Why Does Productivity Growth Stink?

The slowdown in productivity growth is well known, and there are less stars in the sky than articles trying to explain it.  

I haven't read anyone looking at the concomitant rise in inequality: the poor, medium and ordinary rich getting richer at a slower rate than the filthy rich. 

If you are filthy rich, most of your wealth will be saved. To the extent you spend, your expenditure will not be productive, relative to other people. 

To use an extreme example, if a billionaire spends money on a car, he is upgrading his Mercedes from a 2015 model to a 2016 model. How much has his personal productivity increased? Not a jot. But if a poor person has a jalopy which keeps breaking down, and he buys a reliable car, his personal productivity improves a lot. 

If a man in Kenya can get some extra money to replace his thatch roof with metal, he can be more productive instead of gathering thatch all the time. 

So the filthy rich should send some of their pile to Give Directly, in short.