Complementarity between product and process innovation in a monopoly setting

Abstract

In this article we study complementarity between market-enhancing product innovation and cost-reducing process innovation in a monopoly setting. First, we consider the possibility for a firm to alternatively invest only along one of the two directions and compare the incentives of process vs. product innovation. Then, we allow the firm to invest simultaneously in both activities, showing that both investment levels and profit are higher than in the case of individual investment. Thus, product and process innovations are complementary, and the firm always prefers the simultaneous adoption of both activities.

Keywords:

• Complementarity
• Product innovation
• Process innovation

Acknowledgements

This paper is part of my PhD Thesis at CORE, Université Catholique de Louvain. I would like to thank Karen Abramyan, Rabah Amir, Claude d'Aspremont, Luca Lambertini, Giordano Mion, Jacques-François Thisse, Vincent Vannetelbosch, the seminar audience at Université Catholique de Louvain, the Editor, Cristiano Antonelli, and two anonymous referees for useful comments and suggestions. The usual disclaimer applies. Financial support by the University of Bologna and the Italian Ministry of Education is gratefully acknowledged for the academic year 2004–2005.

Notes

¹The theory of comparative statistics, initially investigated by Samuelson (1974), resurfaced again in economics thanks to the improvement in the theory of supermodular games, introduced by Topkis (1978) and further studied by Milgrom and Roberts (1990a, b; 1995), Vives (1990), and Amir (1996), inter alia. The issue of complementarity has become a leading field of research both in games with strategic complementarities among the strategies of the players and in games with players that face multidimensional strategy space.

²Abernathy and Utterback (1975; 1982) and Klepper (1996) propose a ‘technological life-cycle’ model in which firms initially direct most of their R&D resources to product innovation and then move to process innovation. The main argument is that the returns to product innovation are at highest at the very beginning because they depend on the acquisition of new consumers, whereas the returns to process are very attractive the second time becuase they are proportional to the level of output produced by the firm. Adner and Levinthal (2001) recently moved some critics to what they called a ‘supply-side’ view of technological change in favor of a ‘demand side’ approach where technology changes are driven by the interaction between technology development and consumers’ heterogeneous demands.

³This initial classification has been widely adopted after the work of Lancaster (1979).

⁴For a discussion of the theories of advertising and the evidence of its use by firms, see Pepall et al. (1999, Chapter 10), Friedman (1983), and Martin (2002, Chapter 9).

⁵Halmenschlager (2004) considers a modification of the standard two-stage model wherein two high-cost firms conduct cost-reducing R&D, in a setting with spillovers, and then compete à la Cournot against a low-cost firm that does not engage in R&D.

⁶If we do not restrict the potential market expansion, the optimal investment in product R&D is still given by Eq. (10) for δ>δ₁, while it would go to infinity for δ≤δ₁, being the profit function convex with respect to R&D investment.

⁷See also Martin (2002, Chapter 9) for a comprehensive discussion.

⁸We draw both pictures by taking b=1, c=1, a=1.5. In the left panel, we further impose that A=3, hence A−a>c, whereas in the right panel A=2 and A−a<c.

⁹It is easy to demonstrate that the same result holds for a multiproduct monopoly. Consider a symmetric differentiated demand system p _i =a−q _i −d q _j , i=1, 2, where d∈[0, 1] denotes product substitutability. Assume the monopolist invests in process innovation to reduce the cost of producing the first product and in product innovation to increase market size a. Given that a is common for both firms, cross-partial derivatives are positive and the two activities are indeed complementary. We prefer to use a more simple presentation, as it is laid out in the article, as no significant qualitative changes are obtained in the multiproduct setting.

¹⁰Second order conditions are always satisfied, as it can be easily checked.

Additional information

Notes on contributors

Andrea Mantovani

Core, 34 Voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium. E-mail: [email protected]