An interesting part of the present scientific debate in urban economics concerns the appropriateness of some theoretical —and consequently empirical— definitions of the city and its role, underlining the reductive character of purely functional approaches in terms of agglomeration economies. Many scientific achievements have been attained exploiting the virtues of these approaches, residing in their strong internal consistency (within their logical assumptions) and sophisticated formalization. What appears to be left is the inspection of the true nature of cities, going far beyond their agglomerated physical form and the consequent benefits on transactions and communications.

The paper suggests that the geographical-functional approach should be complemented by two other approaches, implicit in classical economics and in evolutionary economic theory, which allow the inspection and (perhaps) a proper interpretation of other constituents of the nature of cities: what I call the relational-cognitive approach —interpreting the city as a cognitive milieu, generating knowledge, creativity and innovation— and the hierarchical-distributive one, interpreting the relationships with the non-city, the «countryside» of classical economists, in terms of control and monopolistic determination of relative prices. The former approach looks at the intrinsically generative role of the city and its capability of developing continuously new activities and functions; the latter at power relations on space and control on income distribution.

If the functional approach looks nowadays quite consolidated, the cognitive one needs still in depth reflections, as it implies the (at least partial) abandonment of methodological individualism that permeates neoclassical economics, with the advantage of better utilizing the conceptual achievements of other social disciplines. On the other hand, the hierarchical and distributive approach looks today quite unexplored.

At the end, a tentative, formalized model of agglomeration economies is presented, with the goal of stimulating the attention on the empirical measurement of the effects of the cognitive and control roles of the city. Two main open issues emerge, both referring to income distribution: how are the advantages of increasing returns to urban scale being distributed among the internal production factors (and urban social classes, including land owners) and how could we measure the urban power in terms of income distribution in space.