Title: The Rank-Size Rule of City Populations
Headings: The Rank-Size Rule of City Populations
The Rank-Size Rule of City Populations
The Rank-Size Distribution of US Cities
Reasons for the Rank-Size Rule
See also:

Content: For example, a city grows on average at a rate of 1% per year, regardless of the city’s size. The growth rates between cities aren’t equal. The growth rates within cities also vary over time, but some cities would on average grow faster than others. Gibrat’s law and the unequal growth rates, lead to a strengthening of the multiplicative relationship over time. In the long run, a multiplicative convex (to the origin) relationship would develop even if the initial relationship was linear or multiplicative but concave to the origin, or if the initial population sizes were equal. The following animated gifs show simulated rank-size distributions changing over time. Each example has a different starting distribution (linear, constant or concave to the origin), and each observation within an example is randomly assigned a growth rate. At each step of the simulation, a unit of time passes, and the populations of each city grow proportionately by their assigned growth rate. The rankings change if one city’s population overtakes another. Example 1: