The Reltive Advntges of Flexible versus Designted Mnufcturing Technologies George Normn Cummings Professor of Entrepreneurship nd Business Economics Tufts University Medford MA 055 USA e-mil: george.normn@tufts.edu Abstrct This pper nlyzes the choice between flexible nd designted mnufcturing technologies given tht firms re llowed to determine how flexible the mnufcturing system should be. We llow firms to operte mix of technologies using flexible system to serve some types of consumer submrkets nd designted technology to serve others nd llow firms to offer multiple products even if they commit to the designted technology. We show tht for flexible systems to be preferred they must offer strong economies of scope nd must be cpble of producing without significnt cost penlties customized products tht re lrgely indistinguishble from custom-built products. By contrst we show tht n increse in submrket size nd n increse in the willingness of consumers to py for prticulr types of products encourges the use of designted technologies trgeted t these submrkets. (JEL: D4 L L R)
. Introduction Recent yers hve seen considerble dvnces in the development nd diffusion of flexible mnufcturing systems. "Flexibility" in this context refers to flexibility in product design through which mnufcturers cn dpt bse product to individul consumer requirements t very low dditionl unit costs: see for exmple Milgrom nd Roberts (990) Mnsfield (99). Specificlly flexible mnufcturing system is defined s: production unit cpble of producing rnge of discrete products with minimum of mnul intervention (US Office of Technology Assessment 984 p. 60) Such flexible systems re employed in the mnufcture of n incresingly wide rnge of goods from cermic tiles to Levi jens nd custom shoes to dt-wrehousing. It is now being suggested tht such flexibility will find nturl outlet s e-commerce continues to expnd. For exmple the New York Times recently stted: Wht this mens in prctice is tht rther thn displying the sme set of pges to every visitor Web site would present different informtion to ech customer bsed on the person s dt profile. (New York Times Internet Compnies Lern how to Personlize Services August 8 000) With the dvent of flexible mnufcturing systems technology choice becomes n importnt strtegic issue. The doption of flexible mnufcturing confers dvntges tht re primrily bsed upon economies of scope but imposes penlties with respect to the dditionl setup costs tht re necessry to estblish such flexible systems: see for exmple Chng (99) Röller nd Tombk (990 99) Normn nd Thisse (999). The existing literture tht ttempts to ddress these strtegic issues is limited in severl respects. In prticulr two importnt questions re not considered. (i) (ii) Given tht firm dopts flexible mnufcturing system how does it choose the rnge of products it should offer? will firm wish to operte mix of flexible nd designted technologies? Question (i) is relted to much of the recent literture on product vriety in horizontlly differentited industries nd leds to nother importnt question: (iii) with endogenous technology choice will we see product gglomertion s for exmple is discussed in Hmilton Thisse nd Weskmp (989) nd Anderson nd Neven (990)? 0/5/00
This pper ttempts to shed some light on these questions. Strtegic choice of technology differentition. Applictions of this pproch to flexible mnufcturing hve been developed by Eton nd Schmitt (994) nd Normn nd Thisse (999). They build on the seminl ides of models of product differentition. McLeod Normn nd Thisse (988) show how this nlogy hs the potentil for being pplied directly to the strtegic nlysis of flexible mnufcturing: customers specifictions. This mens tht the firm now produces bnd horizontlly differentited products insted of single product Trnsport cost is no longer interpreted s utility loss but s n dditionl cost incurred by the firm in Almost ll of the current literture on flexible mnufcturing presents firms with reltively strk choice. Choose between flexible or designted technology. If the designted n importnt issue tht is centrl to our nlysis. We consider not just the choice between flexible nd designted mnufcturing technologies but lso the choice of just how flexible the flexible system is cpble of producing should be endogenous to the nlysis with firms trding off incresed width ginst the dditionl set-up costs tht incresed width imposes. This leds nturlly to second importnt element of our nlysis. We explicitly llow firms to operte of technologies using flexible system to serve some types of consumer nd designted technology to serve others. Furthermore we explicitly llow firms to offer possibility tht there will be symmetry in technology choice in tht the strtegic choice of flexible systems by one firm will encourge nother firm to dopt different technology choice. show tht the ttrctiveness of flexible mnufcturing is determined by the blnce between the economies of scope offered by flexible mnufcturing nd the economies of scle offered by
