Alonso and the scaling of urban profiles

Urban characteristics scaling with total population has become an important urban research field since one needs to better understand the benefits and disadvantages of urban growth and further population concentration. Urban scaling research, however, is largely disconnected from the empirics and theory of intra-urban structure for it considers averaged attributes and ignores residential choice trade-offs between transport and housing costs within cities. Using this fundamental trade-off, the monocentric model of Alonso provides theory to urban density profiles. However, it is silent about how these profiles scale with population, thus preventing empirical scaling studies to anchor in a strong micro-economic theory. This paper fixes this gap by introducing power laws for land and for population density in the Alonso model. From an augmented model with land use, we derive the conditions at which equilibrium profiles match recent empirical findings about the scaling of urban land and population density profiles in European cities. We find that the Alonso model is theoretically compatible with the observed scaling of population density profiles and leads to a satisfactory representation of European cities. The conditions for this compatibility refine current understanding of wage and transport costs elasticities with population. Although they require a scaling power of the profile of the share of urbanised land that is different from what is observed, it is argued that alternatives specifications of transport cost functions could solve this issue. Thus our results call for revisiting theories about land development and housing processes as well as the empirics of agglomeration benefits and transport costs.