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

Abstract: Emergent technologies such as solar power, electric vehicles, and 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.