the geography of nanotechnologies: the role of specialization

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The Geography of Nanotechnologies: The role of Specialization and Diversification Nina Menz Karlsruhe Institute of Technology(KIT) § Ludwig-Maximilians-Universität München Ingrid Ott Karlsruhe Institute of Technology (KIT) ** Kiel Institute for the World Economy (IfW) June 23, 2010 Abstract Nanotechnologies as general purpose technologies (GPTs) drive technical progress and economic growth. External effects and uncertainty, inherent in the multiple inno- vation processes that are triggered by GPTs, inhibit an optimal development. Knowl- edge spillovers promote spatial proximity and invert inhibiting external effects to in- novation enhancing scale effects. Not querying agglomeration advantages in general, it isn’t obvious which role specialization and diversification play in the GPTs develop- ment. Examining the optimal shape of a GPT’s cluster, the situation of nanotechnolo- gies in Hamburg suggests that both are impelling. Here, building up an own cluster seems impossible due to technological distances. Instead, nanotechnologies are well connected to the existing clusters of an application sector. If his joint-use of clusters is expanded, application sectors will be widened, diversification advantages be opened and growth effects be multiplied while market failures are solved through specializa- tion effects in the diverse clusters. Key words: general purpose technology, nanotechnology, cluster, specialization, diversifi- cation, spillover JEL-codes: R11, O31 § [email protected] ** [email protected]

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Page 1: The Geography of Nanotechnologies: The role of Specialization

The Geography of Nanotechnologies: The role of

Specialization and Diversification

Nina Menz

Karlsruhe Institute of Technology(KIT) §

Ludwig-Maximilians-Universität München

Ingrid Ott

Karlsruhe Institute of Technology (KIT) ∗∗

Kiel Institute for the World Economy (IfW)

June 23, 2010

Abstract

Nanotechnologies as general purpose technologies (GPTs) drive technical progress

and economic growth. External effects and uncertainty, inherent in the multiple inno-

vation processes that are triggered by GPTs, inhibit an optimal development. Knowl-

edge spillovers promote spatial proximity and invert inhibiting external effects to in-

novation enhancing scale effects. Not querying agglomeration advantages in general,

it isn’t obvious which role specialization and diversification play in the GPTs develop-

ment. Examining the optimal shape of a GPT’s cluster, the situation of nanotechnolo-

gies in Hamburg suggests that both are impelling. Here, building up an own cluster

seems impossible due to technological distances. Instead, nanotechnologies are well

connected to the existing clusters of an application sector. If his joint-use of clusters is

expanded, application sectors will be widened, diversification advantages be opened

and growth effects be multiplied while market failures are solved through specializa-

tion effects in the diverse clusters.

Key words: general purpose technology, nanotechnology, cluster, specialization, diversifi-

cation, spillover

JEL-codes: R11, O31

§[email protected]∗∗[email protected]

Page 2: The Geography of Nanotechnologies: The role of Specialization

1 Introduction

Nanotechnologies are expected to largely dominate the coming decades by increased ap-

plication in various fields. Moreover, it’s widely accepted that nanotechnologies qualify

as future dominating general purpose technology (GPT), which is characterized by wide

variety of uses, technological dynamism and innovational complementarities. Due to their

capacity to spur a set of complementary innovations, GPTs such as nanotechnologies are

expected to interact with other technologies along the value creation chain and thus to

serve as engines of growth. However, it is still unclear how this growth potential actually

may be realized: Arising market failures, such as positive externalities and uncertainty

inherent in the innovation processes of GPTs in general lead to too little innovations that

above all arise to late.

Within a regional context, spillovers that result from non-rivalry of the knowledge pro-

duced can have a positive impact on innovations. Since these spillovers are limited by

geographical distance, regional networks between firms working in similar fields enhance

innovative activity. As nanotechnologies as GPT entail a great variety of innovations it is

reasonable to assume that they act as agglomeration forces in sectors already showing a

tendency to cluster: Externalities are expected to be internalized and uncertainties can be

resolved within functional clusters, thereby improving productivity of innovations. At the

same time, the definition of a cluster - being specialized in one field - seems to contradict

the GPTs feature of pervasiveness, which is crucial for the optimal development of GPTs

regarding productivity and growth effects. This apparent antagonism of specialization

and diversification raises the question to be answered in this paper: As both seem to be

important for the optimal development of nanotechnologies than how does an agglomer-

ation pattern look like that secures both, promising the growth effect of the multi-purpose

property while profiting from innovation enhancing effects specialized clusters offer? Put

differently: To which extent do nanotechnologies strengthen or expand prevailing regional

production structures and how does this feed back to the innovation processes?

To answers these questions a case study on the role of nanotechnologies and on their de-

velopment was conducted in the metropolitan region of Hamburg, Germany By applying

the theoretical reflections on a particular case, we aim to elaborate the implications of

emerging nanotechnologies for already existing as well as for just emerging regional clus-

ters on the one hand and the feedback effects of innovative activity within these clusters

on the enhancement of nanotechnologies on the other hand.

This paper is organized as follows: Section 2 presents determinants and economic aspects

of nanotechnologies as GPT. Section 3 analyzes the geography of nanotechnologies. In

Section 4 we present our case study of nanotechnologies in Hamburg, applying the argu-

ments detailed before. Section 5 briefly concludes.

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2 Economic aspects of nanotechnologies as general purpose

technologies

Nanotechnologies are interdisciplinary and combine a lot of classical basis technologies.

This is what makes it so difficult to find a clear definition. To quote the National Nanotech-

nology Initiative ’nanotechnolgy is the understanding and control of matter at dimensions

of roughly 1 to 100 nanometers, where unique phenomena enable novel applications.

Encompassing nanoscale science, engineering and technology, nanotechnology involves

imaging, measuring, modeling and manipulating matter at this length scale.’ Nanotech-

nologies are expected to be the dominating general purpose technologies (GPTs) of the

coming decades. Bresnahan and Trajtenberg (1995) consider general purpose technolo-

gies as enabling technologies, because they are giving new answers to various kinds of

problems instead of focusing on a solution for a single problem. In fact they offer a

generic function, which can be used productively in a wide range of application fields.

