A multi-factor Uzawa growth theorem and endogenous capital-augmenting technological change

We prove a generalized, multi-factor version of the Uzawa steady-state growth theorem. In the two-factor case, the theorem implies that a neoclassical growth model cannot be simultaneously consistent with empirical evidence on both capital-augmenting technical change and the elasticity of substitution between labor and reproducible capital. In the multi-factor case, balanced growth with capital-augmenting technical change is possible as long as capital has a unitary elasticity of substitution with any single non-reproducible factor, increasing the likelihood that neoclassical models can be consistent with empirical findings. To illustrate the importance of this result, we also build a three-factor growth model with endogenous and directed technical change and show that is has a stable balanced growth path with a strictly positive rate of capital-augmenting technical change.