Fraud, Investments and Liability Regimes in Payment. Platforms

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Fraud, Investments and Liability Regimes in Payment. Platforms"

Transcription

1 Fraud, Invstmnts and Liability Rgims in Paymnt Platforms Anna Crti and Mariann Vrdir y ptmbr 25, 2011 Abstract In this papr, w discuss how fraud liability rgims impact th pric structur that is chosn by a monopolistic paymnt platform, in a stting whr mrchants can invst in fraud dtction tchnologis. W show that liability allocation ruls distort th pric structur chargd by platforms or banks to consumrs and mrchants with rspct to a cas whr such a rsponsibility rgim is not implmntd. W dtrmin th allocation of fraud losss btwn th paymnt platform and th mrchants that maximiss th platform s pro t and w compar it to th allocation that maximiss social wlfar. JEL Cods G21, L31, L42. Kywords Paymnt card systms, intrchang fs, two-sidd markts, fraud, liability. Univrsité Paris Oust Nantrr and Ecol Polytchniqu. Economix, Bâtimnt G, burau 604, 200 avnu d la Républiqu, Nantrr Cdx, Franc; y Univrsité Paris Oust Nantrr, Economix, Bâtimnt T, burau 234, 200 avnu d la Républiqu, Nantrr Cdx, Franc; 1

2 1 Introduction Th dvlopmnt of lctronic data xchang in th banking industry has gnratd an incras in fraud and cybrcrim. For instanc, in th Unitd-tats, according to th Consumr ntinl Ntwork (CN), 1.2 million complaints of consumr fraud hav bn rcordd in As a consqunc, banks can mak substantial losss bcaus of fraudulnt us of paymnt cards, which di r across countris and paymnt systms ( tabl 1). Tabl 1 Loss rat pr $100 paymnt card transaction valu in svral countris 2 Country pain Australia Franc UK U Losss rat 2.24c/ 2.39c/ 5c/ 9.12c/ 9.2c/ Minimizing th occurrnc of fraud in lctronic paymnt systms rquirs costly orts from all th participants to a transaction platforms, banks, consumrs and mrchants. 3 For instanc, consumrs hav to protct thir prsonal data and to rport th fraud rapidly onc it occurs, whras platforms, banks and mrchants may invst substantial amounts in fraud dtction tchnologis. 4 Ths orts in fraud prvntion dpnd on th xpctd amount of losss and thir allocation, which rsponds to svral liability ruls, dtrmind ithr by public laws or by privat ntwork ruls. Currntly, in most paymnt card systms, consumrs hardly bar maningful liability for fraudulnt us of thir paymnt card, bcaus thy ar protctd both by nancial rgulations, which ar public laws (.g. TILA and rgulation Z in th Unitd- tats) 5, and by th zro liability rul, which has bn privatly adoptd by svral paymnt ntworks. It follows that, in most paymnt systms, th burdn of fraud losss is shard btwn banks or platforms and mrchants. 6 Th allocation of liability btwn banks and mrchants 1 ourc Consumr ntinl Ntwork Data Book for January-Dcmbr 2008, Fdral Trad Commission, Fbruary This rport highlights that crdit card fraud is th most common form of rportd idntity thft amounting at 20% of th rportd fraudulnt transactions. 2 ourc Richard ullivan (2010), Fdral Rsrv Bank of Kansas City, Th Changing Natur of Paymnt Card Fraud Issus for Industry and Public Policy. 3 According to th Fdral Rsrv Board, in th Unitd-tats, "On avrag, by transaction typ, issurs incurrd 2.2c/ pr signatur-dbit transaction for fraud-prvntion and data-scurity activitis and 1.2c/ pr PINdbit transaction. imilarly, ntworks incurrd 0.7c/ pr signatur-dbit transaction for fraud-prvntion and data-scurity activitis and 0.6c/ pr PIN-dbit transaction. Finally, acquirrs incurrd 0.4c/ pr signatur-dbit transaction for fraud-prvntion and data-scurity activitis and 0.3c/ pr PIN-dbit transaction.". ourc Fdral Rgistr / Vol. 75, No. 248 / Tusday, Dcmbr 28, 2010 / Proposd Ruls. 4 According to a survy conductd by th Fdral Rsrv Board in th Unitd-tats, issurs ngag in various fraud-prvntion activitis such as "transaction monitoring and fraud risk scoring systms that may triggr an alrt or call to th cardholdr in ordr to con rm th lgitimacy of a transaction". "Mrchants also hav fraud-prvntion data-scurity costs, including costs rlatd to complianc with paymnt card industry datascurity standards (PCI-D) and othr tools to prvnt fraud, such as addrss vri cation srvics or intrnally dvloppd fraud scrning modls, particularly for card-not-prsnt transactions". 5 For a comparison of consumr protction laws across various countris, s Appndix A. 6 For instanc, in Franc, according to th "Obsrvatoir d la sécurité ds carts d paimnt", fraud losss hav bn shard in 2009 btwn banks (41.1%) and mrchants (53.5%). Mrchants hav bn hld liabl mainly for fraud on intrnt transactions. Consumrs wr hld liabl for only 2.3% of th fraud losss. According to 2

3 gnrally dpnds on privat ruls that ar chosn by paymnt platforms. om ntworks may vn us liability ruls to provid mrchants with incntivs to adopt nw tchnologis. For instanc, MastrCard and Visa usd liability shift masurs to induc mrchants to adopt fraud prvntion tchnologis on th intrnt (MastrCard curcod TM and Visa 3-D cur TM rspctivly). 7 Intrstingly, if th mrchant implmnts th 3-D cur TM tchnology, th issur bcoms liabl for fraud losss for all Commrc transactions that wnt through th 3-D cur TM procss. This papr adrsss two major issus rlatd to fraud in paymnt systms What is th incidnc of fraud liability rgims on th pric structur that is chargd by paymnt platforms? How do privat liability rgims di r from th socially optimal rgim that would b implmntd by a social plannr? In particular, w analys whthr privat ntwork ruls provid mrchants with su cint incntivs to invst in fraud dtction tchnologis and whthr ths ruls gnrat th socially optimal allocation of fraud losss. In our framwork, w us a broad d nition of fraud, which is th us of an lctronic paymnt instrumnt (or its information) by a prson othr than its ownr, to obtain goods and srvics without authority for such us. 8 W considr a monopolistic propritary paymnt platform that provids an lctronic paymnt instrumnt to consumrs and mrchants. Consumrs and mrchants dcid whthr or not to adopt th lctronic paymnt instrumnt basd on th pric of th paymnt instrumnt and on th xpctd loss that thy incur in cas of fraudulnt transaction. Fraudulnt transactions ar dtctd with som probability that is positivly rlatd to mrchants invstmnts in fraud prvntion tchnologis. If a fraud is dtctd, thn th participants do not mak losss. Our rsults highlight th following trad-o for th paymnt platform. Whn th lvl of liability for mrchants incrass, th numbr of mrchants who accpt th lctronic paymnt instrumnt falls, but mrchants tnd to invst mor in fraud dtction tchnologis, which incrass consumrs willingnss to us th lctronic paymnt mthod. Th paymnt platform trads o btwn incrasing th lvl of liability to minimiz th xpctd loss on fraudulnt transaction and maximizing th transaction volum by ncouraging mrchants and consumrs Furltti (2005), in th Unitd-tats, "consumrs of crdit cards ar shildd from narly $3 billion in fraud losss ach yar". According to a mor rcnt survy conductd by th Fdral Rsrv Board in th U, in 2009, across all typs of dbit card transactions, 57% of fraud losss wr born by issurs and 43% wr born by mrchants. ourc Fdral Rsrv Rgistr, vol. 75 n 248, Ths srvics provid Intrnt mrchants with th ability to vrify thir consumrs tru idntitis through a scur, lctronic, non fac-to-fac authntication procss. 8 Our modl dos not nabl us to distinguish which typ of fraud is implmntd by th fraudstr. W considr any typ of fraud that can b mpdd by mrchant invstmnt. For instanc, data brachs and phishing do not dpnd on mrchants invstmnts (rathr on platform s invstmnt). On th contrary, idntity thft can b avoidd by th mrchant s ort to vrify th consumr s idntity. 3

