Do Cities Grow by Natural Increase or by Migration?

It has been argued that cities grow mostly by net in-migration and it has also been argued that they grow mostly by their own natural increase. Kingsley Davis finds that cities in the European industrial revolution grew mostly by in-migration but cities of the contemporary less-developed countries are growing mostly by their own natural increase. The case for their growth by migration was expressed as far back as Sussmilch who showed that deaths exceeded births in the principal cities of Europe so that without in-migrants cities would decline. The same view has been developed by Fischer and Wrigley. Most recently Sharlin finds the contrary for the cities of Europe. He adduces evidence that the population native to the city did replace itself and that the excess of deaths over births that appeared in the overall statistics was due to temporary residents especially tradesmen and servants who had no chance to marry but whose deaths would be counted as urban if they died in the city. This paper studies the contributions of the two components of city growth under various hypothetical conditions. It starts from the simple notion that when there is no city population there can be no natural increase and during the time after a city is established but still small its births cannot be numerous. At the other extreme when the country is mostly urbanized there is little rural population left to migrate to cities. Between these two extremes there must be a moment in the course of urban evolution when natural increase begins to exceed in-migration. The model that follows establishes this moment in terms of three parameters: urban rate of natural increase u rural rate of natural increase r and rate of net out-migration from the countryside m. The discussion starts with a special case in which u = r then goes on to arbitrary fixed values of u r and m and finally presents a result for arbitrary functions of time u(t) r(t) and m(t). The first case with u = r can be solved in commonsense terms; distinguishing u from r the urban rate of population increase from the rural requires a pair of differential equations. (excerpt)