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

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 R&D. The considered model yields a number of interesting results. First, normalization can be maintained simultaneously at the local and at the aggregate level, greatly facilitating interpretation of the aggregate production function's parameters in terms of the underlying idea distributions. Second, in line with earlier findings, if capital- and labor-augmenting ideas are independently Weibull-distributed then the aggregate production function is CES; 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 clear-cut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Finally, 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.