AN ANALYSIS OF EQUILIBRIUM RELATIONSHIP BETWEEN PRICE ELASTICITY AND EXPENDITURE LEVEL: A CASE STUDY OF KOREAN MOBILE MARKET DATA

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1 JOURNA OF ECONOMIC DEVEOPMENT 69 Volume 34, Number 2, December 2009 AN ANAYSIS OF EQUIIBRIUM REATIONSIP BETWEEN PRICE EASTICITY AND EXPENDITURE EVE: A CASE STUDY OF KOREAN MOBIE MARKET DATA * ONGJAI REE AND SANGKYU REE Ajou Unversty and Chung-Ang Unversty In most developng countres, telecommuncatons ndustry has been grown fast and stll has more growth potental than n the developed countres. Clearly the telecommuncatons ndustry contrbutes to foster economc developments and also to narrow the communcaton gaps among countres. Among many components relatng to the success of quck developments of telecommuncaton servces, an approprate and optmal prcng strateges s the most vtal element. In ths vew pont, ths paper examnes the optmal prce dscrmnaton strategy for frms n a monopolstcally compettve market. The prmary nterest s the theoretcal relatonshp between prce elastcty and the average expendture level of consumers. Our equlbrum analyss shows that the relatonshp can go ether way (postve or negatve) dependng on the prevalng prce level of the product n concern. As an emprcal example, usng a herarchcal Bayes model we fnd that heavy user of moble servce are substantally more elastc to the prce of calls n Korea. A dscusson of the optmal prcng scheme and market structure s n order. Keywords: Prce Dscrmnaton, Prce Elastcty, Prce Senstvty, Moble Telecommuncatons, erarchcal Bayes Model JE classfcaton: INTRODUCTION In most developng countres, telecommuncatons ndustry has been grown fast and stll has more growth potental than n the developed countres. Snce the telecommuncaton servces are essental nput for all the ndustres, t s clear that the telecommuncatons ndustry contrbutes to foster economc developments and also to narrow the communcaton gaps between countres. Among many components relatng * The authors are grateful to the anonymous referee for hs/her valuable comments. All remanng errors are ours.

2 70 ONGJAI REE AND SANGKYU REE to the success of quck developments of telecommuncaton servces, an approprate prcng polcy s the most vtal element. Therefore t wll be helpful to learn some lessons from the successful countres n telecommuncaton sector such as Korea whch we explore n ths paper. Specfcally, we note that prce dscrmnaton such as n the form of varous tarff optons s mportant to lessen the payment of consumers as well as to ncrease telecommuncaton operators proft margn. In ths vew pont, ths paper examnes the optmal prce dscrmnaton strategy for frms n a monopolstcally compettve market. The prmary nterest s the theoretcal relatonshp between prce elastcty and the average expendture level of consumers. In theory, monopoly and perfect competton comprse two typcal market structures. In realty, however, most markets fall n between the two extremes. Most products n a market have some degree of product dfferentals n the supply sde as well as some degree of consequental swtchng costs n the demand sde. Nevertheless, the exstng marketng practces and researches have not fully utlzed ths structural vewpont. The exstng marketng lterature has shown a great nterest n the cross-segment dfference n prce senstvty of customers when choosng a brand or an outlet (e.g., och et al. (1995), Bolton (1989), Kumar and eone (1988), Allenby and enk (1995)) whle payng much less attenton on the fundamental quantty decson of how much to buy at a gven prce. 1 In contrast, the prcng strategy n economcs lteratures s mostly about prce elastcty n a farly monopolstc envronment. In ths envronment, economcs theory predcts t proftable to have the mark-up (over margnal cost) n a market segment as reverse-proportonal to the prce elastcty of the consumers n the segment. Thus, from a manageral perspectve, t s mportant to apprehend who s more or less prce elastc. In sum, there exsts an obvous dsparty of concern n economcs and marketng lterature. For nstance, och et al. (1995) stated that a smple strategy for reducng promoton cost would be to have smaller prce cuts n the hghly senstve stores coupled wth larger cuts n the nsenstve stores. On appearance, ths suggeston seems contradctng the nverse elastcty rule f we adopt the usual termnologcal nterchange of prce elastcty and prce senstvty. As mentoned, whle the prmary objectve n marketng lterature s to use the cross-segment heterogenety n prce senstvty to maxmze the choce share of a brand n a hghly compettve envronment, the economc theory of nverse elastcty rule s mostly relevant for frms wth a monopoly power n customers choce of the quantty of ther products. avng ths n mnd, one should be careful to apply the fndngs drawn from a compettve envronment to a monopolstc envronment, and vce versa. For example, the expendture level (or basket sze ) and the purchasng frequency of consumers are found the most sgnfcant behavoral factors for underlyng dfferences n prce senstvty of customers (e.g., Ansle and Ross (1998), Bell and attn (1998), 1 A strkng example s Chang (1991) n whch the decsons of whether, what and how much to buy are smultaneously modeled, and appled to coffee purchasng data.