Bresnahan and Trajtenberg refer to a general purpose technology (GPT), if a drastic inno-

vation is distinguished by the following three features: Generality of purpose, technological

dynamism and innovational complementarities.1 First, the generality of purpose, ensured

by the generic function, opens the pervasive application in a wide range of fields. These

fields can be entirely different and can in turn induce new application fields themselves. In

nanotechnologies, this generality of purpose stems from the possibility to rearrange atoms

encompassing new properties, which can be used in effectively any technology providing

a wide spread for improvement by the possible reduction of size and costs and increasing

complexity. Through further development at every level of the value creation chain, the

GPT will be improved continuously. When the quality of the GPT is improved in the GPT

sector (the upstream sector) the application sectors downstream will profit of a better

quality (or ceteris paribus a lower price) of the GPT as intermediate input. As private

return to investment in R&D is increasing with the GPT’s quality, the downstream sectors

have an incentive to improve their technology as well. This holds true for the entire value

creation chain. Moreover, the use of the GPT becomes profitable for other sectors and its

range of use is widened. This process of innovation works upwards the value creation

chain as well, as a wider range of use or an improved downstream product (i.e. a better

technology) enhances potential for improvement as well as commercial opportunities and

thus the incentives to innovate in the GPT sector. Profits in the GPT sector are in the same

way dependent on the application sectors technologies, leading to higher investments in

R&D when a downstream technology is improved. These feedback effects describes the in-

novational complementarities (see figure 1): Profits from innovations in the downstream

1For a sophisticated discussion of the characteristics that define general purpose technologies see Lipsey

et al. (1998).

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sectors rise when the GPT is improved and vice versa as a result of an increase in pro-

ductivity of R&D (see Bresnahan and Trajtenberg 1995, p. 84). In nanotechnologies an

example for innovational complementarities can be found with the technology that made

research on and progress with nanotechnologies possible and which is now an application

sector of nanotechnologies itself: electronic microscopy (see Youtie et al. 2008, Palmberg

and Nikulainen 2006). Likewise, this mechanism emphasizes the linkages between per-

vasiveness and technological dynamics of the GPT, resulting in a widespread technology

with enormous growth potential. Nanotechnologies are accepted to be such a technology.

Its features, especially the innovational complementarities, hold chances for the develop-

ment of economic growth through technological advance on the one as well as problems

on the other hand.

2.1 Externalities

The constitutive features of GPTs emphasize the relevance of the interaction between up-

and downstream sectors and their interdependencies during the innovation processes. The

innovational complementarities trigger a dual-inducement-mechanism: A technological im-

provement of the GPT results in complementary improvements in the downstream sectors.

On the other hand, private return to investment in the quality of the GPT increases with

the technological level of the application sectors. The incentives to innovate for both sec-

tors are thus interrelated with the behavior of the respectively other. Innovation processes

are therefore strategic complements.2 There are two externalities immanent in this dual

inducement mechanism. The positive vertical externality arises from the feedback between

up- and downstream sectors’ profits. Because of the innovational complementarities their

payoffs are interdependent, resulting in appropriability effects in both directions: An in-

novating sector, no matter if GPT or application sector, fails to appropriate the returns of

its investments in innovation entirely because all other sectors of the value creation chain

profit by higher productivity of innovation investments. What follows is an bilateral moral

hazard problem: Neither up- nor downstream have an incentive to invest in innovations

in a range that would be socially optimal (see Bresnahan and Trajtenberg 1995, p. 94).

The positive horizontal externality is a product of the interdependence between the differ-

ent application sectors in combination with the generic function of the GPT. With a higher

number of application sectors, the opportunities for the GPT sector of realizing profits rise.

This is also true for a higher technology level of the applications sectors as a result of in-

vestment in R&D. Consequently these are incentives for the upstream sector to innovate,

the quality of the GPT will thus increase. Suppose only one application sector invests in

R&D, enhancing a growth of the aggregated technology level of the application sectors

2For a mathematical derivation see Bresnahan and Trajtenberg (1995) or the mathematical appendix.

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and in consequence of the GPT’s quality. Not only the productivity of the innovating sec-

tor, but the productivity of all non-innovating application sectors will improve, too. Thus

at least a part of the return of the investment of the innovative sector is a social return.

This is why the quality of the GPT as well as the aggregated technology level of all ap-

plication sectors can, at least partly, be characterized as a public good (see Bresnahan

and Trajtenberg 1995, pp. 94f.). A bilateral moral hazard problem occurs and in equilib-

rium neither the upstream nor the downstream sector have enough incentives to innovate.

Hence the quality of the GPT as well as the aggregated technology level are lower than in

the social optimum.

Figure 1: Linkages and externalities in the innovation process of GPT

2.2 Dynamics of general purpose technologies

Assume a profit-maximizing GPT sector and (for simplicity) only one application sector

with a certain quality of the GPT zt and a certain aggregated technology level of all ap-

plication sectors TA,t at time t. The period of the length τ is the time one sector needs to

adapt its technology to the innovation made by the other sector in the precedent period.

To develop this adaption, the quality- or technology level at time t is thus relevant. Hence

in each sector the quality/technology level remains constant for a length of time of 2τ:

From t − 1 to t the GPT sector adapts to the technology level TA,t−1, from t to t + 1 the

application sector adapts to the new quality zt and so on (see figure 2). Over time, each

firm maximizes payoffs discounting with the discount factor δ. This discount factor can be

considered as the anti proportional measure for the difficulties of forecasting technologi-

cal developments in the respectively other sector. This means that increasing difficulties of

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anticipation (thus decreasing δ) induce lower values for the levels of z,TA for every point

in time and subsequently for the long run equilibrium. In the extreme case of absolute

uncertainty (δ = 0) innovations would be disrupted entirely. Bresnahan and Trajtenberg

assume that, presumed there is information exchange and thus less uncertainty, a part of

the R&D for the adapting innovation can already be done while the other sector has not

finished its technology improvement yet and the innovation period τ could be shortened.

If there is no coordination at all, τ is as long as before, which effectively means a deceler-

ated innovation rate (see Bresnahan and Trajtenberg 1995, pp. 97-102). Uncertainty can

thus be seen as a second market failure in the innovation process.

Figure 2: Dynamics of GPT innovation process

To sum up: GPTs like nanotechnologies introduce two main market failures in the inno-

vation process. Due to innovational complementarities and the resulting appropriability

effect, returns on investments in innovations can’t be appropriated completely (positive

vertical externality) which leads to too little investments. The same problems occur on

the horizontal level: Raising TA by investments of a single application sector in R&D

makes all application sectors better off, which leads to a free-rider-symptomatic and re-

sults in too few application sectors, each innovating too little. Hence externalities as well

as uncertainties decelerate innovations and lower the long-term equilibrium level of the

nanotechnologies’ quality and the application sectors aggregated technology level.

