Strategic Outsourcing with Technology Transfer under Cournot Competition

Transcription

1 Disussion Paper ERU/4 4 February, 4 Strategi Outsouring with Tehnology Transfer under Cournot Competition Tarun Kabiraj Indian Statistial Institute and Uday Bhanu Sinha ** Delhi Shool of Eonomis February, 4 Aknowledgement: We would like to thank Prabal Roy Chowdhury for helpful omments on an earlier version of this paper. Uday Bhanu Sinha would like to thank the Eonomi Researh Unit, Indian Statistial Institute for generous hospitality when this researh was first initiated. Correspondene to : Tarun Kabiraj, Eonomi Researh Unit, Indian Statistial Institute, 3 B. T. Road, Kolkata tarunkabiraj@hotmail.om; Fax: ** Department of Eonomis, Delhi Shool of Eonomis, University of Delhi, Delhi 7. sinhauday@yahoo.om; Fax:

2 Strategi Outsouring with Tehnology Transfer under Cournot Competition Abstrat This paper seeks to show that even though a produt market ompetitor holds the least ost input prodution tehnology, it may outsoure its input prodution to an independent input produer and buy inputs from the firm at a higher prie instead of produing inputs in-house for itself. Tehnology transfer in the form of patent sale ats as a ommitment. Assuming Cournot ompetition in the produt market the paper shows that suh an outsouring ours when the initial tehnologial gap between the input produing firms is small. Under suh strategi outsouring, however, onsumers welfare as well as soial welfare goes down. JEL Classifiations: D43; L; L3; L4 Keywords: Outsouring; Patent transfer; Vertial struture; Cournot ompetition; Welfare.

3 . Introdution Traditional literature on the theory of firm generally fouses on the hoie between integration and outsouring based on ost onsideration. Aordingly, if a firm an buy an input from outside at a prie lower than its in-house ost of prodution, the firm should go for outsouring. Of late, the researhers have foused attention to the outsouring deision of a firm in the ontext of imperfetly ompetitive market and found different strategi reasons for outsouring, whih were not based on ost onsideration alone. It is in this ontext we provide a theory of strategi outsouring based on a new dimension of tehnology transfer. In a reent paper Arya, Mittendorf and Sappington (8) have shown that given the hoie between outsouring and in-house prodution of inputs, a firm may go for outsouring even though it an produe inputs in-house at a lower ost. There are three firms with one whole sale input supplier and two produt market ompetitors. One of the ompetitors, say firm, has apability to produe the input in-house. The input supplier sets input pries sequentially to firm first and then to the other ompetitor. The paper shows that even though firm an produe the input at a ost less than the input prie harged by the whole sale input supplier, firm will outsoure to take advantage in the output market, where the ompetition is a la Cournot. The outsouring by firm ours whenever its prodution ost of input is greater than that of the whole sale input supplier. Firm strategially opts for outsouring to raise rival s ost and in the proess may also get a favorable treatment in terms of a lower prie for input for some parameter values. However, outsouring never ours in their model when the input prodution ost of firm is stritly lower than that of the whole sale input supplier. In this paper, we allow for the possibility of tehnology transfer and show that outsouring may our even when firm has a better tehnology of input prodution than the independent input supplier. In Arya et al. (8), the sequential and disriminating prie offer seems ruial and motivating fator behind the strategi outsouring. This disriminatory treatment by the input For the literature of firm theory see, for instane, Coase (937), Grossman and Hart (986), Hart and Moore (99), Grossman and Helpman (999) and Gibbons (5). There are a number of other interesting ontributions on strategi outsouring. A subset of this literature omprises Shy and Stenbaka (3), Buhler and Hauap (6), Chen, Dubey and Sen (), Chen (), and Mukherjee and Tsai (, 3). A brief outline of these works an be found in Kabiraj (3).

