Intensity of competition and the choice between product and process innovation

Transcription

1 Internatonal Journal of Industral Organzaton 16 (1998) Intensty of competton and the choce between product and process nnovaton Gacomo onanno *, arry Haworth a, b a Department of Economcs, Unversty of Calforna, Davs, CA , USA b School of Economcs and Publc Affars, Unversty of Lousvlle, Lousvlle, KY 409, USA Accepted 8 November 1996 Abstract Two questons are examned wthn a model of vertcal dfferentaton. The frst s whether cost-reducng nnovatons are more lkely to be observed n regmes of more ntense (ertrand) or less ntense (Cournot) competton. We fnd that there are costreducng nnovatons that are pursued under Cournot but not under ertrand competton. The second s whether the regme of competton affects a frm s choce between product and process nnovaton. We show that for the hgh qualty frm, whenever there s a dfference between the choce made by a ertrand compettor and the choce made by a Cournot compettor, the former opts for product nnovaton, whle the latter prefers process nnovaton. For the low-qualty frm the result s reversed Elsever Scence.V. Keywords: Product nnovaton; Process nnovaton JEL classfcaton: L13 1. Introducton There s a vast lterature on the economc aspects of nnovaton. A wde spectrum of ssues has been analyzed, from the tmng of nnovatve ventures, to expendture patterns n R&D races, to spllover effects and ther mpact (for an * Correspondng author. Fax: ; e-mal: gfbonanno@ucdavs.edu / 98/ $ Elsever Scence.V. All rghts reserved. PII S (97)

2 496 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) excellent survey of the latter see De ondt (1997)). The ssue we address n ths paper s the relatonshp between ntensty of competton and the proftablty of nnovatve actvty. A tradtonal lne of reasonng, assocated wth Schumpeter (1943), s that market concentraton s a stmulus to nnovaton. An early challenge to ths vew came from Arrow (196), who sought to establsh the reverse proposton that more compettve envronments would gve a greater ncentve to nnovate. Arrow consdered the case of a frm undertakng a cost-reducng nvestment that cannot be mtated by compettors. He compared a monopoly wth a perfectly compettve ndustry, under the same demand and cost condtons, and showed that the gan from a cost-reducng nnovaton s hgher for a frm n the latter than for the monopolst. A more nterestng comparson would be between two olgopolstc ndustres. It s not clear, however, how ntensty of competton can be measured n such a settng. Delbono and Dencolo (1990) and ester and Petraks (1993) suggested comparng two ndustres (wth the same number of frms and the same lnear demand and cost functons) under dfferent regmes of competton: Cournot (where frms decson varables are output levels) and ertrand (where frms decson varables are prces). Snce Cournot competton normally leads to lower output and hgher prces than ertrand competton, one can thnk of the former as a stuaton where competton s less ntense. Delbono and Dencolo (1990) showed that, under the assumpton of a homogeneous product, the ncentve to ntroduce a cost-reducng nnovaton s greater for a ertrand compettor than for a Cournot compettor: an Arrow-lke result. ester and Petraks (1993), on the other hand, consdered the case of dfferentated products and obtaned a mxed result: f the degree of dfferentaton s large, the ncentve to ntroduce a cost-reducng nnovaton s hgher for the Cournot compettor, whle f the degree of dfferentaton s small, then the ncentve s hgher for a ertrand compettor. ester and Petraks s model s one of horzontal dfferentaton (when prces are equal both products enjoy postve demand). In the frst part of the paper we re-examne the ssue wthn a model of vertcal dfferentaton (f prces are equal, only one product the hgher qualty one enjoys postve demand) and show that the ncrease n profts assocated wth any gven cost reducton s hgher n the case of Cournot competton than n the case of ertrand competton, and ths s true no matter how small the degree of dfferentaton (thus even f the products are vrtually homogeneous). It follows that there are cost-reducng nnovatons that would be pursued under Cournot competton but not under ertrand competton (a Schumpeter-lke result). In the second part of the paper we address a related ssue, whch somewhat surprsngly has receved very lttle attenton n the lterature. It s customary to dstngush between two types of nnovaton: product and process nnovaton. The former conssts n the creaton of new goods and servces, whle the latter leads to a reducton n the cost of producng exstng products. The lterature has dealt prmarly wth overall nnovatve actvty (that s, the sum of product and process

3 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) nnovaton) or one specfc type of nnovatve actvty (ether process or product 1 nnovaton). There have been no attempts to explan what factors mght be mportant n a frm s decson whether to drect R&D expendture towards product nnovaton or towards process nnovaton. In ths paper we take a frst step n the drecton of fllng ths gap, by provdng an explanaton based on the type of compettve regme n whch the frms fnd themselves (Cournot vs. ertrand). We shall thnk of product nnovaton as an mprovement n the qualty of a frm s product (e.g. the ntroducton of a faster computer chp). Process nnovaton wll be nterpreted as a reducton n the frm s costs. We show that, f the choce s between a gven cost reducton or a gven qualty mprovement and the nnovator s the hgh qualty frm, one of three thngs can happen: (1) both the Cournot compettor and the ertrand compettor choose the cost reducton; or () both choose the qualty mprovement; or (3) they make dfferent choces, n whch case the Cournot compettor chooses the cost reducton, whle the ertrand compettor chooses the qualty mprovement. That s, f ertrand competton and Cournot competton lead to dfferent choces, then the ertrand compettor wll favor product nnovaton, whle the Cournot compettor wll opt for process nnovaton. On the other hand, f the nnovator s the low qualty frm, then the opposte s true: whenever the two regmes of competton yeld dfferent choces, the ertrand compettor wll choose process nnovaton, whle the Cournot compettor wll choose product nnovaton. The paper s organzed as follows. Secton develops the model, Secton 3 deals wth cost-reducng nnovatons, whle Secton 4 s concerned wth the choce between process and product nnovaton. Secton 5 contans some fnal remarks and a concluson. The proofs of all the results are omtted and can be obtaned from the authors.. A model of vertcal dfferentaton We use a model of vertcal dfferentaton ntroduced by Mussa and Rosen (1978). There are N consumers wth the same ncome, denoted by E, but dfferent values of the taste parameter u. Each consumer buys at most one unt. If a consumer does not buy the product, her utlty s equal to her ncome E. Ifa consumer wth parameter u buys one unt of a good of qualty k, at prce p, her utlty s equal to E p 1uk. The parameter u s unformly dstrbuted n the 1 See surveys by Kamen and Schwartz (1975); aldwn and Scott (1987); Cohen and Levn (1989); Scherer and Ross (1990); Trole (1988). An excepton s Rosenkrantz (1995) whch s dscussed n Secton 5. We are grateful to Raymond De ondt for brngng ths paper to our attenton.

4 498 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) nterval (0,1]. It follows that, for every x [ (0,1], the number of consumers wth parameter u less than or equal to x s xn. We consder the case where there are two frms. Frm H sells a product of qualty kh whle frm L sells a product of qualty k L, wth k H. k L. 0 (thus H stands for hgh qualty and L for low qualty ). Let p be the prce charged by frm ( 5 H, L). The demand functons are obtaned as follows. Let u0 be the value of u for whch the correspondng consumer s ndfferent between consumng nothng and consumng the low-qualty product. Then u s the soluton to the equaton 0 E 5 E pl1uk L. Thus u05( p L/k L). Let u1be the value of u for whch the correspondng consumer s ndfferent between buyng the low-qualty product and the hgh-qualty one. Then u s the soluton to the equaton 1 E p 1uk 5 E p 1uk. L L H H Thus u 5[( p p )/(k k )]. Hence the (drect) demand functons are gven by 1 H L H L S S ph pl D H( p H, p L) 5 (1 u 1)N 5 1 ]]] k k H L DN D ph pl pl D L( p H, p L) 5 (u 1u 0)N 5]]] ] N. k k k H L L Lke ester and Petraks (1993) and Rosenkrantz (1995) we assume that the two frms operate under constant returns to scale. Thus frm (5H, L) has a cost functon of the form C (q )5c q wth c.0. We also assume that hgher qualty s assocated wth hgher costs: c H.c L. Fnally, we assume that ch and cl are such that both demands are postve when the two products are sold at unt cost (.e. 3 when ph5ch and pl5c L). It s easy to see that ths s the case f and only f the 4 followng two condtons are satsfed k k. c c (1a) and H L H L k c. k c. L H H L The nverse demand functons are gven by (where q and ql the output of frm L) NkH khqh klql f (q,q ) 5]]]]]] H H L N H (1b) denotes the output of frm H 3 Ths assumpton guarantees that at all the equlbra we consder, prces and output levels are postve: cf. Remark 1 below. 4 Note that Eqs. (1a) and (1b) mply that c,k and c,k. H H L L

5 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) k L(N qh q L) f (q,q ) 5 ]]]]]. L H L N We consder two cases: the ertrand case (decson varables are prces) and the Cournot case (decson varables are output levels). We shall use superscrpt for the ertrand case and superscrpt C for the Cournot case. In the ertrand case the proft functons are gven by ph pl P H( p H, p L) 5 N( ph c H) S1 ]]] D, () k k ph pl pl P L( p H, p L) 5 N( pl c L) ]]] ]. k k k S H L H L L Prces and output levels at the ertrand Nash equlbrum are gven by k H(kH kl1 ch1 c L) P H 5]]]]]]]] 4kH kl (kh khkl khch1 khcl1 klc H) qh 5 N]]]]]]]]]]] (4k k )(k k ) H L H L H L L H L H L k k k 1 c k 1 k c ) p L 5]]]]]]]] 4kH kl k H(kHkL kl1 klch khcl1 klc L) ql 5 N]]]]]]]]]]] (4k k )(k k )k H L H L L gvng the followng expressons for the equlbrum profts of frms H and L: [kh khkl khch1 khcl1 klc H] H H L H L (4kH k L)(kHk L) p (k,k,c,c ) 5 N]]]]]]]]]]] k k 5 ]]] (q H) N H L [khkl kl khcl1 klcl1 klc L H L H L H]]]]]]]]]] (4kH k L)(kHk L)kL p (k,k,c,c ) 5 Nk D k L(k H k L) 5 ]]]] (q L ). (4) k N H We now move to the Cournot case, where the proft functons are gven by C NkH qhkh qk L L P H (q H,q L) 5 qhs]]]]]] chd N C k L(N qh q L) P L(q H,q L) 5 qls]]]]] c LD. N (3)

6 500 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) Prces and output levels at the Cournot Nash equlbrum are gven by H H L H H H L H L C kh kl ch1 cl qh5 N 4kH kl 4kH kl C k k k 1 k c 1 k c c k p 5]]]]]]]]]] ]]]]]] H C khkl1 khcl1 klch klcl C khkl1 klch khcl pl 5]]]]]]]] ql 5 N ]]]]]] (5) 4k k (4k k )k H L H L L yeldng the followng expressons for the equlbrum profts of frms H and L: C k H(kH kl ch1 c L) kh C H H L H L ]]]]]]]] ] N H (4kH k L) p (k,k,c,c ) 5 N 5 (q ) C (khkl khcl1 klc H) kl C L H L H L ]]]]]]] ] N L (4kH k L) kl p (k,k,c,c ) 5 N 5 (q ). (6) Remark 1. The followng facts can be checked easly. If the parameter restrctons (Eqs. (1a) and (1b)) are satsfed, then, for each frm (5H, L), Cournot output C s smaller than ertrand output (q, q ), Cournot prce s hgher than ertrand C C prce ( p. p ), and Cournot proft s hgher than ertrand proft (p.p ). Furthermore, all these quanttes are postve and equlbrum prces are greater C than unt cost (p.p.c ). 3. Intensty of competton and the proftablty of cost-reducng nnovatons In ths secton we compare the ncentves for a gven cost reducton between a ertrand compettor and a Cournot compettor and show that the latter s larger. Let D H.0 be a non-drastc cost reducton for frm H and D L.0 a non-drastc cost reducton for frm L, where non-drastc means that after the cost reducton the nnovator cannot drve the other frm out of the market by chargng a prce close to unt cost. That s, we assume that DH and DL are suffcently small for nequaltes correspondng to Eqs. (1a) and (1b) to be satsfed: k k. (c D ) c H L H H L k (c D ). k c L H H H L k k. c (c D ) H L H L L (7a) (7b) (7c)

7 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) k c. k (c D ). L H H L L (7d) C For each frm (5H, L), let Dp be the ncrease n profts expected from the gven cost reducton n the case of Cournot competton and Dp the ncrease n profts expected from the gven cost reducton n the case of ertrand competton: C C C Dp 5 p (k,k,c D,c ) p (k,k,c,c ) (8a) H H H L H H L H H L H L Dp 5 p (k,k,c D,c ) p (k,k,c,c ) (8b) H H H L H H L H H L H L C C C Dp 5 p (k,k,c,c D ) p (k,k,c,c ) (8c) L L H L H L L L H L H L Dp 5 p (k,k,c,c D ) p (k,k,c,c ) (8d) L L H L H L L L H L H L C C H L H L where p and p are gven by Eq. (6) and p and p are gven by Eq. (4). The followng remark confrms ester and Petraks s result (ester and Petraks, 1993, p. 55, Proposton 1) that the margnal return on nvestment n a cost reducton s ncreasng. C C H H H L L Remark. Dp and Dp are decreasng n c and Dp and Dp are decreasng n c L. Proposton 1 below gves a Schumpeter-lke result: less ntense competton s assocated wth a greater propensty to ntroduce cost-reducng nnovatons. Defne a cost-reducng nvestment opportunty for frm (5H, L) as a par (D, a) where a s the cost of mplementng the nnovaton and D s the reducton n unt cost expected from the nnovaton. It s clear that frm wll carry out the nvestment f and only f the expected ncrease n profts s greater than the mplementaton cost, that s, f and only f Dp.a. Proposton 1. For each (5 H, L) there are cost-reducng nvestment opportuntes that are carred out by frm f t operates n a regme of Cournot competton but not f t operates n a regme of ertrand competton. On the other hand, every cost-reducng nvestment carred out under ertrand competton s also carred out under Cournot competton. Proposton 1 follows drectly from the followng fact: for all k H, k L, c H, c L, DH C and DL that satsfy Eqs. (7a) (7d), and for every 5H, L, Dp.Dp. The ntuton behnd Proposton 1 s as follows. A cost reducton by frm has a drect (postve) effect on the profts of frm as well as a strategc or ndrect effect through the change t nduces n the choce varable of the compettor. In a ertrand regme the strategc effect s negatve: the compettor wll respond to a reducton n c by reducng ts own prce, thereby ncreasng the ntensty of

8 50 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) competton. In a Cournot regme on the other hand, a cost reducton has postve 6 strategc effects, that s, t leads to a softenng of competton. Note that Proposton 1 holds no matter how small the degree of product dfferentaton, that s, no matter how close kl s to k H. Thus n a model of vertcal dfferentaton the mxed result obtaned by ester and Petraks (1993) does not hold. 4. On the choce between process and product nnovaton We now turn to the choce between process and product nnovaton. Assume that one of the two frms, say frm H, has nvested n R&D (e.g. t has hred a team of engneers) and the correspondng cost s sunk. Suppose that the frm has two optons: 1. t can nstruct ts researchers to pursue product nnovaton, expected to lead to an ncrease n the qualty of the frm s product from kˆ to kˆ H H1Dk (wth Dk.0); or 5 The strategc effect s gven by P ]] pj c where ±j, P s gven by Eq. () and p s gven by Eq. (3). It s straghtforward to verfy that and so that p j P ]. 0 p j p j ]. 0 c P ]]. 0 p c p j j In the termnology of ulow et al. (1985), n the ertrand case (wth lnear demand) prces are strategc complements: a reducton n c leads to a reducton n p whch n turn leads to a reducton n p j, that s, an aggressve response by the compettor. 6 The strategc effect s gven by P ]] q c C q C j j whch s negatve, as one can easly verfy (cf., n partcular, Eq. (5)). In the termnology of ulow et al. (1985), n the Cournot case (wth lnear demand) output levels are strategc substtutes: a reducton n c leads to an ncrease n q whch n turn leads to a reducton n q j, that s, a submssve response by the compettor.

