Zipf’s law and South African towns

An important question has exercised the minds of many economist over time: why are there differences in the sizes of different towns? For instance, why are all towns in a region not of equal size? The answer has to do with power laws.

There is no Hobbesian significance in the word ‘power’ – it is just a mathematical term. If the value of some quantity q depends on the value of another quantity x according to a power-law relationship, this means that each time x is doubled, y increases by some constant factor (Ball, 2005).

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Of enterprise richness in South African towns

In two recent publications in the South African Journal of Science, we explored the enterprise richness, defined as the number of different enterprise types, of South African towns:

Enterprise richness as an important characteristic of South African towns; and
The enduring and spatial nature of the enterprise richness of South African towns

Remarkable and enduring regularities were observed between the number of enterprise types and the total number of enterprises in towns.

Picture 1Log-log relationships which endured over 70 years were recorded and these relationships raise important issues about the nature of entrepreneurship and its dynamics in different-sized South African towns. The figure shows such a relationship that covers a range of villages with fewer than 10 enterprises to towns with 350 enterprises.

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