The premise of the manga is strange,though.
First of all, global warming(about 0,5 to 1 degree Celsius within the next century) would never cause food shortages in the 1st world, especially not at our current birth rates of between 1,1 to 1,4 children per woman.
2ndly, it's a strange solution to feed humans as prey for other fleshy beasts.
Why not let the 3rd world starve to death first? After all, we sell our huge abundance produced in 1st world agriculture to them for nothing more than little money, and there's still enough for people to speculate with it, so if there was a food shortage,
those overpopulated countries would've to die first (e.g. Yemen, it has an overpopulation of 900% as it imports 90% of its food;
such countries shouldn't exist, every country should only have as much population as it can feed so it can be independent, otherwise it's completely dependent on other nations and thus not a sovereign nation) way before countries like Japan would have to even think about human cattle.
By that day, humanity would've slimmed down to about 2 to 3 billion people (depending on how many in China and India die;
India will probably lose about 800 to 1000 million people since it's already aggressively overproducing, using up precious ground water resources and poisoning the ground with chemicals;
Africa will probably go down to like 100-200 million people in total since they can't do much without imported food&healthcare from Europe, Japan and the U.S., as failed states like Zimbabwe, Kongo and South Africa showcase to what extend the Africans can feed themselves),
which is completely sustainable with our ever-evolving technology and scientific knowledge regarding agriculture (especially Japan, Europe and the U.S.A. are pretty much at the peak of future agriculture, researching into different resistances against drought/wet climates/plant diseases, crop abundance, etc.).
Human cattle will probably only be an option for the Near East and Africa once we've dumped them to save ourselves first.