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Comment on “Labor- and Capital-augmenting technical change”: Does the stability of balanced growth path depend on the elasticity of factor substitution?

Bental, Benjamin and Li, Defu and Tang, Xuemei (2022): Comment on “Labor- and Capital-augmenting technical change”: Does the stability of balanced growth path depend on the elasticity of factor substitution?

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Abstract

In a classic paper, Acemoglu (2003) developed a growth model where firms can undertake both labor- and capital-augmenting technological improvements. According to that paper the balanced growth path with purely labor-augmenting technical change is the unique asymptotic (noncycling) equilibrium, and is stable only when capital and labor are gross complements, i.e., only when the elasticity of substitution between these two factors is no greater than 1. Otherwise, the model not only has two other asymptotic steady-state paths, but also the balanced growth path is unstable. The current comment points out that Acemoglu's conclusion ignores the crowding effect in innovation sector that he has proposed due to the assumption of perfect mobility of scientists between sectors. By replacing the perfect mobility assumption with a smooth adjustment process, implicitly invoking the presence of some adjustment costs, this comment not only points out that the factors affecting the direction of technological progress include both the demand side of innovations (relative price and relative market size) and the supply side of innovations (relative marginal productivity of innovation), but also proves that regardless of whether the substitution elasticity is greater than 1 or less than 1, the balanced growth path is not only unique, but also at least locally saddle-path stable.

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