Extended Abstract for WISE 2005: Workshop on Information Systems and Economics

Transcription

1 Extended Abstract for WISE 5: Workshop on Informaton Systems and Economcs How Many Bundles?:An Analyss on Customzed Bundlng of Informaton Goods wth Multple Consumer Types Wendy HUI Ph.D. Canddate Department of Informaton and Systems Management Hong Kong Unversty of Scence and Technology Clear Water Bay, Hong Kong Emal: Byungjoon YOO Busness School Korean Unversty Seoul, Korea Emal: Kar Yan TAM Department of Informaton and Systems Management Hong Kong Unversty of Scence and Technology Clear Water Bay, Hong Kong Emal: (5 Pages long - excludng ths ttle page) Ths paper wll be presented by Wendy Hu.

2 . Introducton How Many Bundles?:An Analyss on Customzed Bundlng of Informaton Goods wth Multple Consumer Types (Extended Abstract) In versonng of goods, the frm offers multple versons for consumers wth dfferent prvate values to self-select nto the verson desgned for them. Typcally, versonng reures the frm to determne a set of {, p }, where denotes the ualty or uantty of verson, p denotes the prce of verson, and n, where n denotes the number of versons offered. Ths problem has been solved n Maskn and Rley (984). However, the exstng lterature has not fully addressed the problem of fndng the optmal n. Exceptons are Bhargava and Choudhary () and Bhargava and Choudhary (4a). In the absence of network externaltes and assumng constant margnal utlty, t was found that t s optmal to offer only one verson (Bhargava and Choudhary ). In the presence of network externaltes and agan assumng constant margnal utlty, t was found that t s optmal for the frm to offer only two versons (Bhargava and Choudhary 4). Ths paper extends ther work to look at the case n whch margnal utlty s decreasng. Ths assumpton s mportant because nformaton overload s a common problem people face today; and the margnal utlty of a pece of news, musc or other nformaton s lkely to be decreasng. Classc economcs research on second degree prce dscrmnaton suggests that the frm should offer as many versons as there are consumer types (Maskn and Rley 984). However, n realty, we seldom see too many versons offered by a frm. One good reason s that too many optons confuse the consumers (Estelam 3). It also ncreases the cost of managng the menu for the frm (Wu and Anandalngam ). Although the determnaton of the optmal number of versons has not been fully addressed analytcally n the lterature, gudelnes based on understandng of consumer psychology exst. Shapro and Varan (999) suggested that Goldlocks prcng n whch three versons (low, medum and hgh) are offered s a good strategy. People would choose the medum verson because of extremeness averson. Ths paper provdes a rgorous approach to determne the optmal number of versons n the context of customzed bundlng, although our results can be appled to the general ualty versonng problem. Ths paper takes nto consderaton both menu cost and cogntve cost n determnng the optmal number of versons. Both costs decrease the optmal number of versons, but they are found to have very dfferent practcal mplcatons.. The model. The Base Model We use Chuang and Srbu s model (999). There s a monopolstc frm sellng Q goods to consumers. For the utlty functon of consumers, a typcal margnal utlty functon s gven by (, ) = v v and s graphcally shown n Fgure a. The correspondng utlty functon s a typcal concave utlty functon as shown n Fgure b. v

3 v(, ) v v v(, ) = v v V(, ) (a) Fgure. Typcal Consumer Valuaton Profle Htt and Chen (4) nterpreted v as the consumer s overall budget constrant. The assumpton was that the hgher the ncome of a consumer, the hgher her wllngness to pay for the nformaton goods. defnes the consumer s potental consumpton level and consumer type. Potental consumpton level s the maxmum consumpton level when all goods are offered free of charge. Greater means greater potental consumpton level of that consumer. Wthout loss of generalty, we normalze total number of consumers n the market to. We also assume n our model that A. The margnal cost of producng an nformaton good, c, s neglgble. v, = v v/, where v s fxed. A. The monopolst has knowledge of the margnal utlty functon ( ) By assumng v to be fxed, we gnore the effect of varatons n ncome and focus on consumer heterogenety defned by consumpton level. Ths s consstent wth the common assumpton n the lterature that consumer heterogenety s one-dmensonal. Note that ths formulaton of v (, ) satsfes the sngle crossng property. We consder a market wth consumers who are heterogeneous n ther. And we further assume that potental consumpton levels (,Q) A3. The frm knows that the dstrbuton of s Unform[, Q ]. To solve for the customzed bundlng problem, we can apply the standard results on monopolstc prcng under uncertanty from the lterature (Maskn and Rley 984, Spegel 997). Usng Euaton (8) of (Spegel 997), the soluton of the second-degree prce dscrmnaton problem can be obtaned by n solvng for ( ) (b) (, ( ) ) ( ) v F v(, ( ) ) = c+ () ( ), whch denotes the optmal bundle sze that serves consumer type, can be found to be ( ) = ( v c) Fgure shows the optmal bundle sze that serves each consumer type when Q =. The prce for each bundle sze can be found by Qv