3 The geography of general purpose technologies

As the microeconomic analysis by Bresnahan and Trajtenberg showed, the development of

GPTs such as nanotechnologies and with it the positive contribution to economic growth

is above all hampered by externalities and uncertainty. The inhibitory impact of positive

external effects is caused by the appropriability effect: A third party can’t be excluded

from the knowledge produced by the innovating party. In fact, this can affect the incen-

tives to innovate positively, too: In form of the well-known spillover effect. This is possible

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because of the existing technological complementarities, pointing out the idea creating ef-

fect of knowledge spillovers. Knowledge is inherently of a non-rival nature and knowledge

developed for any particular application can easily spill over and develop economic value

in a very different context. For example (Griliches 1992, p. 29) described spillovers as

’working on similar things and hence benefiting much from each other’s research’. If the

positive externalities can thus be internalized, the incentives for innovative activity can

be increased and technological progress can be promoted. Many others can profit from

the produced knowledge and productivity of all investments in R&D would raise. The

extent, to which these spillover effects have a positive impact is limited by geographical

distance: positive spillovers are mostly of intraregional nature (see Freund and Lindgens

2008, p. 383).

3.1 Proximity and the role of spillovers

Developing a theoretical basis for geographically bounded knowledge spillovers, new

growth theory became relevant. Romer (1986) and Krugman (1991) developed mod-

els explaining increased divergence in distribution of economic activity, that are based

on increasing returns to scale in production which are generated by externalities across

firms and industries, which again arise from spillovers: Such concentration forces derive

from the firms’ access to markets and from the relationship between a firms’ productiv-

ity and its proximity to other market players. Prevalently, this relationship is industry

specific: A large pool of specialized suppliers and labor forces is accessible and shared

information leads to what is commonly known as knowledge spillovers: Labor mobility,

observation of economic activity around and particularly face-to-face contacts3 build up

trust, enable higher frequency interchange of ideas and can thus promote the develop-

ment of networks, partnerships and joint projects. Between proximate firms, knowledge

spillovers are far more relevant than between remote ones (see Venables 2006, pp. 5ff.):

The marginal transmitting cost of knowledge is lowest with frequent social interaction

and communication. This is what is important to innovative activity: Proximity enhances

the ability to exchange ideas, to sense important new developments and hence reducing

uncertainty optionally. In the same manner, externalities can be - at least partially - inter-

nalized in between the firms operating in a dense network of similar or complementary

firms and sectors. This enhances innovative productivity: Absolute output levels as well

as tempo of innovations can increase and thus proximity can be described as stimulative

for innovations (see Audretsch and Feldman 2004, pp. 2718f., 2734).

3See Audretsch and Feldman (2004) for a further listing of spillover mechanisms.

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3.2 Specialization vs diversification

Advantages and disadvantages of agglomeration of economic activity can be divided into

localization or specialization effects (Marshallian specialization externalities) and urban-

ization or diversification effects (Jacobian diversification externalities).4 These effects are

external to the firms in a specific region but internal within this region (see Fritsch and

Slavtchev 2008, p. 274). Specialization externalities are expected to arise only between

firms within the same industry and can thus only be supported by concentration of similar

industries, argumenting that knowledge is to a certain degree industry specific. Localiza-

tion advantages are, in addition to knowledge spillovers, a specialized pool of workers,

specialized inputs as well as the existence of specialized demand. Among the disadvan-

tages, and thus spreading forces, are pressure on the firm’s product and input prices (see

Freund and Lindgens 2008, p. 383). A further risk is the possible appearance of lock-in-

effects, especially when specialization inhibits exchange with other regions or (comple-

mentary) industries (see Fritsch and Slavtchev 2008, p. 272). Diversification effects are

market size effects and result from agglomeration of different industries, which makes

inter-industrial spillovers possible. Though, these industries should feature a common

basis of interaction to be able to realize the advantages: A common science basis for ex-

ample facilitates the exchange of existing ideas and promotes generating new ones across

(complementary) industries (see Audretsch and Feldman 1999, p. 412). Furthermore,

urbanization advantages can be described in a cultural program, which again facilitates

interpersonal spillovers and the possibility to co-use infrastructure or public institutions

intra- and inter industrial (see Acs et al. 2002, p. 374). Disadvantages can again be seen in

a pressure on factor prices and congestion. There is a sophisticated debate on the impact

of these effects on innovational behavior: On the one hand, the actors of innovation work

together more closely and cooperatively if they stem from the same industry - which favors

Marshallian effects to be more relevant to innovative activity. On the other hand, there is

a higher level of available knowledge in diversified regions and knowledge-exchange be-

tween industries becomes feasible. Cross-fertilization effects as well as evolving new ideas

are more likely, accompanied by technological advance and economic growth - pleading

for the importance of the Jacobian effects. Instead of favoring either one or another ef-

fect, Paci and Usai (1999) as well as van der Panne and van Beers (2006) argue, that both

externalities take effect on the innovative behavior, but in different stages of the innova-

tion process: While at the beginning specialized Marshallian effects seem to be beneficial,

Jacobian become more relevant in a more advanced stadium.4The former were first brought up in the specialization hypothesis by Marshall (1890), Arrow (1962),

Romer (1986), today known as Marshall-Arrow-Romer model. The latter were argued for by Jacobs (1969).

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3.3 Location decisions of nanotechnologies’ industries

Feldman (1994, pp. 93ff.) suggests that especially innovative activity clusters spatially. For

knowledge-intensive industries, technological spillovers are especially relevant because

innovations can develop faster and more effectively on every level of the value creation

chain. Learning processes will be induced, uncertainties reduced and R&D-activities will

be aligned. The innovation diffuses more easily, feedback will be generated on the next

level and finally this retro acts to the beginning of the value creation chain.5Hence, these

industries locate, where knowledge externalities reduce R&D-costs and increase the pro-

ductivity of innovations. As GPTs in general and nanotechnologies in particular entail a

great variety of innovations, it is reasonable to assume that they act as agglomeration

forces in those sectors that already show a tendency to cluster. Favorably, this will hap-

pen in regions where a wide basis of knowledge, given by universities, research institutes

and qualified labor forces, increases the probability of knowledge creation and knowledge

spillovers. Especially in the context of the need of qualified labor force as dominating

input for knowledge-based innovations and thus for innovation-intensive nanotechnolo-

gies economics, two important commonly known trends become relevant as well: Though

the secondary sector will go on playing an important role in the future, the economic

structure in industrialized countries tends to more and more shift from the first and sec-

ondary to the third sector, the service sector and thus towards a knowledge-based econ-

omy. Consequently, first-nature geography advantages become less significant and contin-

uous availability of qualified labor determines location decisions. In combination with the

demographic change as second important trend, the aging and shrinking of industrialized

countries’ societies corresponds to an once more increased competition for qualified labor

forces, emphasizing the relevance of agglomeration in regions that offer a broad basis of

qualified labor forces.

