No. 20 WORKING PAPER SERIES IN ECONOMICS THE IMPACT OF COMPETITION ON UNILATERAL INCENTIVES TO INNOVATE NADJA TRHAL

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1 No. 0 U N I V E R S I T Y O F C O L O G N E WORKING PAPER SERIES IN ECONOMICS THE IMPACT OF COMPETITION ON UNILATERAL INCENTIVES TO INNOVATE NADJA TRHAL Department of Eonomis University of Cologne Albertus-Magnus-Platz D-5093 Köln Germany

2 The impat of ompetition on unilateral inentives to innovate Nadja Trhal * University of Cologne August 005 Abstrat: We investigate the impat of the degree of ompetition in a Cournot market on one firm s unilateral inentives to invest in R&D. Applying omparative stati analyses we get different preditions depending on the magnitude of the innovation effiieny parameter α. Even inner solutions arose. For α the omparative statis prediate that inentives to invest in R&D are strongest in a monopoly whereas for smaller α the optimal market struture for unilateral innovation varies depending on the ost level. Keywords: innovation inentives; market struture; Cournot ompetition JEL Classifiations: D4, L, O3 * University of Cologne, Department of Eonomis, Albertus-Magnus-Platz, D-5093 Cologne, Germany Tel: , fax: , nadja.trhal@uni-koeln.de I thank Axel Okenfels and Susanne Wied-Nebbeling for helpful omments and suggestions. I gratefully aknowledge the support of the Deutshe Forshungsgemeinshaft.

3 . Introdution A bulk of evidene indiates that there is a positive effet of innovative ativity on firm profits, produtivity, eonomi growth and total welfare. Among others Kamien and Shwartz (975) already stressed the general importane of researh and development (R&D). On aount of all the positive effets innovation has in general on an eonomy, it is important to understand whih onditions promote R&D ativity of the firms. Therefore in this paper we onsider the question whih degree of ompetition in the produt market provides the strongest unilateral inentives for a single firm to innovate. Is it more worthwhile for a firm to invest in R&D if this firm faes more ompetition? Is the inrease in its profits aused by a ost reduing innovation highest in a monopoly setting? Or is it rather more profitable to innovate under moderate ompetition? The question whih market struture provides strongest inentives to invest in R&D is not new. Shumpeter (954) advoates that a monopoly setting guarantees a strong interest for a firm to invest in innovation. Shumpeter thinks of an eonomy as a proess of reative destrution, meaning that in an eonomy produts and proesses are onstantly renewed or replaed by improved ones. This implies that a monopoly position whih an be ahieved by innovation will be temporarily limited. A firm will invest in innovation only if it gets the hane of obtaining monopoly power by innovation at least for a time and it will ontinue investing in innovation due to the threat of losing its monopoly position. 3 Therefore, perfet ompetition whih implies immediate imitation would destroy inentives to innovate. 4 Arrow (96) supports a different view. He states that the inentive to invent is less under monopolisti than under ompetitive onditions, but even in the latter ase it will be less than is soially desirable (Arrow (96), p. 69). So aording to Arrow there is less innovative ativity in a monopoly than in a ompetitive market. 5 Nevertheless, the disussion of this problem has not lead to generally aepted results. Cohen and Levin (989, p. 075) already stated that [e]onomists have offered an array of theoretial arguments yielding ambiguous preditions about the effets of market struture on innovation. Similarly Aghion et al (005, p. ) state that also IO theory typially predits [that] innovation should deline with ompetition while empirial work finds that it inreases. 3 Note that Shumpeter emphasizes the impat of the threat of potential entrant and rivalry, a situation whih is not framed in this paper. 4 For a disussion of the Shumpeterian hypotheses see Kamien and Shwartz (98). 5 This is a more ommon view. For instane, Dasgupta and Stiglitz (980, p. 89) also emphasize that a pure monopolist [ ] appears to have insuffiient inentive [ ] to undertake R&D expenditure. Furthermore, Geroski (990) found strong evidene that monopoly power has a dampening effet on innovative ativity and that ompetition is desirable to improve R&D inentives. In his study he used data on major innovations introdued in the UK during the 970s. Nikell (996) and Blundell et al (995) ame to similar results.

