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Australasian rank-size rule

Appendix Figure 1 shows the structure of the Australasian urban settlement system, and Auckland's position within it, as summarised by the rank-size rule that generally characterises systems of cities (Gabaix (1999a) Soo (2005)). The formula for the fitted regression line is:

ln(rank) = -0.6964 ln(population) + 11.047 (R² = 0.97).

The slope of –0.6964 is flatter than in most other developed countries (Soo (2005), and Brakman et al (2008)), indicating that the Australasian urban settlement system is highly concentrated.

An unusual feature of the graph is that the two largest urban areas (Sydney and Melbourne) are similarly sized, whereas the rank-size relationship suggests that one of them should be twice as large.

Appendix Figure 1 Zipf's Law for Australasian Urban Areas

Source: World Population Rankings, available from http://www.demographia.com/db-worldua.pdf (NZ data verified against Statistics New Zealand (2005)).

Comparison with US Urbanized Areas

Appendix Figure 2 shows the Auckland Urban Area's size in comparison with urbanised areas in the United States. Size is captured by geographic area and employment (both on log scales). The dotted diagonal lines are lines of constant employment density. There is a tendency for density to increase with size. Auckland ranks as a mid-sized US city, with around the expected density. Appendix Table 1 shows some US cities with similar employment, and land area.

Appendix Figure 2 Auckland Urban Area – compared with US Urbanized Areas by Area and Employment

Source: http://www.demographia.com/db-usaua-employ.htm

Appendix Table 1 Comparable US Urbanized Areas

Source: http://www.demographia.com/db-usaua-employ.htm