Urban Hierarchy and the "Rank-Size Rule"
by Prof Kilkenny for Econ 376 “Rural, Urban, and Regional Economics”
The approximate RANK-SIZE RULE equation
is: Rank r = C / popr
In words: The rank of city “r”
in a region
(“rank” = how many cities are at least as large
or larger than it)
is equal to the ratio of the population of the
region’s largest city (“C”)
divided by the population of city r (“popr”).
Equivalently: C = rankr•popr
and Popr = C/rankr
Graphically: plot city populations sorted in descending order. The locus is a linear hyperbola (C=R•P) .
SEE TABLE BELOW
Sources: 2000
city population data from “Ranking Tables for Incorporated Places of 100,000 or More: Population
in 2000 and Population Change from 1990 to 2000 (PHC-T-5)” http://www.census.gov/population/www/cen2000/phc-t5.html
. 1990 data from Statistical
Abstract of the United States, 1991 (Washington, D.C.: Government Printing
Office). Prior years from Table 4, in Mills and Hamilton, Urban Economics
5th Edition, page 74, data: U.S. Department of Commerce, Bureau of the Census. Census
of Population, 1972, 1982.
Note that (i) The largest cities
are port cities.
(ii)
They are as far apart geographically (dispersed) from each other as
possible.
(iii) The relative sizes of cities in rank
persist over time
(e.g.,
NY (#1 in 1870) was twice the size of Philadelphia (#2 in 1870), etc). In other
words, the largest city has had twice the population of the second largest, and
three times the third, and so on; no matter which cities were 2nd
or 3rd, and no matter when.
Fun things to
do with the “rank-size-rule.”
Amaze your friends and family: All you need to remember is the population of New York City
(about 8 million).
1. You’re driving cross-country and pass the
sign “Entering Houston, Population 2 million.”
You can immediately inform everyone in the car that Houston is the
fourth largest city in the USA.
2. Your friend says “L.A. is the second largest
city in the USA. “ You say, “Right, and
it’s population is about 4 million.”
Population of Selected Cities, Selected Years, 1790 to 2000
|
City (not MSA) |
RANK |
Population (in Thousands: 1,000s) |
%
change |
|||||||
|
|
2000 |
1990 |
1910 |
1790 |
1850 |
1910 |
1970 |
1990 |
2000 |
90-00 |
|
New York |
1 |
1 |
1 |
49 |
696 |
4,767 |
7,896 |
7,323 |
8,008 |
9.4% |
|
Los Angeles |
2 |
2 |
15 |
|
2 |
319 |
2,812 |
3,485 |
3,695 |
6.0% |
|
Chicago |
3 |
3 |
2 |
|
30 |
2,185 |
3,369 |
2,784 |
2,896 |
4.0% |
|
Houston |
4 |
4 |
|
|
2 |
79 |
1,234 |
1,631 |
1,954 |
19.8% |
|
Philadelphia |
5 |
5 |
3 |
29 |
121 |
1,549 |
1,949 |
1,586 |
1,518 |
-4.3% |
|
Phoenix |
6 |
9 |
|
|
|
|
584 |
983 |
1,321 |
34.3% |
|
San Diego |
7 |
6 |
|
|
|
|
697 |
1,111 |
1,223 |
10.2% |
|
Dallas |
8 |
8 |
|
|
|
92 |
844 |
1,007 |
1,189 |
18.0% |
|
San
Antonio |
9 |
10 |
|
|
|
|
|
935 |
1,145 |
22.3% |
|
Detroit |
10 |
7 |
10 |
|
21 |
466 |
1,514 |
1,028 |
951 |
-7.5% |