Overpopulation - What's the solution?

We all know that humans have pretty much taken over the world. There are over 6 billion of us and we are overtaxing the Earth's resources. Many of us suffer from hunger, malnutrition, and starvation. Thus, we seek a solution to this problem. The solution that most of us think of first is to increase production and create more food so that we can feed the hungry. But that is what we have been doing since the agricultural revolution: finding more efficient ways of creating food. But the problem is still there: people are still starving. So what went wrong with this brilliant plan?

Each time a revolution in agriculture occurs and more food can be created in a shorter amount of time, our population explodes. With more food, people reproduce more and, thus, more people become hungry. Then, we, once again, face the problem of world hunger and try to produce even more food, resulting in even more people. Unfortunately, it is seemingly never ending cycle. World hunger leads to more efficient food production, which leads to population explosion, which leads to world hunger ...

This is what happens in a biological perspective. By creating more foods, which is a limiting factor, we increase our carrying capacity. However, eventually, we reach that carrying capacity once more. In order to break the vicious cycle, would it not be better if we just stop looking for ways to produce more food and just allow ourselves to reach our carrying capacity? Wouldn't that be the most efficient way to stop world hunger? Afterall, why should we be exempted from the effects of reaching our carrying capacity when every other organism on Earth is not?

What do you think?