5 comments on “Piketty

  1. The Second Law is just L’Hôpital’s rule: if f and g are differentiable functions (say, stored capital and national income), then f/g has the same limit as f’/g’ as t ? ?, provided f, g ? 0 both or f, g ? ±? both, and that f’/g’ has a well-defined limit.

    In some of your experiments you violated those premises (for example by letting national income decline to zero while capital increased). I don’t know if Piketty intended the correspondence to L’Hôpital’s rule (and its premises).

  2. David, it’s not just a problem around zero. There’s a wide range of negative growth rates for which it seems to produce the wrong answer.

    I think the two references I made to economists who criticize the second law provide some deeper explanation of what’s peculiar about the second law, and those references are probably different ways of analyzing the wrongness that I’m observing.

  3. If by negative growth rate you mean a uniform decline in g of X%/year, then g is going to zero exponentially. g(t) = g(0)*(1 – X%)^t.

    [My previous comment may have gotten its character encoding screwed up. Here’s the relevant portion with words instead of symbols: “… then f/g has the same limit as f’/g’ as t goes to infinity, provided f, g both go to zero or f, g both go plus or minus infinity, and that f’/g’ has a well-defined limit.”]

  4. Oh, I was mainly thinking of cases where the decline could last for centuries before income would go to zero. Piketty is talking about changes to capital that happen in something like a decade. I wouldn’t expect the economy to be stable enough to model this way if participants expected income to go to zero within a few decades.

  5. If the ratio f/g is monotonic (as when f increases monotonically from some positive value up to infinity and g decreases monotonically to zero), and it’s not converging in infinite time, then a fortiori it won’t come close to converging in finite time.

Leave a Reply

Your email address will not be published. Required fields are marked *