UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics BERTRAND VS. COURNOT COMPETITION IN ASYMMETRIC DUOPOLY: THE ROLE OF LICENSING

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1 UNIVERSITY OF NOTTINGHAM Discussion Ppers in Economics Discussion Pper No. 0/0 BERTRAND VS. COURNOT COMPETITION IN ASYMMETRIC DUOPOLY: THE ROLE OF LICENSING by Arijit Mukherjee April 00 DP 0/0 ISSN

2 UNIVERSITY OF NOTTINGHAM Discussion Ppers in Economics Discussion Pper No. 0/0 BERTRAND VS. COURNOT COMPETITION IN ASYMMETRIC DUOPOLY: THE ROLE OF LICENSING by Arijit Mukherjee Arijit Mukherjee is Lecturer, School of Economics, University of Nottinghm April 00

3 Bertrnd vs. Cournot competition in symmetric duopoly: the role of licensing Arijit Mukherjee University of Nottinghm, U.K. April, 00 Abstrct: This pper shows the possibility of higher welfre under Cournot competition in n symmetric cost duopoly when the firms hve the option for technology licensing. We find tht if there is licensing with up-front fixed-fee, welfre is higher under Cournot competition compred to Bertrnd competition when the initil cost difference of these firms is moderte; but, for very smll or very lrge cost initil cost differences, welfre is higher under Bertrnd competition. If licensing occurs with per-unit output roylty, welfre is lwys higher under Bertrnd competition. Key words: Bertrnd, Cournot, Licensing, Welfre JEL Clssifictions: D4, L1, O Correspondence to: Arijit Mukherjee, School of Economics, University of Nottinghm, University Prk, Nottinghm, NG7 RD, U.K. E-mil: rijit.mukherjee@nottinghm.c.uk Fx:

4 Bertrnd vs. Cournot competition in symmetric duopoly: the role of licensing 1 Introduction The debte on the effect of competitiveness on socil welfre is going bck to Schumpeter (14) nd Arrow (16). In seminl work Schumpeter (14) rgued tht mrket concentrtion is stimulus to the innovtion. So, society might prefer to scrifice sttic efficiency for the dynmic efficiency. The work by Arrow (16) chllenged this view. In his work Arrow (16) rgued tht the incentive for innovtion would be stronger for competitive industry thn monopolist. Contrry to the erlier literture focusing on the competitive mrket nd monopoly, the recent contributions focus on the oligopolistic mrkets nd exmine the effects of different types of competition (i.e., Bertrnd competition nd Cournot competition) on socil welfre. The conventionl wisdom suggests tht for sme cost of production under Bertrnd nd Cournot competitions, price of the product is lower under Bertrnd competition compred to Cournot competition nd hence, socil welfre is higher under Bertrnd competition (see, e.g., Deneckere, 18). However, the possibility of innovtion before production cn generte higher welfre under Cournot competition (see, e.g., Delbono nd Denicolò, 10, Bester nd Petrkis, 1, Qiu, 17, Bonnno nd Hworth, 18, Mukherjee, 00 nd Symeonidis, 00). Different mounts of investment in R&D under Bertrnd nd Cournot competitions re responsible for this finding. So, even if the sttic welfre is higher under Bertrnd competition, dynmic welfre cn be higher under Cournot competition. 1 In this pper we show tht if the firms produce with different technology (hence, different cost of production) welfre cn be higher under Cournot competition compred to Bertrnd competition even if there is no possibility of innovtion before production. More specificlly, we show tht if the firms hve the option for technology licensing nd licensing contrct consists of up-front fixed-fee only, welfre under Cournot competition is higher when the initil cost difference of these firms is moderte. Hence, our result shows the possibility of higher sttic welfre under Cournot competition compred to Bertrnd competition. 1 One my refer to Delbono nd Denicolò (10) for the mening of sttic nd dynmic welfre.

