Elasticities, revisited
previously: Review: The Triumph of Injustice
Hannes Malmberg commented on my review of Saez and Zucman in response to a point I made about the elasticity of capital supply:
I think you are confusing demand and supply elasticities of capital.
The revenue calculations hinge on the elasticity of capital supply, i.e., how fast capital supply rise with the interest rate (how much more do people decide to save).
The Piketty spiral, in contrast, hinges on the elasticity of capital demand, i.e., how fast the interest rate fall with increasing capital (i.e., how fast firms and companies switch away from using capital when it gets more expensive).
There is nothing theoretically preventing us from having an almost horizontal capital demand curve, and an almost vertical capital supply curve. In such a world, a capital tax raises a lot of revenue, but increasing the savings propensity increase the capital stock without reducing the interest rate. (...)
I think he is basically right, and I'll partially retract section 3A of my prior post. (The rest of the post basically stands independently.)
"Partially", here, because reconciling the TToI revenue assumptions and the Piketty wealth spiral requires taking a specific stance on the slope of the capital demand curve, which should be considered a nontrivial burden that the authors don't even purport to defend. But we'll get there, hold on.
(1)
First, how did I make this mistake? Basically, by forgetting the Intro Econ that I never took, and making an implicit assumption about capital demand.
Specifically, I implicitly assumed (and didn't realize I had assumed) that the capital demand curve was downward-sloping. Why? Probably for the same reason that Bryan