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Process and product innovation: A differential game approach to product life cycle

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  • Luca Lambertini
  • Andrea Mantovani

Abstract

We investigate the timing of adoption of product and process innovation by using a differential game in which firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we demonstrate that the incentive for cost-reducing investment is relatively higher than the incentive to increase product differentiation. Second, depending on initial conditions, (i) firms activate both types of investment from the very outset to the steady state; (ii) firms initially invest only in one R&D activity and then reach the steady state either carrying out only such activity or carrying out both; (iii) firms do not invest at all in either type of innovation.
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  • Luca Lambertini & Andrea Mantovani, 2010. "Process and product innovation: A differential game approach to product life cycle," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(2), pages 227-252.
  • Handle: RePEc:bla:ijethy:v:6:y:2010:i:2:p:227-252
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    References listed on IDEAS

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    Cited by:

    1. Bondarev, Anton & Greiner, Alfred, 2017. "Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers," Working papers 2017/02, Faculty of Business and Economics - University of Basel.
    2. Hinloopen, J. & Smrkolj, G. & Wagener, F.O.O., 2013. "In Defense of Trusts: R&D Cooperation in Global Perspective," CeNDEF Working Papers 13-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    3. Bondarev, Anton A., 2012. "Optimal control over a continuous range of homogeneous and heterogeneous innovations with finite life-cycles," MPRA Paper 40068, University Library of Munich, Germany.
    4. Debasmita Basak & Andreas Hoefele & Arijit Mukherjee, 2014. "Union Bargaining Power and Product Innovation: Relevance of the Preference Function," CESifo Working Paper Series 5007, CESifo Group Munich.
    5. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2016. "R&D Cooperatives and Market Collusion: A Global Dynamic Approach," Tinbergen Institute Discussion Papers 16-048/II, Tinbergen Institute.
    6. Eckel, Carsten & Unger, Florian, 2015. "Credit constraints, endogenous innovations, and price setting in international trade," Discussion Papers in Economics 24858, University of Munich, Department of Economics.
    7. Luca Lambertini & Raimondello Orsini, 2015. "Quality Improvement and Process Innovation in Monopoly: A Dynamic Analysis," Working Paper series 15-12, Rimini Centre for Economic Analysis.
    8. L. Lambertini & R. Orsini, 2014. "Process Innovation and Product Quality Improvement in a Dynamic Monopoly," Working Papers wp926, Dipartimento Scienze Economiche, Universita' di Bologna.
    9. Bondarev, Anton, 2014. "Endogenous specialization of heterogeneous innovative activities of firms under the technological spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 235-249.
    10. Anton Bondarev, 2016. "Intensity of R&D competition and the generation of innovations in heterogeneous setting," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 621-653, July.
    11. repec:eee:proeco:v:193:y:2017:i:c:p:703-712 is not listed on IDEAS
    12. Debasmita Basak & Arijit Mukherjee, "undated". "Unionisation structure and product innovation," Discussion Papers 11/12, University of Nottingham, School of Economics.
    13. Li, Shoude & Ni, Jian, 2016. "A dynamic analysis of investment in process and product innovation with learning-by-doing," Economics Letters, Elsevier, vol. 145(C), pages 104-108.

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