That you could state that there is no relationship between GDP and productivity
I said no such thing. YOU said: "you do realize that productivity - as its measured in GDP". Productivity is NOT measured by GDP total. Yet you claim that I have no economic knowledge? Nice.
I used a
simplified measure of productivity. There are various ways to measure productivity. All depends on what you are doing.
http://it.toolbox.com/blogs/original-thinking/how-to-measure-productivity-30735
As for rich people, they typically are very productive because they provide the companies that provide us jobs and goods and services. If someone doesn't start a company, all that it might provide never happens. If they are not productive, they go out of business, and all the people that work for them loose their jobs as well.
Productivity DOES provide us more time. If you have to walk or take a horse or drive a car...which gives you more time? If takes one hour to make something by hand or 5 min with a machine, which gives you more time?
Increased productivity, and the wealth that comes from it, has ALLOWED the government to pay people to sit home and do nothing.
I'm not even going to take a guess at what kind of fuzzy math you created to arrive at the 1/4 productivity measure that China will 'later' reach.
The same GDP / 4 times the population. Again, a very simplified measure of productivity.