4 Intuitively, one might think that the inentive to innovate is strongest if there is moderate ompetition. 6 Under perfet ompetition the advantages that our beause of innovation might be diretly negated and under a monopoly situation there might be no inentives to invest, beause the firm already possesses monopoly power. However, under moderate ompetition there might be on the one hand enough ompetition to stimulate innovative ativity and on the other hand the probability that an innovator gets at least some benefits out of his investment is also suffiient 7. We will investigate these questions in the ourse of our researh.. The model In a simple Cournot setting we investigate the impat of stati market struture on one firm s unilateral inentives to invest in R&D in the short run using omparative statis. First, we introdue a stati Cournot setting in a one produt ase in whih no firm invests in R&D. Then we explore the question under whih degree of ompetition one deviating, innovating firm among these firms extrats the highest additional profit (i.e. the differene between profits after innovation and profits before innovation) due to its innovation. That is, we assume that firms take a myopi view they maximize their own behavior given the deisions of the other firms.. Investing in Proess Innovation Imagine a market for one homogenous ommodity in whih n idential risk-neutral firms i deide simultaneously what quantity q i (i,,n) of this ommodity they want to produe and maximize their profits π i given the quantities of the other firms. Moreover, we assume for simpliity that every firm i faes the same onstant marginal osts (with /) 8 and there are no fixed osts. The effet of potential entry is negleted. For the inverse demand funtion p Q, in whih p is the prie for the ommodity and Q is the total produed quantity, with Q n q i i, the Nash equilibrium quantity is q i and n + the equilibrium prie is + n ( ) p with profits π i. n + ( n + ) 6 There are also both theoretial as well as empirial studies whih support this view. See Loury (979), p Among others Kamien and Shwartz (976) show analytially that under ertain irumstanes an intermediate degree of tehnologial rivalry inreases innovative ativity most. Aghion et al (005) found empirial evidene for an inverted U relationship between ompetition and innovation. 8 By this we exlude drasti innovation, so the market size remains onstant.

5 If firm i invests unilaterally in R&D it redues its former marginal osts to i, where i α with 0 < α <. α is alled the innovation effiieny parameter. Note that the smaller α the better is the innovation. The n- other firms j still fae osts. If we assume that the fixed osts F of the innovation are the same for every firm i, we an ignore them (F 0), beause we are only interested in the different additional profits of an innovating firm i under different degrees of market onentration. After firm i invested in R&D the + ( n ) αn produed quantities are as follows: q i for the investing firm i and n + + α q j n + p for the remaining n- other firms j. The equilibrium prie is + ( n ) + α, the profit for firm i (negleting the ost of R&D) is n + + ( n ) αn + α π i and for the other firms j is π j. n + n + We define the additional profit D i of the unilateral investing firm i as the differene between its profit after the innovation and its profit before the innovation. Let us now develop firm i s additional profit D i for every possible magnitude of α ( 0 < α < ) using the equilibrium profits from above. We derive: D i n + n n αn αn + αn ( n + ) + α n. D i depends on the number of firms n, the innovation effiieny parameter α and the ost level.. Comparative statis We analyze now under whih market struture the additional profit D i is largest. To get the optimal number of firms n, we differentiate D i with respet to n: 9 D i n ( n + ) [( α )( n ) + n( 3α + )] α 3. Equating this expression with 0 and solving aording to n yields: n. This is the number of firms in the market α + whih provides the strongest inentives to innovate for firm i (negleting the integer problem). The optimal number n varies depending on the ost struture. There even exist 9 The optimal n is defined in the following as the number of firms in a market whih provides the strongest inentives for a firm to innovate (i.e. the market struture under whih the additional profit D i is highest for a firm for given and α ). Note that it is not a deiding variable of the firm. 3

