R&D Activities in a Differentiated Goods Duopoly with Quadratic Cost Function

  • Jacek ProkopEmail author
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


The purpose of this paper is to assess the relationship between the firms’ behavior in the differentiated product market and the decisions regarding the R&D investments. The comparison is made between the case of the Stackelberg-type duopolistic competition in the final product market and the situation of a cartelized industry under the assumption of quadratic cost functions. On the one hand, different levels of product differentiation are considered. And, on the other hand, the impact of the extent of research spillovers is analyzed. The numerical analysis leads to the conclusion that, under the assumption of quadratic cost functions, it is always beneficial for both firms to form an industry cartel. This result is similar to the case of the linear cost functions with one exception: the threat of cartelizing the industry was not present when the final products were homogenous.


R&D activities Industry cartelization Stackelberg competition Heterogeneous products Quadratic cost functions 



This research was supported by National Science Centre, Poland (grant number UMO-2017/25/B/HS4/01632).


  1. d’Aspremont, C., & Jacquemin, A. (1988). Cooperative and noncooperative R&D in Duopoly with spillovers. American Economic Review, 78, 1133–1137.Google Scholar
  2. Geroski, P. (1995). Do spillovers undermine the incentive to innovate? In S. Dowrick (Ed.), Economic approaches to innovation. Aldershot: Edward Elgar.Google Scholar
  3. Kamien, M. I., Muller, E., & Zang, I. (1992). Research joint ventures and R&D cartels. The American Economic Review, 82, 1293–1306.Google Scholar
  4. Prokop, J., & Karbowski, A. (2018). R&D spillovers and cartelization of industries with differentiated products. Journal of International Studies, 11, 44–56.Google Scholar
  5. Prokop, J. (2016). Firm performance and research and development. In A. Vlachvei, O. Notta, K. Karantininis, & N. Tsounis (Eds.), Factors affecting firm competitiveness and performance in the modern business world (pp. 108–128). IGI Global.Google Scholar
  6. Symeonidis, G. (2003). Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D. International Journal of Industrial Organization, 21, 39–55.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Business EconomicsWarsaw School of EconomicsWarsawPoland

Personalised recommendations