0.4 Income distribution  (Page 17/18)

Notably, the country Piketty cites as the one where income inequality increased the most (the U.S.), the U.S. constitution prohibits the use of federal net wealth taxes.

A second problem in the Piketty approach is his assumption concerning the elasticity of substitution between capital and labor. An increasing gap between (r) and (g), as assumed by Piketty, is possible only if the elasticity of substitution (s) is greater than unity. The elasticity of substitution is an important determinant of how a change in the price of capital or of labor will affect the share of total income received by capital or labor: It measures the extent to which the capital-labor ratio changes when the ratio of the price of capital to labor changes. This elasticity is defined as:

When X _K is the quantity of capital employed in production, X _L the quantity of labor employed, and P _K and P _L are the prices of labor and capital respectively.

If S<1 then when the price of labor increases relative to that of capital, then capital’s share in total income will decrease. If S=1 capital’s share will be constant. If, as maintained by Piketty S>1, then capital’s share in total income will increase over time.

The computed value of the elasticity of substitution (S) may be equal to, greater than or less than unity. If S>1, then (as maintained by Piketty) the share of capital income will increase , thereby increasing income inequality. However, if S<1 there will be diminishing, not increasing returns to capital.

Thus, the share of capital income will decrease as the ratio of capital to labor rises, contrary to Piketty. Even as late as the seventies, economists tended to believe that the elasticity of substitution was about one: Studies over the first three quarters of the 20th century consistent found that labor shares in total income was roughly constant, and ranged between 70% to 80% of total real income. But these studies ignored, among other things the effects of technological change. See Ed Mansfield, Microeconomics (3rd edition, New York, NY: Norton 1970).

Piketty assumes that (S) rises over time, so that (r)>(9) rises as well, and there income inequality rises. The preponderance of empirical evidence shows otherwise: See Robert Chirinko (2008, June), “σ: The Long and Short of It”, Journal of Macroeconomics , 30(20): 671. the gross elasticity of substitution in 26 of 31 studies on the topic shows a value of less than one, typically between 0.40 and 0.60, Matthew Rognlie (2014, June 15), “A Note on Piketty and Diminishing Returns to Capital”, Department of Economics, MIT. values wholly inconsistent with a growing share for capital, as claimed by Piketty.