5 In wht follows, in section we describe our bsic model with two firms hving different technology nd producing homogeneous products. In section we compre welfre under Bertrnd competition nd Cournot competition, when there is no possibility of technology licensing. Here, we show tht welfre is lwys higher under Bertrnd competition. If there is no possibility of technology licensing then Bertrnd competition lwys genertes lower price of the product compred to Cournot competition nd genertes lower dedweight loss. As result, welfre is lwys higher under Bertrnd competition. Section 4 extends our nlysis by llowing these firms to engge in technology licensing. We consider two importnt types of licensing, viz., licensing with up-front fixed-fee nd licensing with per-unit output roylty (see, e.g., Wng, 18). In cse of licensing with up-front fixed-fee, both firms produce with the efficient technology. Under Cournot competition, firms engge in licensing with up-front fixed-fee provided the initil cost of production of these firms is sufficiently close. If the firms engge in fixedfee licensing then it increses production efficiency in the industry by llowing both firms to produce with the efficient technology. In contrst to this, licensing does not occur under Bertrnd competition. Hence, under Bertrnd competition both firms compete with their own technology. So, even if competition is fierce under Bertrnd competition, licensing helps to increses production efficiency under Cournot competition. We show tht the former effect domintes the lter effect when the difference in the initil cost of production (i.e., cost of production without licensing) of these firms is sufficiently smll nd therefore, welfre is higher under Bertrnd competition compred to Cournot competition. But, if the difference in the initil cost of production of these firms is not sufficiently smll but smll enough to encourge licensing under Cournot competition, the lter effect domintes the former effect nd welfre is higher under Cournot competition compred to Bertrnd competition. Though, for simplicity, we show our result for homogeneous products, it is cler from our following discussion tht our qulittive result showing higher sttic welfre under Cournot competition in presence of licensing cn hold even for some degree of horizontl product differentition. We define the technology by the mrginl cost of production. Lower mrginl cost implies better technology.

6 In cse of licensing with per-unit output roylty, we find tht licensing never occurs under Bertrnd competition but licensing lwys occurs under Cournot competition. In cse of licensing under Cournot competition the optiml output roylty will be such tht the effect cost of production of the licensee will be equl to its cost of production without licensing. Hence, optiml outputs of the firms re sme under licensing with output roylty nd no-licensing but licensing with output roylty helps the technologiclly efficient firm to increse its profit. We find tht this benefit from roylty income under Cournot competition is not enough to outweigh the benefit from fierce competition under Bertrnd competition. Hence, welfre is lwys higher under Bertrnd competition compred to Cournot competition even if the firms cn engge in licensing with per-unit output roylty. Rest of the pper is orgnized s follows. The next section gives generl frmework for our nlysis. In section, we do our nlysis for Bertrnd nd Cournot competitions without the possibility of licensing. Section 4 exmines the welfre implictions under Bertrnd nd Cournot competitions in presence of licensing. Section 5 concludes the pper. The Model Consider n economy with two firms, clled firm 1 nd firm, producing homogeneous product. Assume tht the constnt mrginl cost of production of firm 1 nd firm re c 1 nd c > respectively. For simplicity, we ssume tht c 0. It is needless to sy tht c 1 1 = no qulittive result will chnge for c to be positive but our simplifying ssumption of 1 c 1 = 0 will mke the lgebr less cumbersome. As nother simplifiction, we ssume tht there neither firm needs to ber ny other cost of production. Assume tht inverse mrket demnd function is P = q, (1) where the nottions hve usul mening. In the following nlysis we will consider two types of product mrket competition, viz., Cournot competition nd Bertrnd competition. Further, we will divide our nlysis in two prts: (i) where licensing of technology is not fesible, nd (ii) where licensing of technology is fesible. 4

