165
POOLING OF
RISKY ASSETS
AND THE
INTENSITY OF
COOPERATION
IN R&D
Eero Lehto
Pooling of risky assets and the intensity of
cooperation in R&D
Eero Lehto
22.6.2000
Abstract
In the case considered, risk...
According to D’Aspremont and Jacquemin (1988), and Katz and Ordover
(1990), spillovers outside can be reduced, if R&D resu...
This study focuses explicitly on the available information structure. In
the basic model the …rms cannot observe the real ...
a contract a paragraph according to which the sharing contract can be can-
celled, if a signal is low. It can be shown tha...
doubt highest when a …rm’s e¤ort is high and when they cooperate. This
situation implies competition in the product market...
A0
s utility is then
UA = pAU((1 ¡ v)(1 ¡ ±B
A) + ®Av) + pBU((1 ¡ v)±A
B + v°A) ¡ eA:
The above (1 ¡ v) describes that par...
that they stay at the di¤erent levels of the vertically integrated production
chain. Then the information utilized by A do...
Notice that condition (4) does not depend on B0
s conduct. In fact, the
negative sign of the left hand side of (4) holds w...
If vc
¸ 1, both …rms always select low e¤ort. Under symmetry optimal
behaviour is determined from
@UL
A
@v
= pL
A(1 ¡ ®A)[...
When vc
< v · 1, however, low e¤ort is chosen. In this case …rms will also
make cooperation very intensive and set v = 1: ...
(9) then transforms into the form
pL
A(1 ¡ vc
+ ®Avc
) + pH
B vc
°A ¡ pL
A®A ¡ pL
B°A > 0:
Taking into account that °A = 1...
results in v = 0: 5) The outcome of R&D projects is materialized as either
success or failure.
We also assume that signal ...
The above notation pH
´ pH
A = pH
B and pL
´ pL
A = pL
B is used. Due to the
strict concavity of U, the …rst term in (13) ...
as well. In this equilibrium …rms also cooperate with maximal intensity, that
is v = 1: A’s utility in this low e¤ort equi...
observes sH
B . When A sets eA = eH
A its utility is
UH
A = pH
A U(1 ¡ v + ®Av) + (qpH
B + (1 ¡ q)pL
B)U(v°A) ¡ eH
A : (16...
Above, strict concavity of U yields kU(1¡v+®Av)¡kU(1)+k(1¡q)U(v°A) >
kqU(v°A) in symmetry. This guarantees that B > 0 from...
When v = vc
B, it obtained for UA and UB
UH
A = pH
A U(1 ¡ vc
B + ®Avc
B) + pH
B U(vc
B°A) ¡ eH
A :
UH
B = pH
B U(1 ¡ vc
B...
deteriorates …rm B0
s situation. In high e¤ort equilibrium the increase in °A
has a direct and also an indirect e¤ect thro...
¡pL
AU0
(®AzA) ¡ pL
BU0
(°AzB):
When asymmetry becomes deep so that vc
B is very small, the partial
derivative @LH1
@°A
ea...
Suppose that during isolation …rms prefer high e¤ort to low e¤ort, which
implies that (5) is valid. But inserting ®A = 1 i...
generated by the innovation. In cooperation the pro…ts generated by innova-
tion are shared. We again make a simplifying a...
is intensive enough. Therefore, it is obvious a cut-o¤ value vc
for v exists
such as in the two-product model too.
Suppose...
It is remarkable that in the one-product model considered it is possible
that a …rm would not deviate from high e¤ort equi...
(12) valid with all v. An analysis in previous sections showed that if there
exists high e¤ort equilibrium with 0 < v · 1;...
by, for example, Katsoulacost and Ulp (1998).
In the case in which two …rms make discoveries independently of each
other b...
Perez-Castrillo J. and J. Sandonis, 1996, ”Disclosure of know-how in re-
search joint ventures”, International Journal of ...
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Pooling of Risky Assets and the Intensity of Cooperation in R&D

In the case considered, risk averse firms agree in advance to share R&D results but not R&D costs. Real R&D expenditure is unobservable, which creates a moral hazard problem. The firms contract at the first stage on the intensity of cooperation and at the secong stage on the research effort. Moral hazard weakens the firms´ motives to invest in R&D during cooperation. But diversifying the portfolio of R&D projects through cooperation increases firms´ utility. It turns out that in the absence of monitoring, the firms choose either high effort and low intensity of cooperation. If a firm can monitor a partner´s real R&D effort through a signal, moral hazard can weaken to an extent that risk averse and independent firms choose high effort and maximal intensity of cooperation, even if they were indifferent between high effort and low effort under isolation.
Published on: Mar 4, 2016
Published in: Government & Nonprofit      
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Transcripts - Pooling of Risky Assets and the Intensity of Cooperation in R&D

  • 1. 165 POOLING OF RISKY ASSETS AND THE INTENSITY OF COOPERATION IN R&D Eero Lehto
  • 2. Pooling of risky assets and the intensity of cooperation in R&D Eero Lehto 22.6.2000 Abstract In the case considered, risk averse …rms agree in advance to share R&D results but not R&D costs. Real R&D expenditure is unobserv- able, which creates a moral hazard problem. The …rms contract at the …rst stage on the intensity of cooperation and at the second stage on the research e¤ort. Moral hazard weakens the …rms’ motives to invest in R&D during cooperation. But diversifying the portfolio of R&D projects through cooperation increases …rms’ utility. It turns out that in the absence of monitoring, the …rms choose either high e¤ort and low intensity of cooperation or, alternatively, low e¤ort and maximal intensity of cooperation. If a …rm can monitor a partner’s real R&D e¤ort through a signal, moral hazard can weaken to an extent that risk averse and independent …rms choose high e¤ort and maximal intensity of cooperation, even if they were indi¤erent between high e¤ort and low e¤ort under isolation. keywords: R&D expenditure, moral hazard, diversi…cation JEL codes: O31, O32,O38 1 Introduction and summary of the results1 We examine cooperation in R&D. In the literature there are various reasons which explain cooperation in R&D. However, if …rms are competitiors, such conditions are not easily met that are su¢cient for cooperation on R&D. 1 This paper will be presented in EARIE 2000 (in Lausanne). This paper is a part of a larger governmental evaluation programme coordinated by the Finnish National Fund for Research and Development. 1
  • 3. According to D’Aspremont and Jacquemin (1988), and Katz and Ordover (1990), spillovers outside can be reduced, if R&D results are shared between two …rms. The need to eliminate duplication of R&D e¤ort may also motivate the …rms to coordinate their R&D investments (see Katz and Ordover (1990) and Kamien et al. (1992)). But cooperation can also be motivated, if the e¤orts are complementary either in research (see e.g. Veugelers and Kesteloot, 1994) or in the product market. Katz and Ordover (1990) have noticed that R&D e¤ort may become complementary when one …rm learns from another’s success. Cooperation which leads to sharing of R&D results leads almost in- evitably to intensi…ed competition in the product market, which weakens the incentives to share R&D results. This is stressed by almost all authors who have studied cooperation in R&D (see D’Aspremont and Jacquemin (1988), Katz and Ordover (1990), Kamien et al. (1992), Katsoulacost and Ulph (1998) and Stenbacka and Tombak (1998)). However, if cooperating …rms belong to complementary industries, this e¤ect vanishes (see. e.g. Kat- soulacost and Ulph (1998)). D’Aspremont and Jacquemin in 1988 and since then many authors have noticed that