The Cobb-Douglas function can be used to represent a wide range of production functions with varying output elasticity. This approach simplifies the process of determining linear input demands without complex mathematical theorems. It also allows for a more flexible version of the CES function, where the elasticity of substitution between inputs can differ. This framework offers a more general and adaptable way to analyze the substitution properties of nested CES functions, particularly in cases involving energy, capital, and labor.