The Impact of Switching Costs on Closing of Service Branches

Transcription

1 The mpac of wiching Coss on Closing of ervice Branches Mira G. Baron Economics Group Faculy of ndusrial Engineering and Managemen Technion srael nsiue of Technology aifa 3000, RAEL EMAL: ubmied o he 4nd Congress of he European Regional cience Associaion Dormund, Germany, Augus ABTRACT The paper deals wih he locaion of service branches. Consumers can receive service from differen firms and branches offering subsiue services. The consumer chooses he firm and he branch. Examples are banking services which firm and branch?, healhcare providers, insurance companies and heir agens, brokerage firms and heir branches. Wih he change in he accessibiliy of he inerne, he service indusry winesses he impac of he change in echnology. More cusomers prefer acquiring services over he inerne or phone, and less require face o face conacs. The indusry has o respond in limiing he number of branches. The paper deals wih he quesion which branches o close. n he firs period, each consumer selecs o receive service from he branch ha minimizes he overall coss incurred, composed of price per service plus ransporaion coss. n he second period, he branches configuraion changes. A branch is closed by one of he firms in alernaive locaions. When consumers swich a firm, addiional coss, exogenous swiching coss are incurred, he cos of informaion, learning coss, ransacion coss. These coss are incurred by he consumers, and are differen from endogenous swiching coss ha are incurred by firms, e.g., he frequen flier case. The paper invesigaes how he marke area and marke share of branches and firms change wih he closure of a branch. The loss varies beween no loss o losing he whole marke. Given he prices, he swiching coss and he locaion, he branches o be closed are idenified.

2 1. nroducion The paper deals wih he locaion of service branches. Consumers can receive service from differen firms and branches offering subsiue services. The consumer chooses he firm and he branch. Examples are brokerage firms which firm and branch?, insurance companies and heir agens, banking services and heir branches. The service indusry winesses he impac of he change in echnology. More cusomers prefer acquiring services over he inerne or phone, and less require face o face conacs. The indusry has o respond in limiing he number of branches. The paper deals wih he quesion which branches o close. Baron 00a argues ha cusomers don swich ofen beween firms, due o he exisence of swiching coss. Von Weizsacker 1984 and Klemperer 1987a inroduced he erm "swiching coss" ino he economic lieraure see also Klemperer, 1987b, 1995, adilla, 1995, To, They assume ha a cusomer incurs coss in swiching from one firm o anoher, like learning coss, ransacion coss, psychological coss. The consumer adops one of he firms in he firs period, when commodiies are offered a differen prices. n he second period, if he consumers wan o swich firms hey incur swiching coss. The resul is ha cusomers are likely o be loyal o he firm from which hey purchased in he firs period. Two cases are analyzed: "endogenous swiching coss" and "exogenous swiching coss". Endogenous swiching coss exis when firms encourage cusomers o become loyal by plans like frequen flier. Cusomers are offered he commodiy a a lower price in he second period, if hey remain loyal o he firm. The firm bears he coss, he foregone revenues. f he consumers change a firm, due o he change in he producs' prices in he second period, he consumers bear exogenous swiching coss. These coss migh deer he cusomers from swiching firms, and makes hem 'capive cusomers'. harpe 1997 examined he implicaions of swiching coss on he banking indusry; olsky e al. 000 examined he mobiliy of pracicing physicians. n Klemperer s basic model and hose of his followers i is assumed ha consumers ener and exi he marke, bu firms have a permanen locaion. Unlike hese assumpions, his model reverses he roles and assumes ha branches are closed in alernaive locaions, bu consumers have a permanen locaion.