insofar as R&D results only are shared, and the costs of ex- erting R&D e¤ort are not, there arises a free-rider problem. According to D’Aspremont and Jacquemin (1988) the possibility to cooperate on R&D would increase R&D expenditure, if spillovers outside are large enough. As Kamien et al. (1992) have shown, the creation of a research joint venture (RJV) that cooperates in its R&D decisions and maximizes the joint pro…t solves the problems of free-riding. Basically, the existence of moral hazard depends on the observability of real R&D investments. Observability makes it possible to contract on R&D and solve free-riding problem as e¤ectively as the establishing of RJV. In this study we focus rather on ex ante cooperation which is not limited to RJVs. The …rms just agree in advance to share R&D results but not R&D costs. Following Katsoulacost and Ulp (1998) the intensity of cooperation is assumed to be endogenous. In most studies the intensity of cooperation is taken as given. Whether the independent …rms can …nally agree on anything depends on the nature of their observations. If only real R&D results, but not real R&D e¤orts, can be observed veri…ably there arise moral hazard and a free-rider problem. Then …rms can contract on sharing R&D results but not on R&D e¤orts (real investments) themselves. 2
  • 4. This study focuses explicitly on the available information structure. In the basic model the …rms cannot observe the real R&D of their partner, whereas we abstract from asymmetric information concerning …rms’ abilities, discussed by Gandal and Scotchmer (1994). In almost all studies which concern R&D the …rms are assumed to be risk-neutral. But we consider a model in which the …rms are risk averters. The implications of this study are founded strongly on the assumed risk- averseness of the …rms. We think that in real life the …rms are rather risk- averters more often than risk-neutral. This is also indicatied by the quite common tendency of the …rms to diversify a product portfolio and to locate production in di¤erent countries in order to lessen the risks associated with the functioning of the labour market and the development of labour costs. In the model considered, …rms contract at the …rst stage on the inten- sity of cooperation and at the second stage on the research e¤ort. A …rm’s utility is assumed to be separable in R&D e¤orts and investments so that there arise no advantages, owing to complementary actions, that could mo- tivate the cooperation of independent …rms. Neither does there exist any kind of duplication that creates an opportunity for costs savings through coordination. It turns out that, in the absence of monitoring, the …rms choose either high e¤ort and low intensity of cooperation or, alternatively, low e¤ort and maximal intensity of cooperation. When …rms are risk averse they can, ceteris paribus, increase their utility through cooperation, which diversi…es their R&D project portfolio. On the other hand, because the partners’ R&D e¤ort is unobservable, the …rms which maximize their pro…ts by equating marginal bene…ts and costs of R&D take into account only the results of their own R&D which results in moral hazard and low level of R&D. Maximal bene…t from a …rm’s own R&D is obtained during isolation. If a …rm is risk averse, there arises a trade-o¤ between increasing the utility by diversifying the portfolio of R&D projects through cooperation and maximizing the results from a …rm’s own R&D through isolation. If there are no complementarities in R&D research or in the product market, the latter motive easily dominates. We enlarge the model to also cover those cases in which a …rm can mon- itor a partner’s real R&D e¤ort through a signal. In the model considered an e¤ort can be either high or low. The signal tells more or less accurately about the nature of real e¤ort. If the signal is low, a …rm can ensure that the partner’s e¤ort has been low. Monitoring gives an opportunity to add to 3
  • 5. a contract a paragraph according to which the sharing contract can be can- celled, if a signal is low. It can be shown that monitoring, before becoming perfect, weakens moral hazard to an extent that risk averse and indepen- dent …rms choose high e¤ort and maximal intensity of cooperation even if they were indi¤erent between high e¤ort and low e¤ort during isolation. The risk-neutral …rms would then choose low e¤ort, given the intensity of coop- eration is above zero. Besides, their attitude toward cooperation would be indeterminate. In the basic model considered, each …rm has an independent research plan which is aimed at a discovery which is located in another area than a partner’s innovation. In cooperation the utilization of these independent innovations does not lead to duplication of R&D and, on the other hand, cooperation reduces risk through diversi…cation in an e¢cient way. We also consider a case which is more frequently discussed in the literature (see e.g. Stenbacka and Tombak, 1998). In this case …rms’ discoveries aim at an innovation in the same area. A …rm’s e¤ort is a perfect substitute of its partner’s e¤ort when both have success in their discoveries. In this case the tendency towards diversi…cation still motivates cooperation. But the duplication which occurs when both …rms are successful, tightens those conditions under which intensive cooperation is chosen. In the simpli…ed model of this study conduct in the product market is not modelled separately. It is, however, implicitly assumed that competition in the product market increases with the intensity of cooperation. I assume that the sum of the pro…ts of the two …rms considered does not change when the intensity of cooperation increases. This situation can arise, if the …rms are engaged in Cournot competition during cooperation, and if they have monopoly in isolation. It is still posible that a part of those pro…ts which are created by an innovation spills to other …rms even if there is no contracted cooperation. We also discuss a case in which the …rms di¤er from each other in their capability to utilize R&D results. When asymmetry in this sense increases, the conditions under which …rms cooperate tighten. The case in which potential cooperators are located in complementary industries is also discussed. For example, e.g. Katsoulacost and Ulp (1998) and many others have noticed that the incentives to cooperate con…rm re- markably, if the …rms are located in the complementary industries. In the model considered this result also holds good. The e¤ect of public subsidies is also analysed. Society’s welfare is no 4
