Effect of Adjacent Product Price on Customer s Willingness to Pay of Focal Brand: A Bayesian Approach

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1 Theoretcal Economcs Letters, 2017, 7, ISSN Onlne: ISSN Prnt: Effect of Adjacent Product Prce on Customer s Wllngness to Pay of Focal Brand: A Bayesan Approach Atanu Adhkar Indan Insttute of Management Kozhkode (IIMK), Kozhkode, Inda How to cte ths paper: Adhkar, A. (2017) Effect of Adjacent Product Prce on Customer s Wllngness to Pay of Focal Brand: A Bayesan Approach. Theoretcal Economcs Letters, 7, Receved: September 9, 2017 Accepted: November 24, 2017 Publshed: November 27, 2017 Copyrght 2017 by author and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY 4.0). Open Access Abstract Psychologcal researchers, whle studyng nternal reference prce, have dealt wth dfferent types of psychologcal effects lke attracton effect and compromse effect. Whle studyng consumer reference prce and wllngness to pay, marketng researchers have focused on consumers percepton about a brand by evaluatng several attrbutes of that brand. Our research nvestgates the ncremental effect on consumers wllngness to pay n a context where an adjacent prce s present, for nstance, when a medum prced brand s assocated wth a hgh prce brand than a moderately hgh prced brand. Unlke other prcng research, ths research deals wth consumer s ndvdual level heterogenety as prce senstvty and consumers wllngness to pay for a partcular brand snce they vary among ndvdual. Herarchcal Bayes methodology s used to ncorporate such heterogenety. The study shows sgnfcant dfference n consumers utlty and her wllngness to pay when a medum prced brand s compared wth a hgh prced brand as aganst a moderately hgh prced brand. Keywords Brand-Choce Decson, Wllngness to Pay, Internal Reference Prce, Consumer Heterogenety, Herarchcal Bayes 1. Introducton Consumer makes purchase decson n dfferent ways whle buyng a brand. Consumers have ther own preferences for product features, whch they used to select a few brands. Preferred features are compared and weghts are assgned for the fnal decson makng. Selected brands are then evaluated based on prce-beneft DOI: /tel Nov. 27, Theoretcal Economcs Letters

2 paradox and then selected for purchase. Behavoral aspect of consumers n prcng research has receved more focus snce early 80s. Utlty theory of consumer surplus provdes a better understandng of the behavoral aspect of prcng research. Consumer surplus s used to form the reference prce whch s consdered to have a unque value for a gven segment. For a partcular product category, the whole populaton behaves n a smlar way n terms of both prce senstvty and choce rules; vared prce effects across ndvdual or wthn ndvdual are not consdered for the research Durng a purchase, a consumer faces prces of several products whch vary from low range to hgh. A consumer can modfy her reference prce and wllngness to pay based on the prce of other products. Ths research deals wth the change n the effect of consumers wllngness to pay when a product wth the prce n low range s placed wth a product that has moderately prce range than to a product that has hgh prce range. 2. Lterature Revew Consumer s evaluaton of brand under uncertanty s supported by ther justfcaton n terms of most preferred attrbute [1] [2]. Psychologcal research showed that consumers act dfferently whle choosng a product. Among two equal utlty brands the consumer tends to buy a brand whch s superor n terms of mportant attrbutes. These attrbutes are evaluated based on prce-utlty paradox and the comparatve wnner takes the purchase share. The predcton of consumer choce behavor s dffcult as the utlty of a brand s weghted summaton of ndvdual preference of several attrbutes. However, ths evaluaton s often uncertan as n most cases consumers are unaware about the beneft of the product untl they use. On the contrary, money spent, for such utlty s often certan and foregone n advance (Japtura et al. 2014). Several researchers [3] [4] studed the role of attracton effect n brand-choce decson makng. They argued that the choce probablty of domnatng alternatve s affected by the presence of nferor alternatve n a set. In other words, the products wth superor attrbutes are preferred more than the products wth nferor attrbutes. However these researchers used expermental research to study the phenomena. 