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Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds

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  • Greiner, Alfred
  • Bondarev, Anton

Abstract

In this paper we present an inter-temporal optimization problem of a representative R&D firm that simultaneously invests in horizontal and vertical innovations. We posit that learning-by-doing makes the process of quality improvements a positive function of the number of existing technologies with the function displaying a convex-concave form. We show that multiple steady-states can arise with two being saddle point stable and one unstable with complex conjugate eigenvalues. Thus, a threshold with respect to the variety of technologies exists that separates the two basins of attractions. From an economic point of view, this implies that a lock-in effect can occur such that it is optimal for the firm to produce only few technologies at a low quality when the initial number of technologies falls short of the threshold. Hence, history matters as concerns the state of development implying that past investments and innovations determine whether the firm produces a large or a small variety of high- or low-quality technologies, respectively.

Suggested Citation

  • Greiner, Alfred & Bondarev, Anton, 2017. "Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds," Working papers 2017/06, Faculty of Business and Economics - University of Basel.
    • Handle: RePEc:bsl:wpaper:2017/06
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    References listed on IDEAS

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    1. Ping Lin, 2004. "Process and product R&D by a multiproduct monopolist," Oxford Economic Papers, Oxford University Press, vol. 56(4), pages 735-743, October.
    2. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
    3. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    4. Luca Lambertini & Raimondello Orsini, 2001. "Network Externalities and the Overprovision of Quality by a Monopolist," Southern Economic Journal, John Wiley & Sons, vol. 67(4), pages 969-982, April.
    5. Bondarev, Anton & Greiner, Alfred, 2019. "Endogenous Growth And Structural Change Through Vertical And Horizontal Innovations," Macroeconomic Dynamics, Cambridge University Press, vol. 23(1), pages 52-79, January.
    6. K. J. Arrow, 1971. "The Economic Implications of Learning by Doing," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 11, pages 131-149, Palgrave Macmillan.
    7. Anton Bondarev, 2012. "The long-run dynamics of product and process innovations for a multi-product monopolist," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 21(8), pages 775-799, November.
    8. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    9. Luca Lambertini & Raimondello Orsini, 2001. "Network Externalities and the Overprovision of Quality by a Monopolist," Southern Economic Journal, Southern Economic Association, vol. 67(4), pages 969-982, April.
    10. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    11. Anton Bondarev & Alfred Greiner, 2018. "Technology lock-in with horizontal and vertical innovations through limited R&D spending," 4OR, Springer, vol. 16(1), pages 51-65, March.
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    Cited by:

    1. Bondarev, Anton & Greiner, Alfred, 2018. "Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 134-156.
    2. Anton Bondarev, 2021. "Games Without Winners: Catching-up with Asymmetric Spillovers," Dynamic Games and Applications, Springer, vol. 11(4), pages 670-703, December.
    3. Bondarev, Anton, 2018. "Does stronger intellectual property rights protection foster structural change? Effects of heterogeneity in innovations," Structural Change and Economic Dynamics, Elsevier, vol. 46(C), pages 26-42.
    4. Ashwin, Julian & Beaudry, Paul & Ellison, Martin, 2025. "Neural network learning for nonlinear economies," Journal of Monetary Economics, Elsevier, vol. 149(C).
    5. Eigruber, Markus & Wirl, Franz, 2024. "Market equilibrium strategies under learning by doing and spillovers," Energy Economics, Elsevier, vol. 131(C).
    6. Qun Chen & Ji-Wen Li & Jian-Guo Liu & Jing-Ti Han & Yun Shi & Xun-Hua Guo, 2021. "Borrower Learning Effects: Do Prior Experiences Promote Continuous Successes in Peer-to-Peer Lending?," Information Systems Frontiers, Springer, vol. 23(4), pages 963-986, August.
    7. Qun Chen & Ji-Wen Li & Jian-Guo Liu & Jing-Ti Han & Yun Shi & Xun-Hua Guo, 0. "Borrower Learning Effects: Do Prior Experiences Promote Continuous Successes in Peer-to-Peer Lending?," Information Systems Frontiers, Springer, vol. 0, pages 1-24.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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