Optimal R&D Investment with Learning-by-Doing: Multiple Steady-States and Thresholds

18 Pages Posted: 18 Sep 2014 Last revised: 28 Jan 2015

See all articles by Alfred Greiner

Alfred Greiner

Bielefeld University - Department of Business Administration and Economics

Anton A. Bondarev

WWZ Universit├Ąt Basel

Date Written: September 16, 2014

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.

Keywords: optimal control, horizontal and vertical innovations, multiple steady-states, thresholds, lock-in

JEL Classification: C61, D92, O32

Suggested Citation

Greiner, Alfred and Bondarev, Anton A., Optimal R&D Investment with Learning-by-Doing: Multiple Steady-States and Thresholds (September 16, 2014). Bielefeld Working Papers in Economics and Management No. 13-2014, Available at SSRN: https://ssrn.com/abstract=2496943 or http://dx.doi.org/10.2139/ssrn.2496943

Alfred Greiner (Contact Author)

Bielefeld University - Department of Business Administration and Economics ( email )

P.O. Box 100131
Bielefeld, 33501
Germany
+49 521 106 4859 (Phone)
+49 521 106 67120 (Fax)

HOME PAGE: http://phoenix.wiwi.uni-bielefeld.de/lehrbereiche/vwl/wipol

Anton A. Bondarev

WWZ Universit├Ąt Basel ( email )

Basel, 4051
Switzerland

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