Before reading any replies at all the initial number I said to myself was 500 mil. After reading a few replies I can tell that was a really good guess. Only with a number that low will all our resources be "infinite".
The current fuel consumption will leave us without any crude oil in aprox 40 years from now (with the current discovered oil reserves), lets asume for the sake of it that we still havent found a lot of oil so lets say we have enough for the next 100 years. The problem is what the hell do we do then? A logical thing to do would be to change to electric cars etc, the only problem is if we replaced all petrol cars today and gave them all a lithium battery we would empty 1/3rd of the lithium resources on the planet. Another move you could do is replace all fossil fuel with CO2 neutral fuel that you make from plants that you grow. Once again we have a problem. With the current population of earth it would simply be impossible to grow enough crops for all the vehicles on earth. Currently it would take 1/3rd of the size of USA to provide the people with a year of renewable fuel, as for the entire planet it would most likely take the entire size of America (the continent) but fact is theres almost a billion people living there. Do we ship them to Africa where they still have lots of room?
That is just one type of resource, yes it is one of the more important ones but we also have non salty water which is low on supply. While overpopulation seems like no problem at all in America and Europe fact is that it is going to bite us in the ass at some point or another.
I once wrote a report on this subject and the only solution I could come to back then is if we start enforcing birth like they do in China, only allow 1 kid per familily for the next 3 generations should do it. However that alone would take arround 100 years and by then we will have exhausted a lot of resources on earth. One issue with something like this however is that it would take some sort of world government to make sure every single country on the planet does the same.