A note on the Cobb-Douglas function

TL;DR

This paper characterizes the Cobb-Douglas production function by a unique property related to constant labor share during cost minimization at fixed output levels.

Contribution

It provides a novel characterization of the Cobb-Douglas function based on the invariance of labor share during cost minimization.

Findings

Cobb-Douglas function is uniquely characterized by labor share invariance.

The property holds for any constant-returns-to-scale firm.

This characterization offers a new perspective on the function's properties.

Abstract

This note observes that the Cobb-Douglas function is uniquely characterized by the property that, if the labour share of cost for a constant-returns-to-scale firm remains constant when the firm minimizes its cost for any given output level, then the firm's production function must be Cobb-Douglas.