3.4 Nanotechnologies clustered?

Embracing the relevance of clustering to knowledge-based industries, and thus for GPTs

and nanotechnologies, the systematization of the proximity-productivity relation by the

concept of a functional cluster will be picked up briefly. A cluster, whose functional prin-

ciple relies on the advantages of spatial and cultural proximity, refers to a specialized

network of firms ant institutions. Porter (2000, p. 254) defines a cluster as ’[...] a geo-

graphically proximate group of inter-connected companies and associated institutions in

a particular field, linked by commonalities and complementarities [...]’ increasing their

5The proximity to markets is important for innovation-intensive industries, too, as they constitute a testing

ground for new products which can be developed following the needs of intermediaries/consumers. As this

is not the focal point here it won’t be considered further.

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productivity and economic performance. Competition advantages within the cluster en-

sure higher profits. Externalities to firms can be internalized in a cluster and coordination

effects can resolve uncertainty problems. No wonder that there is evidence that firms

in clusters are more innovative than outside (see Fromhold-Eisebith and Eisebith 2005,

p. 1250). The knowledge-based approach of spatial clustering by Bathelt et al. (2002)

offers a distinction of dimensions, along which the advantages for innovational activity

through knowledge generation arise. The vertical dimension of a cluster refers to differ-

ent levels of the value creation chain, the horizontal one refers to sectors/firms on the

same one. The shape of these dimensions indicates the degree of internalization of ver-

tical respectively horizontal externalities within the cluster. The institutional dimension

builds the internal structure, consisting of a system of norms and rules, immanent in for-

mal and informal institutions. This dimension is central for the decline of uncertainty. The

power dimension stands for the persuasiveness of the cluster and reflects the willingness

of regional actors to cooperate. The external dimension is crucial for the future prospec-

tus of the cluster. Too close internal cluster ties risk a lock-in, inhibiting the diffusion of

new technological developments from outside into the cluster as well as chances to learn

from actors outside. This makes one sense that there is a trade-off between the external

and the institutional dimension. The arrangement and development of these dimensions

make a cluster become and stay functional. A cluster can resolve - at least partly - the

occurring market failures where they originate: Positive vertical and horizontal externali-

ties arise along the respective dimensions and can be internalized in the cluster, affecting

the innovative activity positively: Incentive-decreasing externalities become idea-creating

intra-industrial knowledge spillovers, creating a network of interactive information cre-

ation and learning. Uncertainties can be reduced via coordination in the institutional di-

mension, thereby accelerating innovations. Other specialization advantages as mentioned

above further increase innovative productivity in general.

Eliminating the market failures via the organization in a cluster, the development of the

GPT is supported at the expense of a specialization on a particular application industry (or

even a particular value creation chain); otherwise the cluster advantages would not work:

The power dimension would be weakened because of a too big technological distance,

thereby impairing the functionality of the cluster as a whole. The supportive effect is thus

restrained on a single application field. Considering the GPT’s feature of pervasiveness,

this is not optimal: It’s the multi-purpose of use that induces continuous technological

improvements thereby allowing for an even wider range of uses, exponentiating the pro-

ductivity and growth effects of GPTs. An increasing number of application sectors leads

to higher innovation incentives in the GPT sector and other application sectors, which

will again feed back. This may also lead to an overlap between so far unconnected ap-

plication sectors via cross-fertilization effects. All in all this results in a generally higher

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level of R&D with increased productivity. Thus a restraint that favors a specialization on

one application field in form of a cluster effectively decreases productivity of innovations

elsewhere, because feedback effects with other sectors and thus further innovations are

prevented. Put differently: Specialization alone cannot be the key for an optimal devel-

opment of GPTs as diversification promises respectable growth effects, too. Within the

dimensions of one cluster, specialization (i.e. functional clustering) and diversification

(i.e. weakening of the cluster) constitute a trade-off. Consequently pure nano-clusters are

not expected to emerge but they have to be discussed in the context of their applications.

The problem to solve is hence how to secure the promising growth effects of the multi-

purpose property of nanotechnologies while profiting from the innovation enhancing ef-

fects of a cluster in a particular application field. What does the optimal pattern of ag-

glomeration for nanotechnologies thus look like?

4 Application to nanotechnologies in Hamburg

To answer this question, a case study on the role of nanotechnologies and on their devel-

opment was conducted in the metropolitan region of Hamburg, Germany, in spring 2010.

Therefore archival and documentary data, including websites and analyses conducted by

chamber of commerce or the Senate of Hamburg was used, expert interviews and a tele-

phone survey were carried out and the specialization pattern was determined.

Hamburg is Germany’s second biggest city with about 1,8 m inhabitants and one of its eco-

nomically most prosperous cities with a GDP of about 90 bn Euros, that is 80.395 Euros

per employee in 2008 (Statistische Ämter des Bundes und der Länder 2008). Hamburgs

economic structure is characterized by a sound industrial base and a well developed ter-

tiary sector, optimal conditions for ongoing success despite structural change. The harbor

plays a central role as first-nature geography advantage in this structure, because it en-

sures easy, and with respect to rising energy prices cheap, access to the world market,

especially for the industrial production. In the secondary sector, specialization advan-

tages in aerospace industries, maritime industries (both condensed in ’manufacture of

other transport equipment’ which exhibits a location quotient6 of 5.83) and life sciences

can be identified. Notwithstanding the specialization pattern in the secondary sector, the

economic structure in Hamburg is coined by the service sector, following the trend of struc-

tural change in Germany. In this sectors, first-nature geography advantages do not exist

6The location quotient is a measure for regional specialization, which calculates the ratio between national

and regional employment shares of the considered branch. It thus informs about the relevance of proxim-

ity/productivity or first-nature geography advantages. For a detailed listing of Hamburgs location quotients

> 1 see Boje et al. (2010)

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and thus proximity-productivity effects and qualified labor play a significant role. Ham-

burg is still disposing of positive population growth rates contrary to the German trend:

The population is forecasted to grow at a rate of 0.5% until 2025. Moreover labor force is

even supposed to grow at a rate of 2.5%, emphasizing that the ageing society will not be

a problem in the next time (see Boje et al. 2010). In the context of structural and demo-

graphic change Hamburg is thus, in contrast to most parts of Germany, in an advantageous

position because labor force shortages may not arise as early as in other regions and the

transition towards a knowledge-based economy can take place. Not suprising thus that

there are distinct specialization advantages in most branches of the tertiary sector. But

also for rather industry-related branches, such as nanotechnologies and its appliers in

genereal, qualified labor and corresponding acitivities such as face-to-face contacts and

knowledge spillovers, play a significant role considering the innovativeness and thus the

knowledge base of this branches. An online survey of 115 nanotechnology-firms in Ger-

many underlined that the most important location factor is availability of qualified labor

(77% state that this is (rather) important), followed by the proximity to research institutes

(71%) and traffic infrastructure (65%).

