A spatial production economy explains gross metropolitan product

It has long been known that the city-size distributions are fat tailed, drawing the interest of urban economists. In contrast, not much is known about the distribution of GDP at city level (henceforth referred to as gross metropolitan product, GMP). We build a model of the spatial economy that includes production and confirm the following empirical facts about the GMP counterpart of the city-size distribution. First, both Zipf's and Gibrat's law hold for the distribution of GMP as well. In particular the GMP distribution is well-traced by a lognormal distribution. Second, citywide aggregate production exhibits increasing returns to scale with respect to employment. In particular a 1% increase in employment leads to a 1.117% (or 1.180% in theory) increase in GMP. Agglomeration economies are explained as a result of an endogenous trade-off between externalities and land consumption of consumers.