20 expermental researches had a very lmted number of sample sze as well as small number of alternatves wth few factors. ths has consequently resulted dluted effect of comparatve attracton of domnated alternatve snce the choces were small and the nose of complcatng factors may not have sgnfcant unt level varaton [3] [5]. Choce justfcaton s another branch of research n the feld of brand-choce behavor. When a choce selecton s followed by explanaton to second person; ndvdual try to fnd reasons for justfcaton. Whle psychologcal researches do show many reasons of justfcaton (Hall and Lndzey, 1978; Kaura et al., 2013), the prmary referred reason s found to be beng ratonal whle evaluatng related attrbute. Economc lterature [6] also provded enough support n terms of utl- DOI: /tel Theoretcal Economcs Letters

3 ty maxmzaton whle consumers select a choce. Consequently, a prce-utlty effect plays a major role n consumer s brand evaluaton (Ha, 2006; Mahamood, 2014). Studes on anchorng effect found that consumers anchor themselves wth ndependent motvaton whle evaluatng a completely dfferent product. Complete body of sgnfcantly, reference prce lterature also has ts base wth psychology. Prcng research on ncdental prce and wllngness to pay [7] documented that a hghly prced product, whch s completely unrelated can also nfluence the wllngness to pay off a less valued product. Monroe [8] ponted out that whle prce of substtute product affect the expected demand, prevous prce of the product also nfluence nternal reference prce of the consumer. Prmary reason for ths s related and unrelated anchorng effect. Change n consumers reference prce s based on assocaton of a product along wth other products. Monroe [9] found that consumer s reference prce vares based on other prce stmul, whle descrbng consumers subjectve percepton. Above revew leads us to nvestgate the mpact of several prce levels on brandchoce decson makng. Hence the objectve s to study whether there s any dfference n consumers utlty and her wllngness to pay when a medum prced brand wth no nferor attrbute s compared wth a hgh prced brand as aganst a moderately hgh prced brand. Our study attempts to propose that there s some assocaton between gven product alternatve wth a hgh prced product alternatve n brand-choce decson and t may nflate the wllngness to pay of the gven product. In other words we also propose that as the prce dfferental between two assocated choce alternatves ncreases, the wllngness to pay of the lower alternatve ncreases. Ths study tres to explore explores the argument that when a consumer s gven a choce set of several alternatves of brands, she makes her reference prce based on the hgher prced alternatve and estmates the prce of lower prced alternatve from that anchor. 3. Consumer Level Heterogenety Reference prce modeled aggregate level effect almost all researchers [10]. The Dfference across between the consumers s not captured both n reference prce as well as n psychologcal lterature. Prce effects are estmated by aggregatng data of entre sample or few segments and then sngle parameter or few segment level parameters are estmated. The effect studed reports total effect or segment level effect, but not ndvdual effect. The mportant aspects lke how utlty relaton, prce senstvty, loss averson and brand preference dffer across ndvduals are also examned n ths study. Understandng consumer level heterogenety s requred whle dealng wth prcng polces, demand estmaton and smlar researches. Here the ndvdual level heterogenety s taken nto consderaton durng the parameter estmaton. Snce the prce senstvty and wllngness to pay are ndvdual specfc, ndvdual heterogenety n preference call for market segmentaton that wll to cater to specfc consumer requrement. However, data DOI: /tel Theoretcal Economcs Letters

