Will world solve the demographic problem?
Pension system and health care is depleting budgets of developed countries and haunting politicians and economists around the world. World is growing old and we haven't found a solution. In fact we did, it is just intractable in most of the systems.
The human rights state that each person has a right to live. This is extended to the fact that in most developed countries noone is denied health care. Particularly in eastern European countries the socialist health care system is very strong. Each pay a health care tax which then pays for most of the medical procedures. Health care for elders became huge burden on economies of these states. In Europe it was in between 6% and 12% in 2012. Netherlands and France ranked at the top in Europe. This yields high borrowing and is never ending problem.
Obviously, as many economists argue, these money could have been spent on different things like better infrastructure or education. They readily propose rather simple solution. Leave health care of elders upon their families. They can decide for themselves whether they would rather prolong life of a grandpa by 3 years or send son to college. Simple, probably very efficient, but completely implausible in Europe.
Yes, tt is politically intractable. But why? Simply the family doesn't have that role it used to have a century ago in Europe and likely even in USA, it became more individualistic. The finance of a family is restricted only to the nuclear family. Once the child leaves the family house and starts to work, it becomes completely independent. Most of the time. Children hardly support their parents anymore nor have strong influence on their decisions. If you would now leave children to pay for health care they will consider it as terribly unfair. And what about those without children?
While Europe is deemed to fall, China could be the country to successfully pioneer with this kind of law. Firstly, the party is powerful enough to push such unpopular or even hated policy. It happened once with one-child policy for example. Secondly, importance of family is strongly rooted in Confucian culture.
As much as it is not obvious, the demographic problem is hunting China as no other in the world. It haven't caught it as it did Japan for example. Yet. One-child policy, once effective and helpful for the economy in 80s, may be huge burden in the future. It is actually one of the main causes of the spectacular Chinese growth. All can berevealed by simple look at the population structure from 2010:

Today, majority of population in China is in their prime. Child dependency ratio and burden of elders is very small and therefore China can run like a horse. But what happens when those in their thirties and forties will grow old? Who will support them?
The horse might hit a brick wall unless the government finds a remedy, very soon. In fact, it is starting to happen. One child policy has been loosen (only at the last party congress in November). The next step coul be "un-socialization" of health care for elders.
Interesting comparison between China and India. The future might look bright for India but they must get their act together.

But, I think there is one trend most economist don't see when assessing the demographic issues. It is often like that. And it is technology and the fact most people don't want to stop working at their sixties. The original reason to employ a pension systems was simply that for example mine workers after 40 years had so destroyed health that they were hardly helpful anymore. But today, a mine worker hardly do any physical work. Most is done by machines. With the bulk of population working with their mind and in offices, we can have much longer productive time span. (Update: This is though not really plausible in China. Most of the people in 40s to 60s are unskilled with just elementary education.)
The main challenge is to restructure our lives so it was sustainable for a human to work for 60 years instead of 40. The pension must be spread over throughout the lifetime. Today, we call that sabbatical and it is rather rare but once this might be prevalent trend. This might lead to much healthier life style with less stress and much more joy.
However, this doesn't solve the problem of health care for people over 80.