designted technologies. Secondly the dvntges of flexible systems re ffected by consumer tstes nd the bility of flexible mnufcturing systems to deliver t low cost customized products tht re truly substitutble for custom-built products. Thirdly we show tht technology choice is ffected by mrket size nd the willingness of consumers to py for products of prticulr types. The reminder of the pper is structured s follows. In the next section we develop the bsic model presenting the choice between designted nd flexible technologies s simultneous three-stge technology/loction/quntity gme. Section identifies the subgme perfect Nsh equilibri for this gme. Finlly we discuss the primry determinnts of technology choice in section 4.. The Model The demnd side is modeled s vrint of the fmilir Hotelling (99) nd Slop (979) nlysis in tht we ssume consumers to be distributed over line mrket. But we deprt from Hotelling (nd the Eton/Schmitt nd Normn/Thisse nlyses) in two wys. First we ssume tht consumers re concentrted in five evenly spced submrkets s in Figure. The "distnce" between submrkets is designted r (we give more detiled interprettion of r below). Secondly demnd in ech submrket is ssumed to be identicl nd liner: inverse demnd in ech consumer submrket is: () p i = - Q i /s (i = - 5) where s is mesure of submrket size. On the production side we ssume tht the mrket is supplied by duopolists who cn choose from three technologies differentited by their "width": (i) designted technology (d) with width of 0 tht cn be used to serve t most one consumer submrket; (ii) prtilly flexible technology (p) with width of tht cn be used to serve centrl consumer submrket nd t most one submrket on ech side of this centrl submrket; Eton nd Schmitt (994) do introduce this possibility in the initil specifiction of their model but drop this cost term in their ctul nlysis. The reson for our not ssuming consumers to be uniformly distributed will become clerer below. The choice of five submrkets is not totlly rbitrry. It is lrge enough to llow considertion of the strtegic issues in which we re interested while being smll enough to be nlyticlly trctble. 0/5/00 4
(iii) flexible technology (f) with width of tht cn be used to serve centrl consumer submrket nd t most two submrkets on ech side of this centrl submrket. If firm opertes the d technology to supply some or ll of the consumer submrkets the loction i of prticulr d product is just the consumer submrket for which the product hs been designed. For the p or f technologies i defines the loction of the bse product on which the p or f technology is centered. We use the terminology "designted product i" to refer to the output of d technology locted in consumer submrket i nd "bse product i" to refer to the consumer submrket on which p or f technology is centered. Consumers in submrket i re ssumed to consider designted product i or bse product i produced by either of the duopolists to be perfect substitutes. Firms cn choose to serve some or ll consumer submrkets by estblishing multiple products. Thus for exmple if technology d is chosen firm cn choose to estblish up to five d products if technology p is chosen the firm cn serve the remining mrkets by estblishing number of d products nd if technology f is chosen the firm if it hs not locted its bse f product in the centrl submrket (submrket in Figure ) cn choose to serve the remining submrkets by estblishing dditionl d or p products. When we refer to technology choice t below we men the most flexible technology tht firm chooses. (Figure ner here) In specifying technology costs we distinguish between two types of vrible costs. First there re the vrible costs of producing prticulr designted or bse product costs of rw mterils intermedite inputs lbor nd so on which cn resonbly be ssumed to be constnt cross ll three technologies. Without loss of generlity these costs re normlized to zero. Secondly there re vrible costs of customizing bse product centered in one consumer submrket to the specific requirements of consumers in other submrkets. We consider these costs in more detil below. In ddition to vrible costs ech technology is ssumed to incur set-up costs. Specificlly technology of width w is ssumed to incur set-up costs of F(w). Clerly: () F(0) < F() < F(). We do not consider technologies with widths greter thn given tht we confine ttention to mrket contining five submrkets. 0/5/00 5
We ssume tht there re economies of scope s the width of the technology increses. In other words () F(w) < (w + ).F(0) for w =. In the nlysis below it will prove convenient to ssume tht set-up costs increse with width ccording to reltionship of the form: (4) F(w) = (+ w.k).f(0) (i = 0 ) where > k > 0 is n inverse mesure of the economies of scope of the flexible technologies. We hve lredy indicted tht d product cn be sold only in the consumer submrket in which it is locted. In the loction theoretic interprettion of our model this is equivlent to ssuming tht the cost of trnsporting d product between djcent consumer submrkets is t lest per unit; in the horizontl product differentition nlogy it is equivlent to ssuming tht consumers in submrket j consider designted product i to be worth t lest less thn designted or bse product j. By contrst the cost of