  • 6. doubt highest when a …rm’s e¤ort is high and when they cooperate. This situation implies competition in the product market that bene…ts consumers, and higher R&D investments, which narrows the gap between public and private incentives to invest in R&D. At best, these subsidies can improve social welfare and raise e¤orts without weakening the motives to cooperate. If public subsidy is e¢cient it should be based on monitored R&D e¤orts. Alternatively, a subsidy can be based on observed success. Lately, Horvath (1999) has discussed the fact that debt-ridden …rms who cannot contract on sharing of information could be inclined to disclose some information voluntarily. This e¤ect is based on the fact that the …rms in debt are interested only in an upper section of their pro…t distribution, which may make a …rm’s marginal bene…ts from R&D respond positively to other …rms’ R&D. As a result of larger leverage the …rms would share some R&D knowl- edge. If this is true, public aid in the form of loans can promote information- sharing through a leverage e¤ect. 2 Basic model-symmetric …rms We consider a two …rm-model in which the …rms may share information orig- inating in individual R&D projects. The …rms decide about the amount of real R&D investments, called e¤orts, which a¤ects the success of the project. The …rms also agree on the intensity of co-operation. A decision on co- operation is by nature a strategic decision and this decision is made at the …rst stage of the game. An e¤ort decision is made on the second stage. The …rms considered are referred to by subscript A and B: Let v denote the inten- sity of co-operation. Then v is continuous and v 2 [0; 1]: Gross-bene…ts from …rm A0 s own innovation are normalized to be one. Firm B0 s gross bene…ts are also of size one. Let ®A denote that part of the shared pro…ts from A0 s innovation which is captured by …rm A: Respectively, °A denotes that part of the shared pro…ts from B0 s innovation which is captured by …rm A. It is still possible that under isolation, due to involuntary spillovers, part ±B A of gross pro…ts leaks to …rm B: Then ±A B denotes that part of B0 s pro…ts which involuntarily leaks to …rm A: Using these de…nitions, …rm A bene…ts from its own innovation by amount (1 ¡ v)(1 ¡ ±B A) and from B0 s innovation by the amount (1 ¡ v)±A B + v°A. Let pA denote the probability that A0 s project is succesful and, respectively, pB the probability for the succes in B0 s project. 5
  • 7. A0 s utility is then UA = pAU((1 ¡ v)(1 ¡ ±B A) + ®Av) + pBU((1 ¡ v)±A B + v°A) ¡ eA: The above (1 ¡ v) describes that part of a …rm’s own e¤orts which are not shared with a partner. If …rms do not cooperate, v = 0 and UA = pAU(1 ¡ ±B A) + pBU(±A B) ¡ eA: On the other hand, during fully intensive cooperation v = 1, and UA = pAU(®A) + pBU(°A) ¡ eA: From all viewpoints, involuntary leakages ±B A and ±A B are very small so that 1 ¡ ±B A is, in any case, much larger than ®A, and °A respectively much larger than ±A B. This lets us simplify the model by assuming that ±B A = 0 and ±A B = 0 without any loss of generality. It must be noticed that it is still possible that …rm A0 s and B0 s R&D results are imperfectly approbriable in the sense that part of it leaks to the rest of the industry. This spillover must not be taken explicitly into account, because cooperation between …rms A and B only is considered. It is supposed that if the …rms are competitors, then ®A + °B = 1 (1) ®B + °A = 1: This assumption is a simpli…cation as well. It implies that sharing R&D knowledge which, in the product market, increases competition does not change total pro…ts accrued from innovation. This is possible when a …rm obtains monopoly pro…ts while being alone, and, respectively, duopoly pro…ts ala Cournot competition during cooperation. Total pro…ts remain constant, especially if there are decreasing returns, or if, despite the similarity of inno- vation, …rm A0 s …nal product di¤ers a little from …rm B0 s …nal product. We assume that ®A ¸ °A; which says that each …rm is more capable of utilizing its own R&D results than R&D produced by another …rm. If these …rms are equally e¢cient in absorbing shared information, then ®A = ®B and °A = °B. But if …rm A is more e¢cient, then ®A > ®B and °A > °B. If the …rms do not compete with each other it is possible that ®A +°B > 1 and ®B + °A > 1. It is possible, for example, that …rm B is …rm A0 s client and 6
  • 8. that they stay at the di¤erent levels of the vertically integrated production chain. Then the information utilized by A does not, necessarily, hurt …rm B. For simplicity is assumed that an e¤ort is a dichotomous variable. Firm A is not able to observe or control …rm B0 s e¤ort, and vice versa. This yields a moral hazard problem. High e¤ort is denoted by eH and low e¤ort by eL (< eH ). The monetary cost of e¤ort is directly related to the e¤ort levels. In the considered setting, e¤ort only a¤ects the probability of success, not the amount of gross bene…ts. If …rm A0 s e¤orts are high, the probability of success is pH A . This probability exceeds pL A, which denotes the probability of success when A0 s e¤ort is low. It is assumed that failure gives zero gross bene…ts. In the basic model, considered in this section, the …rms A and B are similar in the sense that pH B = pH A , ®A = ®B and °A = °B.The …rm’s utility function U is assumed to be strictly concave and U0 strictly convex. Given these de…nitions A0 s utility is UH A = pH A U(1 ¡ v + ®Av) + pBU(v°A) ¡ eH A (2) when A exerts high e¤ort. In the case in which …rm A0 s e¤ort is low its utility is respectively UL A = pL AU(1 ¡ v + ®Av) + pBU(v°A) ¡ eL A: (3) From (2) and (3) it is seen that the utility function is separable in success probabilities and does not depend on a partner’s e¤ort costs. Thus, research e¤orts do not complement each other and there is no duplication in research activity which could give reasons for cooperation. Let Ui(eH i ; eH j ) describe …rm i0 s utility when both …rms exert high e¤ort. For (eH i ;eH j ) to be a Nash equilibrium in terms of chosen e¤ort it is required that Ui(eH i ; eH j ) > Ui(eL i ; eH j ); i = A; B. The respective Nash condition for (eL i ;eL j ) is Ui(eL i ; eL j ) > Ui(eH i ; eL j ); i = A; B. We assume that eH A = eH B and eL A = eL B and use notation eH for high e¤ort and eL for low e¤ort. From equations (2) and it (3) follows that there exists an equilibrium for high e¤orts, if UH A > UL A. This requires that (pH A ¡ pL A)U(1 ¡ v + ®Av) ¡ (eH A ¡ eL A) > 0: (4) Because of symmetry similar conditions, however, concern …rm B. If condition (4) is valid (eH A ; eH B ) is a Nash equilibrium for …rm A. If, however, the left-hand side of (4) were negative, (eL A; eL B) would be a Nash-equilibrium in the considered setting. 7
  • 9. Notice that condition (4) does not depend on B0 s conduct. In fact, the negative sign of the left hand side of (4) holds when it does not pay for A to deviate from low e¤ort equilibrium. Proposition 1 When cooperation becomes more intense, the incentives to set high e¤ort weaken. Proof. ®A < 1, wherefore in (4) (1 ¡ v)zA + ®AvzA decreases in v; which proves the proposition. When …rm A does not co-operate v = 0, and condition (4) can be written in the form (pH A ¡ pL A)U(1) ¡ (eH A ¡ eL A) > 0: (5) Because the left-hand side of (4) decreases in v, it is clear that the motive to exert e¤ort weakens when the intensity of co-operation increases. If …rm A were indi¤erent or almost indi¤erent between eH A and eL A in isolation, …rm A would select low e¤ort in any kind of co-operation with v > 0: Corollary 1 If a …rm in isolation is indi¤erent between low and high e¤ort, it always sets low e¤ort when there is any kind of cooperation. Proof. When (5) is binding condition (4) transforms into (pH A ¡ pL A)U(1 ¡ v + ®Av) > (pH A ¡ pL A)U(1); which is invalid because 1 ¡ v + ®Av < 1 when v > 0. This result shows that the moral hazard e¤ect is dominant. The opportu- nity to diversify the research project portfolio and decrease risk in this way is still too weak. If (pH A ¡pL A)U(1) is, however, much above eH A ¡eL A, it is possible that there exists such a cut-o¤ value for v, denoted by vc , that is located in the range (0; 1) and speci…es the level at which the agent is indi¤erent between being e¢cient and ine¢cient. If v < vc , the …rm exerts high e¤ort. If, on the other hand, v < vc , …rms set low e¤ort. A cut-o¤ value vc is determined by the equation (pH i ¡ pL i )U(1 ¡ v + ®iv) ¡ (eH i ¡ eL i ) = 0 (6) for i = A; B. We …rst consider an equilibrium at which …rms A and B are identical competitors. Then also pH A = pH B and zA = zB: 8
