China's Population

On Tuesday I happened to watch the following video about calculating the real population size of the PRC:

Which got me thinking. The One Child Policy was put into place in 1979. Although it wasn't as restrictive as it sounds, it still provides an interesting opportunity for a thought experiment.

According to Population Pyramid in 1979 the population of China that was under 50 (still young enough to have children) was a little over 827 million, although perhaps instead I should take the population under 45, or under 40 instead. Assuming that the one child policy was strictly enforced with no exceptions, and assuming that women are 50% of the population, that would mean that each generation is half the size of the previous generation.

Assuming that nobody ever dies of anything, and assuming an infinite number of generations, we get this formula for the total population size:

${lim}_{x \to \infty} \sum_{0}^{x} \frac{1}{2^{x}} = 2$

Which means that under the most ideal circumstances possible, and with a strict uniform enforcement of the one child policy, the population would only ever double itself. Therefor, the largest the population of the PRC could ever be would be 1.654 billion, plus about 100 million or so elderly people who were too old to produce children when the policy was put into effect. Currently the population is slightly over 1.4 billion.

If we take into account deaths and emigration, the maximum would be even smaller, but then we'd need to also take into account that the actual fertility rate didn't flatline at 1 but instead declined gradually and is now reported as 1.09.

It would be interesting if we found out that the PRC had been lying about its population size, just as it had allegedly been lying about its economy for many years. It could have implications about its economic and military might that would negatively affect its international standing, showing the country to be weaker than it projected. As it is, the country should eventually find itself in a crisis as more and more workers become retirees, until a significant majority of the population is no longer working and is supported by the younger generation. I do wonder why that hasn't happened yet, just as I wonder why the US economy hasn't yet imploded under the crushing weight of the colossal national debt.

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