trnsporting p or f product between djcent submrkets or equivlently of customizing bse product i to the consumer tstes of submrket (i - ) or (i + ) is ssumed to be r per unit. 4 In the product differentition nlogy the prmeter r cn be thought of s composite producer nd consumer mesure of flexibility. From the producer perspective it seems resonble to ssume tht product redesign hs some impct on vrible costs even where flexible mnufcturing systems re introduced. This impct increses the less truly flexible is the flexible technology nd the greter the degree of bse product redesign tht is necessry to customize the bse product to the preferences of nother consumer submrket (the more differentited re consumer preferences between submrkets). This element of r in other words is combined mesure of production flexibility nd consumers' preference diversity. For consumers r cn be considered to contin mesure of the extent to which consumers vlue customized products tht re the output of flexible technologies less thn custom-built products tht re the output of designted technologies. 5 In this ltter respect r is 4 We do not feel tht nything is to be gined from distinguishing p nd f technologies with respect to r. 5 As n illustrtion we cn consider flexible mnufcturing in the production of elevtors. Clients re typiclly offered wide rnge of externl finishes nd cr sizes -- the prts tht users see -- but much smller rnge of drive speeds nd cpcities control systems nd other components -- tht the users do not see. Custom-built elevtors by contrst offer much wider rnge of specifictions of the totl system. 0/5/00 6
mesure of the degree of substitutbility between the products of djcent flexible nd designted technologies. Formlly we ssume: (5) r = r + r where: v c w. r v denotes the unit vrible costs of redesigning bse product locted in submrket i to the desired chrcteristics of submrket (i - w) or (i + w); nd w.r c denotes the extent to which consumers in submrket (i - w) (or (i + w)) vlue product customized from bse product i less thn designted or bse product locted in (i - w) (or (i + w)). This implies tht if the price of designted (or bse) product i is p(i) then the product customized to submrket i from bse product j will hve to be offered t price p( i) rc i j nd the net revenue received by firm from the sle of bse product j customized to submrket i is p ( i) ( r + r ) i j = p( i) r i j per unit. v c In chrcterizing equilibrium we ssume tht firms nd im to mximize ggregte profit from sles to consumers in the five submrkets through their choices of technology loctions (designs) of their products nd outputs. Formlly the technology-loction-output gme is modeled s three-stge duopoly gme using the concept of subgme perfect Nsh equilibrium. In the first stge firms simultneously choose their technologies nd estblish technology configurtion denoted t. In the second stge subgme the firms choose the designs (loctions) of their bse nd/or designted products given the technology configurtion estblished in the first stge. We refer to the outcome of this subgme s mrket loction configurtion denoted l(t). The third stge subgme is modeled s Cournot gme in which ech firm chooses how much to supply to ech consumer submrket (nd from which loction to supply) given the technology nd mrket loction configurtions estblished in the first nd second stges. Tht is in the third stge subgme we identify the Cournot equilibrium for the two firms in ech technology nd mrket loction configurtion. This timing seems resonble in tht it implies technology choice to be the most inflexible decision nd output choice to be the most flexible. 0/5/00 7
. Equilibrium Technology Choice We ssume tht set-up costs re sufficiently low for ech firm to be ble to supply ll consumer submrkets no mtter the technology configurtion estblished in the first stge. A sufficient condition for this is ( 0) s. 9 F. We further ssume tht if firm loctes its bse f product t the mrket center it is ble to supply ll consumer submrkets no mtter the technology choices of its rivl which implies r < /4.. Quntity Equilibrium Consider ny technology nd mrket loction configurtion (t l(t)). Firm m supplies consumer submrket i with its product in (t l(t)) tht offers the gretest net revenue per unit. We m denote the loction of this product ( t l( t) ) ( ) by i t l( t) q m i submrket i by firm m s: m (6) q i l( t) i j nd the ssocited quntity supplied to submrket i i. Stndrd nlysis gives the Cournot-Nsh equilibrium quntity supplied to m n ( ) = s( i j r + i j r) Price in submrket i is: (7) p i ( t l( t) ) t (mn = m n). i i m n ( ) = ( + i j r + i j ) * r nd ggregte profit to firm m is: (8) Π ( t) m where ( t) m = 5 i= s i i m n ( i j r + i j r) i 9 i F m ( t) (m = ) F is the ggregte set-up costs incurred by firm m in the technology nd mrket loction configurtion (t l(t)). Eqution (8) indictes tht the subgme perfect equilibrium in our technology-loctionoutput gme is function of five prmeters F(0) k s nd r. We cn however reduce this prmeter spce to three by formulting the nlysis in terms of the demnd djusted prmeters: ρ = r ; f = F s. (9) ( ) ( ) in which cse ggregte profit in (8) cn be rewritten: (8') Π ( t) m = s. 5 i= m n ( i j ρ + i j ρ) i 9 i f m ( t) 0/5/00 8
