As analyzed in th e previous section, firms do not invest only in one kind of innovation b u t rath er distrib u te their research effort optim ally among process and product innovation. The analysis concerning R&D cooperation has revealed th a t firm s’ investm ent decisions are strongly influenced through strategic externalities and cost sharing agreem ents. How does this optim al in
vestm ent decision change w ith th e m arket size? Does th e size of th e m arket change th e stren g th of externalities? C om parative statics concerning con
sum ers’ prohibitive price helps to answer these questions if th e prohibitive price is in terp reted as th e m arket potential. Up to now, a was considered to be a constant and therefore not given explicitly. To be m ore precise, the sym m etric equilibrium q uantity in case of R&D com petition is in th e first stage given by x* = z*(a, Cj(o), Cj(a), d — d,(a) — d ;(o )). Hence, it is straight forward to analyze com parative static properties. If a changes, th e first-order
conditions have to rem ain satisfied:15
Assume first, firms would increase their investm ent in pro d u ct differentiation, which means th a t dia > 0. For this to be true, expression (25) has to have a
S ubstituting K " into the second-order condition of profit m axim ization, given by (12), shows th a t whenever K " < K " th e existence of a sym m etric pure
K " < K " , this leads to m ore process innovation b u t also to less product innovation because then for an equilibrium to exist, G" > G" is required.
However, if m arginal R&D costs of product innovation increase slowly, th a t is G" < G", product innovation will be increased and process innovation decreased, since again equilibrium requires K " to be sufficiently high. In case the slopes of bo th m arginal cost functions do not differ significantly, an increase in the m arket size will induce firms to invest m ore in product innovation and m ore in process innovation. Clearly, th e higher the outp u t th e larger is th e to tal gain from a given reduction in u n it costs of production.
ft can fu rth er be shown th a t this result still holds if firms cooperate in their R&D decisions, independent from th e specific form of agreem ent.16 B ut does the optim al division between th e two kinds of innovation rem ain unchanged?
Differentiation of (22) w ith respect to a yields:
K "c iaG' - G"diaK ' 4 < 2 « - 2 « d + ciax * J G'2 (2 - cP)2x* + ((2 - d ) x f >
It is easily checked th a t the ratio on the right hand side is positive. Since the ratio of m arginal R&D costs is negative, an increase in this case represents a reduction of th e value of th e ratio. Again, this result does not change under R&D cooperation. We can conclude th a t in a larger m arket firms invest pro
portionally m ore in product differentiation th an in process innovation. Given some initial distribution of investm ent, firms will shift th eir R&D investm ent from process to product innovation if they are confronted w ith a larger m ar
ket if bo th kinds of innovation are characterized by rapidly increasing R&D cost functions. And we observe fu rth er th a t in a sm all m arket firms invest less in R&D th an in a large m arket.
This analysis reveals th a t firm s’ optim al choice between process and product 16See Appendix B2 for a formal proof of this statement.
innovation depends on th e one hand on th e m arket size and on th e other on th e relative slopes of m arginal R&D cost functions.
C ontrary to this result, it can be shown th a t firms always increase their investm ent in both kinds of innovation if m arket size increases, if they coor
dinate th eir R&D strategies and share RfeD costs.
Com paring (in the sym m etric setting) th e relative m agnitude of m arginal rev
enues and externalities for b o th kinds of innovation, one finds th a t for product innovation this relation does not change w ith th e m arket size, while for pro
cess innovation th e m arginal revenue increases m ore th a n th e externality.17
9 7T'
T h at is 13%'c'~ 1 > 0. Obviously, w ith an increase in th e m arket size process innovation gets less “tough” in th e sense defined by Fudenberg &; Tirole (1984).
7 Welfare
W hen analyzing R&D cooperation in this setting it is also interesting to consider welfare im plications. Welfare is given by:
W = 2(a - c,)x, - (1 + d - 2di)x? - ß K (c ,) - ß G (di) (28) w ith ß = 1 and I = s for R&D cooperation in th e sense of R JV -cartelization, and ß = 2 and I = i for com petition. Here th e firms always have an incentive to cooperate in th eir R&D activities because they could have mimicked the non-cooperative strategies, if this were optim al :
d*,c* = argm ax{7r;(ds ,c s) + 7r;(ds,c s) - /<(cs) - G (ds)},
17 Actually, one finds iry > 0 and Hjd ,o > 0. However, a reduction of c,- reduces firm j ’s profit since 7rJc. > 0, so the negative externality is actually captured by —irJc. < 0.
Therefore, one finds also < 0, meaning that the negative externality is reinforced through an increase in market size.
and
d*,c* / di , ci = argmax{7ri(dl-,ct) - K (c t ) - G(dt )|dJ, c*}.
