UNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE


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1 UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN
2 UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE by Arijit Mukherjee Arijit Mukherjee is Lecturer, School of Economics, University of Nottinghm September 004
3 Strtegic second sourcing in verticl structure Arijit Mukherjee * University of Nottinghm nd The Leverhulme Centre for Reserch in Globlistion nd Economic Policy, UK September 004 Abstrct: We show tht monopolist input supplier licenses its technology to crete second source of input supply if second sourcing increses competition in the finl goods mrket. We lso show tht welfre increses under second sourcing. JEL Clssifiction: D43 ; L13 ; O34 Key Words: Entry; Licensing; Downstrem mrket; Second sourcing; Upstrem mrket Correspondence to: Arijit Mukherjee, School of Economics, University of Nottinghm, University Prk, Nottinghm, NG7 RD, UK Emil: Fx: * would like to thnk the prticipnts of the North Americn Summer Meeting of the Econometric Society t the Kellogg School of Mngement, for helpful discussions on n erlier drft. The usul disclimer pplies.
4 Strtegic second sourcing in verticl structure Abstrct: We show tht monopolist input supplier licenses its technology to crete second source of input supply if second sourcing increses competition in the finl goods mrket. We lso show tht welfre increses under second sourcing. JEL Clssifiction: D43 ; L13 ; O34 Key Words: Entry; Licensing; Downstrem mrket; Second sourcing; Upstrem mrket 1. ntroduction f the buyers of product need to ber specific setup costs, the seller cn exproprite the returns to the buyer s specific investment by either incresing price of the product or by reducing qulity of the product. This problem of opportunism in the mrket trnsction reduces profit of the seller nd it cn be resolved if the monopolist seller crtes second source of supply by licensing its technology to competitor. These issues hve been ddressed in Sheprd (1987) nd Frrell nd Gllini (1988). We show tht even if there is no commitment problem bout the future price or qulity of the upstrem product, second sourcing by n upstrem monopolist is profitble if it increses competition in the downstrem mrket. Second sourcing reduces the input price by incresing competition in the upstrem mrket, which my increse competition in the downstrem mrket by ttrcting new firms. The ltter effect increses the demnd for input nd domintes the competition effect in the upstrem mrket. We lso show tht welfre increses under second sourcing. 1
5 Our explntion of second sourcing is consistent with the empiricl evidence. t hs been documented in Sheprd (1987) tht commentry in the trde press nd by industry nlysts ttributes second sourcing to the innovting firm s desire to expnd product demnd in the semiconductor industry. This pper cn lso be relted to works on licensing of innovtion, which shows tht monopolist licenses to the competitor only if the products re imperfect substitutes (see, e.g., FulíOller nd Sndonis, 00). We show tht the upstrem monopolist licenses technology even if the upstrem products re perfect substitutes. The reminder of the pper is orgnized s follows. Section describes the model nd derives the results. Section 3 concludes.. The model nd the results Let us consider n economy with the upstrem nd the downstrem mrkets. Assume tht there is n upstrem monopolist, 1, who hs the technology to produce criticl input for the downstrem firms. The verge cost of input production is constnt nd is ssumed to be, for simplicity. Assume tht there is nother upstrem firm,, 0 who cn produce the input if nd only if it gets the technology of. Assume tht there is n incumbent nd potentil entrnt in the downstrem mrket. We cll these firms s nd D respectively. We consider one downstrem D1 incumbent to show our results in the simplest wy. However, it is needless to sy tht 1 1 our qulittive results hold even if there re n downstrem firms. Assume tht the downstrem firms hve the sme production technology, which requires one unit of 1 To mke second sourcing fesible, it must be profitble for to enter the mrket. To stisfy this in the simplest wy, we ssume wy cost of entry for.
