China unlike to catch up with the US on per capita income in three decades

Comments on Peter Robertson and Longfeng Ye "China’s greatest challenge will be escaping the middle income trap', 30/01/2016

The terms of the richest and most powerful country in the following paragraph is confusing. China will not be the richest country in many decades to the future. One should not be confused by the size of a nation and the average income or per capita income. Most powerful or not, it is also debatable. “China’s slower growth figures have caused jitters in world financial markets. Nevertheless its growth remains at miracle levels. At this pace, China would appear to remain on track to become the richest and most powerful country in the world, bar none.”

Further, the following paragraph is questionable, the implied calculation seems to be incorrect: “In a scenario where Chinese “miracle” growth continues around 5-6% for three decades and gradually slows to the average world growth rate, the average Chinese citizen would be as wealthy as the average American.”Per capita income in China is around one fifth of that in the US. Growth rate of around 5-6% is at the best only 2-3 percentage points higher than the US. Three decades of that greater growth rate does not give a factor of 5!

China in its current stage of development shares more similarities with Japan and Korea in their relative developmental stage than with Brazil or Turkey, in culture and economic characteristics, such as saving rates, education state role in growth. Purely from that perspective, China is more likely to avoid the middle income trap, barring disastrous government policies.

PS: Professor Robertson replied to my earlier comments with the following: "Hi Lincoln
I think you have overestimated the US growth rate and underestimated China’s current per capita GDP in $PPP.
The growth rate gap is more likely to be around 4 percentage points as the US per capita income growth unlikely to exceed 2 percentage points per year.
Also China’s per capita income (in $PPP) today is closer to 26-27% of the USA’s.
Obviously one can question the assumptions but I hope that answers your question."

My tcourtsy to Professor Robertson "Thanks Professor Robertson for your reply and clarification that clears some confusion that I had."

PSS: Notwithstanding Professor Robertson's clarification, I still doubt China could practically catch up with the US on per capita income in three decades. While it is possible for a small economy like Singapore or Hong Kong, it is unlikely for a large economy. Japan's per capita income ($37,500 in 2014, re CIA World Factbook) is still quite a bit below the US's ($54,400 in 2014), not to mention South Korea's (interestingly also $35,400 in 2014).

Both Japan and Korea, with reasonably large economic size, are two of the best examples of catching up in the post war era and up to now as well.

One may argue that Japan has had a period of lost decades, but that is exactly part of the parcel of economic development and catch up processes, and reflects the difficulties for a large country to catch up in a short period.