Given this location determinants, preconditions for the optimal development of nanotech-

nologies are given; Hamburg offers a perfect environment for a case study that shall ex-

amine the agglomeration pattern of nanotechnologies. As the actual impact on growth

nanotechnologies can exhibit depends on the regional production structure, it is impor-

tant that the various opportunities incorporated in GPTs such as nanotechnologies can be

made profit of. The given preconditions will surely not inhibit an optimal development of

nanotechnologies (and thus operate as spreading force) but offer a good basis. Despite

the structural and demographic trends, Hamburgs economy still has a reliable industry

base (which is important for the optimal development of nanotechnologies as GPT) and

offers a broad variety of qualified labor forces, ensuring the knowledge base needed for

innovative activity. Regarding the fact of the well formed tertiary sector, the region ex-

hibits an infrastructure and a (cultural) diversity that can be assumed to be conducive to

innovations. In the context of the city’s mission statement of a responsibly growing city

in order to expand its significance as an European metropolis on a national and interna-

tional level7, the development of nanotechnologies shall be explicitly supported through

industrial policy. Whether, and if yes how this is sensible will be discussed in the following.

7’Vision Hamburg: Responsible Growth’ For further information: http://welcome.hamburg.de/business-

location/1646010/perspectives.html, last checked 02.03.10

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4.1 Nanotechnologies clustered in Hamburg?

There exists a significant number of nano-related firms in the metropolitan region of Ham-

burg, most of them focusing either on nanobiotechnology, thus the application of nan-

otechnologies in life sciences, on nanotools or nanomaterials, again frequently applied in

life sciences. But above all the community is constituted by publicly financed research

institutes like the classical natural science institutes (physics, chemistry) at the University

of Hamburg or public-private partnerships (for example the Center for Applied Nanotech-

nology (CAN)). They act as agglomeration force, as corresponding to an online survey

of nanotechnology firms in Germany (n=101), research institutes are (rather) important

as location factor for 71% of nano-firms, supporting the theoretical considerations above

that assume nanotechnologies to cluster favorably where the probability of knowledge

spillovers is high. The CAN and other institutions (e.g. HanseNanoTec or interdisciplinary

nanotechnologies center Hamburg (INCH)) also aim to coordinate research. Despite these

dispositions, a functional cluster doesn’t exist. A critical mass of firms intending to coop-

erate is necessary in order to establish a broad horizontal and vertical cluster dimension.

The problem of nanotechnologies, and this can be be assumed for every GPT as a pecu-

liarity, is the multitude of application fields. As the pure actitivity in nanotechnologies is

not sufficient for the establishment of a coordinating network, but a technological prox-

imity is needed for a coherent cluster structure, a proper nanotechnologies cluster is vir-

tually impossible. Though, there exist several institutions concerned with nanotechnolo-

gies8 constituting an institutional dimension. A telephone survey of nanotechnology firms

in Hamburg (N=21 phoned firms, answers from n=12) suggests that these institutions

are employed differently, the scale went from ’known’ over ’in contact’ to ’joint projects’.

Notwithstanding, none of the firms esteemed these institutions important enough to name

it as a location factor (which was asked for before in the same survey). This corresponds

to findings from th online survey, where only 29% regarded the availability of regional

nano institutions as (rather) important. This supports the assumption that clustering in

nanotechnologies might be difficult in general because of its multi-purposeness: In het-

erogenous application fields other technologies apart from nanotechnologies are often at

least as important as nanotechnologies themselves which creates a technological distance

between the diverse applications that makes institutions that only support nanotechnnolo-

gies less important. Consequently this inhibits the development of cluster advantages. This

is true for contrast mediums and nano-activated varnish, thus products of different indus-

tries, as well as for contrast mediums and drug delivery systems, hence even products of

the same industry. Consequently, firms differ very much vertically, and with it the require-

ments to the economic environment and the opportunities to realize economies of scale.

8Additional to the above mentioned the chamber of commerce, ’TuTech’ as technology transfer institution

and two innovation foundations can be referred to.

12

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This weakens communication and cooperation incentives and thus the establishment of a

possible power and institutional dimension supported by the cluster members (see Henn

2006, pp. 248f.). Contributing to these difficulties is the fact that a part of nanotechnology

firms wouldn’t understand nanotechnology as their core product and thus themselves as

nanotechnology firms 9, but rather as suppliers or firms of other (application) industries.

This will effectively hamper the development of nanotechnologies, because market fail-

ures are not corrected by a cluster, resulting in too little and too late innovations. The

situation changes if these application sectors depict a cluster structure themselves as it is

the case not too seldom. In Hamburg this can be observed especially concerning firms that

operate in the life science sector as will be seen later.

In a nutshell: Notwithstanding the lack of a functional nano-cluster, actors from sciences

and politics became attentive on the relevance of nanotechnologies and initiated institu-

tions that are supposed to support its development, for example in shape of internalizing

vertical external effects by the promotion of technology transfer, in order to benefit from

the nanotechnologies’ growth potential. Therefore the agglomeration of nanotechnology

firms in Hamburg is not to be seen as unconnected concentration of firms either.

The problems in the development of a nanotechnology cluster do not seem to consist in the

special situation of Hamburg, but in the characteristics of GPTs in general. The concept

of a functional cluster as a solution for the market failures in the innovation process of

nanotechnologies seems to be fitting for nanotechnologies only inasmuch as it offers the

integration of measures against uncertainty and external effects. Regarding the difficulties

of a cluster development in a technology field coined by heterogeneous application fields,

the problems mentioned above arise already at the very beginning of the cluster creation.