(See Rowthorn (99) for similr pproch in different context.) Note tht our restrictions on F(0) nd r imply tht f(0) < /9 nd ρ < /4.. Loction Equilibrium By convention nd without loss of generlity we ssume tht firm loctes to the left of firm if the two firms hve not chosen identicl loctions for their bse products. We denote by L m (t) the set of loction configurtions tht cn be chosen by firm m given the technology configurtion t. A loction configurtion l m (t) L m (t) is quintuplet: 4 5 (9) l m (t) = ( l l l l ) l (m = ) m m m m m where lm i = dm i pm i i or f m l m i if firm m estblishes designted or bse product in submrket i nd = 0 if firm m does not hve designted or bse product in submrket i. A mrket loction configurtion is pir l(t) = { ( t) l ( t) } l. Identifiction of the Nsh equilibrium of the loction subgme requires tht we consider number of different possible technology configurtions. In doing so we mke the further simplifying ssumption tht the d technology domintes the p technology if only two djcent submrkets re to be supplied nd domintes the f technology if only three djcent submrkets re to be supplied: sufficient condition for this to be the cse is k >. 6 This ssumption hs three importnt implictions in our model tht considerbly simplify the nlysis. First neither firm will locte p or f bse product in the most peripherl consumer submrkets nd 5. Secondly neither firm will combine the f nd p technologies. Thirdly neither firm will operte two p technology plnts. The loction subgme for ny given technology configurtion is nlyzed on the ssumption tht ech firm chooses its loction(s) to mximize profits given the loction(s) of its rivl nd the equilibrium quntity schedules identified in section.... t = {dd} Given our ssumption tht ( 0) s 9 estblish designted product in every submrket. F in the technology configurtion {dd} both firms 6 If k > then F() >.F(0) nd F() >.F(0). k > is sufficient but not necessry since the p nd f technologies incur dditionl costs of r per unit in customizing bse product i to the requirements of djcent submrkets. 0/5/00 9
Lemm : The Nsh equilibrium mrket loction configurtion for the technology configurtion {dd} is: 4 5 (0) ( dd} ) = ( d d d d d ) l m (m = ) { m m m m m Profit to ech firm is: d (m = ). () Π ({ d} ) = 5s. f ( 0) m.. t = {pp} In nlyzing loction choice when both firms hve chosen the prtilly flexible technology we cn confine our ttention to cses in which firm () loctes its bse p product in consumer submrkets or (4 or ). 7 The py-off mtrix for the loction subgme is given in Tble. Lemm : The Nsh equilibrium mrket loction configurtion for the technology configurtion {pp} is: () l l 5 ({ pp} ) = ( d 0 p 0 d ); l { pp} 4 5 ({ pp} ) = ( 0 p 0 d d ); l { pp} 4 ( ) = ( d d 0 p 0) 5 ( ) = ( d 0 p 0 d ) with firms nd locting their prtilly flexible bse products in consumer submrkets nd 4 (or nd ) respectively. 8 Profit ({ pp} ) Π m to ech firm is given by the off-digonl entries in Tble. (Tble ner here) Lemm indictes tht gglomertion or the principle of minimum differentition does not pply when technology is strtegic vrible nd the technology chosen is not cpble by itself of supplying the entire mrket. This is in shrp contrst to cses in which technology is not choice vrible (Hmilton et l. (989) Anderson nd Neven (990)). The intuition underlying this result cn be seen by compring for exmple the gross profits in ech consumer 4 5 submrket tht re mde by firm in the loction configurtions ( 0 0 d d ) 5 5 ( d 0 p 0 d ) when firm hs chosen the loction configurtion ( d 0 p 0 d ) given in Tble. or p nd. These re 7 Coincident loction t () nd (44) re equivlent to (). 8 Note tht these re equivlent equilibri. 0/5/00 0
Aggregte output is identicl for both firms in these two mrket loction configurtions (recll equtions (6) nd (8)) but individul firm profit is determined by the distribution of ggregte output. 9 No mtter the loction configurtion firm erns gretest profits from those submrkets in which its product is custom-built rther thn customized: submrkets 4 nd 5 in 4 5 the loction configurtion ( 0 p 0 d d ) nd submrkets nd 5 in the loction 5 4 5 configurtion ( d 0 p 0 d ). However in the loction configurtion ( 0 0 d d ) p firm 's custom-built products re in competition with customized products of firm wheres in the 5 loction configurtion ( 0 p 0 d ) d they re in competition with custom-built products (with the exception of submrket 5 of course). The dditionl profits firm erns in the former loction configurtion from its custom-built products being in competition with customized products more thn offset the lower profits tht result from its customized products being in competition with custom-built products. 0 (Tble ner here).. t = {ff} In nlyzing loction choice when both firms hve chosen the wider of the two flexible technologies we cn s with the technology configurtion {pp} confine our ttention to cses in which firm () loctes its bse f product in consumer submrkets or (4 or ). The py-off mtrix to the loction subgme is given in Tble. Lemm : The Nsh equilibrium mrket loction configurtion for the technology configurtion {ff} is: (i) f ( 0) ( 8ρ 4ρ 5 () ({ ff} ) = ( 0 f 00 d ) l ; ({ f f} ) = 4 l ( d 00 f 0) with firms nd locting their flexible bse products in consumer submrkets nd 4 respectively. (ii) ( 8ρ 4ρ < f ( 0) ( 8ρ + 8ρ 9 Note tht the four mrket loction configurtions of Tble hve identicl totl set-up costs for ech firm. 0 This is reminiscent of gme theoretic models of foreign direct investment in which it is shown tht the reltive profitbility of different loction configurtions is determined by the blnce between the import protection effect of competing with imported products nd the export cost effect of hving to export product to nother mrket: see Mott nd Normn (996). 0/5/00