6 inner solutions at speifi magnitudes of ost redution α and ost levels. Figure gives an example for the additional profit D i subjet to n for a given α and a given. Figure : Example for the additional profit D i as a funtion of n for α /4 and /3 The optimal n is 8/5. As there is always a disrete number of firms in the market the optimal number of firms in this ase is, beause if there are firms in the market firm i s additional profit D i is larger than in a monopoly. Now we investigate the influene of α on the optimal number of firms in a market. Differentiating the optimal number of firms n with respet to α yields: n ( ) α ( α + ). This expression is always smaller than zero whih signifies that the optimal n dereases as α inreases given. So the better the innovation is (the smaller α is) the more profitable is innovation in a more ompetitive environment. Consider the ase α, whih would be equivalent with a marginal ost redution. Here it holds that n. 0 Therefore we an predit if the ost redution is only marginal that in a monopoly the inentives to invest in R&D are the strongest. We are also interested in the impat of the ost level on the optimal number of firms in the market. Differentiating the optimal number of firms with respet to yields: 0 A proof is given in Appendix. 4

7 n α ( α + ). This expression is always larger than zero. Thus, the optimal n inreases as inreases for a given α. As an illustration of the results onsider the example given in Table. Cost level I. e.p. α 4 3 α 4 Monopoly Duopoly 4 firms α 3 Monopoly Duopoly 3 firms α Monopoly Monopoly Duopoly α 3 Monopoly Monopoly Duopoly 3 α 4 Monopoly Monopoly Monopoly Table : Example: Most profitable market struture for the innovating firm for speifi α and I. e. p. innovation effiieny parameter For the further disussion of our results we have to take into aount what happens when we vary the ost level and the magnitude of ost redution. First, regard the influene of the initial level of marginal ost, holding the ost redution and the number of firms n onstant. The lower the ost level, the larger the produed quantity q j of the noninnovating firms and the smaller the differene between the produed quantities q i and q j. Under a low ost level the additional profit D i is largest when there is no ompetition at all. The higher the ost level, the more profitable ompetition beomes for the investing firm. Intuitively, when there are already low osts, the investing firm does not improve its situation too muh by its innovation ompared to the other firms. As we have seen above, the differene in the produed quantities q i and q j dereases as the ost level dereases. However, under an initially high ost level a ost redution leads to omparative advantages inreasing the additional profit a lot, beause the higher the ost level, the larger the differene between the produed quantities q i and q j. Seond, what effet does the magnitude of the ost redution have on the quantities? The stronger the ost redution (i.e. the smaller α ), the larger the produed quantity q i of the investing firm i and the less the quantity q j of all the other firms j holding the other parameters n and onstant. This implies that also the differene in the produed 5

8 quantities q i - q j inreases as the magnitude of the ost redution inreases (i.e. as α dereases). So the omparative advantage of firm i is larger the higher the ost redution. When the new tehnology leads only to a small ost redution (e.g. α is lose to one), the advantages in innovating are the largest, when there are no other firms in the market or only few firms depending on the ost level. But as the ost redution inreases, the inentives for firm i to innovate are larger under ompetition at least at higher ost levels. Combining these two elements we an onlude that a firm has the strongest inentives to unilaterally invest in R&D, when it faes no ompetition, when the ost redution due to its innovation is only small and the ost level is small, too. Considering that the ost level inreases and the ost redution is moderate, then firm i s inentives to invest in R&D are strongest in a duopoly or an oligopoly with three or four firms. Moreover, when all the firms fae high marginal osts and the innovation of firm i leads to a great ost redution, then the inentives to innovate are strongest under ompetition. 3. Conlusion We srutinized a simple Cournot framework to investigate the impat of market struture on innovative ativity. From our omparative statis we derived an interesting result. If the hange in the marginal osts is only marginal ( α ) the inentives to invest in innovation are the strongest under monopoly power, thus supporting the Shumpeterian hypothesis that innovation inreases with market onentration. However, when α is dereasing the optimal number of firms is inreasing, whih means that more ompetition is profitable. So our analysis points to the environmental fators whih speifi market struture stimulates innovation most. In fat, the optimal market struture for the innovating firm depends on the irumstanes whih ost level all the firms fae before investing and how good the innovation is i.e. how muh the marginal osts an be redued. Therefore, inentives an be the strongest under no as well as under moderate ompetition. However, due to the restritive assumptions the results need to be interpreted arefully. We just investigated the question of an optimal degree of ompetition under omparative statis by onsidering the unilateral behavior of one investing firm, having studied the myopi view of one innovating firm. A full equilibrium analysis is beyond the sope of this paper. A proof is given in Appendix. 6