7 We ssume tht c <. This ssumption implies tht the (unrestricted) monopoly price of firm 1 is greter thn the constnt mrginl cost of production of firm nd hence, ensures duopoly mrket structure. Compring Bertrnd nd Cournot without licensing In this subsection we will exmine the implictions of Bertrnd nd Cournot competitions on socil welfre when the firms cnnot engge in technology licensing. We define socil welfre s the summtion of consumer surplus nd totl industry profit..1 Cournot competition Given the demnd nd cost specifictions, if the firms compete like Cournot duopolists in the product mrket, totl output is ( c ). The profits of firm 1 nd firm re respectively c, nl ( + c ) c, nl ( π 1 = nd π = competition is c ). Therefore, welfre under Cournot ( + c ) + ( c ) ( ) = +. () 18, c W c nl. Welfre under Bertrnd competition Since the firms re producing homogeneous products, the price under Bertrnd competition is equl to c. Therefore, industry output is ( Bertrnd competition is c ). So, welfre under ( ) = c ( c ) +. () W c b, nl. Welfre comprison under Bertrnd nd Cournot competitions Compring () nd (), we find tht () is greter thn () provided 8c + 0c < 0. (4) 5

8 Left hnd side (LHS) of (4) is continuous, qudrtic nd convex with respect to c over [ 0, ]. Further, LHS of (4) is negtive for c = 0 nd zero for c =. This implies tht (4) holds for ll c 0, ]. [ The following proposition summrizes the bove discussion. Proposition 1: If technology licensing is not fesible, welfre is lwys higher under Bertrnd competition compred to Cournot competition. 4 Compring Bertrnd nd Cournot with licensing Now we extend the nlysis of the previous section by incorporting the possibility of licensing between the firms. In cse of licensing, the technologiclly superior firm, firm 1, licenses its technology to the technologiclly inferior firm nd chrges price for its technology. In the following nlysis, we will consider two populr types of licensing contrct (see, e.g., Wng, 18), viz., licensing with up-front fixed-fee nd licensing with per-unit output roylty Fixed-fee licensing In this subsection, we consider tht in cse of licensing the licensee licenses its technology with n up-front fixed-fee before production. Hence, in cse of licensing, both firms produce with the technology of firm Licensing under Cournot competition Let us first consider the sitution under licensing. If licensing occurs, ech firm will produce. So, the profit of firm 1 nd firm re respectively It is esy to check tht industry output under Bertrnd competition is greter thn the industry output under Cournot competition for ll c <. 4 As shown in Rockett (10), fixed-fee licensing is the optiml licensing contrct when the licensee cn imitte the licensed technology costlessly nd licensing with output roylty is optiml when the licensee cnnot imitte the licensed the technology due to sufficiently higher cost of imittion. If it is difficult to verify the output of the licensee, fixed-fee licensing is the only wy of licensing the technology (see, Ktz nd Shpiro, 185). 6

9 c, l π = + F, (5) 1 nd c, l π = F. (6) where F is the fixed-fee chrged under licensing. In our nlysis we ssume tht firm 1 gives tke-it-or-leve-it offer to firm under licensing nd firm ccepts the licensing contrct if it is not worse off under licensing compred to no-licensing. Therefore, the mximum mount of fixed-fee tht cn be chrged by firm 1 is the difference of firm s profit under licensing nd no-licensing. So, the fixed-fee chrged by firm 1 is F ( ) =. (7) * c However, firm 1 will license its technology provided it is better off under licensing compred to no-licensing. This implies tht firm 1 will license provided c, l * ( + c ) c, nl π 1 = + F > = π 1. (8) From (7) nd (8) nd fter simplifying, we find tht firm 1 will license its technology to firm provided c <, () 5 where 5 <. 5 Hence, the following lemm is immedite Lemm 1: Under Cournot competition, fixed-fee licensing occurs for c 0, ). ( 5 rerrnging) Therefore, for c (, ), licensing occurs nd welfre is given by (fter 4, 0 5 W c fl =. (10) 5 One cn find similr result in Mrjit (10). 7