A modification of the concept seems to be necessary in order to make it feasible for the

improvement of development processes in nanotechnologies.

4.2 Specialization pattern of nanotechnologies in Hamburg

In order to develop a cluster coherence within nanotechnologies nonetheless, a focus on a

very tight profile within an application field is the only way (see Henn 2006, p. 251).

9The telephone survey of nanotechnology firms in Hamburg mentioned above showed that three firms

though they once were enrolled by an employee into the nano-map, which lists relevant nano-enterprises

and institutions in Germany (see www.nano-map.de for further information), did not want to answer because

they said they had not anything to do with nanotechnology.

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4.2.1 Life Sciences as a focus

In Hamburg, such a focus is existing: Here, life sciences is the central application field of

nano-activated products, equal if nano-materials, nano-tools or nano-particles in general.

The center for applied nanotechnology (CAN) mainly produces the nanoparticles needed

in Hamburg. This center’s research is focused on nano applications in life sciences, as it

was co-founded as a public private partnership by industrial enterprises focusing on life

sciences.10 No wonder thus that the CAN is concerned with life science topics in three

of four foci: Cosmetics, medicine and pharmacy; their single strategic partner is again an

enterprise stemming from life sciences. The interdisciplinary nanotechnology center Ham-

burg (INCH), as a further institution in the nanotechnologies field, states its key activity

likewise as the connection of nanotechnologies and life sciences and hence the nano-

industry is often considered as being part of the virtually existing life science cluster (see

Handelskammer Hamburg 2006, p. 34)sing on life sciences.11 No wonder thus that the

CAN is concerned with life science topics in three of four foci: Cosmetics, medicine and

pharmacy; their single strategic partner is again an enterprise stemming from life sciences.

The interdisciplinary nanotechnology center Hamburg (INCH), as a further institution in

the nanotechnologies field, states its key activity likewise as the connection of nanotech-

nologies and life sciences and hence the nano-industry is often considered as being part

of the virtually existing life science cluster (see Handelskammer Hamburg 2006, p. 34) 12.

Here, cross-linked competence in research institutes, firms, politics and institutions exist

as well as access to infrastructure and markets (see Bundesministerium für Wirtschaft und

Technologie 2008, pp. 27f.). Complete value creation chains from fundamental research

to the end product are capable of processing nanotechnologies and the demand of nano-

activated inputs is assured by several big enterprises. As already indicated, nano-suppliers

can profit extraordinarily well from the advantages of the life science cluster, as nanotech-

nologies are implemented rather at the beginning of the value creation chain: Institutions

coordinate and manage technology transfer, knowledge spillovers are effective, a pool

of specialized workers and suppliers and a publicly funded research infrastructure exist.

Like this, nanotechnological competence can be shaped and developed, strengths can be

bundled and top performances be generated. How is this possible?

10For further information see http://www.can-hamburg.de/company/background.php, last checked

16.03.2010.11For further information see http://www.can-hamburg.de/company/background.php, last checked

16.03.2010.12For further information about this cluster see Handelskammer Hamburg (2006).

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4.2.2 Joint-use of the life science cluster

Nanotechnologies can be seen as well associated to the existing life science cluster, con-

sidering nanotechnology-research as upstream sector of the life sciences’ value creation

chains. Vertical coordination between this sector and the intermediaries, the actual up-

stream sectors of the value creation chains consisting of ’pure’ life science sectors, is fore-

most arranged by the CAN as important interface. Here, cross-fertilization effects in the

development of nanoparticles for different applications can be generated (see Henn 2008,

p. 110). At the point where nanotechnologies expand into the life science cluster, market

failures occurring along the value creation chain can be (at least partly) eliminated by the

cluster advantages of the life science cluster resulting in positive incentives to innovate on

every level of the extended value creation chain; thus also in the upstream nano-sectors

as well as the basic research sector. This is secured by the described feedback mechanisms

of innovative complementarities. Figure 3 illustrates schematically how the affiliation of

nanotechnologies to the life science cluster works. Like this, cluster advantages can be

present without a proper nanotechnologies cluster but rather by a ’joint-use’ of the life

science cluster (thus a clustered nano-applier) and nanotechnological research and core

enterprises.

In order to built up a ’joint-use cluster’, a focus on an application field is surely conducive,

if not necessary in order to built up a reciprocal awareness of nanotechnologies and their

scope for application in within life sciences, to strengthen nanotechnological competences

and to create an efficient interface (instead of a proper cluster coherence) between nan-

otechnologies and the associated life science cluster. At this stage of development, special-

ization and not diversification is what drives innovation at the end. But if the benefit of

this joint-use of the life science cluster by nanotechnology actors stays restrained on this

single application field once this joint-use works, the same problems an own nanotech-

nology cluster would produce will reoccur: The dynamism of nanotechnologies as GPT

is inhibited and the effects on economic growth are slowed down. Thus the diversifica-

tion matter reoccurs. As argued for above, a diversification of the cluster would equal

its destruction. This is counterproductive, because at this stage of development both,

diversification and specialization are conducive to an optimization of nanotechnologies’

innovation processes. But the modification of the functional cluster that could be found in

Hamburg, namely a joint-use of an application sector’s cluster offers another possibility of

diversification without destroying the specialization in form of the cluster:

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Figure 3: Affiliation of nanotechnologies to the life science cluster4.3 Diversification and specialization

As considered here, the nano-related sectors (nano core enterprises and basic research)

constitute the very upstream sector of the applicating life science cluster. The main cluster

advantages do not arise in this part but in the clustered sectors downstream. A diversi-

fication in form of connecting this upstream nano-sector to other (clustered) application

sectors hence would not affect the functionality of the cluster in life sciences: It is the ap-

plication clusters that diversified instead of a diversification within one cluster. Therefore,

the correction of the arising market failures in the life science cluster would not be af-

fected either, but the opportunity to profit from the described diversification effects would

be opened. In figure 4 this multiple joint-use is illustrated: The nano-upstream sectors

would than ideally be the very upstream sector of several downstream clusters, connected

by an institution that organizes the vertical connection (e.g. in form of technology trans-

fers) to all the application clusters.

The probability of profiting from cross-fertilization effects would increase at this inter-

face, the arising market failures in the innovation processes of the various value creation

16

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Figure 4: Affiliation of nanotechnologies to various application clusterschains would be corrected by the respective clusters and technological dynamism as well

as a widening of the range of uses of nanotechnologies would be secured by the increas-

ing application sectors. The more applicated, the more complementary technologies for

nanotechnologies will be developed, inducing innovations to their part that would (via

innovational complementarities) feed back to other sectors of the value creation chains,

increasing innovative activity in general. Like this, diversification and specialization could

be conducive at the same time.

