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

Greiner A, Bondarev A (2014) Working Papers in Economics and Management; 13-2014.
Bielefeld: Bielefeld University, Department of Business Administration and Economics.

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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.
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Greiner A, Bondarev A. Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds. Working Papers in Economics and Management. Vol 13-2014. Bielefeld: Bielefeld University, Department of Business Administration and Economics; 2014.
Greiner, A., & Bondarev, A. (2014). Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds (Working Papers in Economics and Management, 13-2014). Bielefeld: Bielefeld University, Department of Business Administration and Economics. doi:10.4119/unibi/2915528
Greiner, A., and Bondarev, A. (2014). Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds. Working Papers in Economics and Management, 13-2014, Bielefeld: Bielefeld University, Department of Business Administration and Economics.
Greiner, A., & Bondarev, A., 2014. Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds, Working Papers in Economics and Management, no.13-2014, Bielefeld: Bielefeld University, Department of Business Administration and Economics.
A. Greiner and A. Bondarev, Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds, Working Papers in Economics and Management, vol. 13-2014, Bielefeld: Bielefeld University, Department of Business Administration and Economics, 2014.
Greiner, A., Bondarev, A.: Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds. Working Papers in Economics and Management, 13-2014. Bielefeld University, Department of Business Administration and Economics, Bielefeld (2014).
Greiner, Alfred, and Bondarev, Anton. Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds. Bielefeld: Bielefeld University, Department of Business Administration and Economics, 2014. Working Papers in Economics and Management. 13-2014.
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