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2 Hypothesis

Our main hypothesis is that city size matters. Since larger cities are more diverse, both in terms of economic profile and of human and social capital, their functions demonstrate a higher level of complexity in terms of urban economy. In that way, the propagation of innovation among towns and cities has been formalized as a hierarchical diffusion process. Indeed, the largest cities are the first to capture the benefits of the innovation, and later on they let them filter down the urban hierarchy. Larger cities concentrate a larger part of anything "new" at any time and they become larger because they were successful in adopting many successive innovations. This is explained by the higher levels of information, of skilled labour and the diversity and capacity of infrastructures that are the distinctive attributes of large cities (Bretagnolle et al., 2009).

As a consequence, they have also developed broader diversity of activities, and

attained higher levels of social and organizational complexity. These characteristics explain why they have a greater probability to adopt any further innovation at an early stage. Later, many of these innovations become part of the activity of all towns and cities, since they meet needs that become commonplace. But the functioning costs in these large urban areas are also much higher, and many activities are forced to migrate out to smaller settlements where they can sustain their economy (Pumain et al., 2009).

Besides the effects of hierarchical selection, there is a second type of asymmetry

that is created in urban systems by the innovation process. Sometimes, the resources for which exploitation becomes profitable are not available in every location; this gives rise to urban specialization because the related economic activities can only develop in a few urban sites. Thus urban specializations are partly explained by the unequal diffusion of some innovation cycles that are linked to spatially concentrated resources. But they may also result from the hierarchical diffusion process itself. That is, when a plant relocates from a large city to a small town, this small town becomes specialized in the activity of the plant (Duranton & Puga, 2000, 2005).

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