Paper Title:

The Degree of Homogeneity: Definition, Geometric Interpretation and New, Direct Proofs of Euler's Theorem

Author(s):

Olivier de La Grandville

Faculty of Economics, Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We show how the degree of homogeneity of a function is a highly useful, precise measure of the sensitivity of a function to a change in its variables. This measure can be evaluated directly thanks to a simple geometric construct, entirely independently of measurement units. The usefulness of this concept is also illustrated by the fact that it leads to new, direct proofs, geometric as well as algebraic, of Euler's theorem; this is in contrast to the traditional approach that requires a limiting process.

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