This paper is written in a two layer format consisting of a managerial layer and a technical layer. The managerial layer emphasizes strategic interpretation and organizational value, while the technical layer focuses on formal procedures, mathematical structure, and operator level rigor. Cognitive Amplification Inequality Theory (CAIT) formalizes how economically relevant intelligence is transformed under LLM mediated augmentation. The theory introduces a multiplicative production operatorAP =C×A, where C denotes intrinsic cognition and A denotes AI amplification capacity. It demonstrates that amplification induces nonlinear productivity gains and structurally increases dispersion, satisfying Var(C ×A) > Var(C). CAIT frames AI integrated economies as socio-cognitive systems in which productivity, inequality, and occupational structure emerge from heterogeneous access to and integration with amplification systems. The framework provides a unified basis for analyzing cognitive underutilization, AI adoption gaps, and amplification driven divergence in modern economies.
Usman Zafar (Mon,) studied this question.