10 4.1. Licensing under Bertrnd competition Since these firms produce homogeneous products, licensing will encourge the firms to chrge price equl to zero. Hence, in cse of licensing, both firms receive zero profit under Bertrnd competition. So, it is trivil tht firm 1 hs no incentive to offer licensing contrct under Bertrnd competition. 6 Hence, the welfre under Bertrnd competition is given by the expression () Welfre comprison under Bertrnd nd Cournot competitions It is trivil tht if c, ), fixed-fee licensing will not occur either under Bertrnd [ 5 competition or under Cournot competition. So, our conclusion bout the reltive welfre under Bertrnd nd Cournot competitions becomes similr to Proposition 1. If c 0, ), licensing occurs under Cournot competition only nd welfre ( 5 under Bertrnd nd Cournot competitions is given by the expressions () nd (10) respectively. After rerrnging, we find tht () is greter thn (10) provided c <. (11) Since, < 5, it implies tht, in presence of fixed-fee licensing, welfre under Bertrnd competition is greter thn tht of under Cournot competition provided c 0, ). But, welfre under Cournot competition, in presence of fixed-fee licensing, is greter thn tht of under Bertrnd competition for c, ). 7 ( 5 The following proposition summrizes the bove discussion under licensing with up-front fixed-fee. ( Proposition : Assume tht the firms hve the option for licensing with up-front fixed-fee only. 6 Licensing cn occur under Bertrnd competition with homogeneous product if the firms ply infinitely repeted gme nd try to collude tcitly (see, Lin, 16). 7 It is esy to check tht industry output is higher under Cournot competition for c (, ). For other vlues of c, industry output is higher under Bertrnd competition. 5 8

11 (i) Welfre is higher under Bertrnd competition compred to Cournot competition for either c 0, ) or c, ). ( [ 5 (ii) Welfre is higher under Cournot competition compred to Bertrnd competition for c, ). ( 5 If we consider tht these firms produce imperfect substitutes then licensing is possible even under Bertrnd competition. However, s evident from the previous work (see, Wng nd Yng, 1 nd Wng, 00), the possibility of licensing is lower under Bertrnd competition compred to Cournot competition when licensing contrct involves up-front fixed-fee only. 8 Hence, there re situtions, where licensing is possible under Cournot competition but not under Bertrnd competition even if the products re imperfect substitutes. So, it is esy to understnd tht our qulittive result like the bove proposition holds even under some degree of horizontl product differentition. 4. Licensing with per-unit output roylty Now we exmine nother type of licensing contrct, viz., licensing with per-unit output roylty Licensing under Cournot competition If firm 1 licenses its technology with per-unit output roylty, the effective mrginl cost of firm is ( 0 + r), where r shows the optiml per-unit output roylty. If firm 1 offers the licensing contrct nd firm ccepts the offer then, given the per-unit output roylty, ( + r) the optiml outputs of firm 1 nd firm re nd ( r) respectively. Therefore, ( + r) r( r) ( given r, the profits of firm 1 nd firm re + nd r) respectively. So, while choosing the optiml mount of output roylty, firm 1 mximizes the following expression: Mx r ( + r) r( r) + (1) 8 Mukherjee nd Blsubrmnin (001) hve exmined the optiml ptent licensing contrct under Cournot duopoly nd lso exmined the implictions of imittion on the qulity of the licensed technology.

12 subject to the constrint r c. Mximizing (1) nd ignoring the constrint r c, we find tht the optiml output roylty is. However, is greter thn for ll c <. c This implies tht the incumbent will chrge the optiml output roylty equl to c. becomes With the optiml output roylty, the effective constnt mrginl cost of firm c. Therefore, optiml outputs of firm 1 nd firm re sme under licensing nd no-licensing. So, the profit of firm nd consumer surplus re sme under licensing nd no-licensing but the profit of firm 1 rises by the mount of roylty income, which is equl to c ( c ). This immeditely gives us the following lemm. Lemm : Licensing with per-unit output roylty lwys occurs under Cournot competition. Therefore, if the firms hve the option for licensing with per-unit output roylty, welfre is given by c, rl ( + c ) + ( c ) c )( c ) ( c ) W = + + (1) Licensing under Bertrnd competition Like licensing with up-front fixed-fee, it is esy to understnd tht even if we consider licensing with per-unit output roylty, licensing does not occur under Bertrnd competition. For ny positive per-unit output roylty tht is less thn c, 10 the output of firm is zero nd this licensing contrct reduces the profit of firm 1 compred to the sitution with no-licensing. This is becuse the optiml output of firm 1 under this type of licensing is greter thn the optiml output of firm 1 under no-licensing, which is greter thn the monopoly output of firm 1. The entrnt will be better off under no-licensing compred to licensing if r > c nd hence, will not ccept the licensing contrct with r > c. 10 There is no mening in considering the output roylty greter thn c since firm cn lwys produce with its own technology. 10