3 AN ANAYSIS OF EQUIIBRIUM REATIONSIP 71 Manchanda, Ansar and Gupta (1998), Km and Ross (1994)). Ths suggests that some preference parameters are well pcked up by those shoppng style varables. owever, the effect (not only n magntude but even n drecton) of expendture level or purchasng frequency can be qute dfferent f we rather focus on the quantty decson and so the prce elastcty of customers. Ths concern n partcular as well as the wdespread practce of volume-based prce dscounts drove us to test f there s a systematc relatonshp between prce elastcty and the average expendture level of consumers. Instead of drectly testng t wth an emprcal data, we frst queston whether the relatonshp has a theoretcal support. To prevew, we verfy under some techncal condtons that the cross-segment dfference n expendture can explan the dfference n prce elastcty so that an optmal expendture-based prce dscrmnaton strategy s possble. More mportantly to our emprcal nterest, we fnd the equlbrum relatonshp between prce elastcty and expendture level s not determnstc a pror. Rather, the relatonshp goes ether way, postve or negatve, dependng on the prevalng prce level of a focal product and the margnal utlty of the outsde alternatves. Therefore the relatonshp can be countryand/or product-specfc, and a case-specfc emprcal nvestgaton s necessary. As an emprcal example, we demonstrate that the relatonshp s strongly postve (.e., heavy users are more prce-elastc) for a sample data of Korean moble telecommuncaton servce market. The rest of ths paper s organzed as follows. Chapter 2 derves the demand functon for a product. An analyss shows that a theoretcal but ndetermnate cross-sectonal relatonshp exsts between the expendture and prce elastcty. Chapter 3 estmates a case relatonshp usng a panel data for moble telecommuncatons servce n Korea. Chapter 4 dscusses a manageral mplcaton and a possble ntegraton of prce senstvty and elastcty research n the future. Chapter 5 concludes the paper. 2. AN EQUIIBRIUM ANAYSIS Ths secton ntroduces a model to analyze the behavor of consumers and a frm. The model s based on Trole (1988) wth a modfcaton to our objectve to establsh a theoretcal lnk between the prce elastcty and the sze of demand Model et q be the ndvdual s quantty demanded for the product (or servce) of concern. et p be the prce for unt of consumpton, r the fxed access charge to the product. Employng the utlty functon n Trole (1988), ndvdual s preference s as follows. W T, q ) = U ( M T ) + V ( q ), (1) (

