This is an oversimplification, if not actually wrong. If you assume that population is positively correlated to food supply, then this is correct, but population does not correlate strongly with food supply; some nations with exceedingly abundant food supply (Italy, Japan, Russia) actually have declining populations; what causes the very high fertility rate in sub-Saharan Africa is poor education, high infant mortality and poverty. As countries become richer, the fertility rate drops to the at or below replacement rate which is prevalent in the developed world (the so-called "Demographic Transition").
Different groups are going to reproduce at different rates. However, I have heard that even groups in the US that would be expected to reproduce more have reduced their rates albeit not down to the lowest rates. That said, the article I posted argues that the Demographic transition is only temporary. Read the article; it's famous and not right wing ideological bs: the guy is a progressive I believe.
The present solution to overpopulation seems to be slaughtering babies (abortion). Also, people get caught up with their careers, projects, standards of living, etc. However even if this continues, those who abuse the commons will replace those who do not. Eventually population growth will surge back upwards. Whether due to culture or due to genetics, those with the tendency to breed more will replace those who tend to not (incl those who breed more but abort their babies).
Some degree of racial differences can enter the discussion here, but it's not entirely necessary to break that taboo. Even in a homogenous society such as Japan (98.5% Japanese I believe though importing foreigners up to 3% of their population and probably more afterwards), those individuals who are favoured will replace those who are less favoured. And the welfare state or charity will support any babies who cannot be supported by their parents and relatives. So in summary, those who have many babies replace those who have fewer.
An interesting extension of this is if the government pays to correct genetic illnesses (symptom not cause - and I dread correcting the cause with science but such meddling is probably inevitable), having a genetic illness will not be or will be less of a hindrance on reproduction. As a result, more will inherit genetic diseases.
Of course the elite doesn't have your or my best interests at heart, the only thing the elite is interested in is preserving its hold on wealth, power and influence (much like a corrupt dictator).
What you say of the elite is true according to the Machiavellians. I'd like to think they need to help their nation as a part of their justification to themselves though. Also, I want them to become attached to their nations. I'm not an expert on that school of thought, and in writing the following response I ran into some issues I haven't resolved. The entire elite isn't going to be power hungry, but most of it will though not conscious of it.
Ideally they should have some sense of duty to their people. If feeding the poor is wrong as has been argued, perhaps they could be neutered and then fed? - awful suggestion I know, then the elite should desire to help their people in some other manner. An entirely selfless elite is probably too much to ask for, but a local foundation has done a great deal with what it has. For this area, it's a part of the elite. Its driving force is probably attachment to the area and a justification to themselves for their power. However, the foundation wasn't created intentionally but as the result of two nonprofit hospitals selling (having to sell really - competition was too fierce though the playing field wasn't level) to a for profit hospital corporation. And the driving force for building the hospitals was probably 1. to become powerful and important but also 2. to serve the area. The area needed them or at least the first one... I was not around when they were built.
Oh, and one other caveat on overpopulation, disease naturally checks it. It looks like AIDS is going to cut global population severely. Other diseases will likely spring up as well though we might be able to fend them off using technology.
but the world's population then was a tiny, tiny fraction of what it is now (so not as many people to get displaced by rising sea levels etc).
It will still be habitable is the argument I believe. Also, whatever fossil fuels exist will be consumed no matter what is done.
In addition to populations and capital having to be relocated, death, loss of capital, etc., I read something interesting at the Nature Conservancy. Important ecological areas will move as well. Even if preserves survive all of the change (powers that be prevent their being paved over), some will no longer be as important or as unique.