13 4.. Welfre comprison under Bertrnd nd Cournot competitions Compring () with (1) nd fter rerrnging, we find tht () is greter thn (1) provided + c 8c > 0. (14) LHS of (14) is continuous, qudrtic nd concve with respect to c over [ 0, ]. Further, LHS of (14) is positive t c = 0 but zero t c =. This implies tht (14) holds for ll c 0, ). ( Hence, the following proposition is immedite. Proposition : Consider the possibility of licensing with per-unit output roylty. In this sitution, welfre is lwys higher under Bertrnd competition compred to Cournot competition. 5 Conclusion There is n existing debte on the effect of mrket competition on socil welfre. Previous works on oligopolistic mrkets suggest tht even if sttic welfre is higher under Bertrnd competition, dynmic welfre my be higher under Cournot competition when the firms hve the possibility of innovtion before production. In this pper we show the possibility of higher sttic welfre under Cournot competition compred to Bertrnd competition in n symmetric duopoly with homogeneous product. We show tht sttic welfre cn be higher under Cournot competition if the firms cn engge in technology licensing nd licensing contrct consists of up-front fixed-fee only. If the firms engge in licensing with up-front fixedfee only, welfre is higher under Cournot competition for moderte initil cost difference of these firms. But, for very smll or very lrge initil cost differences, welfre is higher under Bertrnd competition compred to Cournot competition even if the firms hve the option for licensing with up-front fixed fee only. If there is no possibility of licensing or licensing involves per-unit output roylty only, welfre under Bertrnd competition is lwys higher thn tht of under Cournot competition. 11

14 References Arrow, K., 16, Economic welfre nd the lloction of resources for invention, in R. Nelson (Ed.), The Rte nd direction of inventive ctivity, Princeton University Press, Princeton. Bester, H. nd E. Petrkis, 1, The incentives for cost reduction in differentited industry, Interntionl Journl of Industril Orgniztion, 11: Bonnno, G., nd B. Hworth, 18, Intensity of competition nd the choice between product nd process innovtion, Interntionl Journl of Industril Orgniztion, 16: Delbono, F. nd V. Denicolò, 10, R&D investment in symmetric nd homogeneous oligopoly, Interntionl Journl of Industril Orgniztion, 8: 7 1. Deneckere, R., 18, Duopoly supergmes with product differentition, Economics Letters, 11: 7 4. Lin, P., 16, Fixed-fee licensing of innovtions nd collusion, Journl of Industril Economics, 44: Mrjit, S., 10, On non-coopertive theory of technology trnsfer, Economics Letters, : 8. Mukherjee A. nd S. Blsubrmnin, 001, Technology trnsfer in horizontlly differentited product-mrket, Reserch in Economics (Richerche Economiche), 55: Qiu, L. D., 17, On the dynmic efficiency of Bertrnd nd Cournot equilibri, Journl of Economic Theory, 75: 1. 1

15 Rockett, K., 10, The qulity of licensed technology, Interntionl Journl of Industril Orgniztion, 8: Schumpeter, J., 14, Cpitlism, socilism nd democrcy, Alln nd Unwin, London. Symeonidis, G., 00, Compring Cournot nd Bertrnd equilibri in duopoly with product R&D, Interntionl Journl of Industril Orgniztion, 1: 55. Wng, X. H., 18, Fee versus roylty licensing in Cournot duopoly model, Economics Letters, 60: Wng, X. H., 00, Fee versus roylty licensing in differentited Cournot duopoly, Journl of Economics nd Business, 54: Wng, X. H. nd B. Yng, 1, On licensing under Bertrnd competition, Austrlin Economic Ppers, 8: