Wednesday, 7 May 2014

Piketty and the Marginal Product of Capital

Like hordes of others I'm reading Capital in the 21st Century and so far I'm very impressed. But when I came to this, on page 213, I was shaken, not stirred:
Concretely, the marginal productivity of capital is defined by the value of the additional production due to one additional unit of capital. Suppose, for example, that in a certain agricultural society, a person with the equivalent of 100 euros’ worth of additional land or tools (given the prevailing price of land and tools) can increase food production by the equivalent of 5 euros per year (all other things being equal, in particular the quantity of labor utilized). We then say that the marginal productivity of capital is 5 euros for an investment of 100 euros, or 5 percent a year.
Why do economists do this sort of thing? Keynes gave the world a very useful term for the return which a capital asset offers, expressed as an interest rate. He called it the marginal efficiency of capital:
More precisely, I define the marginal efficiency of capital as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price. This gives us the marginal efficiencies of particular types of capital-assets. The greatest of these marginal efficiencies can then be regarded as the marginal efficiency of capital in general.

Now I think it's clear that Keynes and Piketty are using the same concept, but giving it different names. "So what" you ask; "isn't an author entitled to choose his own terminology?" Well yes, but the name Piketty chose happens to be the name usually given to something quite different. The marginal product of an input, as Wikipedia tells us "is the extra output that can be produced by using one more unit of the input ... assuming that the quantities of no other inputs to production change." (I know Wikipedia isn't always reliable, but trust me I can find plenty of better authorities to cite if I need 'em).

The reasons why this pisses me off somewhat are twofold. Students are regularly warned not to confuse the marginal product of capital (usually abbreviated MPK) with the marginal efficiency of capital (MEC). The MPK should be understood as units of additional output per unit of additional input, while the MEC is akin to an interest rate (it can be thought of as an internal rate of return). It's important to avoid confusion because the two terms often rub shoulders in a discussion.

The other reason why Piketty's choice of jargon is unfortunate is that there are plenty of hacks out there looking to diminish the impact of his work. It's a shame that he has given them an opening.

But it may be for the best. Samuelson remarked that one reason why Keynes's General Theory made such an impact was that the many obscure points give rise to a lot of arguments and, in order to participate, people first had to read the book. Piketty's writing is mostly clearer than that of Keynes, but it may be that it is precisely the few infelicities of language which will keep the conversation going.