The allometry of housing prices in urban scaling laws and an equalised dwellers’ utility across settlement sizes

Large cities have benefits offset by costs. Since the inter-urban Rosen–Roback model, economists interpret the attractiveness of a city in terms of spatial equilibrium: a cost-benefit balance across locations. High incomes are counterbalanced by high prices or disamenities. A cross-sectional regression analysis on the ∼ 8000 Italian municipalities whose population sizes range from around 30 to 3 million, found the following association: by doubling the population of a settlement, holding constant its per capita income and touristic presences, its house price rises by 9%. House price increases are not offset by an increase in income. Bigger cities are more expensive than smaller. This opens reasoning upon indirect economic valuations of the value - or cost  if you see it differently - (opportunities, services, vibrancy…) that urban size has for people who choose - or must  choose - bigger settlements. At the best of my knowledge, this is the first work, in this form, finding a scaling coefficient for house price. It resulted around 0.13, namely, by passing from a town of 10˙000 inhabitants to a city of 1 million inhabitants (even if holding constant tourism and income), the average house price would almost double (+82%), almost tripled (+183%) from a village of 1˙000 inhabitants to a 3 million inhabitants’ city, and almost quadrupled (+282%) from a hamlet of 100 inhabitants to a 3 million inhabitants city.