9 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) t can nstruct them to pursue process nnovaton, expected to lead to a reducton n the frm s unt cost from cˆ to cˆ Dc (wth 0,Dc<c ˆ ). H H H Assume that there are no other costs nvolved n the mplementaton of the nnovaton. The choce facng the frm s llustrated n Fg. 1. For example, the frm s product could be a computer chp wth qualty represented by the operatng speed (measured n MHz) and the choce could be between ncreasng the speed from 166 MHz to 00 MHz or reducng the unt cost of ts present product (the 166 MHz chp) from $800 to $70. Defne a product/process nvestment opportunty as a trple (Dc, Dk, a) where a s the cost of mplementng the nnovaton (e.g. the cost of hrng a team of researchers), whch s the same for both types of nnovaton, Dc s the expected reducton n unt cost f process nnovaton s pursued (e.g. f the researchers are nstructed to seek a cheaper producton process for the exstng product) and Dk s the expected qualty ncrease f product nnovaton s pursued (e.g. f the researchers are nstructed to mprove the qualty of the product). A process/ product nvestment opportunty (Dc, Dk, a) sproftable f the expected ncrease n profts from at least one of the two types of nnovaton (cost reducton or qualty mprovement) s greater than a, the (common) cost of mplementng the nnovaton. We shall frst consder the case where the nnovator s the hgh qualty frm. The followng proposton states that a ertrand compettor s more prone to choose product nnovaton, whle a Cournot compettor s more prone to choose process nnovaton. Fg. 1. oth ertrand and Cournot choose product nnovaton.

10 504 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) Proposton. The followng s true for the hgh-qualty frm. Gven a proftable product/process nvestment opportunty (Dc, Dk, a), ether both the ertrand and the Cournot compettor choose the same type of nnovaton or, f they make dfferent choces then the ertrand compettor chooses product nnovaton, whle the Cournot compettor chooses process nnovaton. As llustrated n Fgs. 1 3, Proposton follows from the followng fact whch apples to the hgh-qualty frm. Fx arbtrary k H, k L, c H and c L that satsfy restrctons Eqs. (1a) and (1b); then n the (k H, c H)-plane both the ertrand so-proft curve (obtaned from Eq. (4)) and the Cournot so-proft curve (obtaned from Eq. (6)) that go through the pont (k H, c H) are ncreasng; furthermore, the ertrand so-proft curve s steeper (at that pont) than the Cournot so-proft curve. It follows that the two so-proft curves cannot cross more than once. Fgs show the three possble cases. Case 1 (Fg. 1): both the ertrand compettor and the Cournot compettor choose product nnovaton. Case (Fg. ): both the ertrand compettor and the Cournot compettor choose process nnovaton. Case 3 (Fg. 3): the ertrand compettor and the Cournot compettor make dfferent choces. In ths case the ertrand compettor opts for product nnovaton, whle the Cournot compettor chooses process nnovaton. Fg.. oth ertrand and Cournot choose process nnovaton. 7 It s useful to consder not the so-proft curve that goes through the status quo (or pre-nnovaton) pont, but rather the so-proft curve that goes through the pont that represents process nnovaton.