4 to accpt th lctronic paymnt instrumnt. In th short trm, th xistnc of a fraud liability rgim a cts th pricing structur of th paymnts systm. With rspct to th standard pric structur in two-sidd markts (Rocht-Tirol, 2003), th pric structur that w obtain taks into account th platform s trad-o btwn maximising its pro t and minimizing th xpctd loss on fraudulnt transactions. If th zro liability rul for consumrs applis, th allocation of fraud losss that is chosn by th paymnt platform dos not plac nough liability on mrchants to maximis social wlfar. Thrfor, liability rgims can b usd by monopolistic paymnt platforms to xtract rnts from mrchants, as it nabls thm to charg highr prics. W also nd that this rsult dos not hold if invstmnts ar shard btwn th platform and th mrchants. W also dtrmin th incidnc of th liability rgim on th choic of th intrchang f. W nd that, if th issurs ar imprfctly comptitiv, whras th acquirrs ar prfctly comptitiv, th pro t maximising intrchang f dcrass with th lvl of liability that is born by mrchants. Th rst of th papr is organizd as follows. In ction 2, w summariz th litratur rlatd to our study. In ction 3, w dvlop a thortical modl to analyz th optimal allocation of fraud losss btwn th paymnt platform and th mrchants. In sction 4, w dtrmin th pro t maximising allocation of fraud losss. In sction 5, w study th wlfar maximising allocation of fraud losss. In sction 6, w analyz th rol of intrchang fs. In sction 7, w xtnd th modl by studying th optimal allocation of invstmnts btwn th paymnt platform and th mrchants. Finally, w conclud. 2 Rlatd Litratur To our knowldg, this papr is th rst attmpt to modl fraud dtction tchnologis and liability rgims in th litratur on paymnt systms. Our approach thus rlis on thr di rnt strands of litratur th litratur on paymnt platforms, on invstmnt in two-sidd markts, and nally th litratur on liability issus in law and conomics. Most paprs on paymnt systms focus on xplaining th divrgnc btwn th pro t maximising pric structur that is chargd by paymnt platforms and th pric structur that maximiss social wlfar (s Chakravorti (2010) for a rviw). In particular, svral paprs aim at dtrmining whthr paymnt platforms charg xcssiv intrchang fs whn thy maximis banks joint pro t (as survyd by Vrdir, 2011). Our papr contributs to this litratur by xtnding Rocht-Tirol (2003) to study how th allocation of th xpctd fraud loss btwn th platform and th mrchants changs th pro t-maximising pric structur. 4

5 Th litratur on invstmnt in two-sidd markts is scarc. For instanc, Vrdir (2010) dtrmins th optimal pric structur of a paymnt card platform in which monopolistic banks can invst to improv th quality of th paymnt srvic. Hr modl studis how invstmnts should b allocatd btwn monopolistic banks in four-party paymnt platforms. In particular, sh nds that a rduction of intrchang fs can improv th allocation of invstmnts by ncouraging acquirrs to invst, whn invstmnts incras consumrs dmand. Our modl dparts from that papr, as w considr a monopolistic propritary paymnt platform, and w focus on th optimal allocation of fraud losss btwn th platform and th mrchants. Th four-party modl is usd in sction 5 of our papr, whr w show that th pro t maximizing intrchang f dcrass with th lvl of liability born by mrchants. Th only papr that considrs mrchants invstmnts in two-sidd platforms is th papr by Pitz and Bll amm (2010), who study th ct of th intrmdiation mod (for-pro t compting platforms vrsus fr accss) on sllrs invstmnt, in a modl whr sllrs invstmnt incras th buyrs utility of blonging to th platform. Thy show that for-pro t intrmdiation may lad to ovrinvstmnt whn innovations incras buyrs surplus, bcaus compting intrmdiaris ract by lowring th accss fs on th sllr sid. Our focus is di rnt from thirs, as w tak th intrmdiation mod as givn, and focus on th impact of liability ruls on sllrs invstmnts incntivs. Our modl is also rlatd to th vast litratur on tort law whos main goal is to nhanc socially optimal dcisions on th lvl of prcaution (Brown, 1973). Mor prcisly, our framwork shars th sam background of x post liability rgims, whil nglcting th problm of non complianc and nforcmnt of x ant rgulation. 9 In this contxt, strict liability allocats th losss to th injurr by ntitling th victim to compnsation, whras no liability allocats th losss to th victim, by dnying th right to compnsation (Lands and Posnr, 1987). Indd, liability provids incntivs for prcaution. 10 W xtnd this argumnt to th cas of a thr party systm intrrlatd through ntwork cts, which is uncommon in law and conomics modls. In fact, in our framwork, th pric of a transaction implis not only a choic for a consumr, which gnrats a loss risk (as also pointd out by law scholars lik Cootr and Robin, 1987), but also a pricing stratgy by th platform and an incntiv for th mrchant to invst in fraud dtction. 9 Ex ant rgulation is mant to prvnt accidnts from occurring through th nforcmnt of minimum safty standards or complianc rstrictions. Ex post liability, xrcisd aftr an accidnt has occurrd, is a lgal dvic that nabls victims to su for damags, forcing injurrs to intrnaliz part of th harm thy caus. 10 Whn both partis hav to tak prcaution in ordr to avoid an accidnt, strict liability crats no incntivs for victim prcaution, whil no liability would shift th ntir rsidual liability on th victim, inducing optimal victim car. It follows that strict liability and no liability can giv incntivs to tak cint prcaution only to on party, rspctivly ithr th injurr or th victim (Dari-Mattiacci, Parisi, 2006). 5

6 3 Th modl W build a modl in which a monopolistic paymnt platform o rs an Elctronic Paymnt Instrumnt (hraftr th EPI) to consumrs and mrchants. W xtnd Rocht and Tirol (2003) along svral dimnsions. W considr that thr is an xognous probability that th EPI is fraudulntly usd, in a stting whr mrchants can invst in fraud dtction tchnologis. W d n fraud as th us of an lctronic paymnt instrumnt (or its information) by a prson othr than its ownr, to obtain goods and srvics without authority for such us. Th fraud ntails a lump sum loss which dos not dpnd on th transaction valu. Our framwork nabls us to dtrmin how fraud liability should b allocatd btwn th participants to maximis th platform s pro t. It also nabls us to compar th privat optimal allocation to th on that maximiss social wlfar. Paymnt systm and allocation of fraud A monopolistic paymnt platform provids an lctronic paymnt instrumnt (.g. th paymnt card) to consumrs and mrchants. Th marginal cost of procssing a transaction is dnotd by c. Consumrs and mrchants pay transaction fs to th platform, which ar dnotd by f and m rspctivly. Whn consumrs us th EPI, thr is an xognous probability x 2 (0; 1) that th paymnt instrumnt is intrcptd by fraudstrs. 11 Thr is also a probability q 2 [0; 1] that th fraud is dtctd, which dpnds on mrchants invstmnts. If th fraud is not dtctd, all th participants to th transaction mak an xognous loss that w dnot by L > 0. Th loss is allocatd btwn th consumr, th mrchant and th paymnt platform as follows th consumr (or buyr B) and th mrchant (or sllr ) bar rspctivly a shar B and of th loss, whr + B 2 [0; 1]. Th rst of th loss, P = 1 ( + B ), is born by th paymnt platform. W assum that th paramtr B is dtrmind by public laws and w considr it as xognous to th modl. In particular, if B = 0, th zro liability rul applis for consumrs. Th paramtr is privatly chosn by th paymnt platform. 12 W choos to normaliz th fraud on cash paymnts to zro Th assumption that x is xognous is mad for simplicity. Indd, ndognizing x would introduc anothr trad-o for th mrchant. Highr invstmnts in fraud dtction tchnologis hav two cts on hackrs incntivs to fraud. On th on hand, highr invstmnts in fraud incras th volum of transactions, which incrass th hackrs incntivs to commit fraud. On th othr hand, highr invstmnts incras th probability that a fraud is dtctd, which may discourag hackrs to commit fraud. 12 In our modl, w do not study how th losss ar allocatd btwn banks and th paymnt platform. In practic, paymnt platforms dsign ruls to allocat th losss btwn issuing and acquiring banks and also to allocat th losss btwn banks and th platform itslf. This issu would dsrv a sparat study. W rintroduc banks in sction 4 and choos to focus on th rol of intrchang fs in fraud prvntion issus. 13 Introducing th probability that a fraudulnt paymnt is mad by cash would not chang th trad-o s that w highlight in our modl. W would only hav to modify assumption (A2) to tak into account th losss that ar du to fraud on cash paymnts. 6

