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: In short, the rank-size rule occurs because: The relationship between population size and population rank is inherently negative. This is obvious and accounts for much of the strong fit, but alone doesn’t account for the multiplicative and convex (to the origin) relationship. Growth rates are independent of city size (or at least weakly related) and absolute growth is roughly proportional to city size. This is known as Gibrat’s Law or Gibrat’s rule of proportional growth. 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.