Piketty (11) Elasticity of Substitution

The biggest debate about Piketty's book has been about the elasticity of substitution between capital and labour. Economists have traditionally believed that as the supply of capital increases, the rate of return will decline, ie there will be diminishing marginal returns to capital. Therefore, even if the capital/income ratio increases, then the rate of return on capital will decline. This will cause share of income going to capital to decline.

Piketty’s formulation implies that over the long term, the elasticity of substitution between capital and labour seems to have been greater than one. This means that an increase in the capital/income ratio seems to have led to a slight increase in α, the capital share of national income (221).

If this elasticity is greater than one, as more capital is added to the productive process, the owners of capital push aside wage demands and claim a increasing share of output as their reward for investing.

Several economists have challenged this result. Matthew Rognlie argues that Piketty has confused gross and net elasticities.

Economists generally talk about gross elasticity in the context of a gross production function. Piketty uses net concepts, so he means elasticity of substitution in a net production function. This a different concept. Net elasticity is always less than gross elascitiy, and almost always less than one.

Lawrence Summers claims in the Inequality Puzzle that,

As the capital stock grows, the increment of output produced declines slowly, but there can be no question that depreciation increases proportionally. And it is the return net of depreciation that is relevant for capital accumulation. I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1, and I know of quite a few suggesting the contrary.

There will be continuing debate on this issue.