Yes, figuring out how to keep the global population sustained is eventually going to be a problem once (if, given capitalism) all developing countries fully industrialize and nowhere has a high birth rate.

Educated women work instead of having kids because two incomes is almost required at this point and having kids ruins career prospects. If it were somehow possible to have kids and maintain a job, e.g. by the spouse taking on an appropriate and equal amount of responsibility, or with free and government-funded daycare, women would probably be more likely (but not certain) to have kids. This can be seen in the 1970s in the GDR, where birth rates increased (at least temporarily) when free daycare was introduced. Also, employers need to give more vacation time all around so parents are not disproportionately taking vacation time and putting their careers at a disadvantage. This is actually, in combination with the fact that women are expected to do most of the parenting, a large contributor to the wage gap; Employers see women as a liability and pass over them for promotions and such because they believe they will have children and miss work, regardless of the truth of that for any individual.

However, this doesn't mean people will have many kids if circumstances allow, just that it would be more likely that a couple would have kids at all. As the other user mentioned, three kids is a lot.

TL;DR Economic conditions matter when having a kid only when the women are educated and required to be in the workforce but parenting is not accommodated by employers or governments (in non-financial ways). In countries where women are not expected to join the workforce, economic conditions and government policy have less influence.