  • 10. If vc ¸ 1, both …rms always select low e¤ort. Under symmetry optimal behaviour is determined from @UL A @v = pL A(1 ¡ ®A)[¡U0 (1 ¡ v + ®Av) + U0 (v°A)]: (7) Due to U0 s concavity and the fact that in (7) 1 ¡ v + ®Av > v°A, expression (7) is positive. This means that the …rms set v = 1 when e¤ort is low. The intensity of cooperation is then the highest possible. Let us then consider the cases where 0 < vc < 1: Because a partner’s choice has no e¤ect on the …rm’s own choice and because of symmetry, only one of two Nash conditions can be valid. Firm A0 s optimization problem is to …nd out maxv UH A ´ ~UH A when v < vc max v UL A ´ ~UL A when v > vc : Finally …rm A chooses max( ~UH A ; ~UL A ): The choice at this stage also determines the chosen the intensity of co-operation. Because of symmetry, …rm B0 s choices are similar to …rm A0 s choices. This is also noticed by …rm A. Suppose that 0 < vc < 1. When v is on the range (vc ;1) the …rm maximizes UL A with respect to v, which gives v = 1: When 0 < v < vc both …rms exert high e¤ort and the agent maximizes UH A with respect to v on the range. The following is obtained @UH A @v = ¡pH A (1 ¡ ®A)U0 (1 ¡ v + ®Av) + pH B °AU0 (v°A): (8) Due to symmetry and the fact that 1 ¡ ®A = °A, @UH A @v above is positive if U0 (1 ¡ v + ®Av) < U0 (v°A). Because U is strictly concave and assumptions °A + ®A = 1 and °A · ®A imply that °A < 1 2 , this requirement is met. Thus @UH A @v > 0 in (8). In other words, intensity v is set as high as possible which is vc . Proposition 2 The higher the cut-o¤ value vc is, the more likely it is that high e¤ort is chosen. Proof. Firm A now knows that insofar as 0 · v < vc ; …rm B also chooses high e¤ort. The highest possible v which still guarantees high e¤ort is arbi- trarily close to vc . Therefore, ~UH A has, in the case considered, the expression ~UH A = pH A U(1 ¡ vc + ®Avc ) + pH B U(vc °A) ¡ eH A : 9
  • 11. When vc < v · 1, however, low e¤ort is chosen. In this case …rms will also make cooperation very intensive and set v = 1: If v = 1, …rm A knows that …rm B will set eB = eL B. Thus the following is obtained for ~UL A ~UL A = pL AU(®A) + pL BU(°A) ¡ eL A: The …rms choose low e¤ort and v = 1, if ~UL A above exceeds ~UH A . Using the fact that (pH A ¡ pL A)[U(1 ¡ vc + ®Avc )] ¡ (eH ¡ eL ) = 0; the following is obtained for inequality ~UH A > ~UL A: pL AU(1 ¡ vc + ®Avc ) + pH B U(vc °A) ¡ pL AU(®A) ¡ pL BU(°A) > 0: (9) Taking into account that pL A = pL B and pH A = pH B , the left-hand side of (9) is negative when vc = 0 and positive when vc = 1. Besides, the left-hand side of (9) increases in vc . This shows that when the cut-o¤ point vc is near 1, the intensity of cooperation is almost vc and e¤ort is set at a high level, whereas when the cut-o¤ point vc is remarkably lower than 1; …rms decide to co-operate very intensively so that v = 1. This, however, exacerbates the free-rider problem and leads to low e¤orts. As a conclusion to this section one can state that at the second stage, when an e¤ort decision is made, the moral hazard (or free-rider) problem creates pressure towards low e¤ort. The decision at the …rst stage, which concerns the intensity of co-operation, is strategic and takes into account the …rst stage decision. Being a risk averter a …rm faces a trade-o¤ between higher incentives to exert e¤ort and diversi…cation of its R&D asset portfolio. More intense co- operation promotes diversi…cation at the expense of e¤orts. These motives appear when the optimization problem is broken down into two stages. At the …rst stage, when the intensity of cooperation is decided, given the e¤orts (see conditions (8) and (7)), a risk averse …rm will intensify cooperation without limit. If the utility function U is linear which, means that …rms are risk- neutral, there arises no tendency at the …rst stage to intensify cooperation. In fact, risk-neutral …rms were indi¤erent about the value of v in their …rst stage decisions. Because a risk-neutral …rm is not interested in diversi…cation, the …nal equilibrium is also quite di¤erent from the case in which …rms are risk avert- ers. This is seen by assuming that U is linear in inequality (9). Condition 10
  • 12. (9) then transforms into the form pL A(1 ¡ vc + ®Avc ) + pH B vc °A ¡ pL A®A ¡ pL B°A > 0: Taking into account that °A = 1 ¡ ®A, the above inequality reduces to (pH A ¡ pL A)vc °A > 0; which is always true. This means that when …rms are risk-neutral, they prefer always a combination of high e¤ort and low intensity of cooperation to a combination of low e¤ort and high intensity of cooperation. Furthermore, when risk-neutral …rms decide to restrict the intensity of cooperation to value lower than vc they are indi¤erent between various values for v in the range [0; vc ): 3 Contracting on e¤orts in symmetry We suppose in this section that the …rms can observe signals which denote more or less credibly the type of e¤ort chosen. These signals are denoted by si; i = A;B: When …rm A observes that sB = sH B , the probability that B actually exerts high e¤ort denoted by p(eH B =sH B ) is q: Then p(eL B=sH B ) = 1¡q. Because the signal sH B is informative, q > 1 2 . If A observes sL B, A has got veri…able evidence that eB = eL B. Thus p(eL B=sL B) = 1 and p(eH B =sL B) = 0. It is also assumed that if A exerts high e¤ort, it can ensure that the signal is sH A : In other words, p(sH A =eH A ) = 1, from which it follows that p(sL A=eH A ) = 0. If …rm A sets eL A, the signal observed by B can, however, be either sL A or sH A . It is assumed that p(sL A=eL A) = k and that k > 1 2 . Then p(sH A =eL A) = 1 ¡ k. It is evident that set sH A is larger than set eL A, wherefore 1 ¡ k > 1 ¡ q (and k < q), but this property is unimportant as far as it concerns the implications of the model. Signal comes after e¤orts. Firms are assumed to be able to use signals in revising the contract concerning R&D co-operation. The time structure in the considered setting is the following: 1) Firms contract on the intensity of co-operation. 2) Firms set e¤ort levels. 3) Firms observe signals concerning e¤ort levels. 4) If signal sL i is observed …rm j (6= i) has su¢cient evidence to cancel co-operation, which 11
