A microfoundation for normalized CES production functions with factor-augmenting technical change

Jakub Growiec

No 98, NBP Working Papers from Narodowy Bank Polski

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 R&D. The considered model yields a number of interesting results. First, normalization of the production function 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 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.

Keywords: CES production function; normalization; Weibull distribution; direction of technical change; directed R&D; optimal technology choice (search for similar items in EconPapers)
JEL-codes: E23 E25 O47 (search for similar items in EconPapers)
Pages: 39
Date: 2011
New Economics Papers: this item is included in nep-eff, nep-ino and nep-mac
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: A microfoundation for normalized CES production functions with factor-augmenting technical change (2013)
Working Paper: A Microfoundation for Normalized CES Production Functions with Factor-Augmenting Technical Change (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:nbp:nbpmis:98

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