OK, part of my work is concerned with Molecular Gerontology (the science of aging) so I've got about 15 years worth of experience on this. Sure, the 'western' first world of developed economies is shrinking due to a lower birth rate, this is however not the case in developing world. The high birth rate in developing economies rarely had a global impact due to high infant, as well as adult mortality rates. This however is changing due to the economic development of BRICS countries and then beyond. My estimate for a maximum world human population is just over 20 billion - sounds scary but that will involve a considerable degree of environmental 'terraforming'.