In Defence of Social Security Against National Security: A Lotka-Volterra Model of Military Expenditures and Civilian Expenditures

Abstract

This paper introduces a novel application of the Lotka-Volterra model to analyze the dynamic interplay between military and civilian government spending in the United States from 1960 to 2019. Drawing on the classical ‘guns versus butter’ framework, we conceptualize military spending as a predator and civilian spending as prey, both constrained by GDP as a shared resource. By constructing a system of nonlinear differential equations, we model inter-sectoral competition, long-term memory effects, and time-varying growth and carrying capacities. The model reveals strong asymmetries in budgetary interaction: military expenditures exert a disproportionately negative impact on civilian spending, while being more sensitive to shared constraints, suggesting a prey-like vulnerability. Using a genetic algorithm for parameter estimation, we