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## Piketty's Capital and Actual Capital

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Thomas Piketty's book, Capital in the Twenty-First Century, has received lots of press and been reviewed dozens of times, so I'm not going to write a general review, but I do want to comment on his depiction of capital, contrasting it with a more Austrian approach.

Piketty's main conclusion is that the return on capital is greater then the overall growth in income, so owners of capital will see their incomes and wealth rising faster than the general population, causing rising inequality over time.  He has an impressive data set, and his analysis shows fairly convincingly that inequality has been rising since 1980.

There are a number of issues one could raise regarding Piketty's analysis, but I will just raise one here: the way he identifies the relationship between the stock of capital and the income that is generated by it.

Piketty identifies what he calls "the first fundamental law of capitalism" as α=rxβ, where α is the income derived from capital, r is the return on capital, and β is the value of the capital stock.  (As Piketty defines them, both are divided by income, but we can safely ignore this by multiplying both sides of the equation by income, which simplifies the discussion that follows.)

As Piketty sees it, the return paid on capital is determined by the value of the capital times the rate of return, as the equation shows.  Piketty confirms that this is his view in examples he gives in the book.  But this is backwards.  The return on capital isn't determined by the value of capital; the value of capital is determined by the return it produces.  The correct view on this is clearly stated in Carl Menger's Principles of Economics.

While Piketty measures capital by the value of the capital stock, in fact capital is a collection of heterogeneous inputs into production processes, and capital only earns a return if it is employed productively.  The value of capital is determined by the return it earns, and the return it earns depends on the value it adds to the economy.

If capital is productive and earns a high return, it will have a high value.  If it is used unproductively and earns little or no return, its value may be low, and may go to zero.  The capital employed by Wal-Mart has been productive, giving the company value, while the capital used by Circuit City was not, and its value fell to zero.

Capital does not just earn a rate of return, its return comes from the decisions its owners make as they employ it in various uses.  A better statement of Piketty's first fundamental law is β=α/r, which is equivalent to Piketty's law in a mathematical sense, but more correct in an economic sense because it says the value of capital is a function of the income it produces, rather than that the income it produces is a function of its value.

Does this make a difference?  Piketty argues for a global tax on capital as a mechanism for lowering inequality, and the economic impact might be minimal if people own capital and it just earns a return based on ownership as Piketty implies.  But if the owners of capital have to make decisions about how to allocate their heterogeneous assets to get the best return on them -- or even to get a positive return -- a tax on capital can have a devastating effect on economic growth and productivity.

Piketty's law amounts to an accounting identity as he defines it, and in that sense it is not wrong.  But giving some thought to the components in the aggregate variables in that identity, we can see that it does not give a clear picture of the individual components that are being measured, nor the causal relationships among them.