3 3 As is shown in he paper, i will be o he firm's advanage o close branches locaed adjacen o each oher, since he firm will no lose any cusomer. n closing branches beween he compeior's branches or adjacen o hem, he firm migh lose all is cusomers or reain some or all of is cusomers under cerain condiions. Under condiions specified in he paper, he firm can avoid losing cusomers, despie he closure of a branch. ecion describes he baseline model a line wih wo branches belonging o wo firms ha co-exis in he firs period a oelling framework. ecion 3 discusses he general impac of closing a branch and inroduces he erminology. ecions 4-5 have proposiions regarding he marke share of a firm closing a branch when prices, swiching coss and locaion vary. ecion 4 discusses he case when a branch is closed in an edge adjacen o he firm's branch or beween wo branches of he firm. We conclude ha a firm should adop such a policy. ecion 5 discusses he case when he branch is closed adjacen o is compeior's branches, or beween branches of wo firms he firm iself and is compeior. Closing a branch migh be profiable o he firm, under condiions specified in he proposiions. ecion 6 summarizes he resuls.. Basic Model Firs eriod Assumpions 1. The marke is represened by a line segmen of lengh 1 [0, 1], along he line cusomers and service branches are locaed;. The branches belong o wo differen firms, ; {A, B, C} a se of leers designaing he locaion of branches on he line. {a, b, c} he respecive disances from he origin. For example, locaion A is in disance a from he origin 0<a<1. Branches are designaed by firm, and locaion a, b, c, A, B, C, A Only firm closes branches in he second period. 3. The branches offer subsiue goods; 4. Branches of differen firms charge differen f.o.b. prices, in branches belonging o firms and respecively. Branches belonging o he same firm charge he same price. The prices don change from one period o anoher; 5. No capaciy consrains apply o he branches. The marginal coss are consan;

4 4 6. Consumers are disribued uniformly along he line. A consumer is locaed a x 0<x<1; 7. wiching coss,, are incurred when swiching from one firm o anoher. There are no swiching coss in swiching beween branches belonging o he same firm; 8. When he oal coss in wo branches are equal, he cusomers adop he closer branch; 9. Consumers don move-in or move-ou of he marke; 10. Demand is inelasic. Each cusomer purchases one uni per period; 11. The model is of wo periods. Definiions Marke area, he boundary of he area from where cusomers paronize a branch, will be designaed by [ ]. For a horough discussion of he law of marke areas, see arr Marke share is he size of he marke area: upper boundary less lower boundary, will be designaed by Ψ. Ψ x i denoes he marke share of firm he closing firm wih respec o he cusomers ha in he firs period belonged o he branch closed i. The Model There are branches in he marke e.g., A, B belonging o firms,, where 0<a<b<1. Consumers choose a branch ha minimizes he oal cos of service. The consumer bears he price per service, and he ravel cos, since he service is offered in he branch as is rue wih discussing a loan, consuling a physician, ec.. The ravel cos equals he disance beween he place of residence x and he locaion of he branch a, b imes he cos of ravel per disance uni ; ravel coss are independen of he firm which provides he service. Toal Coss, denoed C A, of geing service a branch A of firm locaed a a, when he cusomer is locaed a x are: C A = + x-a A consumer locaed a x chooses branch A if he oal cos, C A, is smaller han he oal cos, C B, of geing service of branch B of firm locaed a b. C B = + x-b

5 5 The consumer ha is indifferen beween he branches, is locaed a z: a + b z = + All consumers wih x<z choose branch A locaed a a; all consumers wih x>z choose branch B locaed a b. ince he price per service is differen beween he branches, he exreme case is when one branch dominaes he whole marke. f charges a very low price i will capure all he cusomers. roposiion 1 The marke has branches from wo differen firms, only if he following relaionship beween he prices holds: b a + b a roof The proof is by conradicion. Le us assume ha he price firm charges is below he price range: < b a By comparing C A and C B we conclude ha for all cusomers in he segmen [0, 1] i is cheaper o ge service a A han a B, and nobody will ge service a B. To exemplify, le us examine a single range which is closer o branch B: [b, 1] C A = +x-a<[ -b-a]+x-a=c B b<x<1 We conclude ha firm conrols he whole marke, which conradics he presumpion regarding he marke. f he price firm charges is above he range, i is equivalen o claiming ha he price firm charges is relaively low, and firm conrols he whole marke, which is a conradicion: > + b a < b a f he sign urns from inequaliy o equaliy, where = - b-a hen: for cusomers residing in he range [0, b] i is cheaper o receive service in A and hey will adop branch A. n he marke area [b,1] he cusomers are indifferen beween he branches. According o assumpion 8 equaliy beween coss he cusomers in he range [b,1] adop he closer branch, i.e., branch B. Boh branches co-exis, and heir marke areas

