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A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change

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  • Gregory Casey
  • Ryo Horii

Abstract

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.

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  • Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," ISER Discussion Paper 1051, Institute of Social and Economic Research, Osaka University.
  • Handle: RePEc:dpr:wpaper:1051
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