How Cities Grow: the Standard Urban Model This post is the second in my Living Literature Review project, Scaling in Human Societies. The post can be found here, though it is the same content. It’s a little on the technical side, but I find the standard urban model to be a foundational principle in understanding how cities grow. Like last week, the Quick Hits section can be found after the references. There are thousands of cities in the world, each with its unique history. There are, nevertheless, regularities in how cities grow, which can be captured in the monocentric standard urban model (SUM). In his 1967 paper, Mills (Mills (1967)) presents a simplified model that nevertheless helps to explain many common features of cities. That we have cities at all is something that is necessary to demonstrate. Mills assumes reasonably that most goods are produced, with the exception of land and labor, which are non-produced goods. If we assume that land is homogeneous-one acre is just as good as another for economic purposes-and if we assume constant returns to scale, then we should expect all people to spread out evenly to avoid bidding up land prices. In this scenario, there would be no cities. First, land is clearly not homogeneous; some sites are more advantageous to certain industries than others. In particular, Mills notes that most major cities in the United States are located at strategic waterways to facilitate trade. In Mills’ formulation, production of goods is a function of land, labor, and capital goods. The phrase constant returns to scale means that if the three inputs change by a certain percentage, then the output will change by the same percentage. More formally, Mills presents production of goods as follows. Here, X₁ is the total production of goods, A₁ is a constant, and the three factors respectively are land, labor, and capital. 1. By 1967, the concept of agglomeration was already well-established and discussed by Mills.