Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/185826
Authors: 
Greiner, Alfred
Bondarev, Anton
Year of Publication: 
2017
Series/Report no.: 
WWZ Working Paper 2017/06
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.
Subjects: 
optimal control
horizontal and vertical innovations
multiple steadystates
thresholds
lock-in
JEL: 
C61
D92
O32
Document Type: 
Working Paper
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