6 the input to produce one unit of the finl goods. For simplicity, we consider tht the finl product requires only the criticl input produced by the upstrem firm(s). Assume tht the inverse mrket demnd function for the finl product is P = q 1 q, (1) where nd re outputs of nd D respectively nd q1 q D1 P is price of the finl good. Assume tht the firms in the upstrem nd the downstrem mrkets choose outputs to mximize their profits. n cse of competition in the upstrem nd/or in the downstrem mrkets, the respective firms compete like Cournot duopolists with homogeneous products. So, we consider n economy with successive Cournot oligopolists like Sheprd (1987). Therefore, the upstrem firm(s) chooses output(s) nd the input price, w, is determined from the input demnd function. Further, like Sheprd (1987) nd Frrell nd Gllini (1988), we ssume wy verticl restrints nd verticl integrtion between the upstrem nd the downstrem firms. 3 We lso ssume tht the ntitrust uthority prevents collusion in the finl goods mrket, which will be justified lso by our nlysis. We consider the following gme. At stge 1, 1 decides whether to license to or not. n cse of licensing, it gives tkeitorleveit offer to, which either ccepts or rejects the offer. At stge, the domestic entrnt D decides whether to enter or not. At stge 3, ( nd ) produces (produce simultneously) if there is 1 1 no licensing (licensing) t stge 1. At stge 4, (D nd ) produces (produce D 1 1 D One my, e.g., refer to Abiru (1988), Slinger (1988) nd Abiru et l. (1998) for other works with successive Cournot oligopolists. 3 Hrt nd Tirole (1990) rgued tht verticl integrtion would not occur for significnt cost of integrtion. 3
7 simultneously) if D does not enter (enters) t stge nd the profits re relized. We solve the gme through bckwrd induction..1 No licensing Let us consider the sitution where does not license its technology to. n this 1 sitution, we hve two possibilities: (i) where D enters the downstrem mrket nd (ii) where D does not enter the downstrem mrket. f enters then, given the input price, both nd D produce D D1 ( w). 3 So, the demnd for input is q ( w) =. () 3 1 produces to mximize the following expression: Mx( q ) q. (3) 1 q Optiml input supply nd the input price re respectively 3 nd. Profit of 1 is 6 nd profits of D nd D re respectively 1 nd E. So, if 1 is monopolist in the upstrem mrket, D enters provided > E. f < E, is monopolist in the downstrem mrket nd the input demnd D 1 is So, 1 q ( w) =. (4) produces to mximize the following expression: 4
8 Mx 1 1 ( q ) 1 q q. (5) Optiml input supply nd the input price re respectively 4 nd. Profits of 1 nd D 1 re respectively 8 nd. 16. Licensing to crete second sourcing Now ssume tht licenses its technology to. To show our results in the simplest 1 wy, following Ktz nd Shpiro (1985), Mrjit (1990), Mukherjee (001) nd others, we ssume tht, under licensing, 1 chrges n upfront fixedfee 4 for its technology, nd ccepts the offer if it is not worse off under licensing thn no licensing. So, under licensing, both nd produce the input t zero verge cost of production. 1 We normlize the pyoff of under no licensing to 0. Agin we hve to consider two situtions: (i) where D enters the downstrem mrket nd (ii) where D does not enter the downstrem mrket. f D enters, the input demnd is given by (). The i th firm, i = 1,, in the upstrem mrket produces to mximize the following expression: 3 i 3 j i Mx q q q q i ( ), i j. (6) 4 Noninfringing imittion or inventing round the licensed technology by the licensee or lck of informtion needed for roylty provision might be the reson for licensing contrct with upfront fixedfee only (see, e.g., Ktz nd Shpiro, 1985 nd Rockett, 1990). 5
9 Both nd produce 1. Totl input supply nd the input price re respectively 9 4 nd. Therefore, optiml profits of both nd re nd optiml Profits of nd D re respectively D1 4 nd E So, D enters provided 4 4 > E 81. f 4 < 81 E then is monopolist nd the demnd for input is given by (4). D 1 The i th firm, i = 1,, in the upstrem mrket produces to mximize the following expression: Mx( q q ) q, q i i j i i j. (7) Both nd produce 1. Totl input supply nd the input price re respectively 6 3 nd. Profits of both 1 nd re 3 18 nd profit of D 1 is. 9.3 ncentive for second sourcing We hve seen tht D enters the mrket under no licensing nd licensing in the upstrem mrket if > E nd 4 > E 81 respectively, where 4 >. 81 Proposition 1: (i) f either E < or E > 4 81, second sourcing is mot profitble. 4 (ii) Second sourcing is profitble if E (, ). 81 6
