Can the Nexus of Scaling Laws Coupled with Constant or Variable Elasticity of Substitution Predict AI and Other Technology Adoption?

TL;DR

This paper demonstrates that the interplay of scaling laws and elasticity of substitution can predict the adoption patterns of emergent technologies like AI, solar power, and electric vehicles, linking price declines to adoption curves.

Contribution

It establishes a theoretical connection between scaling laws, CES and VES utility models, and the shape of technology adoption curves, providing a foundation for empirical modeling.

Findings

Price declines follow Moore's, Wright's, and AI scaling laws.

Adoption curves are Logistic or Log-Logistic, influenced by elasticity and experience parameters.

Functional relations can inform complex models and empirical specifications.

Abstract

Emergent technologies such as solar power, electric vehicles, and artificial intelligence (AI) often exhibit exponential or power function price declines and various ``S-curves'' of adoption. We show that under CES and VES utility, such price and adoption curves are functionally linked. When price declines follow Moore's, Wright's and AI scaling "Laws,'' the S-curve of adoption is Logistic or Log-Logistic whose slope depends on the interaction between an experience parameter and the elasticity of substitution between the incumbent and emergent good. These functional relations can serve as a building block for more complex models and guide empirical specifications of technology adoption.