4 supplier may be realisti but is not very robust. A better assumption would be that input supplier fixes a prie and anyone willing to pay that prie should reeive the input supply. In their model the independent input supplier possesses the least ost input prodution tehnology. Hene simply on the ost onsideration firm ould go for outsouring. Most importantly, it is not lear how, in the presene of firm, a higher prie to firm above firm s marginal ost is sustained. Finally, if firm ould possess the superior tehnology, in their model there would be no possibility of outsouring. Hene the purpose of the present paper is to reestablish their main result but under more appealing onditions. We retain their three firm struture and market ompetition but assume firm to have the superior input prodution tehnology ompared to that of the independent input supplier. We get rid of their sequential ontrating for inputs with the final good produers and introdue a single prie setting input market ondition. Yet, we show, there are parametri situations where firm will go for outsouring. Clearly, under the usual ost onsideration outsouring should never our. Hene we provide a stronger version of the result, that is, even when a firm possesses the least ost input prodution tehnology, a firm may opt for outsouring and buying inputs from outside at a higher prie may be profitable. Another interesting aspet of our paper is that we have introdued sale of patent of the input prodution tehnology in the ontext of outsouring. Patent sale in our model ats as a ommitment that the firm, in spite of having the superior tehnology, will buy inputs from outside. This is absolutely a new dimension in the strategi outsouring literature. The layout of the paper is the following. Setion provides the analytial framework. Setions 3 and 4 disuss respetively the ase of in-house prodution and outsouring. Finally, setion 5 onludes the paper.. Analytial Framework Consider three firms interation. Firm is an independent input supplier. Firm and firm are produt market ompetitors with having idential tehnology to produe a homogeneous good whih requires a non-speifi key input and they ompete a la Cournot in the produt market. Firm also possesses input prodution tehnology whih is superior to that of firm. 3

5 Firm has to depend on either firm or firm for inputs. Let and be the per unit ost of produing inputs by firm and firm respetively, and. To simplify the analysis we further assume that one unit of the key input is required to produe one unit of the final good, and no other inputs are required, hene the ost of produing final goods is the ost of inputs only. Let the inverse market demand for the final good be linear and given by P a ( q q ), () where P is the prie of the produt and q i is the supply of the i-th firm, i,, and a. We onsider the following three-sage game. Stage : Firm deides whether it will outsoure the input prodution to the independent input supplier or produe inputs in-house. The outsouring deision is assoiated with the offer of sale of its patent of input prodution tehnology on a take-it-or-leave-it basis against a fee whih firm an either aept or rejet. Firm s option of not selling the patent an be thought of as making an unaeptable offer. Stage : Patent sale leads to monopoly of firm in the input market. It deides its input prie and sells inputs to firm and firm. Under in-house prodution firm deides whether to ompete in the input market with the independent input seller to sell inputs to firm or stay away from input market ompetition. In the latter ase firm will supply inputs to firm. Stage 3: The final good produers ompete in quantities in the final good market. 3 At this stage we need to explain the role of patent sale in the ontext of outsouring. First note that in our model liensing of the input prodution tehnology annot our beause after liensing the tehnology, firm retains its right to produe inputs and ompete in the input market, and given prie ompetition in the input market firm will not agree to pay any liense fee for the tehnology. Moreover, under liensing, firm annot ommit that it will not produe inputs for itself. On the other hand, patent sale by firm to firm strips the right of firm to use the tehnology; hene in our model patent sale ats as a redible ommitment that firm will not produe inputs by itself, whih essentially means that firm will buy the 3 We retain here the Arya et al. (8) framework. For the ase of prie ompetition in the produt market see Kabiraj and Sinha (4). 4

6 input from the input market where firm would be the monopoly seller. Our purpose is to show that firm, may hoose outsouring rather than in-house prodution of the input to maximize its profits. Although firm will have to pay a higher prie under outsouring for the input, but under some parametri onditions the loss of profits for firm will be overompensated by the revenue from patent sale. 3. In-house prodution Under in-house prodution firm is to deide whether it will ompete in the input market with firm to supply inputs to firm or leave the input market to firm. However, we show that not-ompeting by firm in the input market will not be redible; hene in equilibrium both firm and firm will ompete in the input market. If firm ould ommit not to ompete in the input market, then firm would harge a prie w b a for inputs sale to firm (see Appendix ). The orresponding payoff of 4 firm would be b (5a 7 ) 44 () The above is derived on the assumption that both firm and firm are ative by produing positive output in the output market. In partiular, at the input prie b w, firm s output is q b ( a )/6. Hene the relevant ondition is:, (A) a Now onsider the senario when firm not only produes for itself but also ompetes in the input market with firm. Given their input prodution tehnologies and prie ompetition, the optimal input prie will be the limiting prie w C at whih firm will supply inputs to firm. 4 The equilibrium payoffs in this subgame (under input market ompetition) are: 4 Given the open set problem in Bertrand ompetition we assume that the firm with the lower ost mathes the prie quoted by the higher ost firm and get the entire demand in the market. Under asymmetri ost Bertrand ompetition there exists another possibility that the ost effiient firm harging monopoly prie ould be an 5

