Price Discrimination of Digital Content

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1 Prce Dscrmnaton of Dgtal Content Prce Dscrmnaton of Dgtal Content Koj Domon Faculty of Socal Scences, Waseda Unversty -6- Nshwaseda, Shnjuku-ku, Tokyo , Japan Tel/Fax: , E-mal: domon@waseda.jp February, 2006 Abstract: Ths paper consders the smplest DRM, whch permts ether free or no copyng, wth ncomplete nformaton about the type of consumer. We frst obtan results concernng separablty of consumers n a general stuaton, and show that there s a crtcal type of consumer. A hgher utlty type selects a menu of free copyng whereas a lower one chooses not to copy. n a two-type model we ndcate that optmal prcng for a producer s dfferent from that under two-part tarffs. Ths prce strategy brngs about greater profts and socal welfare f, and only f, self-producton s more effcent than that of a producer. JEL classfcaton: D82, L, L86 Keywords: Prce dscrmnaton, Two-part tarff, ncomplete nformaton, Copyng, Dgtal Rghts Management Ths paper was supported by Grants-n-Ad for Scentfc Research for the Promoton of Scence ((B) , (C) (2) ) n Japan.

2 Prce Dscrmnaton of Dgtal Content. ntroducton One of the greatest mpacts of dgtalzaton s the drastc cost reducton of personal copyng. Most people copy musc CDs onto PC hard dsks, portable hard dsk players, or empty CDs. The same phenomenon arose n TV. PCs wth a TV tuner, as well as a hard-dsk DVD recorder, have spread nto people s homes. Facng such stuatons, copyrght owners have managed to control personal copyng through Dgtal Rghts Management (DRM). Recent onlne store DRMs gve consumers menu optons to select smlar to those of moble phone servces. The smplest menu s to choose free copyng or not. Ths paper consders prce dscrmnaton n ths basc case. Areas of our dscusson are self-selecton and self-producton. Self-selecton s a key element for prce strateges, under ncomplete nformaton about a consumer type, n prncpal-agent ncentve schemes. Laffont and Martmort (2002) brefly summarze these ssues. Under the constrant of self-selecton, Spence (980) consders prcng formulas for maxmzng socal welfare, whle Maskn and Rley (984) generalze monopolst non-lnear prcng. Kolay and Shaffer (2003) prove that bundlng of quantty and prce s superor to two-part tarffs for proft maxmzaton. Consderng self-producton, there are varous artcles relatng to personal copyng. Whenever a new copy technology, such as a photocopy machne, a home vdeo-recorder, or an nternet fle-sharng on the nternet, emerged, copyrght owners complaned of copyrght nfrngement. Dscussons have centered on the defnton of Far Use. Lebowtz (985) ndcated that photocopyng n the lbrary could be reflected by subscrpton fees of journals, that s, copyrght owners have ndrect approprablty. Concernng unauthorzed fle-sharng on the nternet, Lebowtz (2003) consdered ts effects on CD sales. Domon and Yamazak (2004) also consdered a prcng strategy under unauthorzed fle-sharng. Domon and Joo (2006) consdered dgtal broadcastng DRM from the pont of ndrect approprablty, ndcatng a case n whch a strct DRM s unproftable for a producer. 2. Consumer Behavors A producer provdes two menus for consumers, one wth a free personal copy and the other wth a copy control. n the frst menu, Menu, they may copy as many tmes as they wsh f they use coped content. n the second menu, Menu, they cannot physcally copy content due to the technology of the Dgtal Rghts Management. The prce of Menu s composed of only a fxed charge denoted as F. A margnal 2