4 defcency exsts n studes on consumer preference due to consumer heterogenety [11]. Earler studes shows [12] [13] that herarchcal Bayes (HB) ndvdual estmates are more consstent and relable than the estmates of fnte-mxture models. 4. The Study Three products were selected from a plot study. These three product square automoble detergent powder and wrst watch. Automoble was elected because t has both tangble and ntangble product features whch consumers gve almost equal weghted whle selectng ther automoble. Detergent powder s a frequently purchased product and selected by the consumers prmarly because of that tangble attrbutes lke cleanng ablty, fragrance comma softness et cetera. Wrst watch was selected because of hgher degree of ntangblty of ts features whch consumers consder whle buyng the product. Table 1 represents the attrbutes and levels of these 3 products below. Snce full factoral desgn s too large n number for realstcally data collecton, fractonal factoral desgn has been used to dentfy the choce sets for the respondents to respond. The expermental desgn was not strctly orthogonal nor was strctly level balanced snce the objectve of the research was to see the effect of anchor ponts on wllngness to pay of a partcular alternatve choce set. Snce proflng the part of utlty of the choce set was not prmary objectve, search method would gve more precse estmate of utltes. Hence, we needed choce sets that are dstnct n terms of prce compare ablty whle sacrfcng the orthogonalty and level balancng to some extent. However, requred correctve Table 1. (a) Automoble; (b) Detergent powder 1 kg pack; (c) Wrstwatch. (a) Brand Engne Capacty Type Hunda, Mercedes, Toyota, Skoda 1500 cc, 1600 cc, 2400 cc, 3300 cc Small SUV, Medum SUV, Large SUV and Sedan Mleage (Km/Ltr) 18, 16, 14 Prce 750,000; 1,100,000; 1,250,000; 1,500,000; 3,000,000 (b) Type Brand Commercal, Fne, Supreme, Arel, Surf, Rn Prce 80; 100; 170 (c) Look Band Brand Ordnary, Offcal, Ornamental Chromum Platng, Leather, Gold Coated HMT, Ttan, Rcho Prce 1200; 2500; 15,000; 60,000 DOI: /tel Theoretcal Economcs Letters

5 measures were taken by measurng desgn effcency to keep t wthn acceptable lmt as prescrbed by the prevous researchers. Huber and Zwerna [14] ponted out that, mnmal overlap s mportant to reduce the probablty of duplcatng an attrbute level n dfferent alternatves of a choce. Sxteen choce Set Square gven to the respondents for ther response. Out of these 16 choce sets 4 sets for expermental whch was repeated twce. Remanng 8 sets where for fller sets. Fller sets were used to elmnate response bas. The frst poston n each of the four expermental choce sets where allotted to anchor alternatve. The alternatve under study s kept n second poston and rest 8 alternatves where mxed alternatves. Anchor prces were recorded separately to capture the prce senstvty. 42 respondents partcpated n the survey. Two dependent varables were collected for each choce profle. These two dependent varable square wllngness to pay and ntenton to buy a prce varable was used as a proxy for dependent varable, wllngness to pay. Both the dependent varables were measured usng 7 pont Lkert scale. Respondents were requred to provde ther opnon about the prce of the second alternatve of the choce set n a 7 pont Lkert scale. The value of ths major vares from very low to very hgh. Smlarly the dependent varable ntenton to buy was measured n a 7 pont scale that arranged from not at all by to defntely buy. 5. Indvdual Level Estmates Usng Herarchcal Bayes In the last one decade applcaton of Bayesan methodology of applcaton used has occuped sgnfcant area n the area marketng research have wtnessed wde usage of the applcaton of Bayesan methodology. The usefulness of Bayesan method was recognzed qute long back, however, computatonal lmtaton was the man hurdle n ts applcaton. Ths computatonal burden can be solved by Markov Chan Monte Carlo (MCMC) smulaton method facltated to overcome computatonal burden of whch uses models drawn from stepwse condtonal dstrbutons. MCMC method s facltates a chan process drawng from arbtrary posteror dstrbuton that converges to target dstrbuton. Consequently, several marketng ssues lke ntra-unt behavor, consumer level heterogenety could be consdered for more effcent marketng decsons. A basc problem n marketng research s lmted amount of ndvdual level nformaton to calculate consumer specfc parameters as well as predct preferences s an mportant problem n the area of marketng research. Ths s due to large number of attrbute and many levels n each attrbute whch call for hgher number of observatons for estmaton. Aggregate level nformaton poolng s a method s based on the fxed effect model whch assumes that the parameters are same across all respondents. Ths partcular assumpton focuses on mean value of the estmate and does not consder ndvdual level heterogenety. Ths s a nave smple and easy way of estmatng prce related parameters. The process of Marketng acton often needs to DOI: /tel Theoretcal Economcs Letters

