TITLE:
Explaining Cobb-Douglas with the New Mathematics of Inteduct
AUTHORS:
Michael Grabinski, Galiya Klinkova
KEYWORDS:
Cobb-Douglas, Production Function, Taylor, Inteduct, Climate Change
JOURNAL NAME:
Theoretical Economics Letters,
Vol.13 No.6,
November
14,
2023
ABSTRACT: The Cobb-Douglas production function is used for around a hundred years
and describes the macro economic reality very well. Though nobody doubts its
validity, there is no rigorous derivation of it. Giving this derivation is done
in this publication for the first time. We start with the most general version
of a production function just assuming that there exists such function of an
arbitrary number of variables (all possible input factors). We then make a
Taylor expansion of this function still containing many variables. We then average over groups of variables via an
inteduct. The groups can be e.g. labor and capital leading exactly the
well-known version of the Cobb-Douglas production function. As we know how to
derive this function, we also know the origin of the normally small deviations
between Cobb-Douglas and the reality.