3 Prce Dscrmnaton of Dgtal Content cost for personal copyng s constant and expressed as c, and there s no fxed cost for personal copyng. We do not have to consder a per-unt prce n ths case, snce consumers select ths menu because they are allowed to copy freely. The prce of the second menu s composed of two parts: a per-unt prce, denoted as P, and a fxed prce, denoted as F. n order for our analyss to be meanngful, the followng assumpton s necessary: As.. F > P + F and P > c. Reverse nequalty of these condtons s excluded from prce strateges, because, n such a case, consumers select a menu wth no personal copyng by payng a hgher prce. A consumer selects a menu from these and maxmzes the followng utlty functons, ( θ, ) U = V F cn, for Menu () ( θ, ) U V P F =, for Menu (2) where V s a gross consumer surplus, θ a type of consumer, ( ) 2 the amount of content consumpton, n ( 0) personal copy tme, and = n + for menu. V As.2. > 0, V 2 < 0 2 V, and Lm = 0. V As.3. > 0, and θ 2 V θ > 0. A crtera for self-selecton can be expressed by usng θ. Before obtanng the crtera, we prove two lemmas. Frst ( θ ) > ( θ, P ) s obvous from As. From that, the level of utlty at the optmal content consumpton s expressed as: 2 How to defne the unt of consumpton s not theoretcally mportant. However, n our model, we count t from n order to take nto account copy tme. Theoretcally, we do not mnd the frst unt of consumpton,. When the frst unt s nfntesmal, we have a techncal problem countng the amount of self-producton. 3

4 Prce Dscrmnaton of Dgtal Content ( θ, ) U V F V c d = ( θ,) + ( θ, ) ( θ, ) = V( θ,) F + V c d + V c d, (3) V( θ, ) U = V( θ,) P F + P d. (4) Lemma. U ( >=< ) U f and only f F ( )( ) P F < f ( θ, ) P + = >, where f ( θ, P ) ( P c) d V( θ, ) c d +. Proof. Ths s drectly derved from (9) and (0), that s, U U V F V c d V c d = ( θ,) + ( ) + V V( θ,) P F + ( P ) d V = ( P + F F ) + ( P c) d + c d = ( P + F F ) + f( θ, P ).. E. D. A functon f expresses a utlty ncrease when a consumer selects Menu nstead of Menu, when we exclude ntal costs, F and P + F. The frst term of f s a beneft from free copyng nstead of purchasng content wth DRM. The second term s a beneft from ncreased consumpton under free copyng. Lemma 2. f ( θ, P ) s strctly ncreasng wth respect to θ. Proof. From the envelope theorem, 4

5 Prce Dscrmnaton of Dgtal Content f ( θ, P ) V( θ, ) ( θ, P ) V( θ, ) ( θ, c) = P c + θ θ θ V( θ, ) V( θ, ) + θ θ V( θ, ) V( θ, ) = > 0. (from As. 3). E. D. θ θ Proposton. f there s * P, then * θ satsfyng F ( P F ) f( θ*, P ) + = gven F, >=<. θ s unque and U ( >=< ) U ( ) f and only f θ * θ F and Proof. F ( P F ) 0 + > s from As., and f s ncreasng wth respect to θ from Lemma 2. Therefore, when there exsts θ *, then θ * s unque and ( + < )( = > ) f and only f θ ( ) θ * F P F f proposton.. E. D. >=<. Ths result and Lemma lead to ths Ths proposton ndcates that consumers are dvded nto two groups, hgh utlty consumers selectng Menu and low utlty ones selectng Menu. ntal costs of Menu, whch s ncurred by the frst purchase of content, are greater than those n Menu, snce Menu permts unlmted copes. Therefore, those who want one unt of content due to low utlty select Menu. Consumers wth hgh utlty want more unts, and can effcently obtan them by personal copyng. At some pont the merts from personal copyng exceed the demerts of ntal costs. Consumers wth hgh utlty enjoy these merts by copyng freely. 3. A Two-Type Model We consder a two-type model n whch consumers are dvded nto two types: a hgh utlty type wth θ H L H and a low one wth θ ( θ ) <. Ths type of model has been dscussed n ncomplete nformaton analyses. We suppose that the number of consumers s normalzed to one, and the proportons of a hgh and a low utlty type are 5

