Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds
Alfred Greiner and
Anton Bondarev ()
Working papers from Faculty of Business and Economics - University of Basel
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 steadystates; thresholds; lock-in (search for similar items in EconPapers)
JEL-codes: C61 D92 O32 (search for similar items in EconPapers)
Date: 2017-04-15
New Economics Papers: this item is included in nep-ino and nep-mic
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Citations: View citations in EconPapers (7)
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Persistent link: https://EconPapers.repec.org/RePEc:bsl:wpaper:2017/06
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