A Microfoundation for Normalized CES Production Functions with Factor-Augmenting Technical Change

Abstract

We derive the aggregate normalized CES production function from idea-based microfoundations where firms are allowed to choose their capital- and labor-augmenting technology optimally from a menu of available technologies. This menu is in turn augmented through factor-specific RD if they are independently Pareto-distributed, then it is Cobb–Douglas. Third, by disentangling technology choice by firms from R&D output, one can draw a clearcut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Fourth, it is argued that the Weibull distribution should be a good approximation of the true unit factor productivity distribution (and thus the CES should be a good approximation of the true aggregate production function) if a 'technology' is in fact an assembly of a large number of complementary components. This argument is illustrated with a novel, tractable model of directed (factor-specific) R&D. Finally, it is shown that all our results carry forward to the general case of n-input production functions.