"How do we acieve an orderly stabilisation in the worlds population and maybe a gradual reduction."
Is population not already starting to decline in many of the 'developed' nations? Was the greying of France and Italy predicted by anybody 30 years ago? It may well be the case that the world population will continue to expand, but the truth is that we are relying on a large helping of research plus an inevitable element of guesswork.
Following the curves, its not that difficult to see that 9 billion will be the peak in 40 - 50 years time, followed by a stabilisation / reduction. The greying of western countries is largely irrelevent as they make up such a small proportion of the total demographic.
Population most dense in richest countires - certainly not true. The largest / most densely populated cities are almost all in second / third world countries. Only 4 of the 20 largest are 1st world;
http://www.mongabay.com/cities_pop_01.htm
Regarding capitalism correlating to population growth, this is true to a certain extent, but the greying / falling polulations of western capitalist countries contradicts this. Certainly the type of capitalism we have will evolve as the population stabilizes.
Assuming energy supply meet this requirement, the real problem for population down the line will be the next ice age (somewhere within the next 1000 years) which will dramatically reduce the worlds population due to reduced precipitation and hence arable land.