Optimal Pricing Scheme for Information Services


 Camilla Perkins
 3 years ago
 Views:
Transcription
1 Optml rcng Scheme for Informton Servces Shny Wu Opertons nd Informton Mngement The Whrton School Unversty of ennsylvn Eml: eyu (Shron) Chen Grdute School of Industrl Admnstrton Crnege Mellon Unversty Eml: G. Anndlngm Decson nd Informton Technologes R. H. Smth School of Busness Unversty of Mrylnd nd Opertons nd Informton Mngement The Whrton School Unversty of ennsylvn Eml: August 00
2 Optml rcng Scheme for Informton Servces Abstrct Ths pper exmnes whch, mong three commonly used prcng schemes: the fltfee, pure usgebsed nd the twoprt trff prcng, s optml for monopolst provdng nformton servces. Our nlyss suggests tht under zero mrgnl costs nd montorng costs, when customers re homogeneous or when customers hve heterogeneous mrgnl wllngness to py (whch corresponds to dfferent downwrd slopng demnd curves), fltfee prcng nd twoprt trff prcng lwys cheve the sme proft level, nd domnte usge bsed prcng. However, when customers re chrcterzed by heterogeneous mxmum consumpton levels (or usge levels), the two prt trff prcng s the most proftble mong the three. We lso exmne how senstve the optml prcng scheme s to mrgnl costs nd montorng costs. Our nlyss shows tht when mrgnl cost s below certn vlue, the flt fee prcng s the optml scheme regrdless how lrge or how smll montorng cost s (s long s t s postve) when customers re homogeneous or hve heterogeneous mrgnl wllngness to py. But s montorng cost becomes zero, the twoprt trff wll lso become one of the optml prcng schemes.
3 . Introducton The dvnce of the Internet nd other telecommuncton networks hs mde mny new nformton servces vlble. For exmple, number of softwre pplctons servces re provded by onlne Applcton Servce rovders (AS) over the Web or prvte networks for busnesses or end users. Onlne dscounted brokerge s lso n exmple of nformton servces whch end users could get ccess to over the Web. Short Messgng Servces (SMS) nd WA servces re mong the most populr servces for moble users. Moreover, s crrers roll out ther.5g nd 3G networks, host of other new servces re beng offered from moble eml to multmed messgng servces (MMS) tht represent vluble new revenue opportuntes (Mer, 00). However, these nformton servce provders generlly fce one dffculty n provdng the servces, tht s, how to prce nd bll these nformton servces (Mer, 00), whch re chrcterzed by neglgble mrgnl, dstrbuton, nd montorng cost. In ths pper we exmne the ssue of prcng nformton servces. In prtculr, we re nterested n knowng whch mong the three most populr prcng schemes used n prctce: flt fee, usgebsed nd twoprt trffs, s the best for monopolst provdng nformton servces. Whle some reserchers beleve tht reducton n montorng cost or dstrbuton cost mkes usgebsed prcng reltvely more ttrctve opton (Cho, Sthl nd Whnston, 997; Metclfe, 997), some rgue tht neglgble mrgnl producton cost mkes fltfee prcng more proftble (Fshburn, Odlyzko nd Sders, 997). There s so fr no cler gudelne bout when the nformton servce provders should dopt flt rte prcng nd when pure usgebsed prcng (wthout subscrpton fee) or even twoprt trff (usgebsed prcng plus subscrpton fee) s more proftble. Mny nformton servce provders hve struggled to fnd best wys to prce ther servces nd bll ther customers, nd ths s reflected from the non 3
4 greedupon prcng schemes offered by dfferent nformton servce provders. For exmple, Verzon Wreless, whch rolled out ts 3G Express Network n lte Jnury, 00 hs chosen flt fee prcng scheme, whle AT&T Wreless hs mplemented usgebsed prcng scheme tht bll for the mount of dt customer uses. et nother scheme dopted by NTT DoCoMo's Imode servce n Jpn chrges users $.50 monthly fee, plus 5 cents per dt pcket (one pcket s equvlent to 8 bytes of dt), s twoprt trff scheme. Outsourcng of IT servces uses both fxedfee prcng n some cses, nd usgebsed prcng wth or wthout subscrpton fees n some other cses (Gopl et l., 00). For exmple, the newly sgned contrcts between Amercn Express Co. nd IBM, nd convenencestore chn 7Eleven Inc. nd EDS re both bsed on usgebsed prcng wth some fxed fees,.e., the twoprt trff prcng (Greenemeer, 00). Whle there hs been ncresng nterest on how to prce nformton goods (Bkos nd Brynjolfsson, 999; Chung nd Srbu, 999; Vrn, 000), much of the work ether does not ddress nformton servces, or s only ndrectly pplcble to such cses. For exmple, the dvntges of pure bundlng n Bkos nd Brynjolfsson (999) result from reducton n the vrnce for customers vlutons for bundle of dfferent nformton goods. Ths modelng technque cnnot be ppled to nformton servces, snce ech unt of nformton servces s essentlly dentcl, nd therefore, we cnnot expect vrnce to be reduced through ggregton of dentcl unts. We use frmework n whch both buyers nd sellers of nformton goods optmze ther net vlues n order to determne whch prcng scheme works best under dfferent condtons. Recent works tht re relted to nformton servce prcng nclude Fshburn, Odlyzko nd Thus they wll hve perfect correlton cross unts n customers vlutons. 4
5 Sders (997), Esseger, Gupt nd Zhng (00) nd Sundrrjn (00). Our pper s complementry to these ppers. Sundrrjn (00) consders fxedfee nd nonlner usgebsed prcng schemes. But the focus of ths study s dfferent from ours n ths pper. He shows tht n the presence of contrct dmnstrton costs, such s montorng cost for usge bsed prcng, monopolst cn mprove ts profts by offerng fxedfee prcng n ddton to usgebsed contrct. However, whle ths study hs suggested tht frm could mprove ts profts by doptng mx of prcng schemes, the results re bsed on utlty functon tht hs to stsfy the SpenceMrrlees snglecrossng property, whch llows frm to possbly segment customers through ther selfselecton proftbly. When ths property does not hold, t s not cler whether doptng multple schemes wll stll be proft mprovng. In ddton, ths pper does not offer drect gudelne bout whch prcng scheme s most proftble when the frm could only opt for one prcng scheme, the mjor focus of our pper. There re severl stutons where frms my fvor to dopt one prcng scheme only. For exmple, when new nformton servce s just beng provded, the frm my prefer to dopt only one prcng scheme to keep the mrketng smple; eser dmnstrton nd mngement my lso mke the frm my prefer one prcng scheme only. Fshburn, Odlyzko nd Sders (997) compre the flt fee nd the usgebsed prcng nd show tht flt fee s better thn metered rte for monopolst offerng nformton servces on the Internet. However, they hve smplfed the problem wth some very restrctve ssumptons. For exmple, they ssume tht consumers choose the quntty of servce to buy nd stck to t before exmnng the vlble prces. It s not cler whether ther results could be generlzed to more generl demnd functons,.e., downwrd slopng demnd functon. And fnlly, both of these works do not consder the twoprt trff prcng, whch s populr both n theory nd prctce; we exmne ths cse lso. Esseger, Gupt nd Zhng s (00) lso 5