7 Mrchants W considr local monopolist mrchants that supply th sam good to consumrs. Th marginal cost of producing th good is dnotd by d and th pric of th good is dnotd by p. W assum that th non-discrimination rul holds, such that a mrchant cannot not charg a pric that dpnds on th paymnt mthod. Each mrchant can dcid whthr or not to accpt th lctronic paymnt instrumnt. If h dcids to accpt th EPI, th mrchant may invst an amount in fraud dtction tchnologis. Invstmnt to improv fraud dtction costs C ( ) to th mrchant, whr C ( ) is paid pr transaction, C 0 ( ) 0, C 00 ( ) 0 and C 000 ( ) 0. Mrchant s invstmnts incras th probability q that a fraudulnt transaction is dtctd, that is, w assum that dq=d > 0 for all > 0. W also assum that d 2 q=d 2 0 for all 0 and that d 3 q=d Th amount invstd in fraud dtction tchnologis is common knowldg, such that banks and consumrs ar awar of th scurity masurs implmntd by th mrchants. 15 By accpting th EPI, ach mrchant obtains a transaction bn t that w dnot by b, whr b > 0. As in Rocht and Tirol (2003), w assum that mrchants ar htrognous ovr thir transaction bn t b which is distributd ovr b ; b according to th probability dnsity h and th cumulativ H. W assum that h 0 0 to nsur dmand (quasi) concavity. W normaliz th bn t of accpting cash to zro. Th mrchant pays a f m to th paymnt platform ach tim a consumr pays with th EPI and bars th cost of invsting in fraud dtction tchnologis. W also assum that mrchants ar risk nutral. Consumrs Consumrs obtain a surplus v > 0 if thy buy th good that is supplid by th mrchants. Thy ar assumd to hold two paymnt instrumnts cash and th Elctronic Paymnt Instrumnt. Each consumr is randomly matchd to on mrchant and chooss btwn paying cash or paying with th EPI, if th mrchant accpts th EPI. W assum that consumrs ar risk nutral and that thy can obsrv mrchants invstmnt in fraud dtction tchnologis bfor dciding whthr or not to us th EPI. If h pays with th EPI, th consumr obtains a transaction bn t b B which is distributd ovr b B ; b B according to th probability dnsity hb and th cumulativ H B. W assum that h 0 B 0 for concavity to hold. Th consumr pays a f f to th paymnt platform, and anticipats that, with som probability x(1 q), h bars a shar B of th loss L, bcaus th EPI is fraudulntly usd without bing dtctd. 16 Th bn t of paying cash is normalizd 14 Th assumption that d 2 q=d 2 0 nsurs that th scond-ordr condition is vri d whn th mrchant chooss its lvl of invstmnt. Th assumption that d 3 q=d 3 0 nsurs that th scond-ordr condition is vri d whn th platform maximiss its pro t. 15 Mrchants can inform consumrs about thir orts to ght fraud. For instanc, onlin sllrs can communicat on th us of a softwar or a spci c tchnology that improvs consumr authntication. 16 W rul out th possibility that consumrs do not anticipat prfctly th dtction probability. Howvr, 7

8 to zro. It follows that, if a consumr can choos btwn cash and th EPI, undr th nondiscrimination rul, a consumr wishs to us th EPI if and only if b B f B x(1 q)l 0, (1) that is, if his transaction bn t is highr than th cost of th transaction f and th xpctd fraud loss. Additional assumptions h B (x) (A1) Th hazard rat is incrasing. 1 H B (x) 1 (A2) In quilibrium, min v d; h B(f + B (1 q)xl) xl B 1 H B (f + B (1 q)xl). Assumptions (A1) is similar to Wright (2002) and standard in th litratur on paymnt cards. Assumption (A2) nsurs that (i) consumrs obtain a much highr surplus from buying th good that from making a transaction with th Elctronic Paymnt Instrumnt. 17 (ii) th amount of th xpctd shar of th fraud loss for consumrs is not too high, such that it dos not xcd th surplus that consumrs obtain from making a transaction. 18 Timing Th timing of th gam is as follows 1. Th platform chooss th liability lvl and th transaction fs f and m. 2. Th mrchants dcid whthr or not to accpt th EPI and how much to invst in fraud dtction tchnologis. Thy also choos th pric of th good p. 3. Each consumr is matchd randomly to on mrchant. Consumrs dcid on whthr or not to buy th good and how to pay for th good (ithr by cash or with th EPI). In th following sction, w look for th subgam prfct quilibrium and solv th gam by backward induction. in practic, consumrs may ovrract to th risk of fraud. This can b studid in our framwork by doing som comparativ statics about B. 17 Part (i) of Assumption (A2) is standard in th litratur (s Wright (2002)). Formally, this corrsponds to th Assumption that v d h B(f + B(1 q)xl)=(1 H B(f + B(1 q)xl). 18 Part (ii) of Assumption (A2) is nw, as our papr is th rst to modl th incidnc of fraud losss on consumrs and mrchants paymnt choics and platform prics. Formally, this corrsponds to th Assumption that (1=xL B) h B(f + B(1 q)xl)=(1 H B(f + B(1 q)xl). 8

9 4 Th quilibrium 4.1 tag 3 consumr paymnt dcisions W start by dtrmining th probability that a consumr wishs to us th Elctronic Paymnt Instrumnt. Considr a consumr whos transaction bn t is b B 2 b B ; b B. This consumr is randomly matchd to on mrchant, who may or may not accpt th EPI. If th mrchant accpts th EPI, th consumr chooss his paymnt mthod by comparing his xpctd utility if h pays cash and if h pays with th EPI. Lt us start by th cas in which th mrchant dos not accpt th EPI. If th mrchant sts p v, th consumr wishs to buy th good by paying cash, as his surplus v p is positiv. Othrwis, h dos not buy th good. Now considr th cas in which th mrchant accpts th EPI. If th mrchant sts p v, th consumr wishs to buy th good, as h obtains at last a positiv surplus if h pays cash. H dcids to us th EPI if his xpctd utility is highr than if h pays cash. It follows that, if p v, a consumr wishs to us th EPI if and only if v p + b B f B (1 q)xl v p, that is, if and only if b B f B (1 q)xl 0 If th mrchant sts p > v, th consumr nvr uss cash. Th consumr buys th good and pays with th EPI if and only if v p + b B f B (1 q)xl 0. W dnot by D B th probability that a consumr wishs to us th EPI. Considring consumrs htrognity, it follows from th prvious analysis that 8 < 1 H B (f + B (1 q)xl) if p v D B = 1 H B (f + B (1 q)xl + p v) if p > v. Not that th probability that th consumr wishs to us th EPI dcrass with th transaction f, th consumr s liability, th xpctd amount of fraud loss, but incrass with th probability that th fraud is dtctd. 9

10 4.2 tag 2 EPI accptanc and invstmnts in fraud dtction Prics and card accptanc condition W now dtrmin th pric that is chosn by ach mrchant, along with th dcision to accpt th EPI and invst in fraud dtction tchnologis. W start by showing that, bcaus of assumptions (A1) and (A2), th pro t of a mrchant who accpts th EPI is maximisd whn h sts a pric such that cash-usrs ar not xcludd from th markt. It follows that mrchants who accpt th EPI and mrchants who do not accpt th EPI choos th sam pric. This nabls us to driv th EPI accptanc condition. Lmma 1 Each monopolistic mrchant maximiss its pro t by stting p = v. Proof. Appndix B. W ar now abl to driv th condition undr which a mrchant accpts th lctronic paymnt instrumnt. A mrchant accpts th EPI if h maks mor pro t by doing so, that is if v d + D B (f + B (1 q)xl)(b x(1 q)l m C ( )) v d. inc D B (f + B (1 q)xl) 0, this condition is quivalnt to b x(1 q)l m C ( ) 0. (2) Not that a mrchant dos not accpt th EPI if th mrchant f is high or if th amount of th xpctd fraud loss is high Invstmnt in fraud dtction tchnologis A mrchant that accpts th EPI can invst in fraud dtction tchnologis. Th amount of invstmnt in fraud dtction tchnologis, which w dnot by, maximiss th mrchant s pro t undr th constraint that th mrchant accpts th EPI. Lmma 2 If th mrchant f is not too high, all mrchants such that b b ( ; B ; x; L; m; f) accpt th lctronic paymnt instrumnt, whr b ( ; B ; x; L; m; f) 2 b ; b. Th pro t maximising invstmnt for a mrchant who accpts th EPI solvs xl dq d C( 0 ) = [b x(1 q)l m C ( )] Bj ; (3) 10

11 whr B = dd B=d D B = ort. dnots th lasticity of th consumr s dmand to th invstmnt Proof. Appndix C. Th mrchant chooss its fraud prvntion ort so as to qualiz th marginal bn ts of invstmnts in fraud dtction tchnologis and th marginal cost of invstmnts. Th marginal bn ts of invstmnts ar qual to th marginal gains from lowr xpctd fraud losss (trm xl(dq=d ) in (3)), and to th marginal bn ts that ar du to an incras in th volum of lctronic transactions (trm [b x(1 q)l m C ( )] ( Bj = ) in (3)). Lt us dtail ach of th two cts that will b rfrrd to as th xpctd loss ct and th transaction volum ct. First, if th mrchant invsts in fraud dtction tchnologis, this incrass th probability that a fraudulnt transaction is dtctd, and thrfor, this rducs th amount of th xpctd loss that h has to bar whn h accpts th EPI. Th xpctd loss ct has a positiv impact on mrchant s invstmnts. cond, if consumrs bar a positiv shar of fraud losss, th probability that a consumr wishs to us th lctronic paymnt instrumnt is impactd positivly by th mrchant s invstmnts, as th xpctd loss dcrass. Th transaction volum ct has also a positiv impact on mrchant s invstmnts. Rmark that, bcaus of th transaction volum ct (if B 6= 0), th mrchants invst in fraud prvntion tchnologis vn if thy bar no liability for fraud, that is if = 0. In two-sidd markts, th liability rgim is not th only incntiv that can b usd to ncourag mrchant invstmnt, as mrchants car about th transaction volum, which is rlatd to consumr dmand. This ct is not prsnt in th litratur on law and conomics that w mntiond in sction 2. Not also that mrchants xrt a positiv xtrnality on th paymnt platform and on consumrs if B 6= 0, bcaus thir invstmnt in fraud dtction tchnologis rducs th amount of thir xpctd fraud loss. If B = 0, th zro liability rul applis for consumrs. In this cas, all mrchants who accpt th EPI invst th sam amount in fraud dtction tchnologis, which is implicitly d nd by xl dq d = C( 0 ) (4) As invstmnts do not impact consumr dmand, th transaction volum ct is null undr th zro liability rul. A mrchant who obtains a highr transaction bn t dos not hav highr invstmnt incntivs, as th marginal bn ts obtaind through a highr transaction volum ar qual to zro. 11