Hence, it m ust be th e case th a t th e following holds:
- | ( A ( < ) + < ? (« )) > » ( < ? ,« ) - ( A ( < ) + G « ) ) . (29)
P r o p o s itio n 4 I f firm s have an incentive to cooperate in their R& D activi
ties and share their R& D costs, this cooperation increases welfare.
P roof: N ote th a t (29) can be rew ritten as:
( » - < ) < - ( i +
+
g w»
> (« - < ) < - (1 + d ) x ? - (A '(< ) + G « ) ) ,
w ith d = d — 2d* for th e com petitive case and d = d — 2d* under cooperation.
W hereas welfare is increased whenever:
(« - - | ( i + < j > : 2 - |( a « ) + g « »
> (« - - ~(1 +
d)x’2 -
(/<(e?) + G « ) ) .Given th a t (29) is satisfied, welfare is increased if:
j ( l + < W - j ( l + < W 2 > 0
O ( l + d X 2 > ( l + d)x*2.
Substituting x* and x* and rearranging leads to:
> (1 + d ) ( 2 + rip (« - c*)2 (1 + d)(2 + d fi
This inequality holds, because due to c* > c* the right hand side of (30) is larger th an one and due to d < d th e left hand side is sm aller th a n one.
Obviously, if (29) is satisfied, and cooperation leads to m ore investm ent into bo th kinds of R&D, also welfare will be increased. □ It is easily seen th a t welfare is increasing in a reduction of (c, d) as long as the increase in R&D costs does not overcom pensate th e gains of producer and consum er surplus or, in other words, as long as firms have an incentive to cooperate. This is not surprising since consumers as well as producers benefit from an increase in product differentiation and from reducing m arginal costs.
The only lim iting factor is th e increase of R&D costs.
If firms do not share th eir R&D costs when they cooperate, welfare im pli
cations are ambiguous. If th e slopes of m arginal R&D cost functions do not differ substantially, cooperative firms differentiate th eir products m ore which benefits th e consumers. B ut m arginal costs are higher under this kind of co
operation th a n under com petition. Therefore th e effect on consum er surplus depends strongly on th e relative strength of th e two effects. W ith o u t assum
ing concrete functions for R&D costs no general conclusion can be drawn.
But when m arginal costs for product innovation do not increase too rapidly, also cooperation in th e sense of R& D -cartelization increases welfare.
8 Conclusion
In this paper we have used a simple linear dem and stru c tu re which enables us to analyze firm s’ R&D decision in a differentiated industry, when they can determ ine m arginal costs and product su b stitu tab ility simultaneously.
In p articu lar, we com pare firm s’ R&D decision under com petition and co
operation and conduct some com parative statics concerning th e m arket size.
The m ain findings are th a t firms do not necessarily specialize in one kind of innovative activity bu t ra th e r allocate their R&D budget optim ally among the two altern ativ e forms of innovation, process and product innovation. Only
if th e R&D costs for one of th e two innovations is such th a t investm ent would be inefficient, we find th e extrem e case of com plete specialization, which is m ostly discussed in th e R&D literatu re. Furtherm ore, the optim al division between the two kinds of innovative activity changes w ith th e m arket size.
U nder R&D com petition th e business stealing effect induces firms to increase (reduce) th eir investm ent in process (product) innovation, com pared to non- strategic decisions. As far as product innovations are concerned, investm ent is fu rth er reduced through th e public good effect. The larger th e m arket, the m ore firms invest in R&D and th e m ore th e investm ent is driven to product innovations provided th a t R&D efficiencies are similar.
We therefore find th a t an increase in th e m arket size affects th e stren g th of com petitive spillovers: “Tough” investm ent becomes less “to u g h ” . (In this scenario th e positive spillover is not affected through an increase in th e m ar
ket size. It rem ains to be shown if in different m arket settings also “soft”
investm ent becomes m ore or less “soft” .)
If firms coordinate their R&D activities and share th e costs for innovation, they will reduce m arginal costs and product su b stitu tab ility m ore th a n un der com petition. They will also proportionally invest more into product in
novation since th e strategic im portance of m arginal costs diminishes if firms cooperate (internalization of com petitive spillovers). In this case of R&D com petition, th e welfare im plications of joint research are positive. T he cost sharing agreem ent together w ith th e internalization of positive com petitive spillovers outweigh the incentive to reduce investm ent in process innovations.
If firms cooperate, b u t for any reason cannot share their R&D costs, they still proportionally invest m ore into product innovation. However, in this case they differentiate their products m ore b u t reduce m arginal costs less th an under com petition. The welfare im plications of an R JV in which firms
only elim inate strategic com ponents b u t do not reduce overall R&D costs are ambiguous. Only if product differentiation is not too expensive, firms increase th eir investm ent for both kinds of innovation, and welfare increases.