6 6 are [0, b], [b, 1] respecively. imilarly, when = + b-a he marke areas are [0, a], [a, 1]. Examples: f he branches charge he same price, = =, hen he marke area of A is [0, a+b/] and he marke area of B is [a+b/, 1]. Each cusomer in he range [0, a] will adop branch A, each cusomer in he range [b, 1] will adop branch branch B, he cusomers in he range [a, b] are spli beween he branches. f he branches are locaed a he edges a=0 and b=1 and he prices are equal, hen he firms spli he marke area, else he marke area will depend on he locaions a, b. f he branches are locaed a he edges, and charge differen prices, hen A and B dominaes respecively a: 1 1 [0, + ] [ +,1] 3. econd eriod - Closing a Branch When a firm closes a branch, he cusomers are forced o move o anoher branch. They migh move o a branch belonging o he same firm, or of anoher firm. ince he cusomers don know he firm s fuure policy regarding he opening of new branches or closure of branches, i is reasonable o assume ha in he firs period hey are myopic, and make decisions disregarding fuure changes in he availabiliy of branches. Closing a branch has differen implicaions on branches and on firms. The branch closed loses is marke area, and consequenly is marke share. The implicaions on he firm are differen. f he cusomers move o anoher of he firm's branches, he firm loses only some or none of is cusomers. f some of is branches gain cusomers, he issue is he sum of changes in marke share see ecion 4. f he cusomers move o a branch of anoher firm, he firm loses is marke share. Five proposiions are presened and discussed. The deailed proofs appear in Baron 00b. n ecion 4, cases where he firm closes a branch adjacen o is own branches are discussed, eiher on he edge ecion 4.1 or beween wo branches ecion 4.. is claimed ha, as expeced, his firm loses no cusomers, and closing a branch will

7 7 acually increase is profis. These proposiions are rivial, bu are brough for compleeness. n ecion 5 we examine cases where he closed branch is adjacen o he compeior's branches. Moving o he compeior's branches implies ha he consumer bears swiching coss exogenous swiching coss. Under cerain condiions he cusomers will move in he second period o remoe branches of he closing firm from which services were purchased in he firs period. is argued, ha under specified condiions, a non-coninuous marke area is generaed. We explore he impac of he swiching coss on he shape of he marke area coninuous or no and on he size of he marke share. Noaion Firms operaing in he firs period in differen scenarios: i, where i=a, B,.. G - branches belonging o firm. A, B - branches belonging o firm. Branches closed by firm in he second period: C - A branch in he edge, adjacen o A. D - A branch beween branches A, B. E - A branch in he edge, adjacen o B. F - A branch beween branches A, B. G - A branch beween branches A, B. 4. Closing a Branch Adjacen o ncumben Branches of he Firm 4.1 A Firm Closes a Branch in he Edge Firm has branches a a and c, branches A, C, which share he marke wih branch B in he firs period 0<c<a<b<1. n he second period, firm closes branch C in he range [0, a]. Branch C has a single adjacen neighbor, branch A, belonging o he same firm. roposiion Closing a branch beween he firm s branch and he edge, will no change he firm s marke share, bu will increase is profis. The adjacen branch will gain all he cusomers of he closing branch.. The firm's marke share in he range will correspond o:

