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29.07.2017 | Research paper

Technology lock-in with horizontal and vertical innovations through limited R&D spending

verfasst von: Anton Bondarev, Alfred Greiner

Erschienen in: 4OR | Ausgabe 1/2018

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Abstract

In this paper we analyze an inter-temporal optimization problem of a representative firm that invests in horizontal and vertical innovations and that faces a constraint with respect to total R&D spending. We find that there can exist two different steady-states of the economy when the amount of research spending falls short of an endogenously determined threshold: one with higher productivities and less new technologies being developed, and the other with more technologies being created and lower productivities. But, for a higher amount of R&D spending the steady-state becomes unique and the firm produces the whole spectrum of available technologies. Thus, a lock-in effect may arise that, however, can be overcome by raising R&D spending sufficiently.

Vorheriger Artikel Block rearranging elements within matrix columns to minimize the variability of the row sums

Nächster Artikel Two-stage stochastic modeling of transportation outsourcing plans for transshipment centers

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Or assuming revenue function to be linear in the state of quality with prices being linear functions of quality.

The budget on R&D could be set endogenously by a specific firm’s R&D policy. It could positively depend on total profits, but, this is difficult to model. Pure exogenous dynamics will not change the qualitative results: the constraint is either binding or not.

It is fairly straightforward to relax this assumption by allowing decreasing efficiency of investment in new technologies, \(\xi (n):\,\frac{\partial \xi (n)}{\partial n}<0\). Qualitative results of the paper will continue to hold, but the dynamics is more elaborated. We assume a bounded state space to keep the analysis simple and clear.

Condition (5) points to the fact that it requires efforts g(i, t) and time to develop a new technology up to the level that it becomes productive, \(q(i,t)>0\).

For an increasing \(\psi (i)\) function there would be no trade-off between expanding the range of technologies and improving the existing ones and, thus, a lock-in could not arise.

Since horizontal and vertical innovations are interrelated, it also leads to an increased complexity of invention of new products.

We do not distinguish between complex and real roots, since this affects only stability and not the existence of steady states

For \(R=4\), the lower \(\dot{\lambda }_n=0\) isocline starts at \(n=1,\lambda _n=0\), the upper \(\dot{\lambda }_n=0\) isocline starts at \(n=1,\lambda _n>0\). For \(R>4\), the lower \(\dot{\lambda }_n=0\) isocline also starts at a value \(\lambda _n>0\) and \(n=1\).

Formally, this is seen from (A.5) as follows: \(\dot{n}=0\) implies \(u=0\) leading to \(l=\xi \tilde{\lambda }_n\), giving \(\dot{q}=\psi _c \sqrt{1-i}\left( \frac{\psi _c \sqrt{1-i}}{r+\beta }-\xi \tilde{\lambda }_n\right) -\beta q\). Since the first term is constant, q converges to its steady-state value.

Further, there is no way to usefully spend the additional R&D on quality improvement because all invented technologies have already reached their maximal quality levels in the steady-state.

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Titel: Technology lock-in with horizontal and vertical innovations through limited R&D spending
verfasst von: Anton Bondarev
Alfred Greiner
Publikationsdatum: 29.07.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: 4OR / Ausgabe 1/2018
Print ISSN: 1619-4500
Elektronische ISSN: 1614-2411
DOI: https://doi.org/10.1007/s10288-017-0348-0

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