Optimal R&D investment with learning‐by‐doing: Multiple steady states and thresholds. (11th January 2017)

• Record Type: Journal Article
• Authors: Greiner, Alfred; Bondarev, Anton
• Is Part Of: Optimal control applications and methods. Volume 38:Number 6(2017)
• Page Start: 956
• Page End: 962
• Publication Date: 2017-01-11
• Subjects: horizontal and vertical innovations -- lock‐in -- multiple steady states -- optimal control -- thresholds; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2301
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: 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.