From a 3-22-16 article by Laurie Mazur for Yes! magazine

Perhaps the best answer comes from Joel Cohen of Rockefeller University, in his aptly titled How Many People Can the Earth Support? It’s an exhaustively researched 532-page book, but his conclusion can be summarized in two words: It depends. That is, the planet’s capacity to sustain human life depends on how resources are used and distributed and on the values and social structures that shape the way we live.

Take food – the number of mouths we can feed depends on what’s for dinner. If all of the world’s people ate like carnivorous Americans – 1,763 pounds of grain each per year, some eaten directly, but most fed to livestock, the 2-billion-ton world grain harvest would support only 2.5 billion people (there are now 7.4 billion of us). But if we all ate like people in India – a mostly vegetarian diet of just 440 pounds of grain per person each year, the same harvest would support a population of 10 billion.

So, there’s some elasticity in the planet’s carrying capacity: better, fairer resource use can expand it. But, in the coming world of scarce fossil fuels, that capacity will contract. In recent decades, for example, food production has pretty much kept pace with skyrocketing population growth, partly thanks to mechanization and cheap oil. Reductions in the oil supply would curtail food production, at least in the short term.

Shortages of natural gas would also make it harder to synthesize nitrogen fertilizer, which has helped triple crop yields since 1950. Vaclav Smil, of the University of Manitoba, told the New York Times that, without nitrogen fertilizer, there wouldn’t be enough food for 40% of the world’s current (much less future) population.

And that’s without considering climate change, which could dramatically reduce crop yields in many parts of the world at a time when global food production must increase by 70% to keep pace with current trajectories of growth and consumption.

So, how many people can the earth support? We don’t know. But, given the uncertain supply of fossil fuels and the grim realities of climate change, it makes sense to aim for the low end of the United Nations’ population projections – about 9 billion people, rather than 13 billion, by the end of this century.

The good news is that we know how to do this. A half-century of experience has shown that the best way to slow population growth is by ensuring access to voluntary family planning services, educating girls, and providing opportunities for women.