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

Greiner A, Bondarev A (2017)
OPTIMAL CONTROL APPLICATIONS & METHODS 38(6): 956-962.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper, we present an intertemporal 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 2 being saddle point stable and 1 unstable with complex conjugate eigenvalues. Thus, a threshold with respect to the variety of technologies exists that separates the 2 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.
Erscheinungsjahr
Zeitschriftentitel
OPTIMAL CONTROL APPLICATIONS & METHODS
Band
38
Ausgabe
6
Seite(n)
956-962
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Greiner A, Bondarev A. Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds. OPTIMAL CONTROL APPLICATIONS & METHODS. 2017;38(6):956-962.
Greiner, A., & Bondarev, A. (2017). Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds. OPTIMAL CONTROL APPLICATIONS & METHODS, 38(6), 956-962. doi:10.1002/oca.2301
Greiner, A., and Bondarev, A. (2017). Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds. OPTIMAL CONTROL APPLICATIONS & METHODS 38, 956-962.
Greiner, A., & Bondarev, A., 2017. Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds. OPTIMAL CONTROL APPLICATIONS & METHODS, 38(6), p 956-962.
A. Greiner and A. Bondarev, “Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds”, OPTIMAL CONTROL APPLICATIONS & METHODS, vol. 38, 2017, pp. 956-962.
Greiner, A., Bondarev, A.: Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds. OPTIMAL CONTROL APPLICATIONS & METHODS. 38, 956-962 (2017).
Greiner, Alfred, and Bondarev, Anton. “Optimal R&D investment with learning-by-doing: Multiple steady states and thresholds”. OPTIMAL CONTROL APPLICATIONS & METHODS 38.6 (2017): 956-962.