Unpriced Quality. Pascal Courty 1. September 2010

Transcription

1 npricd Quaiy Pasca Coury Spmbr 200 Absrac: A monopois dibray chargs h sam pric for diffrniad producs whn high uaiy producs ar mor iky o b assignd o ow vauaion consumrs undr uniform pricing. Th argumn can xpain h us of unpricd uaiy for concr icks, movi hars, and in ohr siuaions. JE: D42, D45. Kywords: Pric discriminaion, scond dgr pric discriminaion, raioning. Pasca Coury, Dparmn of Economics, Europan nivrsiy Insiu, Via San Paoo, Via Da Piazzuoa 43, 5033 Firnz, Iay, Pasca.Coury@IE.i.

2 Firms somims charg h sam pric for producs of diffrn uaiis dspi h fac ha a consumrs sricy prfr h high uaiy producs. Examps incud icks for sas of diffrn uaiy for spors and music vns. Connoy and Krugr 2006 rpor ha 43 prcn of concrs for popuar music in 2003 s a sas in h hous a h sam pric. Consumrs aso hav o wai o njoy h mos popuar aracions in hm parks Pass, 995. Rsaurans do no charg xra o hos consumrs who com during pak hours or pak days. Movi hars do h sam and in addiion hy do no charg mor for bockbusrs Einav and Orbach, In a hs xamps, uaiy is unpricd; ha is, a producs ar sod a h sam pric indpndny of uaiy. Can uniform pricing domina pric discriminaion vn whn hr is no addiiona cos associad wih impmning pric discriminaion? ndr pric discriminaion, h high uaiis producs nd up in h hands of h consumrs who vau uaiy h mos. ndr uniform pricing, his may no b h cas. Br producs may b snappd by h puggd in informd consumrs, by consumrs who can com on h firs day of sa, or by ucky consumrs. W ak h ru ha assigns producs o consumrs as givn and show ha uniform pricing can b opima for som assignmn rus. This is mor iky o b h cas for rvrs monoon rus, which assign high uaiy producs o ow yp consumrs. A coroary is ha advrizing mdiums and disribuion channs ha incras h chanc ha ow yps g h high uaiy producs ar compmn wih uniform pricing. This coud xpain why som pop ariss iniiay ras concr icks ony o fans rgisrd on h aris s officia wbsi or ony a h box offic on a spcific da. If corrc, his xpanaion impis ha pric discriminaion shoud b ss common among hos ariss.

3 Dspi h xnsiv conomic iraur on pric discriminaion, hr is surprisingy i work on why firm somims absain from pric discriminaing Crids 2004 and So Andrson and Dana 2008 sudy whn h opima produc in dominas sing a uniu produc uaiy. Insad, w ak h produc in as givn and invsiga whhr h firm wans o s diffrniad producs a diffrn prics. Mirav 2007 shows ha h rurn o compx ariffs may b ow and impmnaion coss coud xpain h prvanc of simp produc ins. W show ha uniform pricing can domina pric discriminaion vn in h absnc of impmnaion coss. -Examp Assum hr ar wo yps of consumr, wo yps of good, and ach consumr can consum a mos on good. Consumr =,H vaus v s a good of uaiy s=,h such ha v h>v, v s>v s, and v H h-v H >v hv. A consumrs vau h high uaiy good mor, h high yp vaus any uaiy mor han h ow yp, and h high yp vaus an incrmn in uaiy mor han h ow yp. In addiion, w aso assum ha v H >v h. Thr ar high yp consumrs and - ow yps. Thr is a uni coninuum of goods. To simpify, w assum ha h fracion of high uaiy goods is ua o and w show ar ha h rsus gnraiz. ndr pric discriminaion, h monopois fuy xracs h surpus of h ow yp consumrs, p = v, binds h incniv compaibiiy consrain of h high yps, p h = v +v H h-v H, and arns rvnu R d =v +v H h-v H. ndr uniform pricing, w assum ha h goods ar assignd according o an invrs monoon assignmn ru: high uaiy goods ar firs assignd o ow yps. ndr uniform pricing, h monopois chargs v h and arns profis R u v h hr ar nough 2

4 high uaiy goods for h ow yps and high yps buy sinc v H >v h. 2 Th gains from using uniform pricing insad of pric discriminaion, RR u -R d, can b xprssd as R v hv v H h-v H. Th monopois uss uniform pricing whn his xprssion is posiiv, ha is, whn v H h-v H /v hv <. This condiion is mor iky o hod whn hr ar no oo many high yps and whn high yps do no vau uaiy oo much raiv o ow yps so ha aocaion infficincis ar no oo arg. Th inuiion is ha h rvrs monoon assignmn ru incrass h wiingnss o pay of h ow yps mor han wha is os from h high yps undr pric discriminaion. Nx, w gnraiz h anaysis o a coninuum of consumrs and goods and o arbirary assignmn rus. 2-Anaysis W ak h sandard mod of scond dgr uaiy pric discriminaion Mussa and Rosn, 978 bu assum ha h s of producs is givn and ha i is opima o s a producs. This is h cas in h moivaing appicaions discussd arir and i aows us o focus on rvnu considraions aon. W argu ar ha h anaysis can b gnraizd. Th monopois has o pric a givn coninuum of goods of uaiy disribud according o G, [, h ]. Thr is a uni mass of consumr wih yp disribuion F, [, H ]. Consumr gs uiiy -p from buying a good of uaiy a pric p, whr >0, <0, and >0. Th sing crossing condiion impis ha i is fficin o 2 Th monopois coud arn mor by charging mor for ow uaiy goods. This prdicion is odd bu dos no chang h main poin of h papr. Quaiy is invrsy pricd! 3

