There's been a lot of hand-wringing over China's population crunch, shown by its recent decision to allow 3-child families. It's mostly wrong, or at least focused on the wrong thing.
There are two things the hand-wringing gets wrong. First, the numbers game for supporting the elderly isn't about the ratio of workers to non-workers, but about whether the total and per-capita wealth and income of the working population in the future is growing fast enough to keep up with growing numbers of elderly who are unable to pay for their retirement. Compared to 40 years ago, China has much smaller ratio of workers to retirees, and still this smaller percentage of workers is in much better shape to take care of their elderly than in 1980's China. Future economic growth will be slower than the past, but even 2-3% per-capita annual economic growth will go a long way.
China does have an extreme demographic shift, and that gets to the other error in the hand-wringing. To the extent there's a problem, it's not because China's population will fall but because it will fall so fast. A very gradual population decline doesn't pose economic problems, and certainly not the same extent of the economic problems created by a system that relies on there always being far more young people than old people. It's weird that pundits who pride themselves on their economic sophistication are unable to recognize that they're advocating a Ponzi scheme of ever-enlarging amounts of new people paying for prior people.
There are four options:
1. Fast population growth: this results in short to medium term economic growth but long term economic problems when you get off the Ponzi-scheme train. It is also an environmental disaster.
2. Stable population levels - economic growth and increased environmental problems as the same number of people consume more resources.
3. Slow decline in population - economic growth outweighs the slow decline in numbers. There's an increased chance for environmental restoration.
4. Fast decline in population - per capita economic growth, but potential economic problems supporting the elderly. More chances for environmental restoration.
It is not clear to me that a single country on Earth, including China, is in Category 4. The goal, for earthbound populations anyway in the next century or two, should be Category 3.