Cooperation or non-cooperation in R&D: how should research be funded?

ABSTRACT

This article investigates two research funding policies in a cooperative and a non-cooperative R&D setting: subsidising private research (Spr) and subsidising public research (Spu). We show that R&D cooperation with subsidies (either Spr or Spu) always performs better than R&D cooperation with no subsidy. Furthermore, the Spr policy leads to better performance than the Spu approach does in terms of overall net surplus whether the firms cooperate or not in R&D. Nevertheless, comparing the two research funding policies for the same level of public spending shows that the Spu policy with R&D cooperation is in some cases more effective than the Spr policy, the latter becoming too costly for the government when spillovers are high.

KEYWORDS:

• R&D Cooperation
• R&D spillovers
• knowledge public externalities
• subsidies
• public policy

JEL CODES:

• C7
• H2
• H4
• L3
• L5
• 03

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 This point is emphasised by Marinucci (2012) in a survey on R&D cooperation.

2 AJ also consider a third scenario (non-investigated in our analysis) in which firms cooperate in both stages.

3 The R&D cooperation models proposed by d'Aspremont and Jacquemin (1988) and Kamien, Muller, and Zang (1992) (KMZ) have been compared several times. In contrast with the KMZ model, AJ's does not consider diminishing returns for research when calculating spillovers, which are outside the research process. This tends to make the R&D process in the AJ model more productive and to increase the level of the equilibrium results. One can switch between the two models by replacing γ with $(1+\beta )\gamma$ (see Amir 2000 pp. 1030–31, Hinloopen 2000). Changing the R&D cost structure qualitatively does not affect any of the conclusions presented here. The corresponding calculations are available from the authors upon request.

4 In practice, governments can offer firms direct support via grants, loans or procurement or can use fiscal incentives, such as R&D tax incentives (R&D tax credits, R&D allowances, reductions in R&D workers' income taxes and social security contributions, and accelerated depreciation of R&D capital). In our model, we do not distinguish between these different R&D and innovation support tools. We assume that the subsidy is provided based on the R&D output as in Hinloopen (1997), Hinloopen (2000), Hinloopen (2001), Gil-Molto, Poyago-Theotoky, and Zikos (2011) and Gil-Moltó et al. (2018). We could consider the case in which the government subsidises R&D expenditure $\left(s\gamma \right(x_i^2/2\left)\right)$, but this would not change our equilibrium results: the subsidy term disappears from the social welfare function. The relevant calculations are available from the authors upon request.

5 When governments support public research sector, the public money spent on R&D goes to universities and public research institutes (PRIs).

6 This amounts to considering that the government funding public research does not evaluate the effectiveness of this research in terms of costs.

7 As a reminder, the higher the spillover level is, the higher the cooperative effort in R&D is; conversely, non-cooperative R&D output decreases with β, which highlights the disincentive effect of technology leaks on research investments. R&D cooperation induces better performance (in terms of R&D levels, consumer surplus, profit and welfare) than R&D non-cooperation provided the spillovers are sufficiently high ($\beta >0.5$).

8 A RJV cartel is then a R&D cartel with $\beta =1$. In this case, firms coordinate their R&D efforts and share their information completely. In our model, this form of cooperation can also be considered.

9 The second order condition is that $4.5\gamma >2(1+\beta {)}^2$.

10 The second-order condition is similar to the non-cooperative case in the Spr approach: $4.5\gamma >(2-\beta {)}^2$.

11 The second-order condition is $4.5\gamma >(2-\beta )(1+2.5\beta ).$

12 The second-order condition is similar to the non-cooperative case: $4.5\gamma >2(1+\beta {)}^2$.

13 The second-order condition is similar to the one in the cooperative case under Spr: $4.5\gamma >(1+\beta {)}^2$.

14 The second-order condition is $4.5\gamma >1.5(1+\beta {)}^2$.

15 We would like to thank the referee for this suggestion.

16 We can trace the functions $h(\gamma ,\beta )=0$ and $f(\gamma ,\beta )=0$ as a function of the two parameters γ and β.

17 Second-order conditions require that 4.5γ>(2–β)².

18 The second-order condition is 4.5γ>(1+β)².