I'm writing a science fiction novel which is set a few centuries after a devastating series of events, some of which are population growth related, nearly wiped out civilization. There are vast regions of the planet which are uninhabitable, and even more which are unpleasant and dangerous. At the same time, there is still lots of arable land. Especially given that Earth now has a fairly constant, sustainable population of somewhere between 300 - 600 million people, and an inclination to keep it that way. Population is stabilized by a number of factors, including a perception of low infant mortality, societal pressure, and a 'release valve' of extraterrestrial frontiers for those who don't like the way society is being run.
Earth is a center both of high technology and of food production. It is an economic powerhouse (because the colonies within the solar system are partially to wholly dependent on it for food), and depleted resources are supplied by importing from off planet sources.
I'm trying to get a picture of what population density would look like. How big would a large city be? How sparsely populated would (fertile) rural areas be?
As far as I can tell, the worlds population was in this range between the 14th and 18th centuries, but that's not quite enough data to figure it out. Food production per capita needs to be higher than it was historically (to produce excess for export), but farming techniques and equipment will be such that there would be a higher yield both per acre of land and per agricultural worker. Factories and centers of production would likewise be more efficient.
Any suggestion of a starting point would be appreciated.