7 C ( ( a ) 9 ( a ) 3 ) (3a) C ( a ) C and 9 (3b) Note that input market ompetition leads to a lower prie of inputs for firm, whih makes firm a stronger rival in the final good market. This redues firm s profit earning from the final good market (the first term in the expression of C ). Sine input supply to firm is done by firm, it earns some extra profit from input sales (the seond term in the expression of C ). The net overall benefit of input market partiipation an go either way. Thus, it is quite possible that firm may not like to partiipate in the input market and does better by simply undertaking the in-house prodution for itself only. We an easily hek that, b C 3a ~ (4) 4 We an write then the following proposition. Proposition : In ase it is possible for firm to ommit not to enter into input market ompetition with the independent input supplier, it would do so for all [, ~ ]. And for ( ~, ) firm would like to partiipate in the input market ompetition. Now we argue that though firm would prefer not to partiipate in the input market ompetition for small tehnology gap, but it annot redibly ommit to do so (that is, it is not subgame perfet). The following lemma proves that. Lemma : No equilibrium is possible where firm ommits to stay out of the input market ompetition when it produes the input in-house for itself. Proof: Suppose there exists an equilibrium where firm does not ompete in the input market but it produes in-house. Now onsider the following deviation. Suppose firm harges an input prie, w. Then for any w, firm has inentive to enter the input market by mathing w, thereby it an supply the entire demand of firm. This does not hange the equilibrium if the monopoly prie is below the ost of the ineffiient rival firm. This possibility is ruled out due to the parameter restritions onsidered here. 6

8 outome of the final good market, but by mathing the prie quoted by firm it an always inrease its payoff from selling input to its rival. Thus, firm an retain its market operated b payoff from the final good market, and get an additional profit from the input market by entering into the input market ompetition. Hene, the lemma is proved. In view of Lemma, the only possible outome under in-house prodution will be that both firm and firm ompete to supply inputs to firm. Given the ost advantage of firm in input prodution, firm harges the limiting prie, and firm reeives zero profit in equilibrium. Thus, under in-house prodution the payoffs of the firms will be given by (3). 4. Outsouring deision In this setion we examine the possibility of outsouring of inputs by firm to firm. We have already explained that outsouring deision is assoiated with the sale of patent of firm s input prodution tehnology to firm. Then firm emerges as monopoly in the input market. Under this senario the optimal input prie to be harged by firm will be w O a. The orresponding payoffs of the firms will be O O ( a ) and 36 O ( a ) 6 (5) Given firm s disagreement payoff to be zero, assume that firm will be able to extrat all surplus payoff of firm as fee for patent sale. Hene, firm s total payoff under outsouring will be O O O 7( a ) 36 (6) Then outsouring will our if and only if O C. We an show that O C *, *, * (7) where *.8377a