4.3.1 Joint-use widening in Hamburg

Considering the case of Hamburg, the cluster structure of the joint-used cluster of life

sciences is built up so far (see section above). Hence, specialization advantages are at

work, generating positive development impulses for nanotechnologies. But up to today

evidences of an effective diversification could not be found. As depicted above, a diver-

sification is not only necessary for an optimal development of nanotechnologies, but also

possible considering the joint-cluster structure found in Hamburg. Thus, carrying out our

case study, we finally examined reasonable possibilities of tying the nano sector to other

clustered application sectors (see figure 4).

Looking for other (prospective) functional clusters of industries that are potential nan-

otechnology operators, the aviation sector, renewable energies industries and the maritime

industry seem to be promising application fields in Hamburg, as two of them where identi-

fied before as specializations of Hamburgs secondary sector and in all fields either already

functional or easily to be activated clusters exist (Handelskammer Hamburg 2006). Fore-

most nanotechnologies can become adopted by these industries if basic research focuses

on these fields, too. The research on nanomaterials in Hamburg for example is not only

interesting for applications in life sciences. Composites that, thanks to nanotechnologies,

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combine old with new features (like stability and lightness with conductivity) are not only

interesting in medicine (like for artificial replacements), but also for the endowment of

airplanes (see Airbus S.A.S. 2007, p. 19). This is also true for renewable energies, where

another kind of such composites could be used in rotor blades of wind wheels. To quote

another example, employing nanomaterials new solar cells could be developed by uti-

lizing nanotubes in combination with quantum dots, which has already been tested at

Hamburg’s research institutes. These quantum dots were afore applied in pharmaceutical

applications. In maritime industries nano-materials could improve non-stick coatings and

anti corrosives of paints or generally offer lighter material. If research is conducted in all

these application fields, cross-fertilization effects can arise. Nanoparticle research could

be used as platform, originating nanoparticles with partly the same and partly differing

features, depending on the later application. An improvement of quality and technology

levels of nanomaterials as well as nanotechnologies in general (basing on the feedback

mechanism of innovational complementarities) is due to increased research activity, learn-

ing and cross-fertilization effects. Besides, the joint use of several cluster structures at the

same time opens cluster advantages for other application sectors, in total exponentiating

the positive effects for the development of nanotechnologies.

In aviation and renewable energies industries, first projects have taken place in order to

use nanotechnologies in these industries, mostly stemming from research institutes that

before studied application in life sciences. These projects show that there is a technolog-

ical base in the nanotechnological research particularly driven for the life science sector

that is relevant for other application sector and thus cross-fertilization effects can actually

be realized. The first efforts done in order to make use of nanotechnologies for other appli-

cation fields and to connect economic activities demonstrate that the first step to connect

clusters is easy to be done. Referring to the present focus, a widening of the systematically

supported nanotechnologies application sectors is not self-evident, but entailing valuable

advantages. This is of course also true for maritime industries, especially regarding their

relevance in Hamburg. But other than in the above mentioned application fields, there is

no evident connection of maritime industries and nanotechnologies in Hamburg up to to-

day - which favors this clusters not to be the first to widen the joint-used cluster structure

of nanotechnological appliers. What seems to be important considering this is the need

of an institution that supports the connection of basic research on nanotechnologies as

technological platform with the technological applications, ensuring the technology trans-

fer. Such an institution would advance further clustering around, generating even more

dynamics (see Robinson et al. 2007). Robinson et al. (2007) also underline that regarding

various kinds of technological platforms there will be path dependencies in so far that ear-

lier investments shape what can be done later, which pleads for a well-timed initializing.

From today’s point of view, the CAN could be advanced to such an institution, already

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ensuring the technological basis in combination with established connections to many of

the (possible) nano-operators. Particularly at the beginning of the extension of joint-use of

clusters it seems to be important that there exists one coordinating institutions to bring all

cooperations together. Consequently nano institutions, particularly in combination with

research facilities like in the case of CAN, will become more important when efficiently

connecting different application fields, shortening technological distances.

4.4 Nanotechnologies in Hamburg: Specialization and diversification

In Hamburg, a specialization of nanotechnologies at the very beginning of its development

was needed in order to build up a common interest base through technological proximity

which made the establishment of a cluster-related structure actually possible. Like this, ad-

vantages of a joint-used cluster could become effective and inhibit market failures in the

innovation process of nanotechnologies. As argumented, specialization alone is not the

key for an optimal development of nanotechnologies, but diversification is crucial as well,

augmenting the growth-inducing innovational activity in other application sectors and via

innovational complementarities in the nano-sector, too. While constituting a trade-off in

the classical functional cluster model, in the modified joint-used one specialization and

diversification can coexist: After the establishment of distinct cluster effects within life

sciences (i.e. specialization), an initial cluster structure in the aviation sector and within

renewable energies industries could be achieved, thereby leading to regional diversifica-

tion. This can make another set of cluster structures beneficial, if the coordination at the

interface of nanotechnologies (basic) research is ensured, while supporting technological

dynamics through various (and increasing) application fields. Referring to the Marshall Ja-

cobs debate, localization and urbanization effects can effectively be innovation-enhancing

in this case: For the positive development of nanotechnologies in Hamburg in terms of an

initial positioning and functional tying to an already existing cluster structure, localization

effects (i.e. intra-industrial knowledge spillovers and coordination opportunities) were

advantageous. This specialization was and is conducive by internalizing external effects

within this application field and reducing uncertainty. To ensure an optimal development

of nanotechnologies through advantages of cluster structures in future, an additional di-

versification is beneficial. Spillovers and cross fertilization effects of inter-industrial nature

can generate synergistic effects and induce new innovation impulses for nanotechnologies

in general and established application fields, such as life sciences, as well as new ones, in

particular. The application in as many industries as possible and the simultaneous correc-

tion of market failures through the use of cluster structures would allow for an optimal

development of nanotechnologies. An improvement of the quality of nanotechnologies

would entail a complementary improvement of the technology levels in the application

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sectors and vice versa (i.e. innovational complementarity would positively affect the de-

velopment). Via vertical and horizontal coordination well as lowered uncertainty in the

respective clusters this effect would be exponentiated and would result in more and faster

innovations altogether. Consequently, innovation enhancing cluster advantages can be

generated without affecting the positive dynamic effects for the development of nanotech-

nologies ensured by pervasive use.

