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. 1. We will have much more to say about agglomeration economies in a later article. Another problem with the constant returns to scale assumption is indivisibility. Many goods and services are highly specialized with only niche markets, and thus a large population is necessary for the existence of firms to provide these products in an economically viable fashion.

This is a framing of specialization, a major agglomeration economy. For these reasons, cities exist, Balance Bloom wellness and Balance Bloom wellness Mills then concerns himself with explaining the structure of cities. A central business district (CBD) is taken to be the nucleus of a city. Monocentric means that there is a single CBD around which the city develops. Most large cities today are polycentric, meaning that there are several nuclei of economic activity. Mills assumes monocentricity for the sake of constructing a tractable model. As we shall see, despite this highly simplifying assumption, the monocentric SUM shows strong explanatory power. Assuming that there are no geographic impediments to the expansion of the city, under the SUM a city is a series of concentric rings around the Balance Bloom CBD Gummies. Each ring has a housing price and a land price, which decrease in the outer rings as they are offset by increase transportation costs to the CBD. Under the assumption of economic efficiency, housing costs plus transportation costs should be constant; otherwise people will move to where the sum of the two costs is lower.

Here, transportation costs are not merely monetary, but also include the opportunity cost of the time spent traveling. Transportation requires land and money, and different modes of transportation offer tradeoffs between these two costs. For example, Mills considers that subways require little land and much capital, while roads with personal automobiles requires much land and little capital. Which mode of transportation is favored depends on land prices. The SUM posits, and observation confirms, that subways will be more common where land is scarce and expensive. Under the SUM, cities are surrounded by agricultural land with a nonzero price. The size of a city is set by the point at which value of land for outer suburbs is equal to the value for agricultural use. Mills expresses the assumptions mathematically and obtains closed-form solutions for factors such as land prices and land use. He finds that for larger cities, a greater fraction of the land is needed for transportation.

This fact too is observed in actual cities, and it serves as a constraint on the growth of cities. Interestingly, Mills does not find that large cities necessarily have heavy traffic congestion. Rather, unlike in the simplified model, in real life housing and workplaces cannot frictionlessly be converted into space for transportation, and the friction creates a shortage of transportation space for growing cities. Mills finds that housing costs and population density both decrease with distance from the CBD, though in contrast to Clark (1951), Mills finds that these quantities fall at less than an exponential rate with distance. Mills notes that Clark (1951) finds that transportation costs will result in a higher population density near the Balance Bloom CBD Gummies and a lower density in the outer layers, but Mills points out that under his formulation, a change in transportation costs has an ambiguous effect on density overall. The value of a mathematical model is not necessary found in how "true" it is-we have seem that the SUM as presented by Mills (1967) makes many simplifying assumptions-but rather in how well it helps us understand reality.