6 consder the twoprt trff prcng together wth flt fee nd usgebsed prcng. As n Fshburn, Odlyzko nd Sders (997), they ssume tht consumer usge s nelstc to prce chnge. Moreover, they ssume tht both hevy nd lght users hve the sme totl reservton prce for the servce, whch my be doubtful s users usully hve qute dfferent nd dmnshng mrgnl utlty for ech unt of servce they consume. It s lso questonble to ssume tht mrgnl cost s zero when servce provder hs cpcty constrnt (nother problem wth cpcty constrnt s the possble queung problems, whch s not dscussed n ther pper). Overll, our nlyss suggests tht under zero mrgnl nd montorng costs, when customers re homogeneous or when customers hve heterogeneous mrgnl wllngness to py (whch corresponds to dfferent downwrd slopng demnd curves), fltfee prcng nd twoprt trff prcng lwys cheve the sme proft level, nd re strctly better thn the usgebsed prcng. However, when customers re chrcterzed by heterogeneous mxmum consumpton levels, twoprt trff prcng s the most proftble mong the three. We lso exmne how senstve the optml prcng scheme s to mrgnl costs nd montorng costs when customers re homogeneous or when customers hve heterogeneous mrgnl wllngness to py. Our nlyss shows tht when mrgnl cost s below certn vlue, the flt fee prcng s the optml scheme regrdless how lrge or how smll montorng cost s (s long s t s postve) when customers re homogeneous or hve heterogeneous mrgnl wllngness to py. But s montorng cost becomes zero, the twoprt trff becomes one of the optml prcng schemes. The pper s orgnzed s follows: In secton, we provde the generl model for the mrket for nformton servces. Secton 3 reports on the nlyss of dfferent prcng schemes nd when ech of them s most proftble. Secton 4 outlnes some model extensons. We provde Although they try to extend ther model ner the end of the pper by usng the sme unt reservton prce for the two consumer segments, ths ssumpton stll fls to reflect the truth tht users usully hve qute dfferent nd dmnshng mrgnl utlty for ech unt of servce they consume. 6
7 concludng remrks n secton 5.. Mrket Model for Informton Servces We exmne the optml prcng scheme for n nformton servce provder who sells one knd of nformton servce (such s voce communcton servce or dt trnsmsson servce) to consumers. We consder three prcng schemes: pure flt fee, pure usgebsed nd twoprt trff prcng. The nformton servce provder chooses whch prcng scheme to dopt nd the prce(s) to offer. Consumers then mke decsons bout whether to jon the pln, nd how much to consume gven the prcng scheme nd prces set by the nformton servce provder. Snce nformton servces usully experence some pekhours nd some nonpek hours, we ssume tht consumers my hve dfferent utlty functons n pek hours nd nonpek hours. As result, nformton servce provders my chrge dfferent prces for the two tme segments when usng usgebsed prcng. In ddton, gven lmted tme nd ttenton, we ssume tht consumers fce certn upper bounds n consumng the servces. For exmple, gven tht there re only 4 hours n dy, consumers cn t consume the servce for more thn 4 hours dy... Consumers Optmzton roblem Gven the prcng scheme (flt rte, usgebsed, or twoprt trff) nd prce(s) set by the nformton servce provder, consumer wll decde whether or not she wnts to jon the servce progrm nd her consumpton level of the servce n both pek hours nd nonpek hours to mxmze her totl net utlty. Gven rmeters: 7
8 : the subscrpton fee for the consumer to jon the progrm : the unt prce of the servce set by the provder n pek hours : the unt prce of the servce set by the provder n nonpek hours U(, ): the utlty functon of consumer t the consumpton level of n pek hours nd n nonpek hours : consumer 's mxmum consumpton level of the servce n pek hours : consumer 's mxmum consumpton level of the servce n nonpek hours Decson Vrbles: : consumer 's consumpton level of the servce n pek hours : consumer 's consumpton level of the servce n nonpek hours Z : the decson vrble whch s f consumer chooses to jon the progrm nd 0 otherwse Consumers Optmzton roblem: Mx U, Z (),, Z ( ) s.t. Z () Z (3) (, ) U Z 0 (4) (the Indvdul Rtonlty constrnts) Z = 0or (5) The objectve functon () s to mxmze the consumer surplus gven the prce(s) set up by the nformton servce provder. In our model, we do not consder the ntlzton cost for the consumer to jon the progrm, such s the purchse of 3G moble devces n the 3G wreless servce scenros for two resons. Frst, when we consder the longrun reltonshp between the suppler nd consumers, ths knd of onetmeexpense my not be s mportnt s the monthly usge fee nd the subscrpton fee. Further, ths one tme fee does not ffect the optmzton problem, nd t cn be bsorbed by U (, ). Note lso tht there s no prmeter n ths model 8
9 tht ndctes the prcng scheme dopted by the nformton servce provder. Rther thn usng ddtonl prmeter to ndcte the prcng mechnsm, the prcng scheme chosen ctully s reflected by the vlues of,, nd. For exmple, when nd re both zero nd s postve, t s the pure flt rte prcng; when nd re postve nd s zero, t s the pure usgebsed prcng; nd when,, nd re ll postve, t s the twoprt trff prcng. Addtonlly, n ths pper, we mjorly consder the smple nd most commonly dopted usgebsed nd twoprt trff prcng n whch the unt prce of the servce s constnt nd doesn t chnge wth the consumer s consumpton level. For exmple, lmost ll, f not ll, resdentl long dstnce voce communcton servce (wth or wthout monthly fee) nd wreless dt trnsmsson servce hve constnt unt prce. Gven,, nd, consumer wll decde f she wnts to jon the progrm. If she decdes not to jon by choosng Z = 0, constrnt () nd (3) wll enforce her consumpton level nd to be zero, nd her totl utlty nd cost re both zero. On the other hnd, f she decdes to jon the progrm by choosng =, she then hs to decde her optml consumpton level nd Z, whch cnnot exceed her upper bounds nd, s enforced by constrnt () nd (3). Also note tht the consumpton level nd here could be the consumpton tme, such s n the voce communcton servce, the trffc volume, such s n the dt trnsmsson servce, or number of uses/ccesses, such s n the pplcton servces, or number of messges sent n SMS/MMS servces... The Suppler s Optmzton roblem Gven the optmzton problem fced by the consumers, the nformton servce provder 9
10 wll decde wht prcng scheme to dopt so s to mxmze ts totl proft. We ssume tht mrgnl cost,.e., mrgnl producton cost for provder one more unt of the servce to the customer, nd montorng cost,.e., mrgnl dmnstrton cost or montorng cost for one unt of the servce n usgebsed prcng, 3 re both neglgble,.e., zero. We ll dscuss ths ssumpton n Secton 4. Gven rmeters: * = (,, ) : consumer 's consumpton level of the servce n pek hours * = (,, ) : consumer 's consumpton level of the servce n nonpek hours Z* = Z(,, ) : consumer 's decson vrble regrdng prtcpton U(, ) : the utlty functon of consumer t the consumpton level of n pek hours nd n nonpek hours : consumer 's mxmum consumpton level of the servce n pek hours : consumer 's mxmum consumpton level of the servce n nonpek hours Decson Vrbles: : the subscrpton fee for the consumer to jon the progrm : the unt prce of the servce set by the provder n pek hours : the unt prce of the servce set by the provder n nonpek hours The Suppler s Optmzton roblem: Mx,, ( * + * + Z* ) (6) where ( *, *, * = rgmx U Z ( ) ), Z s.t. Z Z ( ) U, Z 0 3 Snce there s no need to montor customer usge level n fltfee prcng, we ssume tht fltfee prcng does not ncur montorng cost n the nlyses throughout. 0
11 Z = 0or The objectve functon (6) s to mxmze the totl proft gven the optmzton problems fced by the consumers. Note tht we do not consder the ntlzton fxed cost of provdng the servce to ech consumer s t s not s mportnt f we consder the longrun reltonshp between the suppler nd consumers. In ddton, we ssume the servce provder hs enough cpcty, so tht the mrgnl cost of provdng the servce s zero. 4 Bsed on ths model, we cn fnd the most proftble prcng scheme nd prce(s) to chrge the consumers gven the consumers t fces. 3. Anlyss 3.. The Bse Cse: Homogeneous Consumers As the frst cse, we consder homogeneous consumers n the mrket wth the sme utlty functon nd the sme upper bounds nd on the consumpton level n pek hours nd nonpek hours, respectvely. For nlytcl convenence, we dopt the frequently used Cobb ( ) Dougls utlty functon, U, = log + blog, wth one mnor modfcton. 5 U(, ) = log( + ) + blog( + ) (7) Wth ths modfcton, when the consumpton level s zero, consumers wll get zero utlty rther thn negtve nfnte utlty. Note tht ths utlty functon s ncresng nd strctly concve n consumpton level nd tht nd re substtutes n tht one could substtute ech 4 Gven ny cpcty, we cn ssume tht the mrgnl cost wthn cpcty s zero, frm only fces lrge mrgnl cost when t needs to ncrese cpcty, but ths s ctully nother nvestment decson tht needs to be mde by frm, rther thn mrgnl cost of the servce, becuse wth new lrger cpcty, mrgnl cost goes to zero gn. 5 Log denotes nturl log here.
12 other to get the sme utlty. We dopt ths specfc utlty functon for two resons: t not only gretly smplfes our devtons but lso llow us to explore how the homogenety (n ths secton) nd heterogenety (n Secton 3.) of consumer utlty functons (wth dmshng mrgnl untlty property) ffect frm s choce of prcng structure. Workng on the generl form of utlty functon U (, ) would hve mde our nlyss much less trctble nd trnsprent wthout ny pprent promse for new nsghts. Wth ths specfc utlty functon, ech consumer wll then fce the followng optmzton problem: Consumers Optmzton roblem: Mx Z,, s.t. ( ) log + + blog( + ) Z (8) Z (9) Z (0) ( ) log + + blog( + ) Z 0 () Z = 0or () Gven consumers optmzton problem bove, the nformton servce provder tres to solve the followng optmzton problem: The Suppler s Optmzton roblem: Mx,, ( * + * + Z* ) (3) where ( * = rgmx, *, *) Z ( ) log + + blog( + ) Z s.t. Z
13 Z ( ) log + + blog( + ) Z 0 Z = 0or roposton When ll consumers n the mrket re homogeneous nd hve utlty functon gven by (7), the pure flt rte prcng nd the twoprt trff prcng yeld the sme proft, whch s strctly hgher thn the pure usgebsed prcng. roof: We frst mke the followng observtons: Frst, snce ll consumers re ssumed homogeneous, ll consumers wll mke the sme jonornot decson nd the servce provder ether serve ll of them or serve none of them. In order to mxmze the proft, the servce provder wll mke sure tht ll consumers wnt to jon the progrm. Second, snce the mjor prcng mechnsms we re studyng n ths pper re pure flt rte, pure usgebsed, nd the twoprt trff prcng, we cn do the nlyss seprtely nd see wht s the best proft the servce provder cn get by ech prcng pln. ) If the servce provder uses the pure flt rte prcng by settng = 0, = 0, nd > 0: It s cler tht gven ths prcng pln, the consumers wll fully utlze the servce by choosng the consumpton level = nd = wth the mxmum utlty the consumers cn get log( +) + b log( +). It s then obvous tht the mxmum flt rte the servce provder cn chrge s log( +) + b log( +), wth mxmum proft : [ log( +) + b log( +)]. ) If the servce provder uses the pure usgebsed prcng by settng > 0, > 0, nd = 0: 3
14 Tkng frstorder condtons for optmlty of consumer s optmzton problem yeld: = * + b = * + => * = b => * = Supplers Optmzton roblem becomes: Mx ( * + *) = Mx (  + b  ) It s cler tht to mxmze the equton bove, the suppler wll hve to mnmze nd. From FOC bove, we know tht s nd decrese, * nd * wll ncrese. But snce nd re bounded, * nd * wll eventully become nd. In other words, the best nd wll be = + nd b =, wth mxmum proft: ( b  b + ) = [(  + ) + b(  + )]. 3) If the servce provder uses the twoprt trff prcng by settng > 0, > 0, nd > 0: Agn, the frstorder condtons for optmlty of consumer s optmzton problem re: = * + b = * + => * = b => * = Supplers Optmzton roblem becomes: Mx ( * + * + ) = Mx (  + b  + ) Lkewse, t s cler tht to mxmze the equton bove, the suppler wll hve to mnmze nd. From FOC bove, we know tht s nd decrese, * nd * wll 4
15 ncrese. But snce nd re bounded, * nd * wll eventully become nd. In other words, the best nd wll be = + nd b =. The mxmum subscrpton fee + the suppler cn chrge s then the dfference between the mxmum utlty the consumers cn get, log( +) + b log( +), nd the pyment for ther usge, ( b  b + ). Therefore, the mxmum proft chevble by the servce provder s [ log( +) + b log( +)], the sme s n the cse when the servce provder dopts the flt rte prcng mechnsm. Note tht snce log( +) > (  + ) nd log( +)> (  hve log( +) + b log( +)> [(  + ) + b( )] for ll >, 0, we )]. Tht s, the pure flt rte prcng nd the twoprt trff prcng re strctly better thn the pure usgebsed prcng from the servce provder s proft mxmzton pont of vew. QED. 3.. Heterogeneous Customers In prevous nlyss, we hve shown tht flt fee nd twoprt trff s more proftble thn the pure usgebsed prcng. However, the ssumpton of homogeneous consumers my be somewht restrctve, so we relx ths ssumpton by consderng dfferent types of heterogeneous customers. Followng Jn et l. (999), we exmne twosets of customer segmentton: hghend nd lowend n terms of wllngnesstopy (Secton 3..), nd hevy nd lght n terms of level of usge (Secton 3..). We further ssume tht t s the frm s nterest to serve both segments n ech cse; otherwse, the problem s reduced to tht 5
