... This may well mean that, contrary to the opinions of Billy T on the rise of China, that the US may maintain its dominance in the 21st century for demographic reasons, if nothing else. ...
There is much, much, more to the problem of how to support an increasingly older population than just the ratio of the # of retired to # of workers in country. Let’s compare only two of these other factors for country "A" (America) vs. country "C" (China) when considering which will have the greater future problem due to changing demographics.
For example:
(1) How much A has Promised to its retired relative to what C has Promised to its retired.
I designate that as Pa/Pc and note it at least greater than 10.
(2) How rapidly the worker's Incomes in C are gaining in real purchasing power annually compared to the the workers in A. I will designate that as Ic/Ia and note that is also at least greater than 10. US workers have actually lost purchasing power for a decade, but lets hope it returns to a 1% annual gain soon and assume that it does. Chinese workers are rapidly gaining purchasing power by more than 10% annually (buying more cars than Americans now, etc.) I.e. Ic/Ia > 10 also.
Thus with just the increase in his salary (no reduction in his living standard) the typical Chinese worker can support more than 100 times better what the Chinese government has promised as benefits to the retired than the American worker can support what his government has promised. US workers are already complaining about how high Social Security taxes are - the Chinese worker does not pay any.
Furthermore, in China, the retired cannot vote themselves higher benefits in China. I.e. the active AARP voting block does not exist. China could even reduce the meager promises it has made, but organized AARP does vote. Any politician who even suggests the Social Security benefits be reduced will soon be a "one-term" Congress person.
Also note that the Yuan is rising in value and the Dollar is dropping, so it will be the Chinese retired who are drinking French wine and smoking expensive Cuban cigars, etc. while retired Joe American will be drinking home brew and rolling his own, if he can afford even that. Many older Americans are already facing hard choices (medicine or meat? Etc.)
SUMMARY: Paying what has been promised to the retired is at least 100 times less of a problem for the Chinese than for the American Government even if there may be eventually slightly more retired in the US / worker than in China.
Frankly, I expect the US will not be able to keep its Social Security / Medicare promises to the old for more than a decade and China easily will for several decades.
I never met an informed American under 35 who expects to even get his mandated SS tax money back (in purchasing power)! Have you?