4 72 ONGJAI REE AND SANGKYU REE where M denotes ndvdual s ncome, and T = r + pq denotes the expendture on q. It s assumed that U ( 0) 0, U ' > 0, U" < 0, V (0) = 0, V ' > 0, and V "< 0. (2) = If T s much smaller than M (.e., the expendture on ths partcular good s small relatve to ncome), 2 then the preference on ( T, ) can be approxmated as follows: W ( T, q ) = V ( q ) T, (3) 1 where = represents nverse of the margnal utlty of ncome. 3 Trole (1988) U '( M ) attrbuted the heterogenety of consumers only to ther dfferent ncome levels (.e., dfference n ) assumng no dfference n the functonal form of (q) n (3). In fact, ths s equvalent to assumng that all ndvduals have the same preference to the product. More generally n ths paper, we extend the model to allow consumers dfferent not only n but also n ther preference to the servce such that q V 1 q 1 V ( q) =. 1 (4) Ths functonal form s very popular n macroeconomc analyss (e.g., Blanchard and Fsher (1989)) and s also adopted by affont et al. (1998) to dscuss the consequence of prce dscrmnaton n network ndustry. For V '> 0 and V "< 0, we should restrct the range of to (0,1). In sum, consumer s now represented by the par of parameters, 2 In ths artcle, we analyze Korean moble telecommuncaton servce. Thus T represents monthly expendture on moble servce. In 2007, the rato of total expendture on telecom servces (fxed lne servces, broadband nternet servce, moble servces, value-added servces) to household-ncome s 4.18%. Snce the rato of expendture on moble servces to household-ncome s lower than 4.18%, we can say that ths condton holds. 3 A frst-order Taylor expanson of Equaton (1) wth respect to varable T around M yelds Equaton U( M ) 1 (3): W ( T, q ) = U( M ) + U'( M )[( M T) M ] + V ( q ) = U'( M ) T + V ( q ). Therefore U ( M ) U ( M ) U ( M ) 1 we get W ( T, q ) = U '( M ){ v0 + V ( q ) T}, where v 0 =, '( M ) =. U U '( M )

5 AN ANAYSIS OF EQUIIBRIUM REATIONSIP 73 (, ). For brevty of exposton, we further employ a dscrete type of customers n each parameter such that, },, } for =1,2, K, I, (5) { { where 0 < < and 0 < < 1. Then the consumers are classfed nto four dstnct types (or segments): < { I, II, III, IV}, where I =, ), II =, ), ( ( III = (, ) and IV = (, ). One advantage of the above specfcaton s that the parameter s related to the prce elastcty as one-to-one bass. To see ths, we derve the optmal level of * consumpton q for the gven prce of ( r, p) as * q ( p) = arg max q 1 q 1 r pq. (6) 1 And solvng (6) results n the followng demand functon 1 * q ( p) =. p (7) So, 1/ amounts to the constant prce elastcty so that the consumer wth hgher turns out less prce elastc Prce Dscrmnaton Strategy As mentoned before, our man queston s whether there exsts a systematc * cross-segment lnk between the prce elastcty ( 1/ ) and the quantty demanded ( q ). Obvously, Equaton (7) tells that the relatonshp hnges on the margnal utlty of ncome ( ) and the prevalng prce (p). Fgure 1 dsplays typcal demand schedule of each consumer segment accordng to Equaton (7). In order to prce dscrmnate, a frm should be able to separate consumer segments wth dfferent prce elastctes on the observable ground. The followng proposton makes t possble to use the average sze of the demand (or expendture level) as a proxy for the prce elastcty but only n some crcumstances:

6 ONGJAI REE AND SANGKYU REE 74 Fgure 1. Illustraton of Demand Functons for Each Segment Proposton 1. Regardless of, the hgh-demand segments are more prce elastc f the prce level s below p = 1, or less prce elastc f the prce above. 4 p = No systematc relatonshp holds otherwse. p k Proof. The threshold prce level ( ) n Fgure 1 can be obtaned by the par-wse equalty of the type-specfc demands such that.,,, p p p p = = = = 1 The clamed relatonshp between prce elastcty and the sze of demand s evdent from Fgure 1. If ths s the case, what wll be the best prce dscrmnaton strategy from frm s perspectve? Clearly, t wll depend on the current prce level utlzng Proposton 1 such as follows.