8 8 Ψ x C = a + c 4. A Firm Closes a Branch Beween Two Branches of he ame Firm We assume ha in he firs period, he branches wihin a resriced segmen of he marke [a, b] are A, B and D where 0<a<d<b<1. The price per service in he hree branches is he same. n he second period firm closes he inermediary branch, D. roposiion 3 The marke share gained by branches due o he closing of an inermediary branch of he same firm, is independen of he locaion of he closing branch and equals half he disance beween he remaining branches. The marke share of firm remains unchanged; closing he branch increases he firm s profis. 4.3 A Firm hould Close he Branches Adjacen o Oher Branches of he Firm Though he closing branches were profiable, in erms of he closing firm, closing he branches will increase he firm's profiabiliy. The consumers move from one of he firm s branches o anoher; No cusomers are los o he firm in he second period; The firm's revenues remain unchanged by Assumpion 10; The oal coss are lower by Assumpion 5, he variable coss are unchanged, since he number of cusomers is unchanged; he fixed coss of an addiional branch are saved; The firm s profis increase. The conclusion migh change, if Assumpion 5 is relaxed, and he capaciy of he branches is limied or marginal coss are increasing. For compleeness: swiching coss will no change he proposiions, since by assumpion, swiching coss apply only in swiching beween firms and no in swiching beween branches of he same firm. Firm aracs he same cusomers wih or wihou swiching coss.

9 9 5. Closing a Branch Adjacen o ncumben Branches of a Compeior 5.1 A Firm Closes a Branch in he Edge, he Adjacen Branch Belongs o a Compeior Three branches belonging o wo firms are in he marke, A, B, E 0<a<b<e<1. Firm closes branch E. f he cusomers move o branch B, he adjacen branch, hey incur swiching coss. Branch A is more remoe. Will firm lose he marke share of he closing branch, Ψ x E, or under cerain condiions reain is share, since he cusomers move o he more remoe remaining branch, A? There is no adjacen branch closer o he edge nex o he closing branch, since we discuss compeiion over a line. f we analyzed a circle and he closer branch belonged o firm hen see ec f he branch belonged o he compeior, see ec. 5.. roposiion 4 A firm closing a branch, in an edge adjacen o a compeior s branch, will lose cusomers as a funcion of he price charged, he locaion of is remaining branches and he swiching coss. The firm's marke share in his range will correspond o: 0 Ψ x E = 1 -[ b + e/ -/ ] < b a + b a + We conclude ha if is relaively high relaive o, he swiching coss are relaively low and he disance beween he poenial branches b-a is high, he closing firm firm will lose all he marke share of he closing branch. f he cusomers remain loyal o he closing firm, hey move o he more remoe branch of he firm branch A. The resul is a non-coninuous marke share. 5. Closing a Branch Beween Two Branches of a Compeior n he firs period, five branches are locaed wihin a resriced segmen of he marke: A, B and C, E, F 0<c<a<f<b<e<1. The branches divide he marke area beween hem in he firs period. n he second period, branch F belonging o firm and locaed a f is closed. f he cusomers move o he compeior s branches A or B, swiching coss apply, since we analyze wo differen firms. Will hey move o more remoe branches belonging o he closing firm and remain loyal o he firm hey adoped in he firs period?

10 10 roposiion 5 The marke share of a firm closing a branch beween wo branches belonging o a compeior depends on he prices, he swiching coss and he locaion of branches. The cusomers decision depends on he disance beween he poenial branches: A vs. C, B vs. E. As he disance is increasing, i is less likely ha he firm will keep he cusomers. Oher cases ha he firm will lose is cusomers are when he swiching coss are low and he price he firsm charges is relaively high. As he swiching coss are higher, i is more likely ha he firm keeps he cusomers. f he cusomers are loyal o he firm, hen he resuling marke area is non-coinuous. 5.3 Closing a Branch beween Branches of Two Firms n he firs period branches of differen firms co-exis in he marke. We concenrae on four branches a he range [a, b]: branches A, E, G and B 0<a<g<b<e<1. n he second period he closing firm closes he branch a g branch G. s adjacen neighbors are one belonging o he same firm and one o is compeior. We assume ha swiching coss apply when a cusomer moves his business o he compeior branch B, swiching beween firms, and don apply when cusomers move o a branch of he same firm branch A or branch E. roposiion 6 The marke share of a firm closing a branch beween branches of wo firms - one belonging o a compeior and one o he same firm - depends on prices, swiching coss and he locaion of branches. < + + < + + < < + = = Ψ 0 b e c a b e c a f e a b b e c a c f a b b e c a a b F x

