This is from the tail of a post written in response to a Paul Krugman column. The subject is "growth" versus "Return on Capital" in an economy.
GDP = Output = Workers x (Output/Worker);
Output/Worker = Productivity
Profit = Output x Income Share to Capital = (Workers x Productivity) x Inc Sh to Cap
Capital = Workers x (Capital/Worker)
Higher growth comes from adding workers (workforce growth), or increasing output per worker (productivity growth).
SO: Return on Capital =
[Workers x Productivity x Inc Sh to Cap] / Workers x (Capital/Worker)
Is it obvious that increasing growth by adding workers to this mix does not increase the return on capital? Since "Workers" appear in the numerator and the denominator, they cancel. This relects the notion that increasing the scale of an operation does not change the return on capital (unless something is *not* scaling the same way).
The implicit modeling assumption is that new workers do the same tasks as the current ones, with the same average capital usage. If new workers need substantially less capital, then the overall capital/output ratio could fall. But that is not the way it was modeled by Dean Baker, who started us down this road with his Feldstein letter.
Productivity is trickier (and my verbal formulation may be off a bit). Basically, as Output per Worker rises, the Capital team captures some of the benefit. (Normally, I should add, productivity is associated with "capital deepening", where it takes more capital to make workers more productive. I am setting that aside here, since it makes it harder for productivity to turn growth into a higher return on capital).
So, in this formula, if the old Return on Capital was 5%, and the increase in productivity is 1.7%, the new Return on Capital will be (5.0%) x (1.017) = 5.085%. Keep that up for 16 years with no capital deepening, and the Return on Capital will rise to 6.5%. Patient capital, indeed. And remember, we are assuming that, down in the denominator, (Capital/Worker) is not changing.
Suppose we increase Productivity so that it grows by 2.7% per year. Now, the Return on Capital will grow from 5% to 6.5% in just 10 years. And when will it stop growing? Ahh, we have a bit of a glitch here - without some more elaborate assumptions about the relationship of capital to labor and output, the Return on Capital will just keep going up. However, any reasonable adjustment I make will slow the (already slow) improvement in the Return on Capital, so I stand by my point that the most plausible place to look for an improvement in the Return on Capital is not growth, but the Income Share to Capital. Increase the Income Share to Capital, and that can solve the Return on Capital problem right away.
As modeled here, higher growth achieved by adding workers does nothing for the return on capital; higher growth through higher productivity reduces the time it takes the return on capital to grow to the target, with an unlikely assumption about capital deepening and the total ratio of (Capital/GDP). So yes, growth can solve the Return on Capital problem eventually, depending on what one assumes about the relative capital deployed (as I noted originally).
There are many critiques that one could level at the author (who is...?) of the letter to Feldstein.
For one, the author seems to be some sort of loon trapped in the days of 'closed economy macro' era 1980, rather than the 'open economy' macro that everyone of note has been involved in since the 90s.
That is, he takes no note of the US economy in its proper international context. In his world, all production, consumption, saving, and investment takes place inside US borders.
But the firms listed on the stock exchange have large and growing fractions of their production and income in foreign countries. These countries often have much less capital per worker than the US, thus the return on capital is much larger there. This fact also splits the perfect correlation between labor income and capital income that is in the author's analysis.
Posted by: DeadHorseBeater | March 07, 2005 at 07:06 PM
CNN on Wilson:
http://www.cnn.com/2005/US/03/07/CNN25.tan.wilson/
Munger
http://cognitivedaily.com/
RTFR
http://rftr.blogspot.com/
New Editor on Italian journo (not buon journo, bad journo!)
http://www.theneweditor.com/JournalistasRube.html
Posted by: TM | March 11, 2005 at 11:33 AM
Noam Scheiber on bankrup
http://tnr.com/etc.mhtml?pid=2584
Posted by: TM | March 11, 2005 at 01:00 PM