A note on 2-input neoclassical production functions

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.