Note on Idea Diffusion Models with Cohort Structures

In this note I propose two alternative frameworks to study idea diffusion models with cohort structures. Both frameworks fix the Lucas (2009) aggregation mistake while keeping the analytical tractability of the model and its insights. The frameworks differ in their assumptions on the meeting process. I study first a continuous arrival process where agents meet at each point in time, and then a more commonly used Poisson process where meeting opportunities arrive stochastically at some given Poisson rate. I generalize the growth formula in Lucas (2009) and show that both models yield the same growth rate on a balanced growth path. Moreover, I show that the continuous arrival process can be viewed as the limit of Poisson processes where the meeting rate increases but the quality of meetings decreases.