Geography Reference
In-Depth Information
We know that the cost of the output is inl uenced by the costs of external knowledge,
which in turn are af ected by the same number of i rms N :
C = C * / v ( N )
(7.8)
dY / dN = dC / dN / dp / dN
(7.9)
The specii c form of interplay between the positive ef ects on the costs of external knowl-
edge and the negative ef ects on knowledge appropriability can acquire a quadratic
form. In such circumstances the dynamics of the process will follow an S-shaped path.
Formally we see that the dynamics of net positive externalities as dependent on the
number N of i rms may take a quadratic shape:
dN ( t ) = n ( N ( t ) − ( N 2 ( t ))
(7.10)
In fact equation (7.10) admits the standard logistic equation as a solution (see Figure
7.4).
Net pecuniary knowledge externalities provide the incentive to enter the knowledge
pools. Entry will take place as long as they are positive. The l ow of entry will take a
quadratic shape and accelerated l ows of entry are likely to take place in the proximity
of the optimum size of the cluster. Beyond that level, i rms will enter at a reduced pace.
Entry will stop as soon as the negative ef ects of reduced knowledge appropriability are
larger than the positive ef ects in terms of reduced costs of external knowledge.
It is clear in fact that agglomeration is no longer an unconstrained recipe. The size of
the local knowledge pools can be too little or too large. There is also, according to spe-
cii c conditions, an 'optimum' size of the local pools of knowledge.
6. The emergence and decline of knowledge systems
The availability of external knowledge explains, at one and the same time, the emergence
of path-dependent local and sectoral systems of innovations, the features of regional
specialization of regions, and the directionality of technological change. The availabil-
ity of external knowledge in fact pushes i rms to increase the complementarity of their
knowledge base so as to take advantage of emerging pecuniary externalities in knowl-
edge generation.
Technological knowledge cannot be regarded as an undif erentiated homogeneous
body but rather as a bundle of highly idiosyncratic and circumscribed items possessed
by individual agents, localized by their own circumscribed competences, more or less
interconnected by a web of communication channels. At each point in time innova-
tion systems are the nodes of such networks of communication channels. They are the
result of the intentional search and implementation of knowledge complementarities
among agents originally dispersed in knowledge space or clustered in other nodes.
Learning agents, able to generate new knowledge, try to exploit pecuniary externalities
of knowledge and move within the knowledge space, hence they direct technological
knowledge towards well-specii ed characteristics that are shaped collectively. The collec-
tive directionality of technological knowledge that is generated through the convergence
contributes to the emergence of structured collective pools of knowledge. Such innova-
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