16 consdered n Secton 3.. We further ssume tht the nformton servce provder cnnot dscrmnte between these two consumer segments. Ths ssumpton s resonble snce t s usully hrd for the servce provder to tell whch segment the consumers belong to. Note tht f the nformton servce provder cn dscrmnte these two types of consumers, the problem gn becomes tht consdered n Secton 3., nd the nformton servce provder cn smply offer dfferent flt rte prcng or twoprt trff prcng to dfferent consumer segments. 3.. Heterogeneous customers: the hghend customers nd the lowend customers For smplcty, we wll cll the hghend busness consumers, nd the lowend personl consumers. We suppose there re m busness consumers (=) nd n personl consumers (=). To study how heterogeneous wllngness to py ffects frm s prcng scheme, we ssume ech consumer n both segments hs the sme upper bounds nd n pek hours nd nonpek hours, nd, b > b. > Consumers Optmzton roblem: Mx Z,, ( ) log + + blog( + ) Z (4) s.t. Z (5) Z (6) ( ) log + + b log( + ) Z 0 (7) Z = 0or (8) The Suppler s Optmzton roblem: 6
17 Mx,, m( * + * + Z *) + n( * + * + Z *) (9) where ( *, *, * = r Z gmx ( ) ) log + + blog( + ) Z s.t. Z Z ( ) log + + b log( + ) Z 0 Z = 0or m+ n m+ n Lemm : when < nd b < b, 6 f the servce provder uses the pure flt rte, m m the prce chrged wll be ( ) ( be: ( m+ n) log ( + ) + blog ( ) roof : log + + b log + ), nd the mxmum proft chevble wll +. It s cler tht gven = 0, = 0, nd > 0, f consumer chooses to jon the progrm, she wll fully utlze the servce by choosng the consumpton level =, = or =, =. Gven ths, t s obvous tht the servce provder cn chrge ech busness consumer no more thn log ( ) lo ( ( ) ( + ) + + b g + ), nd ech personl consumer no more thn m+ n m+ n log + + b log. It cn be esly shown tht f < nd b < b, the m m 6 These condtons correspond to the cse tht t s more proftble for the frm to serve both segments. 7
18 servce provder wll chrge ( ) ( log + + b log + ) nd serve both busness nd personl consumers wth the mxmum proft chevble ( + ) ( + ) + ( m n log b log +. QED. ) Lemm : If the servce provder uses the pure usgebsed prcng, when m > n, 7 the optml prce n the pek hours s = ; when m > n, the optml nonpek hour prce s + b = +. The mxmum proft s: b b m( + ) + n( + b ) ; otherwse, the optml prces re gven by = + nd b = + wth proft : b ( m+ n) ( + ). + + roof : When > 0, > 0, nd = 0, the frstorder condtons for optmlty of busness/personl consumer optmzton problem yeld: = * = * + (0) b b = * = * + () = * = * + () b b = * = * + (3) The Suppler s Optmzton roblem becomes: 7 If we normlze to be, ths condton mens m > n. 8
19 Mx m ( * + *) + n ( * + *) = Mx m ( + b ) + n ( + b ) To mxmze the equton bove, the suppler wll hve to mnmze nd. From (0) (3), we know tht s nd decrese, *, *, * nd * wll ncrese. But snce,, nd re bounded (constrnts (5) nd (6)), *, *, * nd * cnnot exceed nd respectvely, nd ths suggests tht s prce goes down further, no ncrese n demnd cn be expected. To derve the optml prces, we consder the pekhour problem frst. The pekhour demnd curves of the busness nd personl consumers (constrnts (0) nd ()) re shown n Fgure ( nd D ). D + + D D * Fgure. The pekhour demnd curves of the busness nd personl consumers The suppler s optmzton problem s: Mx m ( *) + n ( *) = Mx m ( ) + n ( ). To mxmze ths equton, the suppler wll hve to mnmze nd therefore the best prce cnnot be lrger thn. On the other hnd, f the suppler sets the prce below +, the proft s not optml snce * nd * cnnot exceed + nd user demnd won t 9
20 ncrese s the prce decreses. Hence, the best prce must be somewhere between + nd. When the prce s n ths ntervl, the demnd of the busness consumer s fxed t + whle the demnd of the personl consumer keeps on ncresng s the prce goes down. Thus, we hve: Mx m ( *) + n ( *) = Mx m ( ) + n( ) = Mx n + ( m n ). When m > n, the best prce n ths ntervl s therefore +, otherwse, = +. Smlr nlyss cn be done on the nonpekhour problem nd we cn get the best b prce = + when m n, or b = otherwse. QED. + > m+ n Lemm 3: If the servce provder uses the twoprt trff prcng, when < nd m b m+ n b, optml m < cn be set nywhere between 0 nd, cn be set nywhere + between 0 nd b + log +, nd = log( + ) b ( + ) wth the mxmum proft chevble: ( m+ n)[ log( + ) + blog( + )]. roof : When > 0, > 0, nd > 0, the frstorder condtons for the busness/personl consumer optmzton problem yeld (0)(3). Lkewse, we use the dvdendconquer technque to do the nlyss. As before, we consder only the pekhour problem here nd the jont problem wth nonpekhour consderton cn be solved n smlr wy. Equtons (0) nd () re the pekhour demnd 0
21 curves of the busness nd personl consumers ( nd D n Fgure..). D + + D D * Fgure.. The best subscrpton fee s equl to the consumer surplus of the personl consumers Frst, we mke the followng observton: no mtter wht usge prce the suppler sets for the servce, the best subscrpton fee t cn chrge the consumers s the consumer surplus of the personl consumers (the trngle re under D nd bove ). 8 Any subscrpton fee more thn ths wll let the suppler lose ll of the personl sonsumers. Note tht gven these demnd functons, f the suppler set the usge prce +, the suppler s optmzton problem wll be: = Mx m ( *) n ( *) ( m n ) Mx m ( ) n ( ) ( m n) d = m + m+ n Mx ( ) ( ) log( ) To mxmze ths equton the suppler wll hve to mnmze nd therefore the best prce 8 Due to our ssumpton tht t s more proftble for the frm to serve both mrket segments, nd the condtons for m+ n m+ n ths to be true re: < nd b < b. m m
22 n ths ntervl s + wth the mxmum proft chevble m + m+ n +). ( ) ( ) log ( Second, f the suppler set the usge prce, the suppler s optmzton + + problem wll be: Mx m ( *) ( *) ( ) Mx ( ) ( ) ( ) + n + m+ n= m + n + m+ n d 0 + = Mx m ( + ) m + ( m+ n ) log( ) The best prce n ths ntervl s + wth the mxmum proft chevble ( m+ n) log( + ). Note tht ths proft s lrger thn m ( ) + ( m+ n ) log ( +) (the proft we cn get from nother boundry pont + ). Thrd, f the suppler set the usge prce 0, the suppler s optmzton problem + wll be: Mx m ( *) n ( *) ( m n ) Mx m ( ) n ( ) ( m n) d = Mx ( m+ n) log( + ) = It s cler tht to mxmze ths equton the suppler cn set the prce nywhere between 0
23 nd + wth the mxmum proft chevble ( m+ n) log( + ). Gven the bove nlyss, we know tht the suppler cn set the optml prce nywhere between 0 nd, nd nywhere between 0 nd + b, nd subscrpton fee equl to + the consumer surplus of the personl consumers, wth the mxmum proft chevble ( m+ n)[ log( + ) + b log( + )]. QED. roposton When there re two types of consumers chrcterzed by heterogeneous wllngness to py n the mrket, the fltfee prcng nd the twoprt trff prcng yeld the sme proft, whch s hgher thn the pure usgebsed prcng. roof : Drcetly from Lemm 3, we lredy get the mxmum profts chevble when the servce provder dopts ech of the prcng mechnsm: pure flt rte, pure usgebsed nd the twoprt trff prcng. It s not hrd to show tht for ll 0 nd 0, m[ log( +) + b log( +)] + n[ log( +) + b log( +)] > m(  + b + b  + ) + n( b  b ). Therefore we cn sy the pure flt rte prcng nd the twoprt trff prcng re strctly + better thn the pure usgebsed prcng from the servce provder s proft mxmzton pont of vew. QED. Note tht the conclusons from ths subsecton s exctly the sme s tht derved n 3