In this scenario, positive com petitive spillovers from the product m arket can play a sim ilar role as technological spillovers on th e R&D m arket. If they are sufficiently strong, any cooperative agreem ent is welfare enhancing.
Of course one could th in k of process and pro d u ct innovations as taking place sequentially. The presented m odel could be extended by separating these decisions in two stages. The question of which decision is taken first is not obvious. E ith er th e production technology is considered to be th e m ore com
m ittin g decision or it is assum ed th a t firms first decide on the m arket niche they w ant to position th eir product in. B oth seem to be reasonable assum p
tions and it should be verified by em pirical evidence which of th em is m ore realistic. If rem aining in th e sim ultaneous framework, the assum ption con
cerning th e separability of th e R&D cost function could be altered. Assuming one cost function could lead to unconditioned results concerning th e welfare im plications of cooperative research or concerning com parative statics in the m arket size. A th ird extension of th e m odel could be to assum e price com pe
titio n on th e product m arket. Furtherm ore, th e com parative static analysis could be extended to changes in th e slope of the dem and function. A m ore technical aspect which could be included into th e analysis is th e description of asym m etric equilibria (in case they exist) w ithin th e existing setting, or to analyze equilibria in an a priory asym m etric setting. It would be interesting to analyze these aspects in future research.
Appendix A
AA»CjC,-The denom inators of b oth functions are negative since th e second-order con
ditions for profit m axim ization are assum ed to be satisfied. Therefore the
holds, since the num erator as well as the denom inator are negative. Therefore, also dCs > 0. Inverting dCs and dCi allows us to depict all functions in one
< 0. (32) And for product innovations it yields:
. , ddy . Slgn ( d Y
> 0 > 0
> 0. (33)
References
[1] A bernathy, W .J. and J.M . U tterback (1982): P a tte rn s of Industrial Innovation, in: Readings in the m anagement o f innovation, eds. M.L.
Tushm an and W .L. Moore, P itm an, Boston, p .97-108.
[2] Albach, H. (1994): C ulture and Technical Innovation: a Cross-Cultural Analysis and Policy Recom m endations, Research R eport 9, The Academy of Sciences and Technology in Berlin, W alter de G ruyter, Berlin, New York.
[3] B ester, H. and E. Petrakis (1993): The Incentives for Cost R eduction in a D ifferentiated Industry, in: International Journal o f Industrial Or
ganization, Vol. 11, p .519-534.
[4] D asgupta, P. and J. Stiglitz (1980): U ncertainty, Industrial S tructure, and th e Speed of R&D, in: Bell Journal o f Economics, Vol. 11, p.1-28.
[5] D ixit, A. (1979): A model of Duopoly suggesting a Theory of E ntry Barriers, in: Bell Journal o f Economics, Vol. 10, p .20-32.
[6] G ilbert, R .J. and D.M.G. Newberry (1982): Pre-em ptive patenting and th e persistence of monopoly, in: American Econom ic Review, Vol. 72, p .514-526.
[7] G ilbert, X. and P. Strebel (1987): Strategies to o u tpaste th e com peti
tion, in: The Journal o f Business Strategy, Vol.XX, p. .28-36.
[8] Imai, K. (1992): The Japanese P a tte rn of Innovation and its Evolution, in: N. Rosenberg, R. Laudan and D. Mowery, (eds.): Technology and th e W ealth of N ations, Stanford, Stanford U niversity Press.
[9] R am ien, M.I. and N.L. Schwartz (1982): M arket S tru ctu re and Inno
vation, Cam bridge: Cam bridge University Press.
[10] Kuem m erle, W . (1993): Explaining Foreign D irect Investm ent in R&D - Evidence from selected Japanese and G erm an Industries, P ap er pre
sented a t th e ’’Global M arkets and C orporate S tru ctu re” Conference, The Science C enter Berlin, Berlin O ctober 1993.
[11] M otta, M. (1992): C ooperative R&D and vertical product differen
tiation, in: International Journal o f Industrial Organization, Vol.10, p.643-661.
[12] Reinganum , J. (1983): U ncertain Innovation a th e Persistence of Monopoly, in: Am erican Economic Review, Vol.73, p .741-748.
[13] Rosenkranz, S. (1995): Innovation and Cooperation under Vertical Product Differentiation in: International Journal o f Industrial Orga
nization, Vol.13, p .l- 22.
[14] Scherer, F.M . (1989): Changing Perspectives on th e F irm Size Problem , Paper presented at the ’’Industrial Econom ics” Workshop, T he Science C enter Berlin, Berlin, July 1989.