() l l 5 ({ ff} ) = ( 0 f 00 d ); l ({ ff} ) = ( 00 f 00) 4 ({ ff} ) = ( 00 f 00); l ({ ff} ) = ( d 00 f 0) or Flexible versus Designted Technologies with firms nd locting their flexible bse products in consumer submrkets nd (or nd 4) respectively. (iii) ( 8ρ + 8ρ < f ( 0) (4) l ({ ff} ) = ( 00 00); l ({ f f} ) = ( 00 00) f with firms nd ech locting their prtilly flexible bse products in consumer submrket. Profit ({ f f} ) Π m to ech firm is given by the pproprite cell in Tble. f Agglomertion is the Nsh equilibrium to the loction subgme with the technology configurtion {ff} only for f ( 0) > ( 8ρ + 8ρ. The resoning behind this result is strightforwrd. If the duopolists consider only the vrible costs of production then the sme forces re t work s those discussed in section.. leding to non-gglomertion of the bse products. Tble indictes tht if set-up costs were ignored the unique Nsh equilibrium 5 4 mrket loction configurtion would be { ( 0 f 00 d ) ( 00 0) d }: recll tht ρ < /4. f Once set-up costs re tken into ccount however there is n dditionl incentive for either firm to wish to locte t the mrket center. Centrl loction offers svings in set-up costs. The greter is f(0) the more likely it is tht these svings will offset the reduced gross profit tht the individul firm mkes with more gglomerted loctions. (Tble ner here)..4 t = {dp} (or {pd}) Our prmeter restrictions imply tht the only loctions for the p bse product tht we need to consider re in submrkets or 4. Lemm 4: The Nsh equilibrium mrket loction configurtion for the technology configurtion {dp} is: Note tht these re equivlent equilibri. 0/5/00
(5) l l l 4 5 4 ({ dp} ) = ( d d d d d ); l ({ dp} ) = ( d d 0 p 0) 4 5 5 ({ dp} ) = ( d d d d d ); l ({ dp} ) = ( d 0 p 0 d ) 4 5 4 5 ({ dp} ) = ( d d d d d ); l ({ dp} ) = ( 0 p 0 d d ) Flexible versus Designted Technologies with firm indifferent between submrkets nd 4 for the loction of its prtilly flexible bse product. Profits in the technology configurtion {dp} re: (6) Π Π 5 + 4ρ + ρ 5 8ρ + 8ρ ({ dp} ) = s. 5 f ( 0) ({ dp} ) = s. f ( 0) f ( )..5 t = {df} (or {fd}) We need only consider the loction of firm 's f bse product in submrkets or 4. Tble 4 gives the profits to the two firms from ech loction choice by firm. Lemm 5: The Nsh equilibrium mrket loction configurtion for the technology configurtion {df} is: (i) f ( 0) ( 8ρ 6ρ 4 5 (7) ({ df} ) = ( d d d d d ) l ; ({ d f} ) =. 4 l ( d 00 f 0) with firm locting its f bse product in submrket 4; (ii) f ( 0) > ( 8ρ 6ρ 4 5 (8) ({ df} ) = ( d d d d d ) l ; ({ d f} ) = l ( 00 00) with firm locting its f bse product in submrket. (Tble 4 ner here) The mrket forces leding to Lemm 5 cn be identified from Tble 5; they re just those discussed in... If firm chooses the loction configurtion ( 00 00) 4 ( 00 0) f f or or f rther thn d it gins some dditionl profit in the centrl consumer submrkets but loses profit in the peripherl submrkets: in submrket becuse it hs replced designted product by customized product nd in submrket 5 becuse the costs of customizing the bse product hve 0/5/00
been incresed. The resulting lower gross profits of centrl loction re moderted by the lower set-up costs firm incurs nd re more thn offset if ( 0) > ( 8ρ 6ρ f. (Tble 5 ner here)..6 t = {pf} (or {fp}) Our prmeter constrints imply tht firm will operte mix of p nd d technologies locting its p bse product t or 4 while firm will operte mix of f nd d technologies with the f bse product locted t or 4. The py-off mtrix is given in Tble 6. Lemm 5: The Nsh equilibrium mrket loction configurtion for the technology configurtion {pf} is: f ρ ρ (i) ( 0) ( 8 6 4 5 (9) ({ pf} ) = ( 0 p 0 d d ) (0) l ; ({ p f} ) = 4 l ( d 00 f 0) with firm locting its f bse product in submrket 4 nd firm its p bse product in submrket ; (ii) f ( 0) > ( 8ρ 6ρ l l l 4 5 ({ pf} ) = ( 0 p 0 d d ); l ({ pf} ) = ( 00 f 00) 5 ({ pf} ) = ( d 0 p 0 d ); l ({ pf} ) = ( 00 f 00) 4 ({ pf} ) = ( d d 0 p 0); l ({ pf} ) = ( 00 f 00) with firm locting its f bse product in submrket nd firm indifferent between loctions nd 4 for its p bse product. Once gin gglomertion is Nsh equilibrium only if set-up costs re "sufficiently lrge". (Tble 6 ner here). Technology Equilibrium In the first stge technology choice gme ech firm chooses its technology to mximize profits given its rivl's technology choice nd given the equilibrium mrket loction configurtion nd quntity schedules tht will be estblished in the second- nd third-stge subgmes. or or Switching the lbels gives the Nsh equilibri nd profits for the technology configurtion {pd}. The sme 0/5/00 4
