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Journal of Quantitative Economics

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14-03-2019 | Original Article

When Spillovers Enhance R&D Incentives

Authors: Rittwik Chatterjee, Srobonti Chattopadhyay, Tarun Kabiraj

Published in: Journal of Quantitative Economics | Issue 4/2019

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Abstract

It is commonly believed that spillover reduces R&D incentives of a firm. This happens because of the appropriability problem. However, some empirical literature shows the possibility of enhanced R&D incentives under spillovers. In the literature this is explained under incomplete information, but we show this theoretically under complete information. We show in particular that in a duopoly there are situations when with no spillovers only one firm invests in R&D, but under spillovers both the firms invest. This occurs when there is complementarity in research and the spillover rate lies in an interval specified by the size of R&D investment.

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For instance, see d’Aspremont and Jacquemin (1988), Suzumura (1992), Kamien et al. (1992) and Ghosh and Ghosh (2014).

A comprehensive analysis on the relation between R&D investment and R&D appropriability can be found in Levin et al. (1987).

This effect is actually absent in Chatterjee et al. (2018), as a result in their paper under complete information spillovers unambiguously reduce R&D incentives of a firm.

Here the parameter R is the cost associated with an innovation, hence it includes the lab set up cost, the cost of installing machines and tools, and the expenses to recruiting scientific personnel (including R&D inputs).

Following the works of d’Aspremont and Jacquemin (1988) and Kamien et al. (1992) and others, the effective cost reduction of firm \( i \) through spillover is \( \varepsilon_{i} = \phi \left( {R_{i} } \right) + \beta \phi \left( {R_{j} } \right) \), where \( \phi \left( {R_{i} } \right) \) is the amount of cost reduction if \( R_{i} \) is invested by firm \( i \); \( \phi \left( 0 \right) = 0 \) and \( 0 \le \beta \le 1 \). In our case, \( R_{i} = R_{j} = R \), \( \phi \left( R \right) = D \) and \( \beta D = d \). Alternatively, we can assume that production of the final good requires one unit of each of the two inputs, say \( X \) and \( Y \), and initial unit costs of \( X \) and \( Y \) are \( c_{X} \) and \( c_{Y} \) respectively so that its initial unit cost of production is \( c = c_{X} + c_{Y} \). Now assume that firm \( 1 \) can reduce unit cost of \( X \) by \( D \) amount if it invests \( R \) in R&D. similarly, firm \( 2 \) can reduce its unit cost of \( Y \) by the same amount by investing \( R \). By this, there is spillover of knowledge, \( d \), from one firm to the other; \( 0 \le d \le D \).

Here “x” stands for the notation of the remaining terms other than \( (a - c) \) in the numerator in the quantity and profit expressions. So \( x \) is a variable. In our paper, \( {{\varPi }}\left( {\text{x}} \right) = ({\text{q}}\left( {\text{x}} \right))^{2 } = (\frac{a - c + x}{3})^{2 } \). Suppose firm 1 has unit cost of production (\( c - D \)) and firm 2 has unit cost (\( c - d \)). Then firm 1’s payoff under Cournot competition is \( {{\varPi }}_{1} = = (\frac{a - c + 2D - d}{3})^{2} = {{\varPi }}\left( {2{\text{D}} - {\text{d}}} \right) \) and firm 2’s payoff is \( {{\varPi }}_{2} = {{\varPi }}\left( {2{\text{d}} - {\text{D}}} \right) \), and so on.

Arrow, K.J. 1962. Economic welfare and the allocation of resources for invention. In The rate and direction of inventive activity, ed. R.R. Nelson, 609–625. Princeton: Princeton University Press.CrossRef

Bakhtiari, S., and R. Breunig. 2018. The role of spillovers in research and development expenditure in Australian industries. Economics of Innovation and New Technology 27 (1): 14–38.CrossRef

Chatterjee, R., S. Chattopadhyay, and T. Kabiraj. 2018. Spillovers and R&D incentive under incomplete information. Studies in Microeconomics 6 (1–2): 50–65.CrossRef

d’Aspremont, C., and A. Jacquemin. 1988. Cooperative and non-cooperative R&D in duopoly with spillovers. American Economic Review 78: 1133–1137.

De Bondt, R. 1997. Spillovers and innovative activities. International Journal of Industrial Organization 15: 1–28.CrossRef

Ghosh, S., and S. Ghosh. 2014. Are cooperative R&D agreements good for the society? Journal of Business & Economics Research 12: 313–322.

Jaffe, A.B. 1986. Technological opportunity and spillovers of R&D: evidence from firms’ patents, profits and market value. American Economic Review 76: 984–1001.

Kamien, M.I., E. Muller, and I. Zang. 1992. Research joint ventures and R&D cartels. American Economic Review 82: 1293–1306.

Levin, R.C., A.K. Klevorick, R. Nelson, and S. Winter. 1987. Appropriating the returns from industrial R&D. Brookings Economic Papers on Economic Activity 18: 783–832.CrossRef

Levin, R.C. 1988. Appropriability, R&D spending, and technological performance. American Economic Review 78: 424–428.

Spence, M. 1984. Cost reduction, competition and industry performance. Econometrica 52: 101–121.CrossRef

Suzumura, K. 1992. Cooperative and non-cooperative R&D in an oligopoly with spillovers. American Economic Review 82: 1307–1320.

Title: When Spillovers Enhance R&D Incentives
Authors: Rittwik Chatterjee
Srobonti Chattopadhyay
Tarun Kabiraj
Publication date: 14-03-2019
Publisher: Springer India
Published in: Journal of Quantitative Economics / Issue 4/2019
Print ISSN: 0971-1554
Electronic ISSN: 2364-1045
DOI: https://doi.org/10.1007/s40953-019-00161-3

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