11 11 The firm s marke share is: b g / + + / Ψ x G = b a / + -/ < e b + e b + f he swiching coss are high, all he cusomers will be loyal o he firm, and he firm reains is marke share as in he firs period. n his case he cusomers will spli beween he adjacen branch belonging o he closing firm and a more remoe branch branches A and E. Due o he swiching coss i is cheaper o ge service in E and no in he closer branch B. This resul also depends on he disance e-b. n his case, he resuling marke area is non-coninuous. f hese condiions do no hold, he firm will lose some of is marke share o is compeior. s marke area will be coninuous. s marke share will depend on he disance beween he compeior s branch and he closing branch, b-g. will increase as he swiching coss are increasing. 5.4 hould a Firm Close Branches Adjacen o is Compeior's Branches? When a firm closes one of is branches adjacen o is compeior s branches, i is faced wih he risk of losing he enire marke area and marke share of his branch. As roposiions 4, 5 and 6 show, he loss depends on he difference beween he prices charged by he firms,, he disance beween poenial branches and he swiching coss. n ecions 5.1, 5., and 5.3, he cusomers of he closed branch are faced wih a choice beween wo branches he poenial branches, each wih a differen cos per service: A branch belonging o he compeing firm, and an alernaive, a remoe branch belonging o he closing firm. f m denoes he locaion of he branch belonging o firm, and n he locaion of he branch belonging o firm, and m<n<x. The coss of service are: C m = +x-m C n = ++x-n The comparison is equivalen o comparing he coss a he same locaion, arbirarily, he locaion of he compeior s branch. f we are locaed a n, receiving service a

12 1 branch n we shall pay he price he firm charges plus swiching coss no ransfer coss, +. The coss relevan for branch m equal he price per service plus he ransfer cos beween he wo branches, +n-m. According o roposiion 1, we know ha he co-exisence of branches in he marke implies +n-m. n he second period, he consumer s comparison of coss includes swiching coss, and hey may reverse he sign of he inequaliy. n such a case, he more remoe branch is adoped by he cusomers branch m, and no he close branch, branch n. As long as he swiching coss are low, all he cusomers move from he closing branch o is closes neighboring branch. n ecions 5.1, 5., a branch belonging o he compeior, firm. n hese cases, firm loses is enire marke share in he considered range. n ecion 5.3 he closing firm loses abou half of is marke share, since one of is closes neighbors is a branch belonging o he firm iself. Once he disance beween he poenial branches is relaively small and he swiching coss are relaively high, i is likely ha he cusomers will remain loyal o firm. f ha is he case, he resul is ha some of firm 's branches have a non-coninuous marke area. ome of he cusomers of hese branches belonging o firm reside adjacen o he branch he cusomers who paronized he branch in he firs period, bu oher cusomers, don' reside adjacen o he branch he ones who moved in he second period from he closing branch. The difference beween he proposiions is in he impac of he swiching coss. n roposiion 4, he change in marke share is no coninuous. For a wide range of values of he swiching coss, firm will lose all he cusomers of he closing branch. Once, he swiching cos is above a 'criical value' he firm reains all is cusomers. The 'criical value' depends on he ravel cos beween he poenial branches. Therefore, eiher firm loses all he cusomers of he closing branch or i reains all of hem. n roposiions 4, he resuls are independen of he locaion of he closing branch. n roposiions 5 and 6, he impac of he swiching coss is more gradual. f one of he compeior's branches is aracive enough, he boundary beween he marke areas depends on he swiching coss. The marke area gained by he compeior depends negaively on he swiching coss.