10 Proof: (i) f > E, totl profit in the upstrem mrket under second sourcing is 4 nd it is lower thn the profit of 1 when it is monopolist, which is. 7 6 f 4 E >, totl profit in the upstrem mrket under second sourcing is 81 9 nd it is lower thn the profit of 1 when it is monopolist, which is. 8 4 (ii) f E (, ), totl profit in the upstrem mrket under second sourcing is 81 4 nd it is greter thn the profit of 1 when it is monopolist, which is 7 8. Q.E.D. f second sourcing in the upstrem mrket does not induce entry in the downstrem mrket, it cretes competition in the upstrem mrket while the input demnd function remins unchnged. This competition effect reduces totl profit in the upstrem mrket nd mkes second sourcing unprofitble. However, second sourcing reduces the input price by creting competition in the upstrem mrket nd my induce entry in the downstrem mrket. f second sourcing increses competition in the downstrem mrket, it increses the demnd for input, for given input price. We show tht the effect of higher input demnd domintes the competition effect in the upstrem mrket nd mkes second sourcing profitble..4 Welfre implictions of second sourcing 4 We hve seen tht second sourcing occurs for E (, ). n this sitution, 81 welfre under monopoly in the upstrem mrket nd second sourcing re respectively 7
11 7 3 nd 56 E 16. (8) Comprison of the welfre vlues in (8) gives the following proposition. 4 Proposition : Suppose, E (, ). Second sourcing increses welfre 81 compred to monopoly in the upstrem mrket. t is strightforwrd to see tht collusion in the downstrem mrket reduces welfre if there is no second sourcing. Proposition 1 implies tht if the upstrem monopolist nticiptes collusion in the downstrem mrket, second sourcing does not occur. Then, it follows from Proposition tht collusion in the product mrket further reduces welfre by preventing second sourcing, which my encourge the ntitrust uthority to prevent collusion in the product mrket s ssumed in our nlysis. 3. Conclusion We show tht monopolist input supplier hs the incentive to license its technology to crete second source of input supply if second sourcing increses competition in the downstrem mrket. So, unlike pervious work on second sourcing by the monopolist input supplier, we show tht even if the upstrem firm does not fce ny commitment problem bout the future price or qulity of its product, second sourcing it still profitble. We lso find tht second sourcing increse welfre compred to monopoly in the upstrem mrket. 8
12 References Abiru, M., 1988, Verticl integrtion, vrible proportions nd successive oligopolies, Journl of ndustril Economics, : Abiru, M., B. Nht, S. Rychudhuri nd M. Wterson, 1998, Equilibrium structures in verticl oligopoly, Journl of Economic Behvior nd Orgniztion, 37: Frrell, J. nd N. Gllini, 1988, Secondsourcing s commitment: monopoly incentives to ttrct competition, The Qurterly Journl of Economics, 103: FuliOller, R. nd J. Sndonis, 00, Welfre reducing licensing, Gmes nd Economic Behvior, 41: Hrt, O. nd J. Tirole, 1990, Verticl integrtion nd mrket foreclosure, Brookings Ppers on Economic Activity, nd Ktz, M. nd C. Shpiro, 1985, On the licensing of innovtion, Rnd Journl of Economics, 16: Mrjit, S., 1990, On noncoopertive theory of technology trnsfer, Economics Letters, 33: Mukherjee, A., 001, Technology trnsfer with commitment, Economic Theory, 17: Rockett, K., 1990, The qulity of licensed technology, nterntionl Journl of ndustril Orgniztion, 8: Slinger, M. A., 1988, Verticl mergers nd mrket foreclosure, The Qurterly Journl of Economics, 103: Sheprd, A., 1987, Licensing to enhnce the demnd for new product, Rnd Journl of Economics, 18:
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