[UPDATE: Note that I clarified the thought experiment to make sure it’s obvious that all physical production is due to labor in an economic sense.]
At Mises Canada I elaborate on an example showing Piketty’s approach is flawed even on its own terms. First I’ll refresh your memory about Piketty’s framework:
Technology naturally plays a key role. If capital is of no use as a factor of production, then by definition its marginal productivity is zero. In the abstract, one can easily imagine a society in which capital is of no use in the production process: no investment can increase the productivity of farmland, no tool or machine can increase output, and having a roof over one’s head adds nothing to well-being compared with sleeping outdoors. Yet capital might still play an important role in such a society as a pure store of value: for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine or perhaps for purely aesthetic reasons (adding piles of jewels and other ornaments to the food piles, perhaps). In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero. In that case, the share of capital in national income, α = rXβ, would also be zero. In such a society, all of national income and output would go to labor. [Thomas Piketty, pp. 212-213]
And now an excerpt of my response to show why this doesn’t work:
[I]magine a world where there are no physical capital goods, machinery, or tools of any kind. Further, land and other natural resources do not contribute to production in any way that can be appropriated by humans.
In this strange world, the only way people can eat is that workers can jump up and grab (edible) birds as they fly overhead. These birds are the sole source of consumption in this economy. However, there is no advantage to standing in one spot versus another; the likelihood of catching a bird is the same on any particular plot of land.
Notice that in this odd scenario, we have satisfied Piketty’s requirements: Technologically speaking, there is no role for capital goods or physical wealth of any kind to contribute to production. Human labor is the sole source of consumption. Therefore, Piketty would conclude that 100% of GDP every period must be attributable entirely to wages, with the capitalists earning 0% of GDP in the form of capital income (whether in the form of interest, dividends, profit, etc.).
Yet hang on. This isn’t correct. Even within the confines of Piketty’s thought experiment, it’s possible that someone in period 1 accumulates a stockpile of the birds, let’s say equal to 50% of that period’s total catch. [UPDATE: Just to clarify what I had in mind, further assume that the reason this person in period 1 catches so many birds is that he figured out a good technique. Then, in subsequent periods, the other workers copy his technique. At any time, the constraint on catching more birds is how much time a person is willing to put into it. Thus there are no rents accruing to those who captured scarce natural resources; production is entirely attributable to the expenditure of scarce labor.] Thus β which is “capital/income” is 50% of GDP in Piketty’s framework. Now since (by construction) there is no way this stockpile of birds can contribute physically to more output, Piketty wants us to conclude that the real return on capital (i.e. the real interest rate) is zero, so that α = rXβ which is “capital’s share of income” is also zero.
But this isn’t necessarily correct, and the possibility of a counterexample shows that Piketty’s framework is wrong. If we suppose that everybody expects the flow of birds to increase steadily over time, and we further suppose that people have subjective preferences in which there is diminishing marginal utility from consuming additional birds in each period, then in equilibrium we will see a premium placed on present consumption versus future consumption. That is, someone will be able to sell a bird in period 1 for a claim to more than one bird in period 2.
For example, suppose the capitalist who starts out in period 1 with the stockpile of birds is able to sell them for claims to twice as many birds available in period 2. This will be physically possible and in everybody’s interest if the “bird catch” grows enough from period to period. Then the real interest rate in this economy is 100% per year.
If you want specific numbers, imagine in period 1 the total bird catch is 100 birds, and one really lucky worker happened to nab 50 of them. So he starts out period 1 with a “capital stock” of 50% of GDP. Then in period 2 maybe the total bird catch jumps to 200 birds and it’s more evenly distributed among the workers, and moreover everybody saw this coming. So in period 1, the workers who were really hungry might agree to pay 100% on a loan from the rich capitalist. He lends out his 50 birds, then next period out of the catch of 200 total, the other workers pay him back 100 birds.
Thus, a macroeconomist looking at period 2 would say GDP was 200 birds, and the “interest income” of the capitalist was 50 birds (because of the total 100 birds given to him, 50 was interest, the other 50 was payback of principal). Piketty would be forced to say that the entire output of 200 birds went to labor in period 2, because capital has no physical contribution to output. Yet it seems undeniable that from an accounting standpoint, the capitalist earned 50 birds in “real” interest income, meaning that the workers must have only earned 150 of the birds in terms of wages.