12 4.2.3 Comparativ statics In Lmma 3, w giv som comparativ statics to xplain how a mrchant s invstmnt in fraud dtction tchnologis vary with th transaction fs, th liability lvls and th bn t that a mrchant obtains of bing paid with th lctronic paymnt instrumnt. Lmma 3 If B > 0, th mrchant s invstmnts in fraud dtction tchnologis incras with th consumr liability, th consumr transaction f, th mrchant s transactional bn t, and th mrchant s liability, but thy dcras with th mrchant f. Proof. Appndix D. W provd in Lmma 2 that a mrchant s invstmnts in fraud dtction tchnologis ar chosn such that th marginal bn ts ar qual to th marginal costs of invstmnts. If th mrchant f incrass (rsp. if th mrchant s transactional bn t incrass), all othr things bing qual, th marginal bn ts from invstmnt dcras, bcaus of a rduction of th transaction volum ct. Th mrchant racts by rducing its invstmnts in fraud dtction tchnologis. If th mrchant s liability incrass, this incrass th xpctd loss ct, bcaus th mrchant has mor to sav whn a fraud is dtctd, whras this dcrass th transaction volum ct, as th mrchant s margin pr transaction is rducd. Undr Assumption (A2), th rst ct dominats and th mrchant racts by incrasing its invstmnts in fraud dtction tchnologis. Morovr, if th consumr liability incrass or if th consumr f incrass, this incrass th transaction volum ct, bcaus th impact of mrchant s invstmnts on consumr dmand incras. Thrfor, th mrchant s invstmnts incras. If th zro liability rul applis, from (4), th mrchant s invstmnts in fraud dtction tchnologis do not dpnd on th transaction fs that ar chosn by th paymnt platform. Thy only dpnd on th mrchant s liability and th xpctd loss. As whn B > 0, thy dcras with th mrchant s liability and it can b shown that thy dcras with th xpctd fraud loss. In Lmma 4, w dtrmin how th transaction fs and th liability lvls impact th probability that a mrchant accpts th lctronic paymnt instrumnt. Lmma 4 Th probability that a mrchant accpts th EPI dcrass with th mrchant f, with th consumr f and with th lvl of liability that is born by mrchants or by consumrs. Proof. Appndix E. 12

13 A highr mrchant f lowrs th transaction margin that th mrchant obtains if h accpts th EPI, whras it rducs th mrchant s incntivs to accpt th EPI, which is a standard ct in th litratur on paymnt cards. Morovr, in our modl, th probability that a mrchant accpts th EPI also dpnds on th consumr f, bcaus mrchants xrt a positiv xtrnality on consumrs whn thy choos to invst in fraud dtction tchnologis. Indd, this intraction, which is novl in th litratur on paymnt platforms, ariss whn B 6= 0 and this is spci c to our modl stting. Finally, a highr consumr f dcrass th probability that a consumr wishs to us th EPI, which rducs th marginal bn ts of invsting in fraud dtction tchnologis and th bn ts of accpting th EPI for th mrchant. Thrfor, th probability that a mrchant accpts th EPI dcrass with th consumr f. Most importantly, our modl is th rst to highlight th impact of liability rgims on mrchants accptanc of paymnt mdia. W show in Appndix E that th lvl of liability has an ambiguous impact on mrchants choic to accpt th lctronic paymnt instrumnt. On th on hand, a highr liability lvl incrass th loss in cas of a fraudulnt us of th EPI, which discourags mrchants to accpt th EPI. On th othr hand, it incrass th lvl of ort mad by mrchants, which rducs th probability that th EPI is fraudulntly usd - and thus incrass th probability that a consumr wishs to us th EPI. From assumption (A2), th rst ct dominats in our framwork, and thrfor, th probability that a mrchant accpts th EPI dcrass with his liability lvl. 4.3 tag 1 Prics and liability lvls At th rst stag, th paymnt platform choss th prics that maximis its pro t, P = (f + m c)v P EL P, whr V P dnots th transaction volum, as follows V P = Z bs EL P dnots th avrag xpctd loss, or cb h(b )(1 H B (f + B xl(1 q ))db ; (5) and Z bs EL P = P xl (1 cb q )h(b )(1 H B (f + B xl(1 q )))db ; (6) q = q( ). 13

14 If B = 0, as q dos not dpnd on b, w hav EL P = P xl(1 q )V P (7) Not that, for all B 2 [0; 1], th transaction volum dcrass with th consumr transaction f and with th mrchant f. Whil this ct is standard in th litratur, anothr qustion ariss in our framwork, that is th impact of th transaction prics and th mrchants liability on th xpctd fraud loss that is born by th paymnt platform Variations of th xpctd loss with th prics W start by dtrmining how th xpctd fraud loss is impactd by th choic of transaction fs and by th lvl of liability that is born by mrchants. Proposition 1 Th xpctd loss incurrd by th paymnt platform on fraudulnt transactions (EL P ) dcrass with th consumr transaction f and with th lvl of liability that is born by mrchants. EL P dcrass with th mrchant f only if th lasticity of th mrchant s ort to th mrchant f is small or if th lasticity of th mrchant s dmand to th mrchant f is high. Proof. Appndix F. An incras in th consumr f dcrass th numbr of mrchants who accpt th EPI, whras it incrass mrchants invstmnts in fraud dtction tchnologis. It follows that a highr consumr f dcrass th xpctd loss that is incurrd by th paymnt platform. Morovr, a highr lvl of liability for mrchants dcrass th xpctd loss that is born by th paymnt platform, as it dcrass mrchants accptanc of th EPI, whras it incrass mrchants invstmnt in fraud dtction tchnologis. An incras in th mrchant f has two cts on th xpctd loss that is incurrd by th paymnt platform. Th highr th mrchant f, th lowr th numbr of mrchants who accpt th EPI, and th lowr th transaction volum. This ct rducs th xpctd loss that is incurrd by th paymnt platform. At th sam tim, a highr mrchant f dcrass th mrchants invstmnt in fraud dtction tchnologis, which incrass th xpctd loss that is born by th paymnt platform. Th impact of an incras in th mrchant f on th xpctd loss dpnds on how both cts compnsat ach othr Th pro t maximising pric structur Proposition 2 givs th pro t maximising pric structur for a givn lvl of mrchants liability. 14

15 Proposition 2 Th pro t maximising pric structur r cts th platform s trad-o btwn balancing pro ts btwn both sids of th markt and minimizing th xpctd loss on fraudulnt transactions. Th total pric is implicitly d nd by f + m f c = 1 " V B (f) P P ; and th pric structur vri s f m = 1 " V (m) P P 1 " V B (f) P P whr " V B (f) = P P ) and " V (m) = P P ) dnot th lasticity of th transaction volum to th consumr f and th mrchant f rspctivly. ; Proof. W dnot by M P = f + m c th paymnt platform s gross margin. Assum that thr is an intrior solution. olving for th rst-ordr conditions of pro t maximisation = M + V = 0; = P + V = 0 Ths quations can b rwrittn as f + m f c = V P P P ; (8) and f + m m c = V P P P P (9) Introducing th lasticitis " V B (f) = P P ) and " V (m) = P P ) and dividing th rst quation by th scond quation yilds th rsult of Proposition 2. In Appndix G-A, w show that th scond-ordr conditions of pro t maximisation ar vri d if B = 0. It is intrsting to compar th prics that w nd in an intrior solution with th prics obtaind in th standard two-sidd markt monopoly pricing formula obtaind by Rocht and Tirol (2003). Equations (8) and (9) show that with rspct to th standard pric structur in two-sidd markts, th pric structur that w obtain ncompasss an additional trm that taks into account th platform s trad-o btwn maximising its pro t and minimizing th 15

