A Comment on Piketty Worth Reading

Not that every pixel spilled, anywhere in the universe, discussing P-dawg isn't worth reading but this one is especially interesting.
From Marginal Revolution:

From the comments:
Krugman correctly highlights the importance of the elasticity of substitution between capital and labor, but like everyone else (including, apparently, Piketty himself) he misses a subtle but absolutely crucial point.

When economists discuss this elasticity, they generally do so in the context of a gross production function (*not* net of depreciation). In this setting, the elasticity of substitution gives the relationship between the capital-output ratio K/Y and the user cost of capital, which is r+delta, the sum of the relevant real rate of return and the depreciation rate. For instance, if this elasticity is 1.5 and r+delta decreases by a factor of 2, then (moving along the demand curve) K/Y will increase by a factor of 2^(1.5) = 2.8.

Piketty, on the other hand, uses only net concepts, as they are relevant for understanding net income. When he talks about the critical importance of an elasticity of substitution greater than one, he means an elasticity of substitution in the *net* production function. This is a very different concept. In particular, this elasticity gives us the relationship between the capital-output ratio K/Y and the real rate of return r, rather than the full user cost r+delta. This elasticity is lower, by a fraction of r/(r+delta), than the relevant elasticity in the gross production function.

This is no mere quibble. For the US capital stock, the average depreciation rate is a little above delta=5%. Suppose that we take Piketty’s starting point of r=5%. Then r/(r+delta) = 1/2, and the net production function elasticities that matter to Piketty’s argument are only 1/2 of the corresponding elasticities for the gross production function!....MORE

Read the comments, there are a couple which display a grasp beyond the usual "I’m just going to agree with which ever side fits my political preferences." (comment by Urstoff April 10, 2014 at 3:20 pm)

Brad DeLong, who has, in some less-than-couth circles been referred to as "the poor man's Krugman" notes a similar argument in his point three here.