A note on 2-input neoclassical production functions

Gwenaël Moysan (1) , Mehdi Senouci (2)

1 Global market solutions
2 LGI - Laboratoire Génie Industriel - EA 2606

In this short note, we show how the space of elasticity of substitution functions maps into the space of 2-input neoclassical production functions. In doing so we derive a general analytical formula for every 2-input neoclassical production function of class C2. We present a simple set of sufficient conditions for the Inada conditions to hold; and prove that the Solow model under capital-augmenting (or investment-specific) technical change is asymptotically balanced if and only if the capital share converges to a non-degenerated limit as the capital-labor ratio tends to infinity.

Mots clés: Production function; Elasticity of substitution; Capital share; Labor share; Solow model

Domaines: Economies et finances

Gwenaël Moysan, Mehdi Senouci. A note on 2-input neoclassical production functions. Journal of Mathematical Economics, 2016, 67, pp.80-86. ⟨10.1016/j.jmateco.2016.09.011⟩. ⟨hal-01383290⟩