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Differences and Connections Between Individual (Leontief Type) Activities and Aggregate (Cobb-Douglas Type) Results

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  • Carlos Esteban Posada Posada

Abstract

Each production establishment is assumed to have, at any given time, a unique combination of capital and labor (a Leontief function), but the aggregate output at that same time must still be modeled with a Cobb-Douglas function (or a CES, although the latter yields less efficiency). This has two implications: 1) the total factor productivity variable of the macroeconomic function is endogenous: It depends primarily on the technical factors of the individual establishments and, secondarily, on their levels of capital and labor.; 2) the optimization processes of any establishment cannot be instantaneous, even in the absence of (monetary) adjustment costs; they are processes occurring over several time stages and depending on expectations. However, these implications do not substantially contradict what would correspond to the optimization of a hypothetical firm described by a Cobb-Douglas (or CES) function.

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  • Carlos Esteban Posada Posada, 2025. "Differences and Connections Between Individual (Leontief Type) Activities and Aggregate (Cobb-Douglas Type) Results," Papers 2512.15520, arXiv.org.
    • Handle: RePEc:arx:papers:2512.15520
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    References listed on IDEAS

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    1. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 517-549.
    2. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    3. H. S. Houthakker, 1955. "The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(1), pages 27-31.
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