R&D incentives to cooperate and invest with licensing

ABSTRACT

In this paper, we evaluate the private incentive to cooperate comparing three different scenarios (R&D cooperation, and R&D competition with and without licensing), in terms of expected profits, industry probability of innovation, and expected welfare. We show that the feasibility of licensing increases the appropriability of returns and may stimulate R&D investment; moreover, licensing an innovation may lead to the highest social welfare. However, some conflict may emerge between the public and private incentive to license the innovation, and between different policy targets.

KEYWORDS:

• Innovation
• licensing
• R&D cooperation
• R&D expenditure

JEL CLASSIFICATION:

• D45
• 032
• L13
• L50

Acknowledgments

The authors wish to acknowledge the editor and three anonymous referees for their contribution. The authors also like to show their gratitude to F. De Stefano for the figures. Any errors are our own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In recent years, programs such as ESPRIT, IST, and EUREKA have been implemented in Europe.

2 See Czarnitzki, Ebersberger, and Fier (2007); Pippel (2014); Pippel and Seefeld (2016).

3 See Capuano and Grassi (2019a).

4 Licensing involves a contractual agreement between a firm (the licensor) which makes available a legally protected asset to another firm (the licensee) in return for royalties, license fees, and other forms of compensation.

5 For a recent contribution see Cabon-Dhersin and Gibert (2019).

6 For an extensive survey on the state of the art in R&D cooperation, patenting, and licensing, see Bhattacharya et al. (2014).

7 A similar approach is followed in Choi (1993); Martin (2002). The latter explicitly compares input and output spillovers.

8 Literature surveys are provided in Zúñiga-Vicente et al. (2014); Castellacci and Lie (2015); Becker (2015). Cantabene and Grassi (2019) provide a summary of some of the results of R&D cooperation.

9 See Czarnitzki, Ebersberger, and Fier (2007); Pippel (2014); Pippel and Seefeld (2016).

10 On this topic, see the seminal contributions by Hinloopen (1997, 2000).

11 Other works include (Choi 1993; Leahy and Neary 1997; Goyal and Moraga-Gonzales 2001); and more recently, Cabon-Dhersin and Gibert (2019).

12 See, inter alia, Kamien and Tauman (1986); Gallini and Wright (1990); San Martín and Saracho (2010, 2015); Duchene (2015); Colombo and Filippini (2015, 2016).

13 See, inter alia, Fauli-Oller and Sandonis (2002); Chowdhury (2005); Sen and Tauman (2007); Cabon-Dhersin and Lahmandi-Ayed (2011); Bertran and Turner (2017); Capuano and Grassi (2019b).

14 See inter alia (Gallini and Winter 1985; Mukherjee and Mukherjee 2013; Colombo 2019; Capuano and Grassi 2020).

15 See Colombo and Filippini (2014).

16 See San Martín and Saracho (2010).

17 See, inter alia, Choi (2001); Pastor and Sandonis (2002).

18 See Martin (2002).

19 We do not consider the case of cooperation where firms avoid duplication of fixed costs by investing in a single research line since in equilibrium, this case is always dominated. Calculations are available upon request.

20 For example, in 2012 BMW and Toyota coordinated their R&D efforts to develop lithium-ion batteries. This provides an interesting case of two long-term rivals joining their efforts, not only to develop a cost savings technology but also to jointly move forward the frontier of the industry itself.

21 Substituting Equation (2(2) ${\rho }_i^N={\rho }_j^N=\frac{\text{β}{c}^2-4c+2\text{β}c}{2\text{β}c-5\text{β}{c}^2+4c^2+9}.$(2) ) in Equation (4(4) $\begin{array}{rll}{W}^N& =({\left({\rho }^N\right)}^2+2{\rho }^N(1-{\rho }^N)\text{β})(2\tilde{D}+\tilde{S})+{(1-{\rho }^N)}^2(2D_0+S_0)& \\ & +2{\rho }^N(1-{\rho }^N)(1-\text{β})(\underset{\_}{D}+\overline{D}+\hat{S})-2\frac{{\left({\rho }_i^N\right)}^2}{2}.\end{array}$(4) ) we obtain the level of expected welfare achieved in the non-cooperative scenario, which value is reported in Table A2 in the Appendix.

22 In this scenario, ${\rho }^{N\ast }=\frac{3c^2-76c-68\text{β}c-50\text{β}+2c^3-c^4+69\text{β}{c}^2-2\text{β}{c}^3+\text{β}{c}^4+50}{4c^3-8c-136\text{β}c-66c^2-100\text{β}-2c^4+138\text{β}{c}^2-4\text{β}{c}^3+2\text{β}{c}^4-62}.$ Calculations are available upon request.

23 Indeed, in this scenario, firms invest in two independent R&D lines. If at least one of them innovates (i.e. innovation occurs with a probability equal to ${\rho }_i+{\rho }_j-{\rho }_i\cdot {\rho }_j=1-(1-{\rho }_i{)}^2$) then both obtain the new technology, since in the cooperative equilibrium ${\rho }_j={\rho }_i$.

24 Substituting Equation (6(6) ${\rho }_i^X={\rho }_j^X=\frac{4c-2c^2}{9-2c^2+4c}.$(6) ) in Equation (8(8) $W^X=(1-(1-{\rho }^X{)}^2)(2\tilde{D}+\tilde{S})+(1-{\rho }^X{)}^2(2D_0+S_0)-2\frac{{\left({\rho }^X\right)}^2}{2}$(8) ) we obtain the level of expected welfare achieved in the cooperative scenario, which value is reported in Table A2 in the Appendix.

25 In this scenario, ${\rho }^{X\ast }=\frac{4c(2-c)}{9+8c-4c^2}.$ Calculations are available upon request.

26 We exclude negative fixed fees, as in Wang (1998).

27 Substituting Equation (14(14) ${\rho }_i^L={\rho }_j^L=\frac{7c+5\text{β}{c}^2-5\text{β}c-6c^2}{3c+\text{β}{c}^2-\text{β}c-2c^2+9}.$(14) ) in Equation (15(15) $\begin{array}{rll}{W}^L& =({\left({\rho }^L\right)}^2+2{\rho }^L(1-{\rho }^L)\text{β})(2\tilde{D}+\tilde{S})+{(1-{\rho }^L)}^2(2D_0+S_0)& \\ & +2{\rho }^L(1-{\rho }^L)(1-\text{β})(\underset{\_}{D}+{\overline{D}}^L+\hat{S})-2\frac{{\left({\rho }_i^L\right)}^2}{2}.\end{array}$(15) ) we obtain the level of expected welfare achieved in the non-cooperative scenario, which value is reported in Table A2 in the Appendix.

28 In this scenario, ${\rho }^{L\ast }=\frac{14c+\text{β}{c}^2+2\text{β}c-9c^2}{18+2\text{β}{c}^2+4\text{β}c-10c^2}$. Calculations are available upon request.

29 There exists a threshold value ${\text{β}}_2$ such that: $\mathrm{\forall }\text{β}\le {\text{β}}_2,$ $W^N\le W^L;$ $\mathrm{\forall }\text{β}>{\text{β}}_2,$ $W^N>W^L$.

30 This variable was computed as the probability that at least one firm innovates.

31 The tables in the Appendix contain some rather long-winded equations. They were arrived at using the mathematical package Mathematica 10.1.

32 To accept the contract, the licensee's profit from licensing must be no lower than its profit from imitation. Increasing β, the profit from imitation increases, reducing the licensor's profit.