11 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) Fg. 3. ertrand chooses product nnovaton, Cournot process nnovaton. The proof of Proposton nvolves a number of rather complex algebrac manpulatons whch are hard to nterpret. To obtan some ntuton as to why a ertrand compettor has a propensty to favor product over process nnovaton, recall that n a ertrand regme a cost reducton has a negatve strategc effect, n that t leads to an ntensfcaton of competton (see Secton ), wth the consequence that at the equlbrum followng process nnovaton both frms charge lower prces than at the pre-nnovaton equlbrum. Product nnovaton, on the other hand, wll always lead to an ncrease n the prce of frm H (the nnovator), even though the equlbrum prce of frm L (the compettor) may ncrease or decrease, as shown n Fg. 4. Of course, ths ntutve explanaton s only partally correct for three reasons: (1) as shown n Fg., even a ertrand compettor wll choose process nnovaton over product nnovaton f the former domnates the latter (thus one can only speak of a tendency of ertrand compettors to favor product nnovaton), () the analogous ntuton for the Cournot compettor cannot be establshed, snce both product and process nnovaton have a postve strategc effect, as shown n Fgs. 5 and 6, and (3) t s easer to understand a comparson between regmes of competton holdng the type of nnovaton fxed (as we dd n Secton ) than a comparson of dfferent types of nnovaton holdng the regme of competton fxed (as we are dong here), because there s no obvous way of makng a change n qualty (e.g. an ncrease of 34 MHz) drectly comparable wth a cost reducton (e.g. $80). We now turn to the case where the nnovator s the low qualty frm.

12 506 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) Fg. 4. ertrand: the effect of product nnovaton by frm H. Proposton 3. The followng s true for the low-qualty frm. Gven a proftable product/process nvestment opportunty (Dc, Dk, a), ether both the ertrand and the Cournot compettor choose the same type of nnovaton or, f they make dfferent choces then the ertrand compettor chooses process nnovaton, whle the Cournot compettor chooses product nnovaton. Fg. 5. Cournot: the effect of process nnovaton by frm H.

13 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) Fg. 6. Cournot: the effect of product nnovaton by frm H. Proposton 3 follows from the followng fact whch apples to the low-qualty frm. Fx arbtrary k H, k L, c H and c L that satsfy restrctons Eqs. (1a) and (1b). Then n the (k L, c L)-plane the Cournot so-proft curve (obtaned from Eq. (6)) that goes through the pont (k L, c L) s ncreasng and steeper (at that pont) than the ertrand so-proft curve (obtaned from Eq. (4)) that goes through the same pont. Note that, whle the Cournot so-proft curve s always ncreasng, the ertrand so-proft curve mght not be (t wll be ncreasng f the degree of dfferentaton s not too small). Indeed, t has been shown n the lterature (Gabszewcz and Thsse, 1979, 1980; Shaked and Sutton, 198) that when there s ertrand competton a low-qualty frm mght refran from ncreasng the qualty of ts product even f t could do so at zero cost. Ths wll happen when the degree of dfferentaton s very small. On the other hand, when competton s Cournot style, the low-qualty frm does have an ncentve to ncrease the qualty of ts product (onanno, 1986). The comparson between process and product nnovaton s therefore nterestng manly n the case where the low qualty frm would proft from a costless qualty mprovement (that s, when the ertrand so-proft curve s ncreasng). In ths case we have a reversal of the result of Proposton : when the nnovator s the low-qualty frm and the ertrand compettor makes a dfferent choce from the Cournot compettor, then the latter wll opt for product nnovaton, whle the former wll choose process nnovaton. As for the case of Proposton, the proof of Proposton 3 nvolves a number of complex algebrac manpulatons whch are hard to nterpret. Some ntuton for