9 Appendix Limit of n * if α : Reall that Appendix n α +. For α it holds that limn lim. Therefore firm i s inentive to invest in R&D is α + strongest in a monopoly situation if the ost redution is just marginal. Appendix Derivation of the impat of on the quantities: Differentiating firm i s quantity q i + ( n ) αn and firm j s quantitiy n + + α q j with respet to leads to n + q i n( α) n + and q j α. Aording to the quantity q j we an reognize that n + the smaller the ost level is, the more the firms j produe ( < 0 ). However, onerning the quantity q i of the investing firm, we annot give an unambiguous predition, beause the numerator of the quantity q i depends not only on the ost level but also on the number of firms n and the magnitude of ost redution α ( an be smaller or larger than zero). For some values of n and α the quantity q i is dereasing with an inreasing ost level and for some values of n and α the quantity q i is inreasing. n( α) > 0 n ( α) > n + n > or α q j q i n α > respetively. n The impat of on the differene between the quantities q i + ( n ) αn and n + + α q j : q i q j ( α). We an see that the higher the ost level is, the n + larger the differene is in the produed quantities between the innovating firm and every other firm in the market. 7

10 Derivation of the impat of α on the quantities: Differentiating firm i s quantity q i + ( n ) αn and firm j s quantitiy n + + α q j with respet to α leads to n + q nn i α + and q j q. i < 0 α n + α q j and > 0. α 8

11 Referenes Aghion, P.; Bloom, N.; Blundell, R.; Griffith, R.; Howitt, P. (005): Competition and Innovation: An Inverted U Relationship, UCL Eonomis Working Paper 04/06, forthoming The Quarterly Journal of Eonomis Arrow, K. (96): Eonomi Welfare and the Alloation of Resoures for Invention in R. Nelson (ed.), The Rate and Diretion of Inventive Ativity, New York, Arno Press, 975 (reprint) Blundell, R.; Griffith, R.; Van Reenen, J. (995): Dynami Count Data Models of Tehnologial Innovation, The Eonomi Journal 05, Cohen, W.; Levin, R. (989): Empirial Studies of Innovation and Market Struture in R. Shmalensee and R. Willing (eds.), The Handbook of Industrial Organization, Volume II, Amsterdam: North Holland Dasgupta, P; Stiglitz, J. (980): Industrial Struture and the Nature of Innovative Ativity, The Eonomi Journal 90, Geroski, P. (990): Innovation, Tehnologial Opportunity, and Market Struture, Oxford Eonomi Papers 4, No. 3, Kamien, M.; Shwartz, N. (975): Market Struture and Innovation: A Survey, Journal of Eonomi Literature 75, Issue, -37 Kamien, M.; Shwartz, N. (976): On the Degree of Rivalry for Maximum Innovative Ativity, The Quarterly Journal of Eonomis 90, Issue, Kamien, M.; Shwartz, N. (98): Market Struture and Innovation, Cambridge: Cambridge University Press, Chap., -48 Loury, G. (979): Market Struture and Innovation; The Quarterly Journal of Eonomis 93, Issue 3,

12 Nikell, S. J. (996): Competition and Corporate Performane, Journal of Politial Eonomy 04, No. 4, Shumpeter, J. A. (954): Capitalism, Soialism and Demoray, Ch.VII The Proess of Creative Destrution, Unwin University Books 0