6 calculate ndvdual level nformaton for better understandng of consumer preference and purchase decson. Hence, a random-effect model whch that assumes that the parameters follow a probablty dstrbuton of heterogenety across respondents s requred for practcal applcaton. A herarchcal Bayes random effect model helps n estmatng ndvdual specfc parameters as well as aggregate level under lmted data for dealng wth ndvdual specfc parameters and lmted data, Herarchcal Bayes Random Effect Model s useful. In such model, ndvduals are consdered as ndependent condtonal on unt level parameters. However, the prors nduced for HB estmaton at ndvdual level are not ndependent pror. Indvdual parameters are consdered as drawn from the whole populaton whch s one way of mxng dstrbuton. The lkelhood of ndvdual parameter {θ } and the common parameter of mxng dstrbuton τ can be wrtten as: ({ θ }, τ) = ( data θ, τ) = N ( data θ) ( θ τ) L p p p (1) denotes the th consumer of total N, L s lkelhood functon, θ s ndvdual parameter vector and p(θ /τ) s the mxed dstrbuton of ndvdual parameter condtonal on τ, a common parameter that comes from populaton. Inference about the parameter τ can be calculated by margnalzng lkelhood through ntegratng out the parameter vector: = 1 ( ) = ( ) ( )d L τ p y θ p θ τ θ Gven the jont pror of parameter vector θ of th ndvdual the posteror dstrbuton can be wrtten as ( θ1, θ2, θ 1, 2,, ) ( θ ) N N ( θ1, θ2, θn τ) p y y y p y p τ s hyper-parameter on whch pror s based. Due to nsuffcent data pont at ndvdual level, specfcaton of functonal form and pror hyper-parameters are mportant for ndvdual level analyss. Ross and Allenby [15] suggested that ths process s useful n choce data sets where many consumers evaluates all the alternatves presented and most standard choce models do not have a bounded ML estmate as lkelhood may be asymptotc n certan drecton n parameter space. In such stuaton, largely, the pror determnes the nference about the consumer. Evaluatng the jont dstrbuton of pror parameter ( θ, θ, θ τ) p s dffcult due to ts hgh dmensonalty. One way of smplfyng the form of the pror dstrbuton s assumng they are ndependent to each other condtonal on τ. Hence, we can wrte above equaton wth assumpton of ndependence as: 1 2 ( θ1, θ2, θ 1, 2,, ) ( θ ) N N ( θ τ) p y y y p y p Once we consder the condtonalty of the pror on the hyper-parameter, t s necessary to defne ts behavor,.e. dstrbuton and condtonalty of the hyper-parameter. Assessng the pror hyper-parameter s also a challengng task. In case of normal pror, a large standard devaton serves the purpose. Ross and N DOI: /tel Theoretcal Economcs Letters

7 Allenby [16] suggested a pror on the scaled verson pooled model nformaton matrx. The pror covarance s then scaled ( shrnked ) and used to represent the expected nformaton n one observaton. Ths follows shrnkage phenome- θ = E θ data, pror ) are non and posteror estmates lke the one posteror means ( [ ] concentrated towards the pror means and less on ML estmates (.e. ˆj θ ). Hence, to model ndvdual level heterogenety, we requre two stages of pror; frst stage to model pror parameter value and second stage to model the parameter on whch the frst stage pror s condtonal. It can be represented through a herarchcal form. So the herarchcal Bayes model n ths research conssts of unt level lkelhood functon and two stages of prors: Lkelhood: p( y θ ), = 1, 2,, N (No. of respondents) Frst stage pror: p ( θ τ ) Second stage pror: p ( τω ) Then we can wrte the jont posteror for the herarchcal Bayes model as follows: P( θ1,, θm, τ y1,, ym, ω) p( y θ) p( θ τ) p( τω) where ( θ θ ),, 1 m are ndvdual level (for th ndvdual) parameter vector and y,, 1 ym are ndvdual level data vector. In above model, the ndvdual level prors are not ndependent, rather calculated based on super-populaton dstrbuton wth an assumpton that ndvdual alone cannot nfluence the pror dependence. However, the descrpton of