I am an Austrian economist. My understanding of capital & interest comes (originally) from Mises, but then it was refined in grad school when I studied Bohm-Bawerk, Fetter, and Fisher.
In case I haven’t been clear: One doesn’t need to be an Austrian to understand what’s wrong with Piketty’s conceptual remarks about capital & interest income. The reason I personally can “see” this is because of my background with the Austrian School, but a true student of the history of economic thought and neoclassical theory (which includes Paul Samuelson but not Paul Krugman) would understand the problem with Piketty’s remarks. So here are some links:
==> Nick Rowe has a great post today walking through standard two-good diagrams with PPFs and indifference curves, to show that interest is not “determined” by the marginal (physical) product of capital. This is standard stuff from Irving Fisher.
==> If you understand formal notation and modeling (like the Solow growth model), then check out the appendix (starts on page 178) to my dissertation. I show that in general, the equilibrium real rate of interest is not equal to the derivative of the production function with respect to K. It’s only under very special conditions that the general formula reduces to “r=MPK.”
==> Finally, go look at Paul Samuelson’s referee reports on my two journal articles where I fleshed out the appendix. I took Bohm-Bawerk’s verbal analysis and put it into a neoclassical model. I showed “with math” that Bohm-Bawerk was right and the naive productivity theory was wrong. As you will see, Samuelson had some quibbles with the conclusions I drew etc. (in particular he denied that some authors were advancing a “naive” theory), but he told them to publish the papers (which they did).
Let me say something in closing: Thomas Piketty isn’t stupid. He is aware of some of these issues. But it’s like the classical economists who adhered to a labor- or cost theory of value. Adam Smith understood full well that if you spent 10 hours making a mud pie, nobody would buy it. Yet it is still correct to say “the labor theory of value is utterly muddled” and to use simple thought experiments to get people to see why it’s utterly muddled.