24 roposton, tht s, the fltfee prcng nd the twoprt trff lwys yeld the sme proft, nd tht the usgebsed prcng s strctly domnted. Whle these results re estblshed under one or two segments of customers, they could be generlzed to contnuous type of customers (s shown s roposton 5 n Appendx). 3.. Heterogeneous customers: the hghdemnd customers nd the lowdemnd customers In ths subsecton, we consder how heterogeneous mxmum consumpton level mght ffect frm s prcng choce. Agn, we ssume two types of customers, the hghdemnd customers (type ) wth mxmum consumpton level t nd nd the lowdemnd customers (type ) wth mxmum consumpton level t nd, where > nd >. As before, there re m type customers nd n type customers wth = = nd b = b =. b roposton 3 When there re two types of consumers chrcterzed by heterogeneous mxmum consumpton levels, the twoprt trff lwys domntes the fltfee prcng nd the usgebsed prcng. roof Sketch: The optml prce(s) nd mxmum proft under ech scheme re chrcterzed n the followng: Under the flt fee scheme : = log ( + ) + log ( ) b +, wth mxmum proft: ( ) ( ) ( m+ n)[ log + + blog + ]. Under the pure usgebsed prcng: 4
25 b b when n m, = nd =, wth proft=( m + n)( + ) b b b when n < m, = nd =, wth proft= m( + ) + n( + ) Under the twoprt trff prcng: = +, b = + nd the subscrpton fee: log ( ) blog ( ) = b ( + ). Therefore, the mxmum proft chevble by the servce provder + + ( + b ) + ( m+ n)( log( + ) + blog( + )), whch s greter thn tht cn be + + s m cheved n the flt fee prcng nd the usgebsed prcng. QED. 4. Model Extenson Mrgnl Cost nd Montorng Cost In prevous nlyses, we ssume tht mrgnl cost (denoted by c) nd montorng cost (denoted by t) re both zero. In ths secton, we relx ths ssumpton nd exmne how mrgnl cost nd montorng cost ffect optml prcng scheme. In generl, postve mrgnl cost s expected to mke the flt fee prcng less ttrctve nd fvor two prt trff prcng nd usge bsed prcng, whle postve montorng cost tend to mke the twoprt trff prcng or usgebsed prcng less desrble thn the flt fee prcng snce there s no need to ncur montorng expenses n the fltfee prcng. The optml prcng scheme thus depends on the trdeoff between these two costs. However, under the cse where customers re homogeneous or re chrcterzed by heterogeneous wllngness to py, the optml scheme becomes nsenstve to these two costs when c s below certn vlue, n prtculr, holdng c constnt, reducng 5
26 montorng cost does not mke the twoprt trff prcng better choce thn the flt fee prcng. roposton 4 Under the cse where customers re homogeneous or re chrcterzed by b heterogeneous wllngness to py, when c mn{, }, the flt fee prcng ( + ) ( + ) domntes the twoprt trff prcng nd the usge bsed prcng. roof sketch: The proof here s bsed on homogeneous customers for smplcty. However, the sme nlyss cn be done on heterogeneous customers cse, the results remn the sme, but only the condton on c chnges. As before, we nlyze the pek hour problem, nd the jont problem wth nonpek hour consderton cn be solved n the sme mnner. Wth postve mrgnl cost nd montorng cost, the proft from ech customer (denoted by π ) for the frm under ech prcng scheme s gven by: Under the fltfee prcng: π= c, nd to mxmze the proft, wll be set t log( + ), wth proft chevble: log( + ) c. Under the usgebsed prcng: π = ( c t) ( ), where ( ) s the demnd functon chrcterzed by ( ) = from the frst order condton n customer s optmzton problem. The proftmxmzton peruse prce cn be shown to be: π * = mx{, ( c+ t)} from the frst order condton = 0, nd the mxmum proft cn + be shown to be: ( * c t) ( *) = ( *) * ( *) ( c+ t). Under the twoprt trff prcng: π = ( c t) ( ) +, gn ( ) s the demnd 6
27 functon chrcterzed by ( ) = from the frst order condton n customer s π optmzton problem. Accordng to the frst order condton = 0, we cn derve the proftmxmzton peruse prce: * = mx{, ( c+ t)}, nd, the subscrpton fee, wll be set + t: log( ( *) + ) ( *) *,.e., to fully extrct customer surplus. The mxmum proft s thus equl to: log( ( *) + ) ( *) ( c+ t). We cn show tht when c ( + ), flt fee prcng lwys domntes the twoprt trff prcng nd the usge bsed prcng no mtter how lrge or how smll the montorng cost s (s long s t s postve), nd when montorng cost, t, goes down to zero, the twoprt trff prcng wll derve the sme proft s the flt fee prcng. Smlrly, we cn show tht n nonpek hours, when b c ( + ), flt fee prcng lwys domntes the twoprt trff prcng nd the usge bsed prcng no mtter how lrge or how smll the montorng cost s (s long s t s postve). QED. Ths result s very nterestng becuse t suggests tht s mrgnl cost goes down (but not necessrly zero), flt fee prcng becomes the optml scheme even though tht montorng cost my goes down t lrger scle. A drect mplcton of ths roposton s tht s mrgnl costs nd montorng costs re both lowered wth the dvnce of nformton technology or wth evoluton of electronc mrkets, fltfee prcng wll become more ttrctve for nformton servce provders. However, when montorng cost becomes neglgble, twoprt trff prcng wll become s ttrctve. 7
28 5. Dscusson nd Conclusons The mn objectve of ths pper s to offer gudelne for nformton servce provders bout wht prcng scheme s most proftble nd wht prce(s) t should chrge. Ths ssue bout how to prce nformton servces hs become ncresngly more mportnt s mrgnl producton nd montorng costs for nformton servces re beng reduced wth the dvnce of modern nformton technology, nd more nd more nformton servces re beng offered wth the evoluton of the Internet. Mny reserchers hve suggested tht zero mrgnl cost wll fvor the fltfee prcng scheme. Overll, our nlyss shows tht when customers re homogeneous or hve heterogeneous mrgnl wllngness to py, f mrgnl cost s below certn vlue, fltfee prcng s ndeed more ttrctve. However, s processng power keeps ncresng nd montorng costs become neglgble, the twoprt trff prcng becomes s ttrctve. Our nlyss lso shows tht under zero mrgnl cost nd zero montorng cost, when customers re frly homogeneous, the usgebsed prcng s strctly domnted by the flt fee nd twoprt trff prcng schemes, wth the ltter two lwys chevng the sme proft level. The sme results sustn when customers hve heterogeneous mrgnl wllngness to py (whch corresponds to dfferent downwrd slopng demnd curves). However, when customers re chrcterzed by heterogeneous mxmum consumpton levels, the twoprt trff prcng domntes both the fltfee prcng nd the usgebsed prcng. Appendx: roposton 5 When consumers re chrcterzed by heterogeneous wllngness to py n the 8
