From a few readers:
On China and the US and growth:
1. The calculation that you are doing is total GDP; when US and Chinese
total GDPs are even there will be around 250 million Americans earning,
say, $50,000/head and 1.25 billion Chinese earning $10,000 each. So you
may want to think about per capita GDP as well. The smaller, richer US
population will be able to afford things that the more numerous, poorer
Chinese will not.
2. Chinese growth statistics are at best back of the envelope
estimates. There is a staff of something like 15 people calculating
Chinese GDP, and a large fraction of the country is not well measured.
3. Most of Chinese growth involves getting people out of peasant villages
(where they practice more or less subsistence agriculture) and into factory
jobs. It is unclear how long this will last (it is possible that to move
another 100 million into factories will require building more factories
than are needed to build all the stuff needed by the world’s
consumers). There is a lot of pressure in the US and Europe to reduce
purchases (or maybe the growth in purchases) of Chinese goods, which will
limit future Chinese growth.
4. India is fast creeping up on China. They speak English and outnumber
the Chinese.
And…
If you are speaking of the date at which you expect per-capita income in China will surpass that in the US, then the following is something to remember. There is something called the “Convergence Hypothesis” which states that under certain conditions, economies that are similar except for their initial level of income, will have their incomes converge over time. The corollary to this result is that economies that are initially poor will gradually approach the level of income of the initially rich, they will never pass them. Another way to say this is that it will take an infinite amount of time for China to pass the US. This is because the growth rate of the poorer economies (e.g. China) gradually slows down and prevents it from passing the richer economies (e.g US).
Of course if the “certain conditions” assumption is not satisfied, then there are other things that could happen in principle. For example, it could then ultimately be that China could surpass the US in per-capita GDP at some future date. On the other hand, the opposite could happen: The differences could stay large forever.
The “Convergence Hypothesis” is something widely studied. People like Robert Barro have made a career out of it. It seems to hold up pretty well in the data, but there are always exceptions. For example, once you include the continent of Africa in your data set, everything gets screwed up since this is a pool of countries that are poor and don’t seem to show any sign of catching up to any developed countries.
And…
Jonah:
While it may be interesting to think about when China might pass us as the largest economy, it is certainly not the whole story. If, in 2056, China has an economy roughtly our size, then it would have roughly one-fourth of the per-capita income, since their population is four times as large. So, even after fifty years of outsized growth, we would still be, on average, four times as wealthy as the Chinese. Now that is interesting.