A production function with variable elasticity of substitution greater than one

TL;DR

This paper proves the existence of a production function with a variable elasticity of substitution greater than one, supporting the idea that technological progress influences capital substitutability over time.

Contribution

It introduces a formal proof for a production function where the elasticity of substitution can exceed one, extending previous models.

Findings

Existence of a production function with variable elasticity > 1

Supports the hypothesis of increasing substitution in high-tech economies

Provides a theoretical foundation for variable elasticity models

Abstract

The idea of this paper comes from the famous remark of Piketty and Zuckman: "It is natural to imagine that $\sigma$ was much less than one in the eighteenth and nineteenth centuries and became larger than one in the twentieth and twenty-first centuries. One expects a higher elasticity of substitution in high-tech economies where there are lots of alternative uses and forms for capital." The main aim of this paper is to prove the existence of a production function of variable elasticity of substitution with values greater than one.