Lemms -5 indicte tht there re five prmeter regions to be exmined. The technology choice py-off mtrices for ech of these prmeter regions re given in Appendix Tbles A-e. Substituting from eqution (4) leds to the following: Proposition : The three-stge perfect Nsh equilibrium is: (i) f ( 0) (ii) (iii) (iv) t* = {dd} 8ρ 8ρ 9 ( k ) m with l*(t*) nd ( t* l * ( t *)) 8ρ 8ρ 9 ( k) t* = {pp} < f q given by (0) nd (6) respectively; i ( 0) 6ρ 4ρ 9 ( k ) m with l*(t*) nd ( t* l * ( t *)) 6ρ 4ρ 9 ( k ) < i t* = {pf} or {fp} q given by () nd (6) respectively; f ( 0) 6ρ 9 ( k ) m with l*(t*) nd ( t* l * ( t *)) 6ρ f 9 k < ( ) t* = {ff} ( 0) q given by (0) nd (6) respectively; i m with l*(t*) nd ( t* l * ( t *)) q given by (4) nd (6) respectively. i The equilibri of Proposition re illustrted in Figure for the specil cse of k =. (Figure ner here) 4. Discussion of the Determinnts of Equilibrium Technology Choice When competing firms cn be multi-product firms no mtter their technology choice the strtegic dvntges of flexible technologies would pper to be somewht more limited thn previous nlysis hs suggested. The explntion is strightforwrd. In our nlysis the firms re not forced to dopt flexible mnufcturing systems if they wish to supply more thn one prt comments pply to the discussion of technology configurtions {fd} nd {fp} below. 0/5/00 5
of the mrket. Rther the choice of flexible mnufcturing is determined by firms blncing the svings in set-up costs these technologies offer ginst the vrible costs of product customiztion they impose. The comprtive sttic effects of chnges in mrket prmeters re lso ffected by our multi-product setting. From eqution (4) the bsolute difference in set-up costs between designted nd flexible technologies in supplying the sme number of consumer submrkets increses with f(0). Proposition nd Figure indicte tht flexible technologies re more likely to be used the greter is f(0). In other words nd s we would expect flexible technologies re more likely to be dopted the greter the bsolute svings in set-up costs they offer. It is lso cler from Proposition nd Figure tht the boundries c n (n = ) fll s k is reduced: () ( 0) df dk c n > 0 (n = ) In other words the ppliction of flexible mnufcturing technologies is encourged when these technologies offer strong economies of scope reltive to the economies of scle offered by designted technologies. A low vlue of ρ lso leds to the more extensive doption of flexible mnufcturing. This cn rise for two resons (eqution (9)): low r or high. Consider the former. (We shll consider below how the demnd prmeter ffects the technology choice.) Our discussion in section indictes tht low vlue of r cn be ttributed to one of three fctors. The first is if the vrible costs of redesigning bse product i to the desired chrcteristics of submrket j re low i.e. if there is high degree of production flexibility. Secondly r is low if there is low degree of differentition in consumer preferences between consumer submrkets i.e. high degree of substitutbility between djcent bse products. In either of these two cses the producer costs (rv i j ) of customizing bse product i to the requirements of submrket j re low. Thirdly r is lower the greter the extent to which consumers view customized products s being close substitutes for custom-built products i.e. the greter the degree of substitutbility between the products of djcent flexible nd designted technologies (recll tht this is equivlent to r c in (5) being "low"). 0/5/00 6
This is consistent with the vilble evidence on the diffusion of flexible mnufcturing systems. These pper to be most prevlent in sectors where there is diversity in consumer preferences nd where the technology cn rect firly ccurtely to prticulr consumer requirements. Cermic tiles shoes utomobiles nd housing re obvious exmples. It lso suggests tht e-commerce should encourge the spred of flexible systems by providing ccurte informtion on consumer tstes while t the sme time offering reltively inexpensive technologies tht llow service providers to trget these tstes ccurtely. Now consider the effect of submrket size s. Recll tht f(0) = F(0)/s. so tht f(0) is decresing function of submrket size. It follows tht n increse in submrket size reduces the strtegic incentive to dopt flexible mnufcturing technologies. This might t first sight pper to be counter-intuitive nd is certinly counter to results derived from lterntive specifictions of flexible technology choice (see for exmple Röller nd Tombk (op. cit.)). The explntion lies in the tension in our model between economies of scope nd economies of scle. While only the flexible technologies exhibit economies of scope ll three technologies exhibit economies of scle. Incresed submrket size llows firms to tke greter dvntge of economies of scle no mtter their technology choice nd reduces the demnd-djusted cost disdvntge of the designted technology. In other words the lrger re the individul consumer