Actually, it's more like with 100 people, 1 of them owns $4 of that $10, 9 people owns $2.8, 40 of them own $2.5, and the other 50 of those own 70 cents.
Some people love this set up, others hate it, it really depends which side of the spectrum you believe in. Some people are happy being that 40 to share the $2.5, not a lot are happy being the 50 who owns the 70 cents.
The biggest fallacy is that meritocracy exist in such an economy, when the reality is that family background, and in almost all instances, luck factors a big deal in whether someone belongs to the 1%, the 10%, the middle class, and the poor.
Some capitalistic countries in the world aren't that rich. Jamaica I believe is capitalist. Canada, and the Scandanavian countries are most definitely socialist, so is Switzerland. The funny thing is, the tax rates in Canada is much exaggerated, the people in the States don't really pay much less in taxes. Canada's tax revenue vs. GDP is 31.7%, US is 27.5%. Countries like Kazakhstan, Samoa, Turkey, Suriname actually have lower tax rates than the States.
The main difference is where the taxes go to, is it used to provide incentives for the rich to stay, or is it used to give a decent standard of living to the poor such that the poor can increase spending, and as such feed into economic growth. There is no magic bullet.
HK, Singapore, and the US are some of the most capitalistic societies, and they don't necessarily are a haven for all people. it's great if you are rich, not so great if you are poor and struggle to pay for the basics of life, let alone self improve.