A Spatial Production Economy Explains Zipf’s Law for Gross Metropolitan Product

This paper provides a theoretical and empirical analysis of the distribution of GDP at city level (henceforth referred to as gross metropolitan product, GMP) with the aim of bridging the gap betwen the literature on agglomeration economies and the city-size distribution. We show that 1) it shares the same characteristics to the city-size counterpart: They are both fat-tailed, and 2) a 1% increase in employment leads to a 1.117% (or 1.180% in theory) increase in GMP. Free mobility of household forces a city to operate at the size where scale economies are present, or else, the city cannot offset the reduced housing consumption and increased congestion due to crowding set off by agglomeration economies, and loses its population and GMP to elsewhere. We establish a production economy model to break down the interplay above and derive the equilibrium GMP distribution, which tests well with the US data on GMP.