  • 13. results in v = 0: 5) The outcome of R&D projects is materialized as either success or failure. We also assume that signal sL B is valuable for …rm A when …rm A has set high e¤ort, and vice versa. This means that if A has observed sL B it pays for A to cancel the contract concerning cooperation, by which v becomes zero. This requires that pH A U(1) > pH A U(1 ¡ v + ®Av) + pL BU(v°A); (10) when v > 0. In the case considered e¤orts are set …rst. After that, signals are observed. So, when a …rm exerts e¤ort it just believes that its partner’s e¤ort is either high or low. If a …rm …nds that the state at which both set high e¤ort is an equilibrium and if this equilibrium dominates the state at which both …rms set low e¤ort, high e¤ort strategy is chosen. It should be noticed that the possibility to observe signals brings about a disadvantage for a …rm who deviates from high e¤ort equilibrium. Suppose …rm A believes that …rm B exerts high e¤ort. When A sets eA = eH A its utility is given in equation (2), whereas, if A sets eA = eL A, …rm B observes sL A with probability k, and cancels the contract concerning cooperation. In that case A0 s utility is UL A = (1 ¡ k)pL AU(1 ¡ v + ®Av) + kpL AU(1) (11) +(1 ¡ k)pH B U(v°A) ¡ eL A: Firm A does not deviate from high e¤ort equilibrium, if UH A from (2) is larger than UL A in (11). That says [pH A ¡ (1 ¡ k)pL A]U(1 ¡ v + ®Av) + kpH B U(v°A) ¡ kpL AU(1) (12) > eH A ¡ eL A Proposition 3 Suppose that a …rm in isolation is indi¤erent between high and low e¤ort. If monitoring is e¢cient enough, it is then possible that high e¤ort equilibrium exists although …rms cooperate. Proof. If (5) is binding then (12) is valid, if pH [U(1 ¡ v + ®Av) + kU(v°A) ¡ U(1)] (13) +(1 ¡ k)pL [U(1) ¡ U(1 ¡ v + ®Av) > 0: 12
  • 14. The above notation pH ´ pH A = pH B and pL ´ pL A = pL B is used. Due to the strict concavity of U, the …rst term in (13) is positive, if k is close enough to one and v > 0. The second term is positive in any case. The left hand side of (13) increases in k. When k = 0, the left-hand side is negative and when k = 1, the left-hand side is positive. From this it follows that there must be a cut-o¤ value kc for k which makes (13) binding. If k > kc , monitoring guarantees that high e¤ort equilibrium exists . When (5) is binding, vc is zero for a risk-neutral agent. This explains why the left hand side of (13) is negative when k < 1 and zero when k = 1 and v > 0. The risk-neutral agent would then exert low e¤ort if v > 0. This shows that monitoring combined with risk aversion strengthens the incentives to cooperate. High e¤ort equilibrium should be compared with low e¤ort equilibrium. It can be shown that when …rm A exerts low e¤ort it does not pay for it to cancel cooperation, if it observes sL B. Under symmetry this implies that in low e¤ort equilibrium a contract is not cancelled, even if a low signal is observed. The accuracy of monitoring has no e¤ect on the conditions which determine the existence of low e¤ort equilibrium. In the setting considered, the existence of low e¤ort equilibrium thus requires that (pH A ¡ pL A)U(1 ¡ v + ®Av) ¡ (eH A ¡ eL A) < 0: (14) If (14) is valid, deviation from the low e¤ort state is not pro…table, if the partner has also set low e¤ort. In fact, condition (14) is the negation of condition (4). So the validity of (14) implies that high e¤ort equilibrium does not exist in the absence of monitoring. Condition (14) can, however, be valid simultaneously with conditions (5) and (13). Corollary 2 If condition (12) is in force, with any positive v, then high e¤ort equilibrium dominates low e¤ort equilibrium (if it exists) Proof. In order to derive ~UH A , UH A = pH A U(1 ¡ v + ®Av) + pH B U(v°A) ¡ eH A is maximized with respect to v. This yields v = 1. So, ~UH A has the expression ~UH A = pH A U(®A) + pH B U(°A) ¡ eH A : (15) Would …rms, however, choose low e¤ort, which is also an equilibrium insofar as condition (14) is in force. Suppose that (eL A; eL B) is an equilibrium 13
  • 15. as well. In this equilibrium …rms also cooperate with maximal intensity, that is v = 1: A’s utility in this low e¤ort equilibrium is ~UL A = pL AU(®A) + pL BU(°A) ¡ eL A: Taking into account that pH A = pH B and pL A = pL B , an inequality ~UH A > ~UL A reduces into the form (pH A ¡ pL A)[U(®A) + U(°A)] ¡ (eH A ¡ eL A) > 0: But the above U(®A) + U(°A) > U(1), because U is strictly concave and ®A = 1 ¡ °A. This, together with the assumed validity of condition (5), ensures that the above inequality is in force. This proves that portfolio diversi…cation can play a major role in R&D cooperation. It must be noticed that with perfect monitoring k = 1. Then there exists high e¤ort equilibrium with v = 1 and …rms prefer high e¤ort equilibrium to low e¤ort equilibrium. This case corresponds to a situation, discussed among others by Kamien et al. (1992), where the …rms also decide to share invest- ments. To be able to contract on R&D investments (e¤orts) they must be observed veri…ably by both parties. High intensity of cooperation combined with high e¤orts is not a new result. From various approaches many authors, Reinganum (1981), Motta (1992) and Vonotars (1994) have come to the con- clusion that cooperative investments are stimulated by larger spillovers. The strengthening of ”spillovers” is equivalent to the intensifying of cooperation in our model. It must, however, be stressed that in our model this e¤ect arises exclusively due to the risk aversion of the …rms. Signals and e¤orts are simultaneous We next consider the time struc- ture in which a …rm observes the signal of its partner’s e¤ort at the same time as it sets its own e¤ort. High e¤ort always leads to signal sH i , which does not, however, tell that ei = eH i with certainty. The behaviour considered now is qualitatively di¤erent from the behaviour discussed in the previous section. Now the reactions through e¤orts are based on real observations. In previous sections they were based rather on beliefs concerning the partner’s behaviour. Let us consider the conditions under which (eH A ; eH B ) is a Nash equilibrium under quick monitoring. Suppose …rm B has set eB = eH B . Then …rm A 14
  • 16. observes sH B . When A sets eA = eH A its utility is UH A = pH A U(1 ¡ v + ®Av) + (qpH B + (1 ¡ q)pL B)U(v°A) ¡ eH A : (16) In (16) the signal sH B does not give 100 percent evidence that eB = eH B . With probability (1 ¡ q) B0 s e¤ort is low, whereas, if eA = eL A and sB = sH B , the following is obtained UL A = (1 ¡ k)pL AU(1 ¡ v + ®Av) + kpL AU(1) (17) +(1 ¡ k)(qpH B + (1 ¡ q)pL B)U(vc °A) ¡ eL A: In (17) the probability that …rm B cancels the contract because of A0 s low e¤ort is k: If the contract is denounced, …rm A gets no bene…t from B0 s R&D. It should also be noticed that when A exerts high e¤ort, B cannot get a low signal (sL A) and a reason to give notice to quit. If UH A in (16) is larger than UL A in (17) it is not worth deviating from the high e¤ort strategy given v. The condition for UH A > UL A in the case considered is (pH A ¡ pL A)U(1 ¡ v + ®Av) + kpL AU(1 ¡ v + ®Av) (18) ¡kpL AU(1) + k(qpH B + (1 ¡ q)pL B)U(vc °A) > eH A ¡ eL A: Comparing condition (18) with condition (12) shows that simultaneous and incomplete monitoring can, in fact, weaken those conditions under which high e¤ort equilibrium is chosen. If in (18) monitoring is accurate so that kq is close enough to one, all the implications of the previous section which concerned behaviour during monitoring hold. So, also during coincidence of e¤ort setting and its observation, risk aversion promotes cooperation. This conclusion is reinforced by the following proposition. Proposition 4 Suppose that a …rm chooses high e¤ort in isolation so that (5) is valid. Then the …rms in cooperation choose high e¤ort at least, if U(1 ¡ v + ®iv) + kqU(v°i) ¡ U(1) ¸ 0: (19) Proof. The left-hand side of (18) can be written in the form (pH A ¡pL A)U(1)+ B; where B = pH A [¡U(1) + U(1 ¡ v + ®Av) + kqU(v°A) +pL A[U(1) ¡ U(1 ¡ v + ®Av) + kU(1 ¡ v + ®Av) ¡kU(1) + k(1 ¡ q)U(v°A)]: 15
