Three Ways of Looking at alpha = r k

Piketty’s “first law of capitalism” is the accounting identity

α = r k





k = s/g





2 thoughts on “Three Ways of Looking at alpha = r k”

  1. I'm studying for the CFA now and I am consitently struck by the connections between how financial analysis is preformed and post keynesian / structalist economics. That you never see this stuff in a mainstream econ undergrad class is really very strange.

    Anyway, I have been thinking on the same lines of applying r as a discount rate. I think it is interesting if you look at it as a present value of growth oppurtunities (PVGO) model. This is the same as the normal model excpet you seperate out the growth aspect:

    aY / r + pvgo

    The first term is the value of the assets in place, and the second one is the value of future investment oppurtunities. My question is what is picketty (or anyone else) measuring when they measure capital. If it is the market value, then it would include growth oppurtunities, but if it is book value it might not. Seems this would have implications for r > g.

  2. (I previously commented on this blog as Random Lurker)

    I like this view (that the amunt of capital is the dependent variable), however I think that there is a question:
    Some capital goods, like factories, are produced, that means that they have a "cost of production".
    One would expect that the market value of factories, on average, cannot be much higer than their production cost (or everyone would be building new factories), nor much lower (or there would be massive disinvestiment).
    However if alpha is exogenous and the cost of these goods is also somewhat technologically determined, "r" has to be the dependent variable, unless you assume that the cost of "reproducible" capital goods is a very small part of "capital" in the sense you use here, so that the cost of a factory is a very small part of the "market value" of a firm.
    Else, we could think that a fall in r really causes a (temporary) boom, as factories become relatively "cheap" to produce, whereas a rise in r would cause a recession, as it causes disinvestiment. On the other hand an increase in alpha would cause a temporary boom, while a decrease in alpha would cause a recession.

    I find this interesting because it looks like a ratchet: slowly, r has to go down, while alpha has to go up, or disinvetiment will ensue. This sounds very much like Marx's tendential fall in the rate of profit (together with a tendential decrease of the wage share).

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