4 ( ) = % % % = % p v d % (, ( )), ( ) ( v c) ( v c) 3 Q 3Qv Optmal Bundle Sze () Consumer Type (theta) Fgure. Optmal Bundle Sze versus Consumer Type (when c =, Q = ). Effects of Menu Costs To determne the optmal number of verson n the presence of postve menu cost for the monopolstc frm, we frst fnd the optmal proft earned under n versons, where n s an arbtrary nteger such that n < Q. Wth the assumpton that margnal cost s neglgble,.e., c =, we show that the proft earned when there are n versons s It s easy to see that ( n ) ( n + ) + Qv Π ( n) = 6 Proposton. Proft ncreases wth the number of versons. The margnal beneft of an addtonal verson, however, s decreasng n the number of versons n. We consder menu cost M( n ), whch s assumed to be ncreasng n n. The optmal number of bundles n can be found by solvng the frst order condton Qv ( n + ) 3 = M ' 3 ( n) () Snce the left hand sde of Euaton () s decreasng n n, t s obvous that Proposton. Menu cost decreases the optmal number of versons offered. Snce the determnaton of the optmal schedule gven n does not depend on M( n ), Proposton 3. For a gven number of versons, n, menu cost does not affect the optmal bundle sze and optmal bundle prce p for all n. 3

5 .3 Effect of cogntve costs For consumers, we assume that cogntve effort to recognze and evaluate n versons s convex n n and t takes the form ( ) e n = kn where k controls the sze of the cogntve cost and s nterpreted here as product complexty. We show that Proposton 4. Cogntve cost decreases the optmal number of versons offered. Fgure 3 shows the relatonshp between the optmal number of versons and k graphcally. optmal number of versons (n) product complexty (k) Fgure 3. The Optmal Number of Versons vs. Product Complexty The effects of cogntve cost are more complcated than that of menu cost. Cogntve cost s born by the consumers, whch s antcpated by the frm. The frm formulates ts versonng strategy takng consderaton consumers cogntve costs and, therefore, both the ualty and prce of each verson wll be affected. We show that Proposton 5a. For a gven number of versons, n, cogntve cost ncreases the optmal bundle sze for n, whle the optmal bundle sze of the hghest verson remans Q. Proposton 5b. For a gven number of versons, n, cogntve cost decreases the optmal bundle prce p for all n. Fgure 4a and Fgure 4b llustrates Proposton 5a and Proposton 5b, respectvely, for n = 9. We can see from Fgure 4b that cogntve cost shfts margnal consumer types to the rght. Each bar s slghtly taller (ualty ncreased), but narrower (number of consumers per verson decreased). Due to cogntve cost, lower types consumers who prevously found the bundles worth buyng decde not to buy. Propostons 5a and 5b suggest that n response to the drop out, the frm would ncrease the verson prces slghtly to mnmze the effect of decreased customer base. 3. Contrbuton We provded a rgorous approach to determne the mportant ueston of How many versons? Wthout assumpton of any versonng related costs, we found that the margnal beneft of an addtonal verson s decreasng. Menu cost and cogntve cost decrease the optmal number of versons. However, 4

6 they have very dfferent practcal mplcatons. For a gven number of versons, ncrease n menu cost s completely born by the frm. It does not affect consumers at all: the ualty of the verson and the prce of the verson stay the same. On the other hand, cogntve cost has more profound mpact on the versonng. As cogntve cost ncreases, the frm should rase the ualty of each verson and at the same tme decrease the verson prce. Management of a menu s often asssted by IT. As IT advances, menu cost wll contnue to drop. Frms should focus on reducng cogntve cost, whch s the key factor that prevents frms from effectvely explotng the versonng strategy. If t s mpossble to keep cogntve cost low due to product complexty, our results suggest that frm should ncrease verson ualty to reduce the pressure on prce reducton and mnmze proft loss due to cogntve cost. Bundle Sze Purchased by Each Consumer Type Bundle Sze Purchased by Each Consumer Type Bundle Sze Consumer Types Bundle Sze Consumer Types (a) e(n) = (b) e(n) =. 4. References Fgure 4. Bundle Szes Purchased by Consumer Types Bhargava, H. and Choudhary, V., Informaton Goods and Vertcal Dfferentaton, Journal of Management Informaton Systems,, 8(), 85-. Bhargava, H. and Choudhary, V., Economcs of an Informaton Intermedary wth Aggregaton Benefts, Informaton Systems Research, 4, 5(), -36. Chuang, J. C-I. and Srbu, M. A., Optmal Bundlng Strategy for Dgtal Informaton Goods: Network Delvery of Artcles and Subscrptons, Informaton Economcs and Polcy, 999, (), Estelam, H. (3) Strategc mplcatons of a mult-dmensonal prcng envronment, The Journal of Product and Brand Management, (5), Htt, L. M. and Chen, P., Bundlng wth Customzed Self-Selecton: A Smple Approach to Bundlng Low Margnal Cost Goods, Workng Paper, 4. Avalable at Maskn, E., and Rley, J., Monopoly wth ncomplete nformaton, RAND Journal of Economcs, 984, 5(), Shapro, C. and Varan, H. R., Informaton Rules: A Strategc Gude to the Network Economy, Harvard Busness School Press, 999. Spegel, Y., Second-degree Prce Dscrmnaton, 997. Avalable at: Wu, S. and Anandalngam, G., Optmal Customzed Bundle Prcng for Informaton Goods,. Avalable at: 5