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Optimal Diversity in Investments with Recombinant Innovation


  • Zeppini Rossi, P.

    () (Universiteit van Amsterdam)

  • Bergh, J.C.J.M. van der

    (Autonomous University of Barcelona)


The notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation is addressed. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next diversity is optimized by trading off the benefits of recombinant innovation and returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. Threshold values of returns to scale and recombination probability define regions where either specialization or diversity is the best choice. In the time domain, when the investment time horizon is beyond a threshold value, a diversified investment becomes the best choice. This threshold will be larger the higher the returns to scale.

Suggested Citation

  • Zeppini Rossi, P. & Bergh, J.C.J.M. van der, 2008. "Optimal Diversity in Investments with Recombinant Innovation," CeNDEF Working Papers 08-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:08-12

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    References listed on IDEAS

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    Cited by:

    1. Zeppini, Paolo & van den Bergh, Jeroen C.J.M., 2013. "Optimal diversity in investments with recombinant innovation," Structural Change and Economic Dynamics, Elsevier, vol. 24(C), pages 141-156.
    2. Griffith, Rachel & Lee, Sokbae & Straathof, Bas, 2017. "Recombinant innovation and the boundaries of the firm," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 34-56.
    3. Anton Bondarev & Alfred Greiner, 2017. "Technology lock-in with horizontal and vertical innovations through limited R&D spending," Working papers 2017/04, Faculty of Business and Economics - University of Basel.
    4. Martin Fiszbein, 2017. "Agricultural Diversity, Structural Change and Long-run Development: Evidence from the U.S," NBER Working Papers 23183, National Bureau of Economic Research, Inc.
    5. Rupert Way & Franc{c}ois Lafond & J. Doyne Farmer & Fabrizio Lillo & Valentyn Panchenko, 2017. "Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves," Papers 1705.03423,
    6. Subtil Lacerda, Juliana & van den Bergh, Jeroen C.J.M., 2016. "Diversity in solar photovoltaic energy: Implications for innovation and policy," Renewable and Sustainable Energy Reviews, Elsevier, vol. 54(C), pages 331-340.
    7. Van den Bergh, J.C.J.M. & Zeppini Rossi, P., 2010. " Competing Recombinant Technologies for Environmental Innovation: Extending Arthur’s Model of Lock-in Abstract: This article presents a model of sequential decisions about investments in environment," CeNDEF Working Papers 10-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    8. Paolo Zeppini & Jeroen C.J.M. van den Bergh, 2010. "Competing Recombinant Technologies for Environmental Innovation," Tinbergen Institute Discussion Papers 10-107/1, Tinbergen Institute.

    More about this item

    JEL classification:

    • B52 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Historical; Institutional; Evolutionary
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • Q55 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Technological Innovation

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