13 13 n roposiions 5 and 6 he marke share los or reained depends on he locaion of he closed branches. The marke share depends on he disance beween he closing branch and he adoped branch e.g., in roposiion 6, b-g. f he firm loses all is cusomers, is profi will decrease in he second period, assuming he branch was profiable in he firs period. As he firm reains more of he cusomers of he closed branch, is profis are more likely o increase. The firm saves he branch's fixed coss, and is revenues migh be close o he iniial level in he firs period. 6. Conclusions The service indusry winesses changes. Face o face conacs are less crucial. The branches are losing many of heir cusomers, and firms survival depends on closing service branches. Though he analysis assumed inelasic demand for services, we can infer from he analysis ino he real world. A firm rying o increase is profis should close all he branches adjacen o oher branches of he firm, according o roposiions and 3. When closure of branches adjacen o he compeior s branches is considered, he roposiions sugges rules for choosing he branches o be closed. The proposiions idenify branches ha heir poenial decrease in marke share is minimal, e.g., he case where he compeior's branch is adjacen o one of he firm's branches. The discussion shows he imporance of swiching coss in he decision o swich a firm and in he size of he resuling marke share. The discussion assumes ha swiching coss are exogenous: he consumer bears he swiching coss. We can reformulae he problem and assume boh exogenous and endogenous swiching coss. The consumer coninues o bear he coss and inconvenience of swiching a firm. owever, he firm ha wishes o reain or arac he old cusomers offers a bonus o any cusomer who moves o is branches when a branch is closed, and is willing o bear endogenous swiching coss. Each firm can use he bonus o increase is marke share, if i is willing o bear he coss. Though i is assumed ha he ransfer rae,, is he same for boh firms, we receive a non-coninuous marke area, a resul arr 1995 receives only when he ransfer coss applying o wo firms are differen. This resuls from consumers loyaly and is an unexpeced resul.

14 14 The resuls show ha swiching coss have an imporan role in changing he marke areas and shares. They can be used by firms o increase heir profis, and canno be negleced. References Baron M.G. 00a wiching Coss and he Locaion of ervice Branches, Working aper, Technion, Faculy of ndusrial Engineering and Managemen, aifa, srael. Baron M.G. 00b, wiching Coss and he Closure of ervice Branches, Working aper, Technion, Faculy of ndusrial Engineering and Managemen, aifa, srael. oelling,. 199, "abiliy in Compeiion", Economic Journal, 39, pp Klemperer,. 1987a, Markes wih Consumer wiching Coss, Quarerly Journal of Economics, 10, pp b, The Combaiveness of Markes wih Consumer wiching Coss, Rand Journal of Economics, 18/1, pp , Compeiion when Consumers have wiching Coss, Review of Economic udies, 6, pp adilla, A. J. 1995, Revisiing Dynamic Duopoly wih Consumer wiching Coss, Journal of Economic Theory, 67, pp arr, J. B. 1995, "The Economic Law of Marke Areas: A Furher Discussion", Journal of Regional cience, 354, pp olsky D. e al. 000, MO eneraion and he Geographic Mobiliy of racicing hysicians, Journal of ealh Economics,19 5, pp harpe. A.1997, The Effec of Consumer wiching Coss on rices: A Theory and s Applicaion o he Bank Deposi Marke, Review of ndusrial Organizaion, 1 1, pp To, T. 1996, Muli-eriod Compeiion wih wiching Coss: An Overlapping Generaions Formulaion, The Journal of ndusrial Economics, 44/1, pp Von Weizsacker C.1984, The Coss of ubsiuion, Economerica, 5/5, pp

15 15 Nomenclaure Ψ Marke share [ ] Marke area A, B, C Locaion C Cos of service, Types of firms i=, A, B, C, A, B Branches of firm i, locaion j i=, ; j=a, B, C, rice charged by firm i wiching coss incurred in moving beween firms rice of ravel per disance uni z The border beween marke areas Acknowledgemen The research was conduced while he auhor was a Visiing cholar a he Regional cience rogram, Universiy of ennsylvania, hiladelphia, A. The auhor hanks Ronald E. Miller for his consrucive and helpful commens. The auhor hanks haron inkas Lifshiz for paricipang in early sages of his research.