For what it's worth the current UN estimate for 2050 population is 9 billion.

Population will regulate itself. When there is a high likelihood that peoples' kids will starve, they will (by and large) stop having kids. Or, alternately, when having kids becomes hugely expensive.

The U.S. saw its birth rate dip even due to the (relatively mild, compared to your apocalyptic visions) 2008-2009 economic downturn. During the 1930s depression the U.S. rate was around 2.0-2.1, which is right around replacement level (i.e. population stays the same). And that was without prevalent birth control.