A new class of production functions and an argument against purely labor‐augmenting technical change

Abstract

This paper derives the macro‐level production function from idea‐based microfoundations. Labor‐augmenting and capital‐augmenting developments are assumed to be Pareto‐distributed and mutually dependent. Using the Clayton copula family to capture this dependence, a new “Clayton–Pareto” class of production functions is derived that nests both the Cobb–Douglas and the constant elasticity of substitution. In the most general case, technical change is not purely labor‐augmenting over the long run, but it augments both capital and labor. Under certain parametrizations, the derived elasticity of substitution between capital and labor exceeds unity and, therefore, gives rise to long‐run endogenous growth.