  • 17. Above, strict concavity of U yields kU(1¡v+®Av)¡kU(1)+k(1¡q)U(v°A) > kqU(v°A) in symmetry. This guarantees that B > 0 from which it follows that (pH A ¡ pL A)U(1) + B > (pH A ¡ pL A)U(1): . Proposition (4) shows that in the trade-o¤ between free rider extrenality which tends to lower e¤ort, and the diversi…cation motive which tends to enforce e¤ort incentives, the latter motive becomes dominant when a …rm tightens control over a partner’s e¤orts. 3.1 Asymmetric …rms Asymmetry in absorptive capacity Asymmetry can exist in several ways. Firstly, another …rm can be more e¤ective than its partner in exploiting R&D produced by itself or by a partner. If …rm A is more e¤ective then ®A > ®B and °A > °B under restrictions ®A + °B = 1 and ®B + °A = 1. In this case it is possible that …rm A can exploit …rm B0 s R&D results even more e¤ectively than …rm B itself. This says that ®A > °B, although ®A > °A and ®B > °B. Secondly, the e¢ciency di¤erences can refer to the ability to produce innovations. If …rm A is more e¢cient than …rm B in this respect, pH A > pH B which implies that pL B > pL A. Let us …rst consider a case in which ®A > ®B and °A > °B. Still, ®A + °B = 1 and ®B + °A = 1, ®A > °A and ®B > °B. It is assumed that °A + °B = C when C is constant. Because ®A > ®B and °A > °B, it follows from equation (5) that vc A > vc B when vc i denotes …rm i0 s (i = A; B) cut-o¤ value. If 0 < v < vc B, eA = eH A and eB = eH B . If vc B < v < vc A, eA = eH A and eB = eL B and …nally, if vc A < v < 1, eA = eL A and eB = eL B. By the de…nition of vc B, when setting high e¤ort …rm B always prefers vc B to vc A. If the intensity of co-operation becomes larger than vc B …rm B starts to set low e¤ort and then it prefers maximal intensity, as …rm A also does. In the setting considered vc A is not an equilibrium level for v: There seem to be two alternatives for …rms A and B: Either v = vc B, which de…nes an equilibrium (eH A ; eH B ): The other alternative is v = 1, which de…nes low e¤ort equilibrium (eL A; eL B): Let us consider how these equilibria react when ®A and °A increase at the expense of parameters ®B and °B. 16
  • 18. When v = vc B, it obtained for UA and UB UH A = pH A U(1 ¡ vc B + ®Avc B) + pH B U(vc B°A) ¡ eH A : UH B = pH B U(1 ¡ vc B + ®Bvc B) + pH A U(vc B°B) ¡ eH B : Taking into account that °B = C ¡°A, ®B = 1¡°A and ®A = 1¡C +°A, the equations above can also be written as UH A = pH A U(1 ¡ vc BC + vc B°A) + pH B U(vc B°A) ¡ eH A : (20) and UH B = pH B U(1 ¡ vc B°A) + pH A U(vc B(C ¡ °A)) ¡ eH B : (21) Respectively, when v = 1, the following is obtained: UL A = pL AU(1 ¡ C + °A) + pL BU(°A) ¡ eL A (22) and UL B = pL BU(1 ¡ °A) + pL AU(C ¡ °A) ¡ eL B: (23) From (6) we obtain the equation (pH B ¡ pL B)U(1 ¡ vc B°A) ¡ (eH B ¡ eL B) = 0; which de…nes vc B as a function of °A. Then @vc B @°A = ¡ vc B °A . Using this result it is possible to examine how the left-hand side of equations (20) - (23) change when °A increases and with it ®A also at the expense of °B and ®B. Di¤erentiating equations (20) - (23) with respect to °A yields @UH A @°A = pH A U0 (1 ¡ vc B°B) °A + °B °A vc B > 0: @UH B @°A = ¡pH A U0 (vc B°B) °A + °B °A vc B < 0: @UL A @°A = pL AU0 (1 ¡ °B) + pL BU0 (°A) > 0 @UL B @°A = ¡pL BU0 (1 ¡ °A) ¡ pL AU0 (°B) < 0: The results above show that the increase of °A which is connected with an increase in ®A and decrease in ®B and °B improves …rm A0 s situation but 17
  • 19. deteriorates …rm B0 s situation. In high e¤ort equilibrium the increase in °A has a direct and also an indirect e¤ect through a decrease in vc B. The direct e¤ect, however, dominates, which explains why …rm A0 s utility increases and …rm B0 s utility decreases. In low e¤ort equilibrium, v is …xed to be one, wherefore there is only a direct e¤ect from °A to utilities UL A and UL B . It is thus clearly in the …rm’s interests to …nd partners which are relatively ine¢cient in utilizing information that has arisen in R&D projects. But other …rms will not cooperate with …rms which are more e¢cient in this respect. It is evident that in the market it is easiest for similar …rms rather than for dissimilar …rms to conclude an agreement concerning cooperation. On the whole, one would expect that the average type of …rms …nd partners more easily than exceptionally e¢cient or ine¢cient …rms. Firms could also trade on dissimilarity. But this requires a more exact contract. It would no longer be su¢cient to decide only about the intensity of cooperation. The relative di¤erences in absortive capacity should also be speci…ed. Naturally, transaction costs related to contract would rise. The required complexity of the contract would also prevent cooperation between dissimilar partners. Let us …nally consider the case in which an e¢cient …rm, however, co- operates with an ine¢cient …rm. Taking into account the assumed restric- tions concerning model parameters, the condition which says when …rm A prefers high e¤ort and low intensity (v = vc B) compared with low e¤ort and high intensity of co-operation is pH A U(1 ¡ vc BC + vc B°A) + pH B U(vc B°A) (24) ¡pL AU(1 ¡ C + °A) ¡ pL BU(°A) ¡ (eH A ¡ eL A) > 0: For …rm B the respective condition is of the form pH B U(1 ¡ vc B°A) + pH A U(vc BC ¡ vc B°A) (25) ¡pL BU(1 ¡ °A) ¡ pL AU(C ¡ °A) ¡ (eH B ¡ eL B) > 0: Let LH1 denote the left-hand side of (24) and LH2 the left-hand side of (25). Then @LH1 @°A = pH A U0 (zA(1 ¡ vc B°B)) °A + °B °A vc BzA 18
  • 20. ¡pL AU0 (®AzA) ¡ pL BU0 (°AzB): When asymmetry becomes deep so that vc B is very small, the partial derivative @LH1 @°A easily becomes negative. This shows that an increase in ®A and °A make low level of e¤ort and very intensive co-operation more tempting for …rm A. From equation (25) it is obtained @LH2 @°A = pH A U0 (vc B°B)) °A + °B °A vc B +pL BU0 (®B) + pL AU0 (°B): Above the sign of @LH2 @°A is ambiguous even when vc B is very small. When U(x) is, for example, of the form ¡e¡x @LH2 @°A is easily positive when vc B is small. If LH2 is positive …rm B prefers very high e¤orts combined with low level co-operation. Asymmetry in ability to succeed in R&D projects Assume that …rm A is more successful in R&D activity than …rm B. Then pH A > pH B and pL A > pL B. We assume for simplicity that pH A ¡ pL A = pH B ¡pL B. In the situation considered the intensity of co-operation in high e¤ort equilibrium is the same as in the symmetric case. But …rm B bene…ts from its more e¤ective part- ner, whereas …rm A loses, owing to …rm B0 s ine¢ciency. Again, one would imagine that, in the market of many …rms, it is easier for similar …rms to contract with each other than for dissimilar …rms. 4 Vertically integrated …rm structure So far we have considered competing …rms only. Then it is reasonable to assume that ®A + °B = 1: Suppose …rm A is either …rm B0 s client or de- liverer. Firms A and B do not compete with each other. But locating in complementary industries may lower their ability to utilize each other’s R&D results. We next assume that one is located in downstream industry and an- other in upstream industry. A …rm does not lose to its partner any part of its pro…ts which are generated by its own R&D. Partners, however, can get ben- e…t from each other’s R&D. Because partners are not located exactly in the same industry they cannot, however, get full bene…t from a partner’s R&D. According to these assumptions ®i = 1 and 0 < °i < 1 when i; j = A; B and i 6= j. 19
