Bullshit. Rich people tend to have far far better health care. The size of your parents' wallet is not genetically heritable, therefore your claim that somehow Darwinism would solve the problem is utter crap. As with all Social Darwinists, you either twist what Darwin was saying, or you just simply don't understand it.
A few points:
1. Cooperation is as much a result of Darwinian selection as competition. Humans are social animals, not solitary hunters. Even Neanderthals appeared to take care of their infirm, for chrissake.
2. You can legally inherit money, but it confers no genetic advantage. A moron can just as easily have a trust fund as a genius.
2a. There is an at least partial caveat to that, in that poor nutrition during the key developmental years that is often found in the poorest societies can in fact stunt cognitive development. But again, that still doesn't mean rich people are genetically superior, it just means good nutrition and health care allows them to reach a sort of maximum of cognitive development that members of poor societies are often deprived of. The same would happen to a baby born in a rich society if it is deprived of protein and calories necessary for development.
3. There may be a genetic component to earning lots of money; in that either intelligence or risk taking behaviors can likely influence a person's ability to earn money, but high intellect and risk taking can also be associated with some potentially deleterious behaviors as well (i.e. links to depression or, in the case of risk takers, to physically or legally dangerous exploits).
4. The wealthier society, the lower the fertility rate, which generally means it isn't the poor societies who are going to be wiped out, but rather the wealthier ones, which is why they end up having to build big walls which they then are forced to open the gates to because to remain economically viable you need to have some way of generating the required 2.1 children per female to at least maintain a stable population over time.
5. As one can see from poorer societies, women can produce a number of offspring even if their average lifespans are considerably less than your average citizen of an industrialized country, so the idea that "Darwinism" (whatever you mean by that) is just going to leave all the nice rich people in place, and all the poor people will drop dead doesn't even make any bloody sense.
6. Social Darwinism has about as much to do with Darwinism/evolutionary biology as horoscopes have to do with astronomy. It was long ago debunked, but remains oddly popular among Libertarians in wealthy countries who either directly or indirectly benefit greatly from the labour of people in poor societies, and who seem to feel that it somehow justifies that pecking order. If Social Darwinism resembles any kind of evolution, it is the Lamarckian evolution that Darwin set about strongly critiquing in his theory.