7 AN ANAYSIS OF EQUIIBRIUM REATIONSIP 75 Corollary 1. It pays to ncrease frms proft to dscrmnate prce n favor of hgh-demand segments (.e., heavy users) f the current prce level s below p 1, or n favor of low-demand segments f the current prce s above p 4. Proof. To maxmze proft, the frm must apply the nverse elastcty rule such that the prce s set reverse-proportonal to the prce elastcty of each segment. More formally, the frst-order condton for proft maxmzaton ends up wth * * c * * c * pi = pii =, piii = piv = where p j denote the optmal prce for segment j { I, II, III, IV} and c the margnal cost. Due to the relatonshp between prce elastcty and the sze of demand as n Proposton 1, the corollary holds. Summng up, the bottom lne predcton s that the quantty-orented prce dscrmnaton s relevant only n certan crcumstance, and the drecton of proftable dscrmnaton can go ether way dependng on the prevalng prce level of the focal product. In fact, the emprcal relatonshp can vary dependng on the compettve market envronment, product lfecycle 5, and many others that affect the prce levels. And ths calls for a careful nvestgaton before employng an expendture-based prce dscrmnaton strategy n practce. 3. EMPIRICA FINDINGS We now proceed to an emprcal model to explore a case relatonshp between prce elastcty and the average expendture of consumers. We select the moble telecommuncatons servces n Korea because of data avalablty and also wth a concern that the moble operators n partcular requre a smart prcng strategy aganst the trend of market saturaton and contnual pressure on regulatory or compettve tarff reducton. In addton, the Korean moble market makes a good case of the monopolstc ndustry structure at least for the sample perod n our dataset. Whle three frms compete wth dfferentated servce and marketng actvtes, consumers bear a substantal churnng cost arsng from the absence of handset and number portablty 6 as well as the loss of loyalty benefts such as accumulated mleages. It s nterestng to note that ths emprcal relatonshp n moble ndustry was 4 It s note worthy that the type-dfference n (.e., margnal utlty of ncome) does not matter n the optmal prce dscrmnaton strategy. It smply drops out of the frst-order condton. 5 If the prce level tends to declne over the lfe cycle of a product, one can also argue that the relatonshp s lkely to be postve n the long run. 6 The moble number portablty has begun only n 2004 after the end of the sample perod, and swtchers are stll subject to the handset ncompatblty among operators.

8 76 ONGJAI REE AND SANGKYU REE exploted n Jan, Muller and Vlcassm (1999). To explan why the moble tarff level n U.S. s stable n contrast to the rapd downturn of the handset prce n the late nnetes, they postulated that moble consumers consst of hgh- and low-usage segments n whch the hgher-use segment s more senstve to the prce of phone calls. Ths assumpton was backed up by a conjont analyss to a focused group of consumers. Obvously, we do not attempt to challenge or valdate ths fndng. Nonetheless, we beleve that our emprcal study usng an actual panel consumpton data could provde a better support to ther proposton too f found consstent Specfcaton We begn wth the demand functon derved n Equaton (7): log q t = α + β log p + ε, = 1, K, I; t = 1, K, T. (8) t t Usng the logarthm n Equaton (7) and comparng wth Equaton (8), α denotes ndvdual dfference n preference (or n ncome), and β denotes the negatve prce elastcty such that log 1 α =, β =, = 1,, I. (9) The error term 2 ε t s assumed to follow an ndependent normal dstrbuton N( 0, χ ). To allow consumer heterogenety n elastcty n most flexble way (e.g., Allenby and Ross (1999)), we use a herarchcal random effect Bayes model whch s popularly utlzed n recent marketng lterature such as n Ross, MuCulloch and Allenby (1996) among many others. That s, we assume [ α, β ] ~ ( X ' δ, Σ), X N = 1,, I, (10) where denotes 1 K vector of K demographc covarates of consumer ncludng ntercept, δ K 2 parameter matrx of the margnal mpact of demographcs st nd n X to the mean of heterogenety n ether n α (the 1 row) or n β (the 2 row), and Σ denotes 2 2 varance-covarance matrx of ( α, ), respectvely Data We use a monthly panel data of 2298 sample customers of a moble operator n Korea. The Korean moble telecommuncaton servce market has rapdly grown to β