16 xpctd loss on fraudulnt transactions. Notic that if th zro liability rul applis for consumrs (that is if B = 0), from (7), th xpctd loss only dpnds on th transaction prics through th transaction volum. It follows that, in this cas, th pric structur is th sam as th on obtaind by Rocht and Tirol (2003), that is f m = "V B (f) " V (m); and th total pric is implicitly d nd by f + m c (1 )xl(1 q ) f = 1 " V B (f) For instanc, if B = 0, with uniforms distribution on [0; 1] for b B and b, with a cost function C ( ) = k( ) 2 =2, with q( ) = and c = 0, w prov in Appndix H that th pro t maximising transaction fs ar m = 1 + xl(1 3 ) + (xl)2 (2 2 ) k ; (10) 3 and f = 1 + xl + (2 2 )(xl) 2 2k 3 Not that th consumr f is highr than th mrchant f if 6= 0, as w hav f m = xl 1 q xl (11) 2k If th dmands ar uniform and symmtric, in th standard cas of th litratur on paymnt cards, th pro t maximising transaction fs ar such that f = m. Equation (11) shows that, if > 0, th paymnt platform tnds to lowr th mrchant f to provid mrchants with incntivs to invst in fraud dtction tchnologis. Th pric structur changs in favor of mrchants. This is not ncssarily th cas if dmands ar not symmtric, or if B 6= 0. If B 6= 0, th paymnt platform can us th transaction prics on both sids of th markt to ncourag mrchants to invst in fraud dtction tchnologis, bcaus of th transaction volum ct that w highlightd in Lmma 2. 16

17 4.3.3 Th pro t maximising lvl of liability W hav assumd that th paymnt platform has th opportunity to choos th mrchant s lvl of liability at th sam stag as th transaction prics. Thus, w start by dtrmining how th mrchant s lvl of liability impacts th plaform s pro t. W know from Proposition 1 that th xpctd loss that is born by th paymnt platform dcrass with th lvl of liability born by mrchants. It rmains to study how th lvl of liability born by mrchants impacts th transaction volum. W b h b b )(1 H B (f + B xl(1 q ))) {z } Trm I Z bs + h (b B(f + B xl(1 q )) db {z } Trm II Th rst trm of (12) is ngativ. It r cts th fact that fwr mrchants accpt th EPI whn th lvl of liability that is born by mrchants incrass. Th scond trm of (12) is positiv. It shows that mor consumrs wish to pay with th EPI whn mrchants invst in fraud dtction tchnologis. It follows that a highr lvl of liability for mrchants has an ambiguous impact on th transaction volum. Not that if th lasticity of th mrchants dmand to thir liability lvl is small (that is, if trm I is small), th transaction volum may incras with th mrchants lvl of liability. Morovr, if th zro liability rul applis for consumrs, th scond trm of (12) is null, and th transaction volum dcrass with th mrchant s lvl of liability. Proposition 3 givs th pro t maximising lvl of liability for mrchants. (12) Proposition 3 A monopolistic paymnt platform chooss a lvl of liability for mrchants that r cts a trad-o btwn minimizing th xpctd loss on fraudulnt transactions and maximising th transaction volum. Th intrior solution for th pro t maximising lvl of liability for mrchants solvs (f + m If th transaction volum incrass with th liability lvl that is born by mrchants, thr is a cornr solution such that th paymnt platform lts th mrchants bar all th losss. Proof. Th paymnt platform chooss th lvl of liability that maximiss its pro t. olving for th rst-ordr condition of pro t maximisation = (f + m P 17

18 In an intrior solution, w hav (f + m From Proposition 1, w know that th xpctd loss dcrass with th lvl of liability that is born by th mrchants. It follows that, if th transaction volum incrass with th lvl of liability born by mrchants, th pro t maximising liability lvl is a cornr solution, with th mrchants baring th maximum shar of th loss. In Appndix G-B, w show that th scond-ordr conditions of pro t maximisation ar vri d if B = 0. Proposition 3 shows that th paymnt platform has an incntiv to shar th losss on fraudulnt transactions with th mrchants, as this ncourags mrchants to accpt th lctronic paymnt instrumnt, unlss mrchants dmand is inlastic to th lvl of liability. Howvr, th choic of a liability rgim is also a mans for th paymnt platform to xtract rnts from mrchants if th lasticity of th mrchants dmand to th liability lvl is small. In Appndix H, w prov that, if B = 0, with uniforms distribution on [0; 1] for b B and b, with a cost function C ( ) = k( ) 2 =2, and a dtction probability q( ) =, th pro t maximising lvl of liability for mrchants is qual to 1 This rsult is not gnral undr th zro liability rul. In othr cass, th liability for fraud is shard btwn th platform and th mrchants Wlfar maximising liability lvls To study wlfar maximizing liability lvls, w assum that th mrchant s lvl of liability is dcidd by a social plannr at th rst stag, who maximiss th sum of th platform s pro t, th consumr surplus and th mrchant surplus. Thn, th paymnt platform chooss th transaction fs at th following stag. Our aim is to compar th pro t maximising lvl of liability for mrchants, which is chosn by th paymnt platform, to th wlfar maximising lvl of liability for mrchants. W start by analyzing th simpl cas in which consumrs bar zro liability on fraudulnt transactions. 20 For this purpos, w nd to dtrmin how th liability lvl that is born by mrchants impacts th transaction fs that ar chosn by th paymnt platform. 19 A gnral rsult undr th zro liability rul is that th paymnt platform chooss th lvl of liability for mrchants that maximiss th probability of fraud dtction ( Appndix G-B). 20 In th futur, our analysis will b xtndd to th cas in which consumrs bar som rsponsibility for fraud. 18

19 Lmma 5 If th zro liability rul applis for consumrs, th transaction fs chosn by th paymnt platform dcras with th lvl of liability that is born by mrchants. Proof. Appndix I-A and I-B. Whn th lvl of liability that is born by mrchants incrass, this has two cts on th paymnt platform s pro t. First, this rducs th shar of th xpctd loss that is born by th paymnt platform, which amounts to a rduction of its marginal cost. Th paymnt platform may dcid to pass through this marginal cost rduction to th usrs by rducing th transaction fs. cond, mrchants invst mor in fraud prvntion tchnologis, which rducs th amount of th xpctd loss that is born by th paymnt platform for ach transaction. This ct can b rinforcd if th paymnt platform dcids to rduc th transaction fs paid by th usrs, as this incrass th transaction volum. Thrfor, if th lvl of liability that is born by mrchants incrass, th paymnt platform has an incntiv to lowr th transaction fs on both sids of th markt. Th paymnt platform loss som rnts from th transaction fs, but this loss is compnsatd by highr rnt xtraction through th liability rgim, which ncourags mrchant invstmnt. W ar now abl to compar th pro t maximising lvl of liability and th wlfar maximising lvl of liability for mrchants if consumrs do not bar any liability for fraudulnt transactions. W assum that social wlfar is a concav function of th transaction fs. 21 Proposition 4 Undr th zro liability rul for consumrs, if social wlfar is a concav function of, th pro t maximising lvl of liability for mrchants is lowr than (or qual to) th wlfar maximising lvl of liability. Proof. Appndix J-B. W showd in Proposition 5 that th transaction fs paid by th usrs dcras with th lvl of liability that is born by mrchants. A dirct consqunc of Proposition 5 is that consumr and mrchant surplus incras whn mrchants liability incras. It follows that, from th point of viw of total usr surplus maximisation, it is socially optimal to lt th mrchants bar th maximum liability on fraudulnt transactions. Howvr, if th rgulator taks into account th paymnt platform s pro t, th wlfar maximising lvl of liability for mrchants is not ncssarily qual to on. 21 W is concav in for instanc if b and b B ar uniformly distributd on [0; 1] undr som assumptions about th cost of fraud prvntion and th snsitivity of th dtction probability which ar prcisd in Appndix J. In gnral, it is possibl to prov that P is concav in, howvr, th total usr surplus is not ncssarily concav in. 19

20 Th paymnt platform dos not plac nough liability on mrchants to maximis social wlfar, xcpt in th cas whr it is maximiss its pro t by ltting th mrchants bar th maximum liability on fraudulnt transactions. This is bcaus th paymnt platform intrnalizs imprfctly th impact of th liability rgims on consumr and mrchant surplus. Not that this rsult is drivn by th assumption that th probability to dtct a fraudulnt transaction only dpnds on mrchants invstmnt. Th rsult could chang if th invstmnts wr shard by th paymnt platform and by th mrchants. 6 Th rol of intrchang fs In this sction, w xamin an important rgulatory challng, which is th impact of mrchant liability on th lvl of intrchang fs. 22 This issu has bn xamind in th Unitd-tats aftr th vot of th Dodd-Frank act in July 2010, which givs to th Fdral Rsrv Board th powr to rgulat intrchang fs on dbit card transactions. Among th rgulatory ruls, th "fraud adjustmnt rulmaking" provids th Board with th opportunity to assss how card ntworks authorization choics and fraud procdurs may burdn th mrchant community and potntially incras th volum of dbit card fraud. Th rulmaking also givs th Board th opportunity to promot th us of th fraud adjustmnt mchanism as a mans of crating incntivs for banks and mrchants to migrat to mor ctiv fraud dtction tchnologis. To study this issu, w modify our modl stting, by making th standard assumption that th paymnt platform is now composd of imprfctly comptitiv issurs and prfctly comptitiv acquirrs. 23 W also assum for simplicity of th modl that consumrs bar no liability on fraudulnt transactions ( B = 0). Th issurs charg a f f (c I a) to th consumrs, whras th acquirrs charg mrchants with thir prcivd marginal cost, that is m = a+c A. As in th litratur, w mak th standard assumption that f is dcrasing with a, and that th pass-through rat is lowr than on, that 1. At th rst stag of th gam, th paymnt platform chooss th lvl of intrchang f that maximiss banks joint pro t. Thn banks choos th transaction prics, mrchants invst in fraud dtction tchnologis and consumrs mak thir paymnts dcisions. W dnot th pro t maximising intrchang f by a P, and study how th pro t maximising intrchang f is impactd by th lvl of liability that is born by mrchants. Proposition 5 If th issurs ar imprfctly comptitiv and if th acquirrs ar prfctly comptitiv, th pro t maximising intrchang f dcrass with th lvl of liability that is born 22 Intrchang fs ar paid by th acquiring bank to th issuing bank ach tim a consumr maks a transaction. 23 For instanc, this assumption is also mad in Rocht and Tirol (2002). 20