  • 21. Suppose that during isolation …rms prefer high e¤ort to low e¤ort, which implies that (5) is valid. But inserting ®A = 1 into condition (4) also produces condition (5), which shows that in vertically integrated structure …rms choose high e¤ort with all values for the intensity of cooperation. Maximizing …rm A0 s utility UH A = pH A U(1) + pH B U(v°A) ¡ eH A with respect to v would yield v = 1: That is, cooperation with maximal intensity is preferred. It is obvious that high e¤ort equilibrium now dominates low e¤ort equilibrium (with v = 1): Taking into account the fact that pH A = pH B and pL A = pL B, condition UH A > UL A has the expression (pH A ¡ pL A)U(1) + (pH A ¡ pL A)U(°A) ¡ (eH A ¡ eL A) > 0: (26) This inequality proves that cooperation of non-competitiors combined with risk-averseness can lead to high e¤ort and fully intensive cooperation even under circumstances where high e¤ort under isolation is not chosen; compare condition (5) with condition (26). Cooperation bene…ts the …rms in the setting considered owing to two reasons. First, it makes it possible to utilize the complementary nature of R&D results and, secondly, cooperation leads to portfolio diversi…cation, which generates cost-savings. If …rms were be risk-neutral, the latter bene…t would vanish. This result is much in ac- cordance with the earlier results obtained by Steurs (1995), who states that inter-industry spillovers stimulate R&D investments, because the competitive e¤ects are lacking. 5 Two discoveries and one product In the literature the cooperation is most often seen as a case where the part- ners aim at an innovation in the same brand (see e.g. Stenbacka and Tombak, 1998). We next discuss the case in which two …rms make discoveries indepen- dently of each other, but both discoveries aim at the same innovation. This innovation creates very similar products, wherefore the model considered is called a one-product model as distinct from the two-product model discussed in previous sections. Because there only is one product in the market, a …rm falls into competition in the market of a new product, if both …rms have success in R&D research. Competition arises even if …rms do not cooperate in R&D. If only one …rm is successful, the fortunate …rm grabs all the pro…ts 20
  • 22. generated by the innovation. In cooperation the pro…ts generated by innova- tion are shared. We again make a simplifying assumption according to which the total pro…ts are of equal size in the monopoly and in the duopoly. In the one-product case there is duplication of e¤orts when both …rms have success. In that respect the one-product case di¤ers from the two- product case. In the one-product model a …rm bene…ts from its partner’s higher e¤ort only if cooperation is intensive enough. Furthermore, in the one-product case the rise of cooperation intensity does not enlarge pro…ts so powerfully as in the two-product case. The bene…ts of cooperation do not appear to be as large in the one-product case as in the two-product case. In the one-product setting considered there are four states de…ned by probabilities of success. If …rm A succeeds and B fails, with the probability PA(1 ¡ PB), …rm A is assumed to get pro…ts of the amount (1 ¡ v) + ®Av. A parameter ®A describes A0 s ability to capture the total pro…ts when pro…ts are shared. If …rm A is more e¤ective than its partner in the product market, ®A > 1 2 . In this section we consider a symmetric case only. Wherefore it is assumed that ®A = 1 2 . We still assume that …rms can share an innovation with various intensities. Firm A0 s pro…ts in the setting considered are UA = pA(1¡pB)U(1¡v+®Av)+pB(1¡pA)U(v®A)+pApBU(®A)¡eA: (27) If both …rms succeed, …rm A gets ®A(1¡v)+®Av = ®A. It is still assumed that e¤orts can be either high or low. When high e¤ort is exerted pA = pH A . If e¤ort is low, pA = pL A. It is remarkable that in the one-product model considered, the …rms also prefer, due to risk aversion, more intensive cooperation to slight cooperation, given the e¤orts. This is proved by di¤erentiating UA from (27) with respect to v which results in @UA @v > 0: The conditions which say whether it pays …rm A to deviate from high e¤ort state (eH A ; eH B ) is of the form (1 ¡ pH B )(pH A ¡ pL A)U(1 ¡ v + ®A) ¡ pH B (pH A ¡ pL A)U(v®A) (28) +pH B (pH A ¡ pL A)U(®A) ¡ eH A + eL A > 0: Condition (28) describes the same phenomen as condition (4) in the two- product model of section(2). Also, condition (28) is invalidated if cooperation 21
  • 23. is intensive enough. Therefore, it is obvious a cut-o¤ value vc for v exists such as in the two-product model too. Suppose that …rms can observe each other’s e¤ort. This corresponds to the case in which the signal discussed in section (3) is fully informative so that probabilities k = q = 1: In this case there is no moral hazard problem and the …rms can also contract on e¤orts. Firms can set severe punishments which eliminate all the deviations from contracted e¤ort level. Firms then choose between low and high e¤orts. Because of risk averseness the intensity of co-operation is always set on the maximal level, which is one. Let ~UH A denote now A0 s utility when eA = eH A ; v = 1 and eB = eH B : ~UL A still denotes A0 s utility UA when eA = eL A; v = 1 and eB = eL B. In the case considered ~UH A > ~UL A if (¡pL A ¡ pL B + pH A + pH B + pL ApL B ¡ pH A pH B )U(®A) ¡ (eH A ¡ eL A) > 0: (29) Due to symmetry pH A = pH B and pL A = pL B. From inequality (29) it is seen that the larger pH A and pH B , and smaller pL A and pL B increase the left-hand side of (29) and thus ease those conditions under which high e¤ort is chosen. The main result of this section concerns the di¤erences between one- product and two-product cases when e¤orts are perfectly monitored. In the two-product model of section (3) a possibility for co-operation eases those conditions under which high e¤ort is chosen. So a high e¤ort equilibrium is always attained when e¤orts are observable (so that k = q = 1) and when a …rm is indi¤erent between high e¤ort and low e¤ort under isolation(v = 0). This result does not hold in the one-product case. Proposition 5 In a one-product case the …rms do not necessarily choose high e¤ort and intense cooperation although the partner’s e¤orts are observed and although they would be indi¤erent between high and low e¤ort under isolation. Proof. We prove that condition (28) with v = 0 does not necessarily imply condition (29). If this implication holds it would require that (2U(®A) ¡ U(1))(pH ¡ pL ¡ (pH )2 + pH pL ) ¡ U(®A)pL (pH ¡ pL ) > 0: The above condition is not necessarily valid. If U is linear it is certainly invalid. The validity of the above inequality also presupposes besides the strict concavity of U that pL is very small in relation to pH . 22
