I think the problem with overpopulation is mostly present in third world countries (especially Africa, the continent which will mostly likely have a population of 1 billion soon enough), and this is partially to blame to the West. No, I'm not going to hang up a teary story about how the West supposedly ruined Africa during the colonial era, but quite the contrary: foreign aid is destroying Africa. Let me explain how.
Imagine that there's a farmer in Senegal who cultivates rice and also happens to own a few chickens, so he earns his living by selling rice (a staple food in West Africa), eggs and poultry. Now imagine that, suddenly, the west starts sending massive food packs for free. Not only is all of this food completely free of charge, but due to the use of hormones, antibiotics etc. etc. this food will be vastly superior to anything our friend the farmer can produce on his own. This means that he can't earn his living and thus also becomes dependent on thse food packs. These food packs allow Africans to eat and quickly reproduce which doesn't only not solve the hunger problem, but only gives the West more mouths to feed. Personally I think the West shoud cut off this kind of aid as soon as possible, since even not helping is better than this. If the West absolutely, positively NEEDS to get involved (which they have absolutely no obligation to, mind you), then the only kind of aid they should give should be constructive aid, ie. Belgian and French Canadian farmers going to Senegal to explain our farmer friend how he can increase his rice output, what kinds of chickens he should breed for maximum egg production etc. etc.
This will solve most of the problems, because:
1. Our farmer friend only has 'fair' competition, ie. other farmers that have more or less the same tech level as himself.
2. The existant farmers will no longer have any reason to quit their work, since they don't get any foreign aid for simply existing
3. Because they no longer receive free food packs, Africans will actually have to do some family planning, which will result in (relatively) smaller families. These families will most likely still be bigger than western families, but most likely lower than the current 5-7 children per family rate*.
The West hardly has an overpopulation problem. Countries like China have a massively decreasing population due to the 1 child policy, and western countries have very small families that are belowe the 2.11 child/family replacement rate. My country, the Netherlands, for example, only has a growing population due to immigration rather than birth rates.
*This might be a bit of a problem in Africa though, since polygamy is completely common in some societies there. I don't want to start a religious discussion here but for (among others) this reason I think Christian missionairy work in Africa is a good thing, even if only to promote monogamy.