5 assign highr uaiy goods o highr yps: consumr gs uaiy dfind by F =G. 3 ndr uniform pricing, consumrs buy a ory ovr uaiy. This is a gnra framwork. Consumrs may no know which produc hy wi rciv. Bu oris coud aso b dgnra in which cas h assignmn is drminisic. Th probabiiy dnsiy ha yp rcivs a good of uaiy is wih associad disribuion. Th oris ar givn. Th assignmn ru is such ha mark caring aks pac, H d=g, for a. In addiion, w assum d for a A h d h This condiion guaranis ha undr uniform pricing a yps paricipa if h ows yp dos. 4 To sabish a bnchmark, w assum ha h assignmn ru dos no induc addiiona coss. 5 This may b xrm bu impmning pric discriminaion aso inducs coss and hr is i on can say in gnra. So w av his asid, and ony compar h rvnus undr uniform pricing and pric discriminaion. ndr pric discriminaion, dno h pricing ru p and h profi maximizing assignmn ru pd. Th paricipaion consrain of consumr, p =, oghr wih h consumrs firs ordr condiions, =p, dfin h pricing ru as a funcion of h assignmn ru pd p d. 3 I is aways opima o s a goods if >-F for a whr.= -.. This condiion impis ha srving [, H ] dominas srving ony [, H ] for any. 4 This condiion hods undr a rvrs monoon assignmn if > for a whr is dfind by G =-F. 5 Quuing, for xamp, imposs a cos if h margina consumr has o b compnsad for hr im cos si and Sornson,

6 5 Taking fu drivaivs in h consumr firs ordr condiion wih rspc o impis ha pd is incrasing, which oghr wih fu mark covrag, impis pd =. Afr ingraion, w obain h rvnu undr pric discriminaion h x pd d g dx x R and afr ingraion by pars, w g h pd d G R. ndr assumpion A, h opima uniform pric is h d wih profis h u d R niform pricing waky dominas pric discriminaion if and ony if R R PD 0 h d G. 2 This sabishs our main rsu which w now discuss. ndr a rvrs monoon assignmn ru h ows yp gs h highs good for sur, =0 for a < h, and condiion 2 bcoms 0 h d G which is h coninuous vrsion of. A sufficin condiion for uniform pricing o b opima is G for a [, h ]. 3 Again, his condiion is uivan o condiion in h wo yp cas wih an invrs monoon assignmn ru. In gnra, i is ss iky o hod if hr is a arg fracion of high yps firs-ordr-sochasic-dominanc shif in G., if h assignmn ru is cosr o rvrs monoon firs-ordr-sochasic-dominanc shif in., and if highr yps

7 ar no wiing o pay much mor han h ows yp for incrmna unis of uaiy so ha infficincis ar no oo high h raio on h righ hand sid of inuaiy 3 is sma. Any assignmn ru away from rvrs monoon rducs h chanc ha uniform pricing is opima. For xamp, undr a random assignmn ru, =G, condiion 2 is vioad, and pric discriminaion is prfrrd. In a mark wih no consumr hrogniy a a, pric discriminaion and uniform pricing ar uivan. Pric discriminaion dominas uniform pricing whn hr much consumr hrogniy condiion 2 is vioad. Thrfor, uniform pricing can b sricy opima whn hr is som consumr hrogniy bu no oo much. Whn uniform pricing is opima, h assignmn of goods is infficin. Toa consumr wfar dcrass sinc ovra wfar dcrass and firm rvnu incrass. Som consumrs, howvr, may b br-off. 6 3-Concusions Th pric discriminaion iraur has ovrookd h possibiiy o dibray s an xognousy givn s of vricay diffrniad producs a h sam pric. This papr maks hr poins:. W show ha no pricing uaiy can domina pric discriminaion. 2. This dpnds on how high uaiy goods ar assignd undr uniform pricing. 3. A sr who uss uniform pricing sricy prfrs advrizing mdiums, disribuion channs, and ohr mans ha hp assigning high uaiy goods o ow yps. W assumd ha h s of goods was givn and focusd on h monopoy rvnu maximizaion probm. Th anaysis coud b xndd o ndognous produc uaiis. 6 h This wi b h cas if d p whr.= -.. 6

8 Cary, h rsus hod for cos funcions ha sufficiny consrain h monopois s choic of produc in, so ha h profi maximizing produc in saisfis condiion 2. Rfrncs Andrson, Eric and Jams Dana Ingraing Mods of Pric Discriminaion. Mimo, Norhwsrn. Connoy, Mari and Aan B. Krugr 2006, Rockonomics: Th Economics of Popuar Music. Handbook of h Economics of Ar and Cuur. Crids, Sofronis Pric Discriminaion wih Diffrniad Producs: Dfiniion and Idnificaion. Economic Inuiry 423, Einav, iran and Orbach, Barak niform Prics for Diffrniad Goods: Th Cas of h Movi-Thar Indusry. Inrnaiona Rviw of aw and Economics, 272, si, Phiip and Aan Sornsn Th Wfar Effcs of Tick Rsa. Mimo, GSB, Sanford nivrsiy. Mirav, Eugnio Th imid Gains from Compx Tariffs. CEPR Discussion Papr No Mussa, M., and S. Rosn 978 Monopoy and Produc Quaiy, Journa of Economic Thory 8: Pass, Pr. Disnyand and h od.s.s.r. Nw York Tim, Apri 27, 995. So, ars. Pric Discriminaion and Compiion. In M. Armsrong and R. Porr: Handbook of Indusria Organizaion, Voum 3. Amsrdam: Esvir,