A New Class of Production Functions and an Argument Against Purely Labor-Augmenting Technical Change

Abstract

Abstract. This paper follows Jones (2005) in his approach to deriving the global production function from microfoundations. His framework is generalized by allowing for dependence between the Pareto distributions of labor-and capital-augmenting developments. Using the Clayton copula family to capture this dependence, we derive a "Clayton-Pareto" class of production functions that nests both the Cobb-Douglas and the CES. Embedding the resultant production function in a neoclassical growth framework, we draw conclusions for the long-run direction of technical change. Jones' result of Cobb-Douglas global production functions and purely laboraugmenting technical change hinges on the assumption of independence of marginal Pareto distributions. In our more general case, the shape of local production functions matters for the shape of the global production function, and technical change augments both factors in the long run. Furthermore, the elasticity of substitution between capital and labor may exceed unity and thus yield endogenous growth.

Knife-Edge Conditions in the Modeling of Long-Run Growth Regularities

“…These works do not solve the Uzawa's fundamental problem of highly restrictive knife-edge conditions, though (cf. Jones, 2005a;Growiec, 2008). 13 Another milestone in the development of this line of discussion is the linearity critique of endogenous growth models (Jones, 2005a).…”

“…Jones, 2005a;Growiec, 2008). 13 Another milestone in the development of this line of discussion is the linearity critique of endogenous growth models (Jones, 2005a). The crux of this argument is that if the vital growth-driving linearity (a knife-edge assumption) is relaxed, exponential growth ceases to be obtained unless exponential population growth is additionally assumed.…”

“…A discussion of the theorem and both proofs has been provided by Jones and Scrimgeour (2008). 13 The objective of Acemoglu (2003) and Jones (2005b) was, of course, not to get rid of knife-edge assumptions but to provide sound economic explanations why purely labor-augmenting technical change could indeed be an equilibrium outcome.…”

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

“…Each of these local techniques is in turn characterized by a pair of technology-specific unit factor productivities (UFPs), (a, b). This model has been first put forward by Jones (2005) and then extended in two subsequent papers by Growiec (2008aGrowiec ( , 2008b). 1 Jones (2005) assumed that firms producing the final good draw both these UFPs randomly from a pair of independent Pareto distributions, so that their technology choice is optimal only on average, or in the limit when sufficiently many draws have been made.…”

“…Two decisive changes in the model setup have been made as compared to the earlier contributions by Jones (2005) and Growiec (2008aGrowiec ( , 2008b. First, we have rewritten the model in terms of normalized CES functions (cf.…”