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

TL;DR

This paper explores the relationship between individual production functions modeled by Leontief and aggregate functions modeled by Cobb-Douglas, revealing implications for productivity and optimization processes in macroeconomics.

Contribution

It demonstrates how aggregate productivity is endogenous and influenced by individual technical factors and shows that firm optimization occurs over multiple stages with expectations.

Findings

Total factor productivity depends on individual technical factors.

Optimization processes are multi-stage and expectation-dependent.

Aggregate output can be modeled with Cobb-Douglas despite individual Leontief functions.

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.