5 Conclusion

Nanotechnologies can remarkably contribute to economic growth. As GPTs the character-

istics of pervasiveness, technological dynamics and innovational complementarities result

in reciprocal prompting of innovative activity in up- and downstream sectors and hence

technological advance and economic growth. The innovational complementarities, on the

one hand origin of innovative activity produce on the other hand market failures in shape

of vertical and horizontal externalities. Innovation processes are interdependent between

sectors along the value creation chain, feedback mechanisms work bidirectionally and on

account of the appropriability effects and uncertainties too little innovations are realized

too late. The aim of this paper was to find a solution for the problems inhibiting the op-

timal development of nanotechnologies and thus their contribution to economic growth.

The core problem inherent in the described market failures is a lack of coordination and

cooperation: Positive external effects can be internalized and uncertainty be reduced if a

technological region instead of incoherent firms and sectors is considered. Analyzing the

advantages of geographical proximity, agglomeration within a region seems to offer far

more than just the simplification of coordination. External and technological effects of

scale become intern within the region and promise increased productivity of innovative

activity.

Though functional clusters constitute an agglomeration pattern that corrects market-failures

such as externalities and uncertainties by advantageous specialization effects such as co-

ordination and spillovers, it per definitionem (i.e. being specialized in a particular field)

contradicts the GPTs feature of pervasiveness, which induces continuous technological

improvements and anew spurs innovations that are crucial for the development of nan-

otechnolgies regarding overall growth effects. Consequently pure nano-clusters are not

expected to arise. Looking for an optimal pattern of agglomeration of nanotechnologies in

particular and GPTs in general, a case study examining the situation of nanotechnologies

in Hamburg was driven. Expectedly no cluster structure of the nanotechnologies industry

could be found, but surprisingly cluster advantages effectively do support the development

of nanotechnologies in Hamburg. The advantages do not arise through a proper nanotech-

20

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Figure 5: Timeline: Specialization and Diversificationnologies cluster but through a joint-use of the cluster of the most important application

field life sciences. Via vertical linkages, the nano sector could be, obviously successfully,

connected to the functional life science cluster. This constituted a possiblity to revisit the

idea of coexisting specialization and diversification. Within one cluster specialization and

diversification do constitute a trade-off but in between various clusters this is very well

possible: Once the connection of the nano sector to a clustered application sector has

been successful, like the distinct cluster effects within life sciences, a further association to

other (clustered) application sectors is possible, leading to regional diversification. Within

the economic structure of Hamburg, two easily to be associated clusters in renewable en-

ergies industries and aviation could be identified. Industrial policies that shall support

nanotechnologies should therefore promote the further affiliation of these clusters into a

network of clustered application sectors, all having the nanotechnological sector as their

very upstream sector in common. The dedicated support of a proper nanotechnologies

cluster in general however is not sensible and therefore not recommended.

To sum up: Within the dimension of joint-used clusters diversification can support nan-

otechnologies’ development while in each cluster specialization advantages still correct

market failures (see time line in figure 5). Consequently, innovation enhancing cluster

advantages can be generated without affecting the positive dynamic effects for the devel-

opment of nanotechnologies ensured by pervasive use.

Transferring this idea to the context of any GPT, the questioning of the cluster concept

for the elimination of market failures in the innovation processes is legitimate. Cluster

policies will not work, if the local actors do not conceive themselves as GPT-actors due to

technological distances, hence inhibiting coordination. For this reason, a specialization of

the region’s GPT industry and the promotion of a cluster or a linkage to an existing ap-

plication sector cluster makes sense. Referring to the relevance of universal applicability

of GPTs, a widening of application fields (i.e. a diversification) should be forced in or-

der to open opportunities to realize urbanization effects and ensure optimal development.

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Whether and if so how this is possible always depends on the regional economic structure.

Though diversification becomes more important with the progression of the development

of GPTs in a region, specializations in clusters and sub-specializations will constantly re-

main important in order to maintain localization advantages and correct market failures.

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A Mathematical appendix: The dual inducement mechanism

Given the GPT with a quality z is provided to the application sectors for the price w.

The profit decreases when w increases. The technology level Ta can be chosen by the

downstream sectors by controlling their R&D-activity. Ta correlates positively with the

profit of the application sectors, as well as with z. The application sectors act profit-

maximizing when

maxTa

πa(w,z,Ta)−Ca(Ta) (1)

where Ca denotes costs for innovation in application sectors, πa is are the gross private

returns to technological advance. With the innovational complementarities given by

πa

zTa =δ2πa(w,z,Ta)

δzδTa≥ 0 (2)

follows, that the marginal value of enhancing the application sectors technology increases

with z. The technology investment function

Ta = Ra(z,w) (3)

follows from the first order condition for (1). With d2Ca

d2Ta> 0 and the second order condition

( δ2Ca

δ2Ta< 0), Ra is upward sloping in z. This implicates that a technological improvement of

the GPT results in complementary improvements in the downstream sectors.

Modeling the profit-maximizing behavior of the GPT sector we get

maxz

πg(z,TA,c)−Cg(z) (4)

with Cg(z) denoting the innovation costs (with dCg(z)dz > 0 and d2Cg(z)

d2z > 0), c is the constant

marginal production costs for the good embodying the GPT and TA the aggregate tech-

nological level of all application sectors. Assumed πg(z,TA,c) ≡ maxw

(w− c)∑a

Xa(w,z,Ta),

whereas ∑a

Xa(w,z,Ta) is the (conditioned) input-demand of all application sectors, this

gives with the first order condition

z = Rg(TA,c) (5)

Because z depends on TA and therefore on every single Ta, the GPT-firm reacts on changes

in Ta:

δRg(TA,c)δTa

≡δ2πg(z,TA,c)

δzδTa

− δ2πg(z,TA,c)δ2z + d2Cg(z)

d2z

(6)

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The innovational complementarities (see 1), from which δ2∑aXa(w,z,Ta)

δzδTa> 0 follows, lead to

δ2πg(z,TA,c)δzδTa

> 0. The second order condition gives δ2πg(z,TA,c)δ2z < 0. Thus

δRg(TA,c)δTa

> 0 (7)

Hence Rg is upward sloping in TA thus private return to investment in z increases with TA.13 Thus, the incentive to innovate for the GPT sector is interrelated with the behavior of

the application sectors. Innovation processes are therefore strategic complements.

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