submrkets the greter the incentive firm hs to design designted or niche products for these submrkets rther thn supply them with products tht re customized versions of bse product trgeted t other submrkets. When seen in this light this outcome seems to ccord well with our intuition. Technology choice is ffected in similr mnner by the consumer reservtion price. Note from (9) tht both f(0) nd ρ re declining functions of. In other words n increse in the consumer reservtion price reduces the vrible costs of production flexibility but lso reduces the set-up cost dvntge of production flexibility. The set-up cost effect is greter thn the vrible cost effect with the result tht n increse in the consumer reservtion price reduces the strtegic incentive to dopt flexible mnufcturing techniques. Simply put greter (lesser) willingness on the prt of consumers to py for products designed to their specific requirements encourges the doption of designted (flexible) technologies. This points to n offsetting influence tht will tend to limit the diffusion of flexible mnufcturing. As incomes rise consumers cn be expected to be willing to py more for 0/5/00 7
products designed to their specific tstes encourging firms to dopt technologies tht re well dpted to stisfying niche mrkets. This is presumbly one of the resons why highly specilized fshion houses such s Dior nd Escd re ble to thrive in high-income mrkets while more flexible compnies such s Wl-Mrt thrive in lower income environments. 5. Conclusions Flexible mnufcturing systems cpble of customizing products to the tstes of heterogeneous consumers re generlly regrded s being superior to technologies tht re cpble only of producing designted or niche products. If tht is so then we should expect over time tht flexible technologies will drive out inflexible ones. There re however resons for questioning this pprently ppeling conclusion. In erlier work Normn nd Thisse (999) rgue tht flexible mnufcturing leds to more competitive pricing regime with the result tht doption of such technologies might ctully reduce profitbility. Our nlysis in this pper suggests other resons for skepticism regrding the evolutionry dominnce of flexible systems. We hve rgued tht the nlysis of competing technologies should llow for the possibility tht firms offer multiple products re ble to choose the degree of flexibility of ny flexible system tht they employ nd re ble to deploy mix of technologies. This leds to rther more complex set of trde-offs. It remins the cse tht flexible technologies re preferred when they offer strong economies of scope reltive to the economies of scle vilble from designted technologies nd when the customized products of flexible technologies cn be mde prcticlly indistinguishble from custom-built products t very little cost penlty. On the other hnd we hve shown tht flexible technologies re not necessrily preferred when consumers differ widely in their preferences. In such circumstnces it my well be better for the firm to offer multiple designted products ech trgeted t prticulr prt of the tste spectrum. By similr rgument our nlysis suggests tht s prticulr prts of the consumer tste spectrum grow in size nd s consumer incomes rise it my be better for firms to produce niche products designed specificlly for prticulr submrkets rther thn try to serve these mrkets by using flexible mnufcturing to customize bse product centered in nother submrket. In other words we would rgue tht the likely future scenrio is likely to exhibit high degree of 0/5/00 8
heterogeneity in the technologies tht firms employ with firms will operte rnge of technologies of vrying degrees of flexibility determined by the precise chrcteristics of the mrkets they re trying to cpture nd the bility of the flexible technology ccurtely to trget prticulr consumer requirements. 0/5/00 9
References Anderson S.P. nd D.J. Neven (990) Cournot competition yields sptil gglomertion Interntionl Economic Review 79-808 Chng M.H. (99) Flexible mnufcturing uncertin consumer tstes nd strtegic entry deterrence The Journl of Industril Economics XLI 77-90. Eton B.C. nd N. Schmitt (994) Flexible mnufcturing nd mrket structure Americn Economic Review 84 875-888. Hmilton J. J.-F. Thisse nd A. Weskmp (989) Sptil discrimintion: Bertrnd vs. Cournot in model of loction choice Regionl Science nd Urbn Economics 9 87-0. Hotelling H. (99) Stbility in competition Economic Journl 9 4-57. McLeod W.B. G. Normn nd J.-F. Thisse (988) Price discrimintion nd equilibrium in monopolistic competition Interntionl Journl of Industril Orgniztion 6 49-446. Mnsfield E. (99) The diffusion of flexible mnufcturing techniques in Jpn Europe nd the United Sttes Mngement Science 9 49-59. Milgrom P. nd J. Roberts (990) The economics of modern mnufcturing products technology nd orgniztion Americn Economic Review 80 5-58. Mott M. nd G. Normn (996) Does economic integrtion cuse foreign direct investment? Interntionl Economic Review 7 757-78. Normn G. nd J.-F. Thisse (999) Technology choice nd mrket structure: strtegic spects of flexible mnufcturing Journl of Industril Economics XLVII 45-7. Röller L.-H. nd M.H. Tombk (990) Strtegic choice of flexible mnufcturing technology nd welfre implictions The Journl of Industril Economics XXXV 47-4. Röller L.-H. nd M.H. Tombk (99) Competition nd investment in flexible technologies Mngement Science 9 07-4. Rowthorn R. (99) Intr-industry trde nd investment under oligopoly: the role of mrket size Economic Journl 0 40-44. U.S. Office of Technology Assessment (984) Computerized mnufcturing Automtion: Employment Eduction nd the Workplce Government Printing Office Wshington D.C. 0/5/00 0
