Krugman has an insightful post on Piketty’s recent book.
I find this easiest to think of in terms of a numerical example. Let’s assume that s = .09 and initially n = .03. Then the capital-output ratio is 3; if the capital share is .3, r=.10. Now let n and hence steady-state g fall to .015. K/Q rises to 6. If the capital share doesn’t change, r falls to .05 – that is, it falls in proportion to growth. If the elasticity of substitution is less than 1, the higher ratio of capital to effective labor means a fall in the capital share, so the return on capital falls more than the growth rate. However, Piketty asserts that the elasticity of substitution is more than 1, so that the capital share rises, and r falls less than g.
And then Piketty tells us something remarkable: historically, r has almost always exceeded g – but there was an exceptional period in the 20th century, a period of rapid labor force growth and technological progress, when r was less than g. And he asserts that the kind of society we consider normal, in which high incomes reflect personal achievement rather than inherited wealth, is in fact an aberration driven by this exceptional period.