the consumers requres nformaton about θ and τ. Only the knowledge of heterogenety by way of assumng dstrbuton often nsuffcent to evaluate optmum marketng decson under less ndvdual level nformaton. Bayesan approach solves ths problem by estmatng τ by maxmzng ts lkelhood functon gven n Equaton (1) and then applyng p ( θ ˆ τ = τ) as pror n the analyss of an ndvdual s condtonal lkelhood. So, P( θ data) ( ) ( ˆ P y θ P θ τ = τ). For reasonably large sample sze, τ can be correctly estmated and any ndvdual cannot nfluence ts estmate. Huber [17] study on herarchcal Bayes wth survey data and Natter and Feursten [18] wth real world purchase data fnd that herarchcal Bayes outperforms latent class model and aggregate model n terms of correctness of parameter estmaton (RMSE) and predctng hold out choces as t ncorporates heterogenety n the model. Ths supports that ncorporaton of heterogenety n the consumer choce model have hgher predctve power. Aggregate models underestmate the standard error of the parameter estmates n presence of heterogenety. 6. Analyss Sawtooth Software s used n ths research for The HB analyss s carred out usng Sawtooth Software. An dentty matrx s assumed as pror covarance matrx whch ndcates a pror varance of 1 for all parameters. Large pror varance pays more mportance on data-fttng of each ndvdual and less mportance on borrowng data (Sawtooth software manual, 2006) from others. An dentty matrx DOI: /tel Theoretcal Economcs Letters

8 ensures a proper balance between two data-fttng and borrowng of data. We mantaned the default opton of pror degrees of freedom, 5 s mantaned and less degrees of freedom helps to restrct mpact of pror varance. As the research s exploratory n nature and very lttle nformaton s avalable about the pror parameter, we consdered less degree of freedom to restrct the mpact of pror varance. All categorcal the ndependent varables that are categorcal, coded through effect codng. In dummy varable codng, one level of each attrbute whch s deleted attrbute takes the value zero. In effect codng, the deleted level has an mpled value whch s equal to suggests that the negatve value of summated coeffcents of rest levels n that category. Hence, wth effect codng, the sum of coeffcents of all levels of any attrbute s zero. 7. Result and Dscusson 20,000 teratons are performed n each case through HB regresson procedure s devsed for performng 20,000 teratons n each case. Every 10 th draws are saved to calculate mean part-worth of every respondent and the result s saved to calculate the mean part-worth of each attrbute across all respondents To calculate the mean part-worth of every respondent and each attrbute, 10 th draws are saved across. No parameter constrant both n value and sgn s mposed n the analyss Parameter constrant does not matter n both value and sgn of the results. In terms of Wllngness to pay and n choces of medum prced study alternatves wth hgh prced reference (anchor) alternatves are sgnfcantly hgher (p < 0.01) n all three studes. It means that consumers perceve utlty of an alternatve when t s assocated wth a hgh prced alternatve whch s sgnfcantly hgher than and also when the same alternatve s assocated wth moderately hgh prced alternatve. At the same tme, the ntenton to buy the alternatve under study s not sgnfcantly dfferent n two both cases (p > 0.05). It also suggests that people s ntenson to buy a moderately prced alternatve do not vary wth the assocaton of a hgher prced alternatve than that of a moderately prced alternatve. Correlaton between part-worth utltes n two both cases s nsgnfcant. Ths advocates the usefulness and effectveness of ths s where fller choce sets are made use of. A possble explanaton s that when smlar types of choce sets are faced by the respondent, as per standard form n memory one choce set s mmedately supplemented by another smlar choce set. No sgnfcant nsgnfcant correlatons suggest that respondents evaluaton of study alternatve along wth each anchor alternatve (.e. wth hgh prce and moderately hgh prce) was ndependent to each other and hence bas free. Evaluated score of wllngness to pay were sgnfcantly dfferent wth value (at p < 0.01) wth value of and 23.5 (Maxmum possble score for each respondent n both cases would be 28 and mnmum wll be 4). However, we found that sgnfcant postve correlaton between two cases Ths whch suggest that wllngness to pay s consstently hgh among respondents when the study alternatve s assocated wth moderately hgh prced one than that of hgh prced one. DOI: /tel Theoretcal Economcs Letters