9 Thus, for low, outsouring is the optimal strategy for firm. Hene, we have the following proposition. Proposition : Firm will outsoure the input prodution to the independent input seller for a all (, *) and it will undertake in-house prodution if [ *, ). 5 Thus, firm would like to outsoure for small tehnology gap but it would not do so if the tehnology gap is large. Note that as the tehnologial advantage inreases, the in-house prodution beomes more and more attrative for two reasons: First, firm an make more profit from selling the input and would have more strategi ost advantage at the final good prodution stage. It should be lear that the strategi advantage of outsouring stems mainly from the advantage of the input prodution tehnology of firm. Seond, when firm sells the patent in order to outsoure from firm, it removes the input market ompetition. This inreases the input prie in the input market thereby softening the ompetition in the final good market. This advantage of extra profit from the final good market and the opportunity to extrat the surplus from firm due to patent sale make the outsouring strategially advantageous for small tehnology gap. Note that under outsouring firm buys inputs from firm at a prie O w whih is muh higher than its in-house input prodution ost per unit. 5. Conlusion In this paper we have shown the possibility that although a firm possesses a superior input produing tehnology, it outsoures the ruial input from outside at a muh higher prie than its in-house prodution ost under some parametri onfigurations. More speifially, the outsouring ours when the tehnologial gap between its in-house input prodution and that of the outside input supplier is not large and it would produe the input in-house and also supply to its rival when the tehnology gap is large. Outsouring leads to a high input prie, whih softens the ompetition in the final good market. We have introdued the issue of 5 Note that we are onsidering the outright sale of the patent and hene it is natural that the payment would be settled upfront. Therefore, we have onsidered a fixed prie for the sale of the patent. However, allowing for a two-part tariff payment (fixed fee and royalty as onsidered in the tehnology liensing ontext) for the sale of patent we find that the optimal payment struture will be fixed prie. 8

10 tehnology transfer in the outsouring literature and provided a new strategi reason for outsouring, whih was hitherto not reognized in the literature. We have analyzed the problem in a setting where an integrated firm ompetes in the final goods market with a rival that has to depend on the input market for input supply and the independent input produer has an inferior input produing tehnology. The integrated firm by selling off the patent of its tehnology to the independent input supplier redibly ommits to purhase inputs from the latter. This raises not only the firm s own prodution ost but also that of the rival. The outsouring firm then aptures the surplus profit of the input supplier by means of a fee for the transferred tehnology, and outsouring beomes profitable. In our set up, however, both industry profit and onsumers welfare fall. Our analysis therefore raises a serious poliy onern over the strategi outsouring. Appendix A Given the demand funtion by (), if firm harges an input prie w to firm, the output a stage equilibrium quantities are w q and 3 q a w, and the 3 ( a w) orresponding payoffs are 9 and ( a w ) 9. Then the optimal w is solved from max w ( w ) q ( w )( a w )/3. This yields the optimal input prie quantities are q b 5 a 7 w w and b q b a 4 a 6. The orresponding equilibrium, and the payoffs of the firms: b (5a 7 ) b ( a ),, 44 4 and b ( a ). 4 9

11 Referenes Arya, A., Mittendorf, B., Sappington, D. (8), The make-or-buy deision in the presene of a rival: strategi outsouring to a ommon supplier, Management Siene 54, Buehler, S. and Hauap, J. (6), Strategi outsouring revisited, Journal of Eonomi Behavior and Organization 6, Chen, Yutian. (), Strategi souring for entry deterrene and tait ollusion, Journal of Eonomis, Chen, Yutian, Dubey, P., Sen, D. (), Outsouring indued by strategi ompetition, International Journal of Industrial Organization 9, Coase, R. H. (937), The nature of the firm, Eonomia 4: Gibbons, R. (5), Four formal(izable) theories of the firm?, Journal of Eonomi Behavior and Organization 58, -45. Grossman, S. and Hart, O. (986), The osts and benefits of ownership: a theory of vertial and lateral integration, Journal of Politial Eonomy 94, Grossman, G. and Helpman, E. (999), Inomplete ontrats and industrial organization, National Bureau of Eonomi Researh Working Paper No Kabiraj, T. (3), Outsouring: some strategi aspets, ERU Disussion Paper No. 5. Indian Statistial Institute, Kolkata. Kabiraj, T. and Sinha, U. B. (4), Strategi outsouring with tehnology transfer under prie ompetition, Paper presented at the Annual Conferene of the Department. of Eonomis, Jadavpur University, Kolkata during 6-7 January, 4. Mukherjee, A. and Tsai, Y. (), International outsouring and welfare redution: An entry deterrene story, The Manhester Shool 78, Mukherjee, A. and Tsai, Y. (3), Multi-souring as an entry deterrene strategy, International Review of Eonomis and Finane 5, 8-. Shy, O. and Stenbaka, R. (3), Strategi outsouring, Journal of Eonomi Behavior and Organization 5, 3-4.