall (992), Micoeconomic Teoy, Noton. 3 An xcel file wit te detailed esults is available fom te auto uon equest.