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There is only so much that can be done to increase food production, but people left to themselves always produce more kids than the previous generation, so at some point population outstrips food supply.
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Not too sure about each generation out-reproducing it's last. Years ago it was far more common to have a dozen spawn than now- here, Mexico, and in many places.
I do think it isn't a totally "free" market though. There are many, many subsidies- income tax deductions, not having parents pay for schools, myriad govt programs for kids not paid for by parents, etc.- for breeders that encourage them to breed more. With no human shortage, I'd think the subsidies are, in fact, counterproductive.
I'd use a good chunk of that 100B to provide sterilizations.