  • 24. It is remarkable that in the one-product model considered it is possible that a …rm would not deviate from high e¤ort equilibrium under isolation, but would not choose a high-e¤ort contract under intense co-operation when e¤orts are observable. Why is the elimination of morald hazard in the case concerned not su¢cient for high e¤ort? Firstly, low intensity con…rms condi- tion (28) but higher intensity does not necessarily strengthen condition (29). In other words, in the one-product model the more intensive co-operation does not increase gross pro…ts more in the high-e¤ort state than in the low- e¤ort state. In fact, the marginal bene…ts from a …rm’s own higher e¤orts are strongly reduced by a partner’s higher e¤orts. One can say that in the one-product model the bene…ts of diversi…cation are necessarily largest when both …rms’ e¤orts are high. In any case, however, the …rms choose maximal intensity of cooperation, which is v = 1, if e¤orts are observable and therefore contractable also. If …rms cannot agree on high e¤orts, then lower e¤orts are chosen. 6 Public subsidy Consider a public entity which subsidizes a …rm’s R&D. If real, cost-generating R&D e¤orts cannot be observed, there is a moral hazard problem which makes public subsidy ine¢cient in raising …rms’ R&D intensity. We assume that a public entity which make subsidizing decisions can monitor a …rm’s e¤ort with the same accuracy as a …rm’s partner. Let u be the subsidy rate. Then total subsidy is ueH , if e¤ort eH is observed. Because e¤orts are not, however, observed directly, a subsidy decision must be based an observed signals. It is assumed that, if a high signal is observed then the total subsidy is of the amount ueH , whereas, if the signal is low, the subsidy is ueL . From this it follows that if …rm A sets eA = eH A , sH A is observed by a public sponsor. Then the subsidy is ueH . When eA = eL A sL A is observed with probability k, and sH A with probability 1 ¡ k. In that case the subsidy is kueL + (1 ¡ k)ueH . Because of subsidies cost di¤erence eH A ¡ eL A are replaced by (1 ¡ ku)(eH A ¡ eL A). Through monitoring the costs from high e¤ort can thus be lowered in relation to low e¤orts, although the gross bene…ts from high e¤ort stay untouched. The subsidies can, for example, make an isolated …rm, with v = 0, to exert high e¤ort when condition (5) is invalid so that incentives without subsidies are not strong enough for this. Subsidies can also make condition 23
  • 25. (12) valid with all v. An analysis in previous sections showed that if there exists high e¤ort equilibrium with 0 < v · 1; the intensity of co-operation is set on maximal level. So, at the best, subsidies can encourage …rms to set high e¤orts and, in addition, to cooperate intensively so that the positive externality of cooperation is internalized. In the model considered subsidies with monitoring have no real e¤ect, if the incentives for high e¤orts and intensive cooperation are strong enough without subsidies. 7 Conclusions We consider the R&D cooperation decisions of the risk-averse …rms. The …rms are assumed to agree in advance to share R&D results but not R&D costs. In the basic case the real R&D expenditure is unobservable, which creates a moral hazard problem. The …rms contract, at the …rst stage, on the intensity of cooperation and, at the second stage, on the research e¤ort. Moral hazard weakens the …rms’ motives to invest in R&D during cooper- ation. But diversifying the portfolio of R&D projects through cooperation increases …rms’ utility. It turns out that in the absence of monitoring the …rms choose either high e¤ort and low intensity of cooperation or alterna- tively low e¤ort and maximal intensity of cooperation. We also allow …rms to monitor a signal which tells more or less perfectly the partner’s real e¤orts in R&D. If this signal is accurate enough, moral hazard can weaken to an extent that risk averse and independent …rms choose high e¤ort and maximal intensity of cooperation, even if they were indi¤erent between high e¤ort and low e¤ort in isolation. It is also shown that asymmetries between the …rms reduce the scope for cooperative agreements. A …rm is reluctant to cooperate with a …rm which is more e¤ective than itself in utilizing new knowledge. Respectively, other …rms would like to cooperate with a …rm which is very e¤ective in creating new knowledge. But such a …rm would require that its partner would also meet the same e¢ciency standards in this respect. The …rms which are located in complementary industries are not nec- essarily technically so close with each other, which reduces the bene…ts of cooperation. But because a …rm in another stage of a vertically integrated industry - as a client or a providor - does not compete with a partner, the moral hazard problem is more or less removed. This strengthens the incen- tives to cooperate in the setting considered. This phenomen is also noticed 24
  • 26. by, for example, Katsoulacost and Ulp (1998). In the case in which two …rms make discoveries independently of each other but both discoveries aim at the same innovation, there arises a dupli- cation of e¤orts when both …rms are successful. This reduces the bene…ts of cooperation, so that the conditions under which both …rms choose high R&D e¤orts and fully intense cooperation are much stricter than in the case where the innovations aim at di¤erent products. Due to risk-averseness, the …rms can also bene…t from cooperation in this case. The diversi…ed portfolio of R&D projects can, at its best, make the …rms invest heavily in R&D and cooperate closely with each other. Public authorities can make the admitted subsidy or loan dependent on the …rms’ success or, alternatively, on some evidence of the R&D exerterd. In this way public authorities can remarkably decrease moral hazard, which for its part promotes cooperation between independent …rms at the high level of R&D. 8 Literature D’Aspremont, C. and A. Jacquemin (1988), ”Cooperative and noncoopera- tive R&D in duopoly with spillovers”, The American Economic Review, 78, 1133-1137. De Bondt, R. , 1996, ”Spillovers and innovative activities”, International Journal of Industrial Organization, 15, 1-28. Gandal, N. and S. Scotchmer, 1993, ” Coordinating research through research joint ventures”, Journal of Public Economics, 51, 173-193. Horvath, R., 1999, ”Information sharing in research joint ventures and the limited liability e¤ect”, draft presented at ESEM 1999 (Santiago Com- postela). Kamien, M., Muller, E. and I. Zang, 1992, ”Research joint ventures and R&D cartels”, The American Economic Review, 82, 1293-1306. Katsoulacost, Y. and D. Ulph, 1998, ”Endogenous spillovers and the per- formance of research joint ventures”, The Journal of Industrial Economics, XLVI, 333- 357. Katz., M. and J. Ordover, 1990, ”R&D cooperation and competition”, Brookings Papers: Microeconomics, Microeconomics, 137-203. Motta, M., 1992, ”Cooperative R&D and vertical product di¤erentia- tion”, International Journal of Industrial Organization, 10, 643-661. 25
  • 27. Perez-Castrillo J. and J. Sandonis, 1996, ”Disclosure of know-how in re- search joint ventures”, International Journal of Industrial Organization, 15, 51-75. Reinganum, J., 1981, ”Dynamic games of innovation”, Journal of Eco- nomic Theory, 25, 21-41. Stenbacka, R. and M. Tombak, 1998, ”technology policy and the organi- zation of R&D”, Journal of Economic Behavior & Organization, 36, 503-520. Stuers, G., 1995, ”Inter-industry R&D spillovers: what di¤erence do they make?”, International Journal of Industrial Organization, 13, 249-276. Veugelers, R. and K. Kesteloot, 1994, ” On the design of stable joint ventures”, European Economic review, 38, 1799-1815. Vonortas, N.S.,1994, ”Inter-…rm cooperation in imperfectly appropriable research”, International Journal of Industrial organization”,12, 413-435. 26

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