6 Prce Dscrmnaton of Dgtal Content respectvely denoted as δ and δ (0< δ < ). A producer knows only these proportons and the margnal cost for content producton s mc. n such a case, a maxmzng problem for a producer s F, F, P { } L L ( ) ( ) (, ) (, ) Max π = δ F mc + δ P θ P + F mc θ P (5) H L ( θ ) ( ) ( θ ) st.. f, P F P + F f, P, (6) ( ) H H H U = V θ, ( θ ) F cn ( θ ) 0, (7) ( ) L L L U = V θ, ( θ, P ) P ( θ, P ) F 0. (8) The condton of (6) s a separablty one of consumers. Condtons (7) and (8) are constrants for ndvdual ratonalty. Due to ncomplete nformaton, a producer cannot obtan all consumer surpluses. n the two-part tarffs, t s well-known that a proft maxmzng per-unt prce for hgh utlty consumers s equal to a margnal cost, mc. n other word, consumers purchase content at the pont where ( θ H, ) self-produce content at the pont of ( θ H, ) we obtan the followng proposton, V = mc. However, n our model, consumers V = c. Consderng ths dfference, Proposton 2. Proft maxmzng solutons are as follows; ( θ, P ) L δ L H P * = mc+ { ( θ, P ) ( θ, P )} > mc, δ P ( θ ( θ )) ( θ ) L L L F * = V,, P P, P, { ( θ ( θ )) ( θ )} F * = V, cn H H H { ( θ ( θ )) ( θ )} H, H, H, V P P P + F *. Proof. A procedure of ths proof concernng optmal prces s the same as that of Kolay and Shaffer (2003).. E. D. 6

7 Prce Dscrmnaton of Dgtal Content A producer does not have a per-unt prce for hgh utlty consumers who can produce copes by themselves under ther margnal cost. Ths means that a producer delegates producton to consumers whose margnal cost s c( < mc). Ths delegaton may be benefcal for a producer, snce an optmal fxed fee, F, stemmng from consumer surpluses, ncreases due to ths effcent self-producton. Ths mples that a producer can derve ndrect approprablty from hgh utlty consumers by allowng personal copyng. MV( θ, ) A E P * mc c H J F G ( θ, P ) L B L MV( θ, ) C H ( θ ) D H MV( θ, ) Fgure. Dfference between two-part tarff and DRM Proposton 3. f only f mc > c, prce dscrmnaton by DRM s more proftable than two-part tarff and mproves the socal welfare. Proof. Ths s explaned n Fgure 3. Frst, snce P * n a model of the two-part tarffs s the same as that n our model, profts from a low utlty consumer n both cases are represented as an area of EFG. Secondly, profts from a hgh utlty consumer under DRM are BDJEF whle those under the two-part tarff are BCEF. Therefore, f mc > c, a producer s profts ncrease by CDJ. The socal welfare under DRM s ADJ whle that under the two-part tarff s AC. Therefore, t ncreases by CDJ whch s equal to ncreases n the producer s profts. 7

8 Prce Dscrmnaton of Dgtal Content Furthermore, t s apparent that the producer s profts and socal welfare ncrease only f mc > c.. E. D. 4. Concludng Remarks Benefts from content depend not only on prce but also on usage. Moreover, unlke physcal goods, dgtal content can easly be coped. Reflectng these facts, DRM offers flexble menus for consumers. Although onlne dstrbuton of musc content began to cope wth unauthorzed fle-sharng on the nternet, t expanded musc markets and enhanced user convenence. The musc ndustry has begun to notce ths fact. We have shown that prce dscrmnaton by DRM s ncentve-compatble under ncomplete nformaton. Our analyss s the applcaton of ndrect approprablty, ponted out by Lebowtz (985), to ncomplete nformaton. References Domon, K. and Yamazak, N., Unauthorzed Fle-Sharng and the Prcng of Dgtal Content, Economcs Letters, 85, Domon, K. and Joo, E, 2006, Copy Control of Dgtal Broadcastng Content: An Economc Perspectve, Dgtal Broadcastng: Polcy and Practce n the Amercas, Europe and Japan, edted by Cave, M. and Nakamura K., Edward Elgar. Kolay, S. and Shaffer G., Bundlng and Menus of Two-Part Tarffs, Journal of ndustral Economcs, 5, Laffont, J. and Martmort, D., The Theory of ncentves: The Prncpal-Agent Model, Prnceton Unversty Press. Lebowtz, S. J., 985. Copyng and ndrect Approprablty: Photocopyng of Journal, Journal of Poltcal Economy, 93, Lebowtz, S. J., Wll MP3 Downloads Annhlate the Record ndustry? : The Evdence So Far, n Advances n the Study of Entrepreneurshp, nnovaton, and Economc Growth, edted by Gary Lbecap, JA Press. Maskn, E. and Rley, J., 984. Monopoly wth ncomplete nformaton, Rand Journal of Economcs, 5, Spence, M., 980. Mult-Product uantty-dependent Prces and Proftablty Constrants, Revew of Economc Studes, 47,

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