9 AN ANAYSIS OF EQUIIBRIUM REATIONSIP 77 about 47 mllon subscrbers as of June 2009 comprsng almost 95% of total populaton. The panel data records the amount of voce calls (n bllng unt of 10 seconds) for 21 months from August 2000 to Aprl 2002, and demographc nformaton on sex and age of the panelsts. It s mportant to note that each panelst n the data uses the same tarff plan (namely the standard tarff). Therefore, we worry lttle about a possble self-selecton of consumers regardng to ther preference to partcular tarff plans. Fgure 2. The Average Change of Moble Prce and Demand (n log scale) To construct a prce measure (per 10 second voce calls), we computed a real prce ndex for each month usng the avalable nomnal prces 7 and the consumer prce ndex (CPI). Fgure 2 dsplays the month-to-month varaton of the real prce ndex (n log scale). In short, we note that the prce gradually decreases over the sample perod except a promnent break n the month #18 (Jan 2000). Because every consumers use the same standard tarff plan durng the entre sample perod, t should be noted that the ndvdual prce measure ( p t ) n Equaton (8) becomes dentcal across every sample consumer n our data such as p t = p t. For the demand varable ( q t ), we take the log unts of voce calls (n 10 seconds) made by each panelst for each month. Meanwhle, as clear n the average demand profle n Fgure 2, an apparent seasonal varaton was notced n the data partcularly n 7 In fact, the operator provdes dfferent rates for day tme, nght tme, and weekends. Wth a known dstrbuton of calls, we computed a weghted average of the rates.

10 78 ONGJAI REE AND SANGKYU REE February (wth fewer days) and the months wth bg holdays (January and August by lunar calendar). Therefore, we adjusted the quantty varables by the exact number of workng days n a month (wth 30-day standard). 8 The other key varable s the average quantty demanded (denoted as y ) of each panelst durng the sample perod. We constructed ths varable by takng the sample average of the number of voce calls for the entre sample perod. Fgure 3 dsplays the hstogram of the average quantty across panelsts Mean=7.12, SD= Fgure The stogram of Average og Demand per Month Across Panelsts In sum, the demographc covarates X n Equaton (10) ncludes four varables ncludng ntercept, log( y ), sex =1 f male, and log( age ) n turn. Of course, the other covarates such as ndvdual ncome level may play a key role n determnng prce senstvty of moble consumers. Due to data lmtaton, we could not suffcently control for possble omtted varable bases. Techncally, we subtracted the means from each non-ntercept varables to have the ntercept parameter nterpreted as ( α, β ) of the average panelst n the sample. 9 Of prmary concern s the regresson coeffcent between the average expendture (log( y )) and the prce elastcty ( β ). 8 Ths adjustment turned out to ncrease the magntude of prce elastcty a lttle bt. owever, we verfed that our man fndng s qualtatvely ntact. 9 The mean subtracton procedure was suggested n Ross, Allenby and MuCulloch (2005).

11 AN ANAYSIS OF EQUIIBRIUM REATIONSIP Estmaton The lkelhood functon for Equaton (8) contans many ndvdual parameters ( α, ). Furthermore, the ndvdual parameters are possbly correlated wth each other β by the random effect specfcaton n Equaton (10). Our objectve s to estmate the predctve dstrbutons of the hyper parameters n Equaton (10), δ and Σ, as well as the ndvdual parameters of 2,298 sample consumers n our data. Therefore, the jont lkelhood seems hard to evaluate analytcally. To sdestep ths dffculty, we use a Markov Chan Monte Carlo (MCMC) method whch becomes popular n the recent marketng lterature (e.g., Ross, Allenby and McCulloch (2005)). To mplement a Bayesan herarchcal model, t s necessary to specfy a pror 2 dstrbuton of the hyper parameters n the bottom of the herarchy,.e., χ, δ and Σ. As usual, we employ qute dffuse but proper prors for the hyper parameters to make the mpact of pror as small as possble. Specfcally, we used R program language, and worked wth the herarchcal Bayes model ncluded n the bayesm package developed by Ross, Allenby and McCulloch (2005). In what follows, all results summarze 1000 posteror draws of each parameter wth 1000 burn-ns and 5 thnnng nterval of sequences. To dagnose the convergence of the sampler, we verfed the posteror descrptve statstcs vary lttle wth the number of sequences after the ntal burn-n perod Result Table 1 summarzes the estmated posteror dstrbuton of parameters (means and standard devatons n parenthess). The average of constant elastcty demand functon was estmated to have the ntercept of and the slope (prce elastcty) of wth strong sgnfcance. For demographc effects, the sex and age do not gve sgnfcant effects on the demand parameters. In contrast, the average log expendture of panelsts turned out to ncrease the demand ntercept (3.36) and to make the prce elastcty even more negatve (-0.792). The latter fndng per se clearly tells about our prmary concern such that the heavy moble users are more lkely to have hgh prce elastcty. The unobserved heterogenety n ndvdual demand parameters s profound as can be seen from the estmates of Σ, and ths s probably due to poor performance of the demographc covarates except the log expendture. Focusng on the key parameters of nterest, Fgure 4 dsplays the posteror kernel denstes of the average prce elastcty (left panel), and of the effect of log expendture on the prce elastcty (rght panel). Because the prors are selected as condtonal conjugate to the lkelhood, both posteror denstes look very smlar to the normal curvature.