21 by mrchants. Proof. Appndix K. Proposition 4 has important implications for rgulatory dcisions about intrchang fs. It mans that, if mrchants bar a highr shar of th loss on fraudulnt transactions, th pro t maximising intrchang f bcoms lowr. Th rsult of Proposition 4 may chang if consumrs ar hld liabl for fraudulnt transactions. In this cas, mrchants invstmnts ar impactd by th transaction fs and by th intrchang f that is chosn by th paymnt platform. Th paymnt platform may dcid ithr to lowr or to incras th intrchang f to provid mrchants with incntivs to incras thir invstmnt in fraud dtction tchnologis, dpnding on th rlativ importanc of th xpctd loss ct and th transaction volum ct that w highlightd in Lmma 2. Anothr intrsting aspct of th problm is that rgulators may wish to x a maximum lvl for th intrchang f, but th paymnt platform can ract by adjusting th lvl of liability that is born by mrchants for fraudulnt transactions. In Appndix K, w show in a simpl xampl that, if th rgulator chooss a low lvl for th intrchang f, th paymnt platform racts by choosing a high lvl of liability for mrchants, which may not b dsirabl from th point of viw of social wlfar. 7 Platform s invstmnts W analyz if our wlfar rsult undr th zro liability rul holds in an xtnsion of th modl that allows th paymnt platform to invst. W assum that th paymnt platform invsts an amount P in fraud dtction tchnologis, which costs C P ( P ) pr transaction, whr C P is a convx cost function. Th probability to dtct a fraudulnt transaction, which w dnot by q( ; P ), incrass with th platform s invstmnts, that is P 0. Th platform chooss its lvl of invstmnt at th sam stag as th prics, and mrchants ar abl to obsrv this dcision bfor dciding on whthr or not to accpt th lctronic paymnt instrumnt. In a supplmntary not, which is availabl upon authors rqust, w show that th wlfar rsult obtaind undr th zro liability rul dos not hold whn th platform s invstmnts ar takn into account. 24 This is bcaus th prics chosn by th paymnt platform do not ncssarily dcras with th lvl of liability born by mrchants. Th intuition of this rsult is th following. Th platform now trads o btwn ncouraging th mrchants to invst in fraud dtction tchnologis and choosing to mak itslf th fraud 24 Excpt in th cas whr th platform s cost function is linar and if th dtction probability is linar in th platform s invstmnt ort. 21

22 prvntion ort. Th rsult of this trad-o is impactd by th rlativ cost of invstmnt for th platform and th mrchants, and by th fact that thir tchnological choics may b ithr indpndnt or may in unc ach othr. 7.1 Indpndnt invstmnts W start by analyzing th cas in which th mrchant s invstmnts and th platform s invstmnt ar b indpndnt. This cas can b illustratd by assuming for instanc that q( ; P ) is linar and sparabl in and P, that is q( ; P ) = d + h P ; whr d 0 and h 0. To undrstand bttr th impact of th platform s invstmnts on our wlfar rsult undr th zro liability rul for consumrs, w spcify quadratic invstmnt cost functions for th mrchants and th platform, such that C ( ) = k ( ) 2 =2 and C P ( P ) = k P ( P ) 2 =2, whr k 0 and k P 0. W also assum uniform distributions on [0; 1] for b and b B. Undr ths assumptions, at th quilibrium of stag 2, ach mrchant invsts an amount = dlpx =k in fraud dtction tchnologis. At stag 1, th prics chosn by th platform ar f = 1 3 (1 + c + Lx) k P 6 ( P ) 2 k 6 ( ) 2 2 ; m = 1 3 (1 + c + Lx(1 3 )) k P 6 ( P ) 2 (1 6 ) k 6 ( ) ; whr ( P ) = hlp=k P dnots th optimal invstmnt of th platform. Not that this illustration shows that th consumr f is not ncssarily highr than th mrchant f, unlik our prvious xampl with uniform distributions undr th zro liability rul. = d2 L 2 x 2 (1 ) 3k ; = xl 3k P k 2k (h 2 xl k P ) + d 2 k P xl (14) From (13), th consumr f dcrass with th lvl of liability born by mrchants, whras from (14), th mrchant f incrass with th lvl of liability born by mrchants if th invstmnt cost of th platform is high and if th mrchants contribution to incras th dtction probability is small (through th paramtr d). This rsult can b xplaind as follows. A highr lvl of liability for mrchants has two cts on th platform s incntivs to 22

23 invst in fraud dtction tchnologis. First, it dcrass mrchants accptanc, which rducs th marginal bn ts of invsting in fraud dtction tchnologis for th paymnt platform. cond, it rducs fraud losss, which amounts to a rduction of th platform s marginal cost. This ct impacts th platform s invstmnts in two opposit dirctions. On th on hand, it dcrass th platform s incntivs to invst, as th platform bars a lowr shar of fraud losss. On th othr hand, it incrass th platform s margin pr transaction, which can rsult in highr invstmnt incntivs. From th point of viw of mrchants, an incras in thir liability raiss th valu of th platform s invstmnts, as this improvs th quality of srvic providd by th platform. Th paymnt platform trads o btwn xtracting this additional surplus from th mrchants through th mrchant f and incrasing th transaction volum through lowr fs. Th variation of th mrchant f with th mrchants shar of fraud losss r cts this trad-o, which is not prsnt on th consumr sid. 7.2 Rlatd invstmnts W now analyz th cas in which th platform s dcision to invst in fraud dtction tchnologis impacts positivly th mrchant s invstmnt ort. This cas can b illustratd by assuming for instanc that q( ; P ) is a product of th mrchant s invstmnt ort and th platform s invstmnt ort, that is q( ; P ) = d P + h P ; whr d 0 and h 0. At th quilibrium of stag 2, th mrchant s invstmnts in fraud dtction tchnologis ar positivly rlatd to th platform s prvntion ort, and w hav = d P xl =k. Thrfor, th platform taks into account this ct in its trad-o btwn ncouraging mrchants invstmnts and choosing to bar itslf th fraud prvntion ort. At stag 1, th platform chooss th transaction fs f = 1 3 (1 + c + Lx) hlx P 6 ; m = 1 3 (1 + c + Lx(1 3 )) + k 2 ( ) 2 hlx 3 P (1 3 ) + hlx P ; 6 whr P = hk Lx=(k P k d 2 L 2 x 2 (2 )). Not that th platform s lvl of invstmnt incrass with th shar of liability born by mrchants. This rsult can b xplaind as follows. An incras in th lvl of liability born by mrchants amounts to a rduction of th platform s marginal cost, which rsults in highr invstmnt incntivs for th platform. A highr lvl of liability also raiss th impact of th platform s ort on mrchants invstmnt incntivs, 23

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc

More information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse Selection and Moral Hazard in a Model With 2 States of the World Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,

More information

Question 3: How do you find the relative extrema of a function?

Question 3: How do you find the relative extrema of a function? ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating

More information

Foreign Exchange Markets and Exchange Rates

Foreign Exchange Markets and Exchange Rates Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE METHODS CLASSES WEEK SEVEN QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.

