Overpopulation is not a problem in first world countries. Most first-world countries today, in fact, have decline population due to birth-control and socio-economic decisions that result in most families having two or less children.
Most of the countries that do have a rapidly exploding population are in Africa where people are still having 6+ kids per family. These are typically not the people that will have access to cures for cancer and other such diseases due to the high cost. Millions in Africa die every year from malaria, a diease that is treatable here in North America. I doubt very much that advances in medial technology would contribute to an huge population explosion.
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