The Mechanics of Endogenous Diffusion: A Tractable Analytical Framework

This note develops a growth model in which the diffusion of capital goods is endogenized through the interaction between monopolistic suppliers and a final-goods sector. We introduce a distinction between private and social returns to adoption: while individual firms operate under constant or diminishing returns-ensuring a stable micro-foundation for profit maximization-aggregate production exhibits increasing returns driven by system-wide diffusion complementarities and adoption externalities. The model derives a closed-form solution for the long-run growth rate, which is shown to depend on the user cost of capital and the strength of these aggregate complementarities. Specifically, we find that lower financing costs and declining relative prices for capital goods accelerate diffusion. By explicitly modeling the transition from microlevel adoption to macro-level increasing returns, this framework provides a structural mechanism explaining how economies sustain growth through the propagation of innovations, complementing standard R&D-based approaches.