More information

Expert-Mediated Search

Expert-Mediated Search Exprt-Mdiatd Sarch Mnal Chhabra Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA chhabm@cs.rpi.du Sanmay Das Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA sanmay@cs.rpi.du David

More information

Rural and Remote Broadband Access: Issues and Solutions in Australia

Rural and Remote Broadband Access: Issues and Solutions in Australia Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity

More information

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 08-16-85 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book. Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs

More information

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity

More information

Performance Evaluation

Performance Evaluation Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism

More information

Electronic Commerce. and. Competitive First-Degree Price Discrimination

Electronic Commerce. and. Competitive First-Degree Price Discrimination Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg

More information

Statistical Machine Translation

Statistical Machine Translation Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) 92.222 - Linar Algbra II - Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial

More information

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers) Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly

More information

IMES DISCUSSION PAPER SERIES

IMES DISCUSSION PAPER SERIES IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003-E-13

More information

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D

Remember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D 24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd

More information

(Analytic Formula for the European Normal Black Scholes Formula)

(Analytic Formula for the European Normal Black Scholes Formula) (Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually

More information

Basis risk. When speaking about forward or futures contracts, basis risk is the market

Basis risk. When speaking about forward or futures contracts, basis risk is the market Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also

More information

Lecture 3: Diffusion: Fick s first law

Lecture 3: Diffusion: Fick s first law Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th

More information

Gold versus stock investment: An econometric analysis

Gold versus stock investment: An econometric analysis Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin

More information

Economic Insecurity, Individual Behavior and Social Policy

Economic Insecurity, Individual Behavior and Social Policy Economic Inscurity, Individual Bhavior and Social Policy By Indrmit S. Gill igill@worldbank.org and Nadm Ilahi nilahi@worldbank.org Th World Bank Washington, DC 20433 First Draft: March 27, 2000 Papr writtn

More information

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13 Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

Asset set Liability Management for

Asset set Liability Management for KSD -larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv

More information

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

The Constrained Ski-Rental Problem and its Application to Online Cloud Cost Optimization

The Constrained Ski-Rental Problem and its Application to Online Cloud Cost Optimization 3 Procdings IEEE INFOCOM Th Constraind Ski-Rntal Problm and its Application to Onlin Cloud Cost Optimization Ali Khanafr, Murali Kodialam, and Krishna P. N. Puttaswam Coordinatd Scinc Laborator, Univrsit

More information

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through Liquidity and Information-Basd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among

More information

Theoretical aspects of investment demand for gold

Theoretical aspects of investment demand for gold Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is

More information

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms

Analyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas

More information

Efficiency Losses from Overlapping Economic Instruments in European Carbon Emissions Regulation

Efficiency Losses from Overlapping Economic Instruments in European Carbon Emissions Regulation iscussion Papr No. 06-018 Efficincy Losss from Ovrlapping Economic Instrumnts in Europan Carbon Emissions Rgulation Christoph Böhringr, Hnrik Koschl and Ulf Moslnr iscussion Papr No. 06-018 Efficincy Losss

More information

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif

More information

Parallel and Distributed Programming. Performance Metrics

Parallel and Distributed Programming. Performance Metrics Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:

More information

High Interest Rates In Ghana,

High Interest Rates In Ghana, NO. 27 IEA MONOGRAPH High Intrst Rats In Ghana, A Critical Analysis IEA Ghana THE INSTITUTE OF ECONOMIC AFFAIRS A Public Policy Institut High Intrst Rats In Ghana, A Critical Analysis 1 by DR. J. K. KWAKYE

More information

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives. Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud

More information

STATEMENT OF INSOLVENCY PRACTICE 3.2

STATEMENT OF INSOLVENCY PRACTICE 3.2 STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr

More information

Key Management System Framework for Cloud Storage Singa Suparman, Eng Pin Kwang Temasek Polytechnic {singas,engpk}@tp.edu.sg

Key Management System Framework for Cloud Storage Singa Suparman, Eng Pin Kwang Temasek Polytechnic {singas,engpk}@tp.edu.sg Ky Managmnt Systm Framwork for Cloud Storag Singa Suparman, Eng Pin Kwang Tmask Polytchnic {singas,ngpk}@tp.du.sg Abstract In cloud storag, data ar oftn movd from on cloud storag srvic to anothr. Mor frquntly

More information

A Theoretical Model of Public Response to the Homeland Security Advisory System

A Theoretical Model of Public Response to the Homeland Security Advisory System A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial

More information

Incomplete 2-Port Vector Network Analyzer Calibration Methods

Incomplete 2-Port Vector Network Analyzer Calibration Methods Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar

More information

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009 Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft

More information

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s1660-015-0741-1 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans Wi-Mao Qian

More information

Constraint-Based Analysis of Gene Deletion in a Metabolic Network

Constraint-Based Analysis of Gene Deletion in a Metabolic Network Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany

More information

Increasing Net Debt as a percentage of Average Equalized ValuaOon

Increasing Net Debt as a percentage of Average Equalized ValuaOon City of Orang Township Warning Trnd: Incrasing Nt Dbt as a prcntag of avrag qualizd valuation Nt Dbt 3 yr. Avg. qualizd Valuation Incrasing Nt Dbt as a prcntag of Avrag Equalizd ValuaOon rc 1.20% 1.00%

More information

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost

Improving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 50-54 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin

More information

A Project Management framework for Software Implementation Planning and Management

A Project Management framework for Software Implementation Planning and Management PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company

More information

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst RACSAM Rv. R. Acad. Cin. Sri A. Mat. VO. 103 2, 2009, pp. 373 385 Matmática Aplicada / Applid Mathmatics Th pric of liquidity in constant lvrag stratgis Marcos Escobar, Andras Kichl, uis Sco and Rudi Zagst

More information

Use a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects

Use a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a high-lvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End

More information

Production Costing (Chapter 8 of W&W)

Production Costing (Chapter 8 of W&W) Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary

More information

Important Information Call Through... 8 Internet Telephony... 6 two PBX systems... 10 Internet Calls... 3 Internet Telephony... 2

Important Information Call Through... 8 Internet Telephony... 6 two PBX systems... 10 Internet Calls... 3 Internet Telephony... 2 Installation and Opration Intrnt Tlphony Adaptr Aurswald Box Indx C I R 884264 03 02/05 Call Duration, maximum...10 Call Through...7 Call Transportation...7 Calls Call Through...7 Intrnt Tlphony...3 two

More information

A Secure Web Services for Location Based Services in Wireless Networks*

A Secure Web Services for Location Based Services in Wireless Networks* A Scur Wb Srvics for Location Basd Srvics in Wirlss Ntworks* Minsoo L 1, Jintak Kim 1, Shyun Park 1, Jail L 2 and Sokla L 21 1 School of Elctrical and Elctronics Enginring, Chung-Ang Univrsity, 221, HukSuk-Dong,

More information

REPORT' Meeting Date: April 19,201 2 Audit Committee

REPORT' Meeting Date: April 19,201 2 Audit Committee REPORT' Mting Dat: April 19,201 2 Audit Committ For Information DATE: March 21,2012 REPORT TITLE: FROM: Paul Wallis, CMA, CIA, CISA, Dirctor, Intrnal Audit OBJECTIVE To inform Audit Committ of th rsults

More information

Architecture of the proposed standard

Architecture of the proposed standard Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th

More information

HSBC Bank International Expat Explorer Survey 08

HSBC Bank International Expat Explorer Survey 08 HSBC Bank Intrnational Expat Explorr Survy 08 Rport On: Expat Existnc Th Survy Th Expat Explorr survy qustiond 2,155 xpatriats across four continnts about th opportunitis and challngs thy fac. Th survy

More information

7 Timetable test 1 The Combing Chart

7 Timetable test 1 The Combing Chart 7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing

More information

A copy of the Consultation Paper is in the Members Library and further details are available at www.scotland~qov.umpublications/2012/12/5980

A copy of the Consultation Paper is in the Members Library and further details are available at www.scotland~qov.umpublications/2012/12/5980 To: CORPORATE SERVICES COMMITTEE NORTH LANARKSHIRE COUNCIL REPORT Subjct: CONSULTATION: CIVIL LAW OF DAMAGES - ISSUES IN PERSONAL INJURY From: HEAD OF LEGAL SERVICES Dat: 30 JANUARY 2013 Rf: AL LE CSN

More information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 612 Metal Forming and Theory of Plasticity. 6. Strain Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.

More information

Free ACA SOLUTION (IRS 1094&1095 Reporting)

Free ACA SOLUTION (IRS 1094&1095 Reporting) Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 279-1062 ACA Srvics Transmit IRS Form 1094 -C for mployrs Print & mail IRS Form 1095-C to mploys HR Assist 360 will gnrat th 1095 s for

More information

Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling

Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling Planning and Managing Coppr Cabl Maintnanc through Cost- Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Cost-bnfit Analysis, Rliability

More information

Global Sourcing: lessons from lean companies to improve supply chain performances

Global Sourcing: lessons from lean companies to improve supply chain performances 3 rd Intrnational Confrnc on Industrial Enginring and Industrial Managmnt XIII Congrso d Ingniría d Organización Barclona-Trrassa, Sptmbr 2nd-4th 2009 Global Sourcing: lssons from lan companis to improv

More information

Development of Financial Management Reporting in MPLS

Development of Financial Management Reporting in MPLS 1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr

More information

Continuity Cloud Virtual Firewall Guide

Continuity Cloud Virtual Firewall Guide Cloud Virtual Firwall Guid uh6 Vrsion 1.0 Octobr 2015 Foldr BDR Guid for Vam Pag 1 of 36 Cloud Virtual Firwall Guid CONTENTS INTRODUCTION... 3 ACCESSING THE VIRTUAL FIREWALL... 4 HYPER-V/VIRTUALBOX CONTINUITY

More information

CARE QUALITY COMMISSION ESSENTIAL STANDARDS OF QUALITY AND SAFETY. Outcome 10 Regulation 11 Safety and Suitability of Premises

