Essays in Honour of Karl-Göran Mäler
New Horizons in Environmental Economics series
Edited by Bengt Kriström, Partha Dasgupta and Karl-Gustaf Löfgren
Chapter 2: An Optimal R & D for a Patent Race with Uncertain Duration
2. On optimal R&D for a patent race with uncertain duration Thomas Aronsson, Per-Olov Johansson and Karl-Gustaf Löfgren 1 INTRODUCTION In this chapter we consider a patent race where independent firms (or research laboratories) compete in order to develop a ‘winner takes all’ innovation. We look at the optimal strategy for the individual firm, the non-cooperative Nash equilibrium, and how to design policy instruments such that the Nash equilibrium replicates the socially optimal resource allocation. There are several distinct features that distinguish this chapter from the patent races considered by Bhattacharya and Mookherjee (1986), Dasgupta and Stiglitz (1980), Gilbert and Shapiro (1990), Grossman and Shapiro (1986), Gruver (1991), Klette and de Meza (1986), Loury (1979), Scherer (1967) and Tirole (1988). First, previous authors typically consider research and development (R&D) costs as instantaneous, whereas, in our model, a firm builds up a stock of R&D capital. Instead, a research intensity parameter, which captures research intensity at each instant, plays the same role as the constant R&D cost in previous studies. We use the necessary conditions for an optimal control to highlight the difference between flow expenditures on R&D and changes in the stock of R&D capital. Second, in our model the hazard is a function of (among other things) the stock of R&D capital.1 This is an important generalization, since the magnitude of a firm’s R&D capital is central for its chances to win a patent race. Building up competence is not...
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