Heterogeneous Firms and AI Adoption. Dynamic Insights into Market Structure and Global Trade

This paper presents an extended framework building on the Melitz model to analyze the impact of artificial intelligence (AI) adoption on firm behavior, market structure, and international trade. We introduce a log-normal distribution of firm productivity and model heterogeneous AI adoption by incorporating fixed costs and a free-rider effect, where non-adopters benefit indirectly from technological diffusion. A key innovation lies in including AI productivity gains, either symmetric in a simplified manner or stochastic, allowing for firm-level variation in implementation success. This addition generates realistic dispersion in post-adoption outcomes and alters firm dynamics near critical survival, investment, and export activity thresholds. We compare deterministic AI adoption trajectories (sigmoid and exponential) with stochastic scenarios, highlighting how uncertainty in AI outcomes can amplify competitive asymmetries and increase market volatility. Under high fixed adoption costs and weak spillovers, the model exhibits strong endogenous concentration effects, especially when adoption follows an exponential path reinforced by feedback loops, potentially approaching scenarios of artificial superintelligence (ASI) or singularity. A sigmoid adoption trajectory implies bounded gains and a more stable equilibrium. The paper also explores the potential breakdown of monopolistic competition assumptions, suggesting oligopolistic drift in concentrated AI-intensive markets. These dynamics give rise to targeted policy implications to promote inclusive technological diffusion and reduce systemic risk.