CARE QUALITY COMMISSION ESSENTIAL STANDARDS OF QUALITY AND SAFETY. Outcome 10 Regulation 11 Safety and Suitability of Premises CARE QUALITY COMMISSION ESSENTIAL STANDARDS OF QUALITY AND SAFETY Outcom 10 Rgulation 11 Safty and Suitability of Prmiss CQC Rf 10A 10A(1) Lad Dirctor / Lad Officr Rspons Impact Liklihood Lvl of Concrn

More information

Noble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions

Noble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions Valnc lctron configuration dtrmins th charactristics of lmnts in a group Nobl gas configuration Th nobl gass (last column in th priodic tabl) ar charactrizd by compltly filld s and p orbitals this is a

More information

SOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA

SOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA Intrnational Journal on Tchnical and Physical Problms of Enginring (IJTPE) Publishd by Intrnational Organization of IOTPE ISSN 077-358 IJTPE Journal www.iotp.com ijtp@iotp.com Sptmbr 015 Issu 4 Volum 7

More information

Deer: Predation or Starvation

Deer: Predation or Starvation : Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,

More information

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY 1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically

More information

Sci.Int.(Lahore),26(1),131-138,2014 ISSN 1013-5316; CODEN: SINTE 8 131

Sci.Int.(Lahore),26(1),131-138,2014 ISSN 1013-5316; CODEN: SINTE 8 131 Sci.Int.(Lahor),26(1),131-138,214 ISSN 113-5316; CODEN: SINTE 8 131 REQUIREMENT CHANGE MANAGEMENT IN AGILE OFFSHORE DEVELOPMENT (RCMAOD) 1 Suhail Kazi, 2 Muhammad Salman Bashir, 3 Muhammad Munwar Iqbal,

More information

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim

More information

OPTIONS AND FUTURES: A TECHNICAL APPRAISAL

OPTIONS AND FUTURES: A TECHNICAL APPRAISAL Pag 15 OPTIONS AND FUTURES: A TECHNICAL APPRAISAL by David J.S. Rutldg Papr prsntd to Sminar on Trading in Options: Opportunitis in th Intrnational Markt sponsord by Th Sydny Stock Exchang and Th Scuritis

More information

Essays on Adverse Selection and Moral Hazard in Insurance Market

Essays on Adverse Selection and Moral Hazard in Insurance Market Gorgia Stat Univrsity ScholarWorks @ Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc 8--00 Essays on Advrs Slction and Moral Hazard in Insuranc Markt

More information

In the first years of the millennium, Americans flocked to Paris to enjoy French

In the first years of the millennium, Americans flocked to Paris to enjoy French 14 chaptr Exchang Rats and th Forign Exchang Markt: An Asst Approach 320 In th first yars of th millnnium, Amricans flockd to Paris to njoy Frnch cuisin whil shopping for dsignr clothing and othr spcialtis.

More information

Category 7: Employee Commuting

Category 7: Employee Commuting 7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil

More information

Government Spending or Tax Cuts for Education in Taylor County, Texas

Government Spending or Tax Cuts for Education in Taylor County, Texas Govrnmnt Spnding or Tax Cuts for Education in Taylor County, Txas Ian Shphrd Abiln Christian Univrsity D Ann Shphrd Abiln Christian Univrsity On Fbruary 17, 2009, Prsidnt Barack Obama signd into law th

More information

Media Considerations Related to Puerto Rico s Fiscal Situation

Media Considerations Related to Puerto Rico s Fiscal Situation CUNY Graduat School of Journalism Jun, Mdia Considrations Rlatd to Purto Rico s Fiscal Situation Alan Schankl Managing Dirctor Municial Stratgy and Rsarch Economy is Stagnant and Dbt Continus to Grow.%.%.%

More information

The Normal Distribution: A derivation from basic principles

The Normal Distribution: A derivation from basic principles Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn

More information

IBM Healthcare Home Care Monitoring

IBM Healthcare Home Care Monitoring IBM Halthcar Hom Car Monitoring Sptmbr 30th, 2015 by Sal P. Causi, P. Eng. IBM Halthcar Businss Dvlopmnt Excutiv scausi@ca.ibm.com IBM Canada Cloud Computing Tigr Tam Homcar by dfinition 1. With a gnsis

More information

HERO OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working paper 2007: 5

HERO OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working paper 2007: 5 OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: THE CASE OF MEDICAL ERRORS Svrr Grpprud Institut of Halth Managmnt and Halth Economics, Univrsity of Oslo and Norwgian Univrsity of Lif Scincs, Aas, Norway

More information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000 hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails

More information

A Note on Approximating. the Normal Distribution Function

A Note on Approximating. the Normal Distribution Function Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and

More information

User-Perceived Quality of Service in Hybrid Broadcast and Telecommunication Networks

User-Perceived Quality of Service in Hybrid Broadcast and Telecommunication Networks Usr-Prcivd Quality of Srvic in Hybrid Broadcast and Tlcommunication Ntworks Michal Galtzka Fraunhofr Institut for Intgratd Circuits Branch Lab Dsign Automation, Drsdn, Grmany Michal.Galtzka@as.iis.fhg.d

More information

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 2250-2459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt

More information

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W Cllo Tchnology LG has introducd th NON 2, with nwly dvlopd Cllo Tchnology which improvs prformanc and rliability. Up to 320W 300W Cllo Tchnology Cll Connction Elctrically Low Loss Low Strss Optical Absorption

More information

1 Walrasian Equilibria and Market E ciency

1 Walrasian Equilibria and Market E ciency 1 Walrasian Equilibria and Markt E cincy Rading in Txtbook: Chaptr 3 in Stiglitz. 1.1 Motivation Whn thinking about th rol of govrnmnt w hav to considr a numbr of rathr fundamntal qustions, such as: What

More information

Cisco Data Virtualization

Cisco Data Virtualization Cisco Data Virtualization Big Data Eco-systm Discussion with Bloor Group Bob Ev, David Bsmr July 2014 Cisco Data Virtualization Backgroundr Cisco Data Virtualization is agil data intgration softwar that

More information

Voice Biometrics: How does it work? Konstantin Simonchik

Voice Biometrics: How does it work? Konstantin Simonchik Voic Biomtrics: How dos it work? Konstantin Simonchik Lappnranta, 4 Octobr 2012 Voicprint Makup Fingrprint Facprint Lik a ingrprint or acprint, a voicprint also has availabl paramtrs that provid uniqu

More information

C H A P T E R 1 Writing Reports with SAS

C H A P T E R 1 Writing Reports with SAS C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd

More information

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doubl-sidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation

More information

NAVAL POSTGRADUATE SCHOOL

NAVAL POSTGRADUATE SCHOOL NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA MBA PROFESSIONAL REPORT Th Survivor Bnfit Plan: A Cost-Bnfit Analysis By: Advisors: Scott E. Batty, and Tho Kang Dcmbr 2007 William R. Gats, Raymond E. Franck

More information

Category 1: Purchased Goods and Services

Category 1: Purchased Goods and Services 1 Catgory 1: Purchasd Goods and Srvics Catgory dscription T his catgory includs all upstram (i.., cradl-to-gat) missions from th production of products purchasd or acquird by th rporting company in th

More information

Engineering Analytics Opportunity Preview Zinnov Report August 2013

Engineering Analytics Opportunity Preview Zinnov Report August 2013 Enginring Analytics Opportunity Prviw Zinnov Rport August 2013 Enginring Analytics: Prviw Agnda Dfinition Markt Siz Summary 2 Enginring Analytics: Prviw Agnda Dfinition Markt Siz Summary 3 Agnda 1 Enginring

More information

Vector Network Analyzer

Vector Network Analyzer Cours on Microwav Masurmnts Vctor Ntwork Analyzr Prof. Luca Prrgrini Dpt. of Elctrical, Computr and Biomdical Enginring Univrsity of Pavia -mail: luca.prrgrini@unipv.it wb: microwav.unipv.it Microwav Masurmnts

More information

Budget Optimization in Search-Based Advertising Auctions

Budget Optimization in Search-Based Advertising Auctions Budgt Optimization in Sarch-Basd Advrtising Auctions ABSTRACT Jon Fldman Googl, Inc. Nw York, NY jonfld@googl.com Martin Pál Googl, Inc. Nw York, NY mpal@googl.com Intrnt sarch companis sll advrtismnt

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER Cost-Volum-Profit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us cost-volum-profit (CVP) analysis

More information

Relationship between Cost of Equity Capital And Voluntary Corporate Disclosures

Relationship between Cost of Equity Capital And Voluntary Corporate Disclosures Rlationship btwn Cost of Equity Capital And Voluntary Corporat Disclosurs Elna Ptrova Eli Lilly & Co, Sofia, Bulgaria E-mail: ptrova.lnaa@gmail.com Gorgios Gorgakopoulos (Corrsponding author) Amstrdam

More information

Dehumidifiers: A Major Consumer of Residential Electricity

Dehumidifiers: A Major Consumer of Residential Electricity Dhumidifirs: A Major Consumr of Rsidntial Elctricity Laurn Mattison and Dav Korn, Th Cadmus Group, Inc. ABSTRACT An stimatd 19% of U.S. homs hav dhumidifirs, and thy can account for a substantial portion

More information