9 8. Conclusons and Future Research Above all, the fndngs support reveal that consumers compare ther choce alternatves wth the one close to them and form an opnon about ts utlty that modfes ther reference prce accordngly. It s qute consstent wth the standard noton of t s human behavor. They compare thngs and form an opnon about one, whch s consstent wth our fndngs. The study consdered the effect of hgher prce anchor on medum prced brand and found that by consderng the effect of hgher prce anchor on medum prced brand, there s a sgnfcant postve mpact n consumers wllngness to pay. Unlke other studes on reference prcng research and studes on consumers wllngness to pay, we have consdered consumer level heterogenety as ndvduals vary n terms of utlty and prce reference. Further studes can be carred to research and to nvestgate whether there s any negatve mpact of assocaton of lower prced brand on medum to moderately hgh prced brand. Currently, we are workng on a smlar project to nvestgate the effect of such lower anchor prcng and see the effect on consumer s wllngness to pay. However, ths knd of research also requres ncluson of aspects lke ndvdual level heterogenety to study the ndvdual specfc effect. Nunes and Boatwrght [6] conducted a study n that lne but dd not repost as they and dd not fnd any sgnfcant result. The study consdered aggregate level effect and dd not nclude ndvdual level heterogenety. References [1] Montgomery, H. (1983) Decson Rules and the Search for a Domnance Structure: Towards a Process Model of Decson Makng. In: Humphreys, P.C., et al., Eds., Analyzng and Adng Decson Process, North-Holland, Amsterdam. [2] Slovc, P. (1975) Choce between Equally-Valued Alternatves. Journal of Expermental Psychology: Human Percepton and Performance, 1, [3] Huber, J. and Puto, C. (1983) Marketng Boundares and Product Choce: Illustratng Attracton and Substtuton Effects. Journal of Consumer Research, 10, [4] Smonson, I. (1989) Choce Based on Reasons: The Case of Attracton and Compromse Effects. Journal of Consumer Research, 16, [5] Ratneshwar, S., Shocker, A.D. and Stewart, D.W. (1987) Towards Understandng the Attracton Effect: The Implcaton of Product Stmulus Meanngfulness and Famlarty. Journal of Consumer Research, 13, [6] Samuelson, P.A. and Nordhaus, W.D. (2001) Mcroeconomcs. ISE Edtons, McGraw-Hll Educaton, New York. [7] Nunes, J.C. and Boatwrght, P. (2004) Incdental Prces and Ther Effect on Wllngness to Pay. Journal of Marketng Research, 41, DOI: /tel Theoretcal Economcs Letters

10 [8] Monroe, K.B. (1990) Prcng: Makng Proftable Decsons. 2nd Edton, McGraw Hll, New York. [9] Monroe, K.B. (1973) Buyers Subjectve Perceptons of Prce. Journal of Marketng Research, 10, [10] Mazumdar, T., Raj, S.P. and Snha, I. (2005) Reference Prce Research: Revew and Propostons. Journal of Marketng, 69, [11] Adhkar, A. and Rao, A.K. (2013) Indvdual Preference and Barganng Behavor n Famles Buyng Decsons of Restaurant Servce. Cornell Hosptalty Quarterly, 54, [12] Allenby, G.M. and Gnter, J. (1995) Usng Extremes to Desgn Products and Segment Markets. Journal of Marketng Research, 32, [13] Lenk, P., DeSarbo, W., Green, P.E. and Young, M. (1996) Herarchcal Bayes Conjont Analyss: Recovery of Part-Worth Heterogenety from Reduced Expermental Desgn. Marketng Scence, 15, [14] Huber, J. and Zwerna, K. (1996) The Importance of Effcent Utlty Balance f Effcent Choce Desgn. Journal of Marketng Research, 33, [15] Ross, P.E. and Allenby, G.M. (2003) Bayesan Statstcs and Marketng. Marketng Scence, 22, [16] Allenby, G.M. and Ross, P.E. (1999) Marketng Models of Consumer Heterogenety. Journal of Econometrcs, 89, [17] Huber, J. (1998) Achevng Indvdual Level Predctons from CBC Data: Comparng ICE and Herarchcal Bayes. Presentaton Gven at Advance Research Technque Forum (Understandng Taken from Sawtooth Software Techncal Papers). [18] Natter, M. and Markus, F. (2002) Real World Performance of Choce Based Conjont Models. European Journal of Operaton Research, 137, DOI: /tel Theoretcal Economcs Letters