A generalized Uzawa growth theorem

We prove a generalized, multi-factor version of the Uzawa steady-state growth theorem, Balanced growth with capital-augmenting technical change is possible when capital has a unitary elasticity of substitution with at least one other factor of production, Thus, a neoclassical growth model with three or more factors of production can be consistent with empirical evidence on both the capital-labor elasticity of substitution and the declining price of investment relative to consumption, In a three-factor model calibrated to US data, medium-run fluctuations in the investment price explain labor share movements from 1960-2000, but not the subsequent fall in the labor share.