The Addicted Predator–Prey Model: How Substance Abuse Shapes Productivity and Growth-Cycle Dynamics

This paper introduces substance abuse into the Goodwin (1967) predator–prey growth-cycle framework as an endogenous channel linking income distribution to aggregate productivity. Using a continuous-time discrete-choice mechanism, workers transition between drug-abusing and drug-free states in response to the wage share, which in turn feeds back into productivity through a damage function. We ground the model empirically using U.S. state-level data from 1998–2019, and show theoretically that the resulting nonlinear system admits a unique interior equilibrium that loses stability via a Hopf bifurcation as the autonomous wage-growth parameter crosses a critical threshold, giving rise to persistent, bounded fluctuations and, in some regions of the parameter space, coexisting multiple limit cycles.

Recommended citation: Chung, Nara, and Marwil J. Dávila-Fernández. "The Addicted Predator–Prey Model: How Substance Abuse Shapes Productivity and Growth-Cycle Dynamics." Working paper, March 2026.