14 508 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) the result can be obtaned by examnng the strategc effects. Consder, for example, the case of ertrand competton. Process nnovaton by the low-qualty frm has negatve strategc effects, snce t nduces the nnovator to reduce ts prce (frm L s reacton curve shfts down) and the compettor (frm H) wll respond by also lowerng ts prce. Product nnovaton by frm L, on the other hand, would potentally have postve strategc effects, snce t shfts the nnovator s reacton curve up. However, unlke the case of Proposton where a qualty mprovement by the hgh qualty frm ncreased the degree of dfferentaton here a qualty mprovement by frm L reduces the degree of dfferentaton and nduces an aggressve response by the compettor: the reacton curve of frm H shfts to the left. To put t dfferently, a cost reducton for frm L has only an ndrect effect on frm H s profts, through a reducton n the prce of the nnovator. A qualty mprovement by frm L, on the other hand, has a drect effect on the compettor s profts (t reduces frm H s revenue) and therefore nduces a more aggressve response by frm H. 5. Concluson Wthn a model of vertcal dfferentaton (due to Mussa and Rosen (1978)) we examned two ssues. The frst, whch has receved consderable attenton n the lterature, s whether more ntense competton s assocated wth a stronger or weaker ncentve to ntroduce a cost-reducng nnovaton. Followng Delbono and Dencolo (1990); ester and Petraks (1993) we compared two dentcal ndustres (same demand and cost functons, same number of frms) that dffered only n the regme of competton: ertrand style versus Cournot style. Snce Cournot competton leads to lower output and hgher prces than ertrand competton, t can be thought of as a regme of less ntense competton. Our fndng was that the ncentve to ntroduce a cost-reducng nnovaton s stronger for a Cournot compettor. We then turned to an ssue that so far has receved lttle attenton n the lterature, namely what factors mght be mportant n a frm s decson whether to nvest n product nnovaton (mprovement n the qualty of ts product) or process nnovaton (cost reducton). We found that the regme of competton mght be one such factor. For the hgh qualty frm our result s that f there s a dfference between the choce made by a ertrand compettor and the choce made by a Cournot compettor, then the former wll opt for product nnovaton, whle the latter wll prefer process nnovaton. For the low-qualty frm, on the other hand, the result s reversed: whenever there s a dfference, the ertrand compettor wll favor process nnovaton, whle the Cournot compettor wll favor product nnovaton. As far as we know, the only other paper n the lterature that deals wth the choce between process and product nnovaton s Rosenkrantz (1995). She

15 G. onanno,. Haworth / Int. J. Ind. Organ. 16 (1998) consders a model of horzontal dfferentaton, smlar to the model used by ester and Petraks (1993). A two-stage Cournot duopoly model s consdered where n stage 1 the frms smultaneously choose ther unt cost c and ther product characterstc d (the choce of c s called process nnovaton and the choce of d s called product nnovaton); n the second stage the frms choose outputs. Note, therefore, the followng substantal dfferences: (1) for us product nnovaton means an mprovement n the qualty of the product (ours s a model of vertcal dfferentaton), whle for Rosenkrantz product nnovaton means a change n the horzontal characterstc of the product; () whle we compare the nvestment choce of one frm n dfferent regmes of competton (ertrand versus Cournot), Rosenkrantz analyzes the smultaneous choces of both frms wthn the same regme of competton (Cournot); (3) whle we assume that the frm s faced wth the choce between product and process nnovaton, Rosenkrantz allows each frm to mx both types of nnovaton and s nterested n studyng how the optmal mx vares wth the parameters of the model (n partcular the consumers reservaton prce). A natural queston to ask s: how robust are these results? The answer to ths queston s two-fold. Frst of all, one cannot hope to obtan any results whatsoever n a very general model where propertes of demand and costs are specfed only qualtatvely. The reason s that one needs to compare equlbra and n order to do so one needs to be able to compute them. Indeed the model used n ths paper s as general as the models used n the lterature on ths topc (e.g. Delbono and Dencolo, 1990; ester and Petraks, 1993; Rosenkrantz, 1995). The type of ssues consdered can only be analyzed n models that have a lot of structure and the rcher the structure the less general the model. Secondly, although the model s rather specfc, the results can be understood (fully, as n the case of Proposton 1 or only partally, as n the case of Propostons and 3) n terms of qualtatve propertes, such as the strategc effects of dfferent types of nnovaton. Acknowledgements The authors are grateful to two anonymous referees, Raymond De ondt, Lous Makowsk and Klaus Nehrng for helpful comments and suggestons. References Arrow, K., 196. Economc welfare and the allocaton of resources for nventons. In: Nelson, R. (Ed.), The rate and drecton or nventve actvty. Prnceton Unversty Press, Prnceton, NJ. aldwn, W.L., Scott, J.T., Market structure and technologcal change. Harwood Academc Publshers, Chur, Swtzerland.

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