s s s s s 4 5 r r r r Figure : The Mrket Notes: ρ Figure : Three-stge Perfect Nsh Equilibrium -- k =. c : f ( 0) = ( 8ρ 8ρ ( k) ; c : f ( 0) = ( 6ρ 4ρ ( k ) c : f ( ) = 6ρ 9( k) 0 ; b : ( 0) = ( 8ρ 6ρ f ; b : f ( 0) = ( 8ρ ρ ; b : ( 0) = ( 8ρ 4ρ b 4 : ( 0) = ( 8ρ + 8ρ f. f ; ; 0/5/00
Tble : Py-Off Mtrix for {pp} Technology Configurtion Firm 4 5 5 l ({ pp} ) = ( 0 p 0 d d ) ({ pp} ) = ( d 0 p 0 d ) l Firm ({ p p} ) = l 4 d 0 p ( d 0) ({ p p} ) = l 0 p 0 5 ( d d ) 5 4ρ + 6ρ 5 4ρ + 6ρ s. s. f ( 0) f ( ) s. f ( 0) f ( ) 5 4ρ + 0ρ 5 4ρ + 0ρ s. f ( 0) f ( ) 5 4ρ + 0ρ 5 4ρ + 0ρ s. f ( 0) f ( ) s. f ( 0) f ( ) s. f ( 0) f ( ) f ( 0) f ( ) 5 4ρ + ρ 5 4ρ + ρ s. f ( 0) f ( ) Tble : Gross Profits to Firm with Technology Choice {pp} Consumer Submrket Loction Configurtion 4 5 5 ( 0 p 0 d d ) ( d 0 p 0 d ) s. ( ρ + ρ s. 9 s. ( s. ( s. ( ρ ρ s. 9 4 s. ( + ρ s. ( ρ 5 s. 9 s. 9 0/5/00
Tble : Py-Off Mtrix for {ff} Technology Configurtion Firm 5 l ({ ff} ) = ( 0 f 00 d ) ({ ff} ) = ( 00 00) l f Firm l ({ f f} ) = 4 ( d 00 f 0) l ({ f f} ) = ( 00 00) f 5 8ρ + 6ρ : 5 8ρ + 6ρ : s. s. f ( 0) f ( ) : s. f ( ) f 5 4ρ + 8ρ : 5 6ρ + 0ρ : s. ( 0) f ( ) 5 6ρ + 0ρ 5 4ρ + 8ρ : s. f ( 0) f ( ) s. f ( 0) f ( ) : s. f ( ) f ( ) 5 ρ + 0ρ 5 ρ + 0ρ : s. f ( ) Tble 4: Profits in the Technology Configurtion {df} Loction Configurtion of Firm 4 ( 00 0) d s. f ( 0) f ( ) f ( 00 f 00) s. Profit of Firm Profit of Firm 5 6ρ + 4ρ 5 4ρ + 40ρ f ( ) s. s. 5 + 8ρ + 6ρ 5 + ρ + 0ρ 5 f 5 f ( 0) ( 0) 0/5/00
Tble 5: Gross Profits to Firm with Technology Choice {df} Consumer Submrket Loction Configurtion 4 ( d 00 0) ( 00 00) f s. 9. ( 4 ) s ρ 9 s. ( 4ρ s. ( ρ s. ( 4 s. ρ f s. 9 9. ( ) s ρ 9 5 s. ( ρ s. ( 4ρ Tble 6: Py-Off Mtrix for {pf} Technology Configurtion Firm 4 l ({ p f} ) = ( d 00 f 0) ({ pf} ) = ( 00 00) l f ({ p f} ) = l 4 p 0 d 5 ( 0 d ) 5 ρ + ρ : 5 + 0ρ : s. f s. f ( 0) f ( ) : s. f ( ) ( 0) f ( ) 5 0ρ + 4ρ 5 + 4ρ + 0ρ : s. f ( 0) f ( ) Firm ({ p f} ) = l 0 p 0 5 ( d d ) 5 ρ + 8ρ : 5 ρ + 7ρ : s. f s. f ( 0) f ( ) : s. f ( ) ( 0) f ( ) 5 0ρ + 4ρ 5+ 4ρ + 0ρ : s. f ( 0) f ( ) ({ p f} ) = l 4 d 0 p ( d 0) 5 ρ + 8ρ : 5+ 6ρ : s. f s. f ( 0) f ( ) : s. f ( ) ( 0) f ( ) 5 0ρ + 4ρ 5+ 4ρ + 0ρ : s. f ( 0) f ( ) 0/5/00 4
Tble A: Technology Choice Py-Off Mtrix - f ( 0) ( 8ρ 6ρ Firm d p f d : 5s. (/9 - f(0)) : 5s. (/9 - f(0)) : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5+4ρ+ρ )/9 : s. ((5-6ρ+4ρ )/9 - f(0) - f()) : s. ((5+8ρ+6ρ )/9 Firm p : s. ((5+4ρ+ρ )/9 : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-ρ+ρ )/9 - f(0) - f()) : s. ((5+0ρ )/9 - f(0) - f()) f : s. ((5+8ρ+6ρ )/9 : s. ((5-6ρ+4ρ )/9 - f(0) - f()) : s. ((5+0ρ )/9 - f(0) - f()) : s. ((5-ρ+ρ )/9 - f(0) - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) Tble Ab: Technology Choice Py-Off Mtrix - ( 8ρ 6ρ < f ( 0) ( 8ρ ρ Firm d p f d : 5s. (/9 - f(0)) : 5s. (/9 - f(0)) : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5+4ρ+ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+ρ+0ρ )/9 Firm p : s. ((5+4ρ+ρ )/9 : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-ρ+ρ )/9 - f(0) - f()) : s. ((5+0ρ )/9 - f(0) - f()) f : s. ((5+ρ+0ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+0ρ )/9 - f(0) - f()) : s. ((5-ρ+ρ )/9 - f(0) - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) 0/5/00 5
Tble Ac: Technology Choice Py-Off Mtrix - ( 8ρ ρ f ( 0) < ( 8ρ 4ρ Firm d p f d : 5s. (/9 - f(0)) : 5s. (/9 - f(0)) : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5+4ρ+ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+ρ+0ρ )/9 Firm p : s. ((5+4ρ+ρ )/9 : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) f : s. ((5+ρ+0ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) : s. ((5-8ρ+6ρ )/9 - f(0) - f()) Tble Ad: Technology Choice Py-Off Mtrix - ( 8ρ 4ρ < f ( 0) ( 8ρ + 8ρ Firm d p f d : 5s. (/9 - f(0)) : 5s. (/9 - f(0)) : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5+4ρ+ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+ρ+0ρ )/9 Firm p : s. ((5+4ρ+ρ )/9 : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) f : s. ((5+ρ+0ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5-6ρ+0ρ )/9 - f()) : s. ((5-4ρ+8ρ )/9 - f(0) - f()) 0/5/00 6
Tble Ae: Technology Choice Py-Off Mtrix - ( 8ρ + 8ρ < f ( 0) Firm d p f d : 5s. (/9 - f(0)) : 5s. (/9 - f(0)) : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5+4ρ+ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+ρ+0ρ )/9 Firm p : s. ((5+4ρ+ρ )/9 : s. ((5-8ρ+8ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) f : s. ((5+ρ+0ρ )/9 : s. ((5-4ρ+40ρ )/9 - f(0) - f()) : s. ((5+4ρ+0ρ )/9 - f(0) - f()) : s. ((5-0ρ+4ρ )/9 - f()) : s. ((5-ρ+0ρ )/9 - f()) : s. ((5-ρ+0ρ )/9 - f()) 0/5/00 7