12 80 ONGJAI REE AND SANGKYU REE Table 1. Mean and Standard Devaton of Posteror Dstrbuton of Parameters Parameters Covarates effect on the demand parameters (δ ) Constant og(expendture) * Male=1 * og(age) * Demand ** ** Intercept ( α ) (0.25) (0.47) (0.58) (1.46) Demand Slope ( ) β Σ 1, ** ** (0.08) (0.16) (0.19) (0.49) SD( α ) = ** (0.22) SD( β ) = ** (0.07) Σ 2,2 Cov( α, ) = ** (1.50) β Σ 1, 2 2 SD( ε ) = χ ** (0.03) Notes: * These varables were subtracted from ther means. ** The 95% posteror nterval does not nclude zero. Fnally, t s noteworthy that our emprcal fndng s n lne wth the conjont analyss of Jan, Muller and Vlcassm (1999) for U.S. moble servces. owever, as our model predcts that the relatonshp can go ether way dependng on the prevalng prce of the product n a country, ths analogy may be a concdence. 4 Average Prce Elastcty 2.5 Effect of Expendture Mean= -1.19, S.D.=0.08 Mean= -0.79, S.D.=0.16 Fgure 4. The Posteror Kernel Densty of Key Parameters

13 AN ANAYSIS OF EQUIIBRIUM REATIONSIP DISCUSSION So far, we proposed that the theoretcal relatonshp between prce elastcty and expendture level can go postve, neutral or negatve dependng on the characterstcs of the focal product, and then demonstrated a postve case wth an example data for Korean moble telecommuncaton servce market. et alone our two way theoretcal predctons, the emprcal fndng can help to boost the proft of moble operators n devsng a consstent prce dfferentaton or segmentaton strategy. owever, t s also noteworthy that the emprcal fndng seems n contrast to those n the prevous shoppng behavor lterature n marketng. For example, Bell and attn (1998) showed that large-basket shoppers tend to be less senstve to a category-level prce promoton when choosng retalers. owever, one should remnd the dsparty of concerns n prce elastcty and senstvty lterature as was hghlghted before. Whle the marketng lterature focuses mostly on the choce of a suppler n hghly compettve envronment, our elastcty study n ths paper s more vald for the choce of quantty for a gven suppler n a monopolstc envronment wth substantal product dfferentaton and swtchng cost. One may argue that the nverse elastcty rule we explored n ths paper only works for a pure monopoly case. On the other hand, we contend that the emprcal scope of monopolstc prce strategy goes beyond t. In realty, there s no dstnctve borderlne between monopoly and competton. To avod unsustanable prce competton, most products n a market are dfferentated n a varety of dmensons such as brand, qualty, dstrbuton channel and many others. In addton, consumers bear a substantal swtchng cost (both n economc and psychologcal sense) whch hnders them from churnng for a small prce gap among alternatves. Therefore, we beleve our analyss n ths paper can be appled to a broad range of monopolstcally compettve markets n the feld. More generally, though t seems qute nterestng to extend our analyss to more compettve envronment through a smultaneous parameterzaton of the swtchng cost and prce elastcty, ths s left a frutful research track to proceed. 5. CONCUSION Knowng the cross-segment heterogenety n prce elastcty of consumers makes t proftable to devse a relevant prce dscrmnaton strategy for a frm n a monopolstc market. The bottom lne suggeston s to gve relatvely deeper dscounts to the consumers of hgher prce elastcty. Despte the smplcty of ths gudelne, the prce elastcty of demand has not been fully utlzed n the prevous marketng lterature as compared to substantal emphases on the prce senstvty n choosng a brand or a store. Probably, ths s mostly because the lterature has postulated substantally compettve busness envronment. In ths paper, we alternatvely contended that the emprcal relevance of the nverse elastcty rule goes beyond the pure monopoly case. If wth

