A Rigorous Proof of the Index Theorem for Economists

TL;DR

This paper offers a detailed, rigorous proof of the index theorem in economic theory, making it more accessible for economists by filling a gap in existing literature.

Contribution

It provides the first comprehensive, gap-free proof of the index theorem applicable to many economies, enhancing understanding and rigor in economic theory.

Findings

A rigorous proof of the index theorem is constructed.

The proof applies under usual assumptions and continuous differentiability.

It broadens the applicability of the index theorem in economic analysis.

Abstract

This paper provides a rigorous and gap-free proof of the index theorem used in the theory of regular economy. In the index theorem that is the subject of this paper, the assumptions for the excess demand function are only several usual assumptions and continuous differentiability around any equilibrium price, and thus it has a form that is applicable to many economies. However, the textbooks on this theme contain only abbreviated proofs and there is no known monograph that contains a rigorous proof of this theorem. Hence, the purpose of this paper is to make this theorem available to more economists by constructing a readable proof.