You seem to be under the assumption that the population is going to grow towards infinity. The UN projects that we will stay under 10 billion (http://en.wikipedia.org/wiki/Projections_of_population_growt...) and even the highest only have us at 16 billion at the end of this century (compare that to the growth in the 20th century).

So unless there is a relatively low limit for total humans on this planet, we won't reach it before we become a spacefaring race, at which point the limit will be the carrying capacity of the Universe.