14 82 ONGJAI REE AND SANGKYU REE substantal product dfferentaton and/or swtchng costs n the market, frms would prce dscrmnate across segments based on a relable proxy of the prce elastcty. Unlke the conventonal prcng practce n favor of heavy users, our theoretcal model predcts that expendture and prce elastcty can be correlated to ether drecton dependng on the prevalng prce level of the focal product. Therefore, a careful case-by-case nvestgaton s necessary. REFERENCES Ansle, A., and P.E. Ross (1998), Smlartes n Choce Behavor across Product Categores, Marketng Scence, 17, Allenby, G.M., and P.J. enk (1995), Reassessng Brand oyalty, Prce Senstvty, and Merchandsng Effects on Consumer Brand Choce, Journal of Busness and Economc Statstcs, 13, Allenby, G.M., and P.E. Ross (1999), Marketng Models of Consumer eterogenety, Journal of Econometrcs, 89, Bell, D., and J. attn (1998), Shoppng Behavor and Consumer Preference for Store Prce Format: Why arge Basket Shoppers Prefer EDP, Marketng Scence, 17, Blanchard, O.J., and S. Fsher (1989), ectures on Macroeconomcs, The MIT Press. Bolton, R. (1989), The Relatonshp between Market Characterstcs and Promotonal Prce Elastctes, Marketng Scence, 8, Chang, Jeongwen (1991), A Smultaneous Approach to Whether, What and ow Much to Buy Questons, Marketng Scence, 10, och, S., B-D. Km, A. Montgomery, and P. Ross (1995), Determnants of Store-evel Prce Elastcty, Journal of Marketng Research, 32, Jan, D., E. Muller, and N.J. Vlcassm (1999), Prcng Patterns of Cellular Phones and Phones and Phone Calls: A Segment-level Analyss, Management Scence, 45(2), Km, B-D., and P. Ross (1994), Purchase Frequency, Sample Selecton, and Prce Senstvty: The eavy User Bas, Marketng etters, 5, Kumar, V., and R. eone (1988), Measurng the Effect of Retal Store Promotons on Brand and Store Substtuton, Journal of Marketng Research, 25, affont, J-J., P. Rey, and J. Trole (1998), Network Competton II: Prce Dscrmnaton, Rand Journal of Economcs, 29, Manchanda, P., A. Ansar, and S. Gupta (1998), The Shoppng Basket: A Model for Multcategory Purchase Incdence Decsons, Marketng Scence, 18, Ross, P., R.E. McCulloch, and G. Allenby (1996), The Value of Purchase story Data n Target Marketng, Marketng Scence, 15,

15 AN ANAYSIS OF EQUIIBRIUM REATIONSIP 83 (2005), Bayesan Statstcs and Marketng, NJ: Wle. Trole, J. (1988), The Theory of Industral Organzaton, MIT press. Malng Address: Sangkyu Rhee; Department of Economcs, Chung-Ang Unversty, 221 euksuk-dong, Dongjak-Gu, Seoul, Korea. Tel: E-mal: Receved August 24, 2009, Revsed November 5, 2009, Accepted November 23, 2009.