29 mrket, the fltfee prcng nd the twoprt trff prcng lwys yeld the sme proft, whch s hgher thn the pure usgebsed prcng. roof sketch: Assume customer hs type: nd b, whch follow the unform dstrbuton,.e.,, b ~ U [0,]. As before, we solve the pek hour problem, nd the jont problem wth nonpek hour consderton cn be solved wth the smlr procedure. Under the fltfee prcng: Gven ny flt fee,, chrged by the frm, we cn determne the mrgnl customer, 0, who wll sgn up by 0 log( + ) =, wth proft = ( ). To mxmze the proft, the frm wll 0 set = log( + ), wth 0 =,.e., customers wth type hgher thn wll jon the servce. The mxmum proft under ths scheme s thus ( 0 ) = ( ) log( + ) = log( + ). 4 Under the pure usgebsed prcng: As before, the demnd functon s chrcterzed by: =, tht s, when, we hve, nd when <, we hve + + demnd functon, customer wth type hgher thn ( + ) wll consume. =. And gven ths The frm wll choose tht mxmzes ts proft: ( + ) d + ( ( + )). 0 Solvng ths optmzton problem, we get =, wth proft: ( + ) ( + ), whch cn be shown to be lower thn log( + ), the proft n the fltfee prcng. 4 9
30 Under the twoprt trff prcng: The frm wll choose nd the subscrpton fee,, to mxmze ts proft. Note tht gven ny nd, the mrgnl customer,, who wll sgn up the servce s determned by: 0 0 0log( ( 0) + ) ( 0) = 0, whch cn be smplfed to = 0log( ) ( 0 ). The proft gven nd s : 0 ( + ) d + ( (+ )) + ( ). To mxmze the 0 proft, the frm wll set = nd ( + ) = log( + ) +, wth mxmum proft: lo g( ) 4 + QED., whch s exctly the sme s wht cn be cheved n the fltfee prcng scheme. References. Bkos,. nd E. Brynjolfsson. Bundlng Informton Goods: rcng, rofts nd Effcency. Mngement Scence 45, Cho, S., Dle O., nd A. B. Whnston. The Economcs of Electronc Commerce. Mcmlln Techncl ublshng, Indnpols, Indn, Chung, C. I. nd Srbu, M. A. Optml Bundlng Strtegy for Dgtl Informton Goods: Network Delvery of Artcles nd Subscrptons. In Informton Economcs nd olcy, Esseger, S., S. Gupt nd Z. J. Zhng. rcng Access Servces. Mrketng Scence (), Fshburn,.C., A.M. Odlyzko nd R.C. Sders. Fxed fee versus unt prcng for nformton goods: competton, equlbr, nd prce wrs. roceedngs of the Conference on Internet 30
31 ublshng nd Beyond: Economcs of Dgtl Informton nd Intellectul roperty. Cmbrdge MA Gopl, A., T. Mukhopdhyy, M. S. Krshnn, nd K. Svrmkrshnn, Contrcts n Offshore Softwre Development: An Emprcl Anlyss, Workng per, Greenemeer, L. y As you Go, Informton Week, Mr. 4, Jn, D., E. Muller nd N. Vlcssm. rcng ptterns of Cellulr hones nd honeclls: A SegmentLevel Anlyss. Mngement Scence 45 (), 34, Mer, M. How Much Would ou y for Advnced Wreless?. Busness.0, Februry 7, 00. Avlble t 0. Metclfe, R ollnte lets you rent the softwre you need for just the rght mount of tme. Infoworld, June 9, Sundrrjn, A. Nonlner prcng of nformton goods. Workng pper, New ork Unversty, 00.. Vrn, H. R. Buyng, Shrng nd Rentng nformton Goods. Journl of Industrl Economcs, ,
WiMAX DBA Algorithm Using a 2Tier MaxMin Fair Sharing Policy
WMAX DBA Algorthm Usng 2Ter MxMn Fr Shrng Polcy PeChen Tseng 1, JYn Ts 2, nd WenShyng Hwng 2,* 1 Deprtment of Informton Engneerng nd Informtcs, Tzu Ch College of Technology, Hulen, Twn pechen@tccn.edu.tw
More informationJoint Opaque booking systems for online travel agencies
Jont Opque bookng systems for onlne trvel gences Mlgorzt OGOOWSKA nd Domnque TORRE Mrch 2010 Abstrct Ths pper nlyzes the propertes of the dvnced Opque bookng systems used by the onlne trvel gences n conjuncton
More informationNewtonRaphson Method of Solving a Nonlinear Equation Autar Kaw
NewtonRphson Method o Solvng Nonlner Equton Autr Kw Ater redng ths chpter, you should be ble to:. derve the NewtonRphson method ormul,. develop the lgorthm o the NewtonRphson method,. use the NewtonRphson
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationA Hadoop Job Scheduling Model Based on Uncategorized Slot
Journl of Communctons Vol. 10, No. 10, October 2015 A Hdoop Job Schedulng Model Bsed on Unctegored Slot To Xue nd Tngtng L Deprtment of Computer Scence, X n Polytechnc Unversty, X n 710048, Chn Eml: xt73@163.com;
More informationPricing Strategy of Platform: An Investigation to the Internet Service Provider (ISP) Industry
Prng trtegy of Pltform: n Investgton to the Internet erve Provder (IP Industry by WDEH KUMR MT, HUI P Correspondng ddress: Dept. of Computng nd Eletron ystems, Unversty of Essex, Wvenhoe Prk, Colhester,
More informationIrregular Repeat Accumulate Codes 1
Irregulr epet Accumulte Codes 1 Hu Jn, Amod Khndekr, nd obert McElece Deprtment of Electrcl Engneerng, Clforn Insttute of Technology Psden, CA 9115 USA Eml: {hu, mod, rjm}@systems.cltech.edu Abstrct:
More informationMultiMarket Trading and Liquidity: Theory and Evidence
MultMrket Trdng nd Lqudty: Theory nd Evdence Shmuel Bruch, G. Andrew Kroly, b* Mchel L. Lemmon Eccles School of Busness, Unversty of Uth, Slt Lke Cty, UT 84, USA b Fsher College of Busness, Oho Stte Unversty,
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationASP OnDemand versus MOTS InHouse Software Solutions *
ASP OnDemn versus InHouse Softwre Solutons Dn M School of Informton Systems Sngpore Mngement Unversty Abrhm Semnn Xerox Professor of Computer n Informton Systems n Opertons Mngement W. E. Smon Grute
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationBasics of Counting. A note on combinations. Recap. 22C:19, Chapter 6.5, 6.7 Hantao Zhang
Bscs of Countng 22C:9, Chpter 6.5, 6.7 Hnto Zhng A note on comntons An lterntve (nd more common) wy to denote n rcomnton: n n C ( n, r) r I ll use C(n,r) whenever possle, s t s eser to wrte n PowerPont
More informationVector Geometry for Computer Graphics
Vector Geometry for Computer Grphcs Bo Getz Jnury, 7 Contents Prt I: Bsc Defntons Coordnte Systems... Ponts nd Vectors Mtrces nd Determnnts.. 4 Prt II: Opertons Vector ddton nd sclr multplcton... 5 The
More informationIncorporating Negative Values in AHP Using Rule Based Scoring Methodology for Ranking of Sustainable Chemical Process Design Options
20 th Europen ymposum on Computer Aded Process Engneerng ECAPE20. Perucc nd G. Buzz Ferrrs (Edtors) 2010 Elsever B.V. All rghts reserved. Incorportng Negtve Vlues n AHP Usng Rule Bsed corng Methodology
More informationResistive Network Analysis. The Node Voltage Method  1
esste Network Anlyss he nlyss of n electrcl network conssts of determnng ech of the unknown rnch currents nd node oltges. A numer of methods for network nlyss he een deeloped, sed on Ohm s Lw nd Krchoff
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationUNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE
UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN 10438 UNVERSTY OF NOTTNGHAM Discussion
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationSupply chain coordination in 2stageorderingproductionsystembased
As Pcfc ndusrl Engneerng nd Mngemen Sysem Supply chn coordnon n sgeorderngproduconsysembsed on demnd forecsng upde Esuko Kusukw eprmen of Elecrcl Engneerng nd nformon Sysems, OskPrefecure Unversy, Sk,
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationORIGIN DESTINATION DISAGGREGATION USING FRATAR BIPROPORTIONAL LEAST SQUARES ESTIMATION FOR TRUCK FORECASTING
ORIGIN DESTINATION DISAGGREGATION USING FRATAR BIPROPORTIONAL LEAST SQUARES ESTIMATION FOR TRUCK FORECASTING Unversty of Wsconsn Mlwukee Pper No. 091 Ntonl Center for Freght & Infrstructure Reserch &
More informationModels and Software for Urban and Regional Transportation Planning : The Contributions of the Center for Research on Transportation
Models nd Softwre for Urbn nd Regonl Plnnng : The Contrbutons of the Center for Reserch on Mchel Florn Aprl 2008 CIRRELT200811 Models nd Softwre for Urbn Regonl Plnnng: The Contrbutons of the Center
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 12015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationNo 144. Bundling and Joint Marketing by Rival Firms. Thomas D. Jeitschko, Yeonjei Jung, Jaesoo Kim
No 144 Bundlng and Jont Marketng by Rval Frms Thomas D. Jetschko, Yeonje Jung, Jaesoo Km May 014 IMPRINT DICE DISCUSSION PAPER Publshed by düsseldorf unversty press (dup) on behalf of Henrch Hene Unverstät
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationLoyalty Program and Customer Retention of Bank Credit Cards an Logistic Regression Analysis based on Questionnaires
oylty Progrm nd Customer Retenton of Bnk Credt Crds n ogstc Regresson nlyss sed on Questonnres ZHU Qn IN Runyo College of Economcs Zhejng Gongshng Unversty P.R.Chn 310014 strct To Chnese credt crd ssuers
More informationMath Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationHedging InterestRate Risk with Duration
FIXEDINCOME SECURITIES Chapter 5 Hedgng InterestRate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cashflows Interest rate rsk Hedgng prncples DuratonBased Hedgng Technques Defnton of duraton
More informationWhen Talk is Free : The Effect of Tariff Structure on Usage under Two and ThreePart Tariffs
0 When Talk s Free : The Effect of Tarff Structure on Usage under Two and ThreePart Tarffs Eva Ascarza Ana Lambrecht Naufel Vlcassm July 2012 (Forthcomng at Journal of Marketng Research) Eva Ascarza
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationFeasibility of Using Discriminate Pricing Schemes for Energy Trading in Smart Grid
Feasblty of Usng Dscrmnate Prcng Schemes for Energy Tradng n Smart Grd Wayes Tushar, Chau Yuen, Bo Cha, Davd B. Smth, and H. Vncent Poor Sngapore Unversty of Technology and Desgn, Sngapore 138682. Emal:
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationChapter 7: Answers to Questions and Problems
19. Based on the nformaton contaned n Table 73 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationALABAMA ASSOCIATION of EMERGENCY MANAGERS
LBM SSOCTON of EMERGENCY MNGERS ON O PCE C BELLO MER E T R O CD NCY M N G L R PROFESSONL CERTFCTON PROGRM .. E. M. CERTFCTON PROGRM 2014 RULES ND REGULTONS 1. THERE WLL BE FOUR LEVELS OF CERTFCTON. BSC,
More informationAPPLICATION OF QUEUING THEORY TO DYNAMIC VEHICLE ROUTING PROBLEM WeiNing Chen, Kainan University Taiwan
GLOBAL JOURNAL OF BUSINESS RESEARCH VOLUME 3 NUMBER 009 APPLICATION OF QUEUING THEORY TO DYNAMIC VEHICLE ROUTING PROBLEM WeNng Chen Knn Unersty Twn ABSTRACT In ths pper we eelope n nlyze ynmc moel of
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationPositive Integral Operators With Analytic Kernels
Çnky Ünverte FenEdeyt Fkülte, Journl of Art nd Scence Sy : 6 / Arl k 006 Potve ntegrl Opertor Wth Anlytc Kernel Cn Murt D KMEN Atrct n th pper we contruct exmple of potve defnte ntegrl kernel whch re
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, crossclssified
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationPerformance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application
Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdodong,
More informationVoIP for the Small Business
Reducing your telecommunictions costs VoIP (Voice over Internet Protocol) offers low cost lterntive to expensive trditionl phone services nd is rpidly becoming the communictions system of choice for smll
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationChapter 6 Best Linear Unbiased Estimate (BLUE)
hpter 6 Bet Lner Unbed Etmte BLUE Motvton for BLUE Except for Lner Model ce, the optml MVU etmtor mght:. not even ext. be dffcult or mpoble to fnd Reort to uboptml etmte BLUE one uch uboptml etmte Ide
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationLabor Productivity and Comparative Advantage: The Ricardian Model of International Trade
Lbor Productivity nd omrtive Advntge: The Ricrdin Model of Interntionl Trde Model of trde with simle (unrelistic) ssumtions. Among them: erfect cometition; one reresenttive consumer; no trnsction costs,
More informationON THE IMPACT OF A SINGLE SALES FACTOR ON CALIFORNIA JOBS AND ECONOMIC GROWTH
Doc 004 69 pgs ON THE IMPACT OF A SINGE SAES FACTOR ON CAIFORNIA JOBS AND ECONOMIC GROWTH Chrles W. Senson, Ph.D., CPA Professor nd eventhl Reserch Fello Mrshll School of Busness Unversty of Southern
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment
ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks
More informationResearch on performance evaluation in logistics service supply chain based unascertained measure
Suo Junun, L Yncng, Dong Humn Reserch on performnce evluton n logstcs servce suppl chn bsed unscertned mesure Abstrct Junun Suo *, Yncng L, Humn Dong Hebe Unverst of Engneerng, Hndn056038, Chn Receved
More informationFuzzy Clustering for TV Program Classification
Fuzzy Clusterng for TV rogrm Clssfcton Yu Zhwen Northwestern olytechncl Unversty X n,.r.chn, 7007 yuzhwen77@yhoo.com.cn Gu Jnhu Northwestern olytechncl Unversty X n,.r.chn, 7007 guh@nwpu.edu.cn Zhou Xngshe
More informationAlternatives to an Inefficient International Telephony. Settlement System
Alterntve to n Ineffent Interntonl Telephony Settlement Sytem Alterntve to n Ineffent Interntonl Telephony Settlement Sytem Koj Domon Shool of Sol Sene Wed Unverty 6 NhWed Shnjukuku Tokyo 698050 JAPAN
More informationYOU FINALLY FINISHED YOUR FILM. NOW WHAT? Distributor...? Sales agent...? GOT IT: SELF DISTRIBUTION
YOU FINALLY FINISHED YOUR FILM. NOW WHAT? Dstrbutor...? Sles gent...? GOT IT: SELF DISTRIBUTION THE ADVANTAGES OF SELF DISTRIBUTION: A gurnteed openng n NY / LA prme theter nd you keep 100% of the boxoffce.
More informationStrategic Labor Supply
Prelmnry drft My 1999 Do not quote wthout permsson of uthor Comments re welcome Strtegc Lor Supply A dynmc rgnng model nd ts econometrc mplementton Mrm Belo Free nversty of Berln Astrct In ths pper dynmc
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationRevenue Management Games: Horizontal and Vertical Competition
Revenue Mngement Gmes: Horzontl nd Vertl Competton Sergue Netessne he Whrton Shool Unversty of Pennsylvn Phldelph, PA 191036340 netessne@whrton.upenn.edu Robert A. Shumsky Smon Shool of usness Admnstrton
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationCardiff Economics Working Papers
Crdff Economcs Workng Ppers Workng Pper No. E204/4 Reforms, Incentves nd Bnkng Sector Productvty: A Cse of Nepl Kul B Luntel, Shekh Selm nd Pushkr Bjrchry August 204 Crdff Busness School Aberconwy Buldng
More informationExponentiation: Theorems, Proofs, Problems Pre/Calculus 11, Veritas Prep.
Exponentition: Theorems, Proofs, Problems Pre/Clculus, Verits Prep. Our Exponentition Theorems Theorem A: n+m = n m Theorem B: ( n ) m = nm Theorem C: (b) n = n b n ( ) n n Theorem D: = b b n Theorem E:
More informationEfficient Bandwidth Management in Broadband Wireless Access Systems Using CACbased Dynamic Pricing
Effcent Bandwdth Management n Broadband Wreless Access Systems Usng CACbased Dynamc Prcng Bader AlManthar, Ndal Nasser 2, Najah Abu Al 3, Hossam Hassanen Telecommuncatons Research Laboratory School of
More informationLesson 28 Psychrometric Processes
1 Lesson 28 Psychrometrc Processes Verson 1 ME, IIT Khrgpur 1 2 The specfc objectves of ths lecture re to: 1. Introducton to psychrometrc processes nd ther representton (Secton 28.1) 2. Importnt psychrometrc
More informationISLM Model 1 C' dy = di
 odel Solow Assumptons  demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth  Assumptons  supply s rrelevant n short run; assumes economy s operatng below potental
More informationWHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS?
WHAT HAPPES WHE YOU MIX COMPLEX UMBERS WITH PRIME UMBERS? There s n ol syng, you n t pples n ornges. Mthemtns hte n t; they love to throw pples n ornges nto foo proessor n see wht hppens. Sometmes they
More informationVoIP for the Small Business
VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become
More informationBond futures. Bond futures contracts are futures contracts that allow investor to buy in the
Bond futures INRODUCION Bond futures contracts are futures contracts that allow nvestor to buy n the future a theoretcal government notonal bond at a gven prce at a specfc date n a gven quantty. Compared
More informationVoIP for the Small Business
VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become
More informationVoIP for the Small Business
VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become
More informationManaging Cycle Inventories. Matching Supply and Demand
Managng Cycle Inventores Matchng Supply and Demand 1 Outlne Why to hold cycle nventores? Economes of scale to reduce fxed costs per unt. Jont fxed costs for multple products Long term quantty dscounts
More informationON THE EFFECTIVENESS OF SINGLE SALES FACTORS FOR STATE TAXATION
ON THE EFFECTIVENESS OF SINGE SAES FACTORS FOR STATE TAXATION Chrles Senson Professor nd eventhl Reserch Fello Mrshll School of Busness Unversty of Southern Clforn June, 0 ABSTRACT Ths study odels nd eprclly
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationEntry Games in Exogenous Sunk Costs Industries (Sutton, Chapter 2)
Entry Games n Exogenous Sunk Costs Industres (Sutton, Chapter 2) StructureConducterformance aradgm: Models oneway chan of causaton Concentraton to erformance, treatng Conduct as a Black Box ew Industral
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationOn the System Dynamics of the Logistic Risk of Marketing Channels
1194 JOURNAL OF SOFTWARE, VOL. 8, NO. 5, MAY 2013 On the System Dynmcs of the Logstc Rsk of Mrketng Chnnels Yng M School of Mngement, Wuhn Unversty of Technology, Wuhn, Chn Eml: myng331@163.com Fe Feng
More informationVoIP for the Small Business
Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the
More informationVoIP for the Small Business
VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become
More informationProduction. 2. Y is closed A set is closed if it contains its boundary. We need this for the solution existence in the profit maximization problem.
Producer Theory Producton ASSUMPTION 2.1 Propertes of the Producton Set The producton set Y satsfes the followng propertes 1. Y s nonempty If Y s empty, we have nothng to talk about 2. Y s closed A set
More informationVoIP for the Small Business
Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephonyrelted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the
More informationThe Economics of Twosided Markets 2. Platform competition!
U. Porto Doctoral Programme n Economcs The Economcs of Twosded Markets 2. Platform competton! Paul Belleflamme, CORE & LSM! Unversté catholque de Louvan! Aprl 1013, 2012 Learnng objectves At the end
More informationThreePhase Induction Generator Feeding a SinglePhase Electrical Distribution System  Time Domain Mathematical Model
ThreePhse Induton Genertor Feedng SnglePhse Eletrl Dstruton System  Tme Domn Mthemtl Model R.G. de Mendonç, MS. CEFET GO Jtí Deentrlzed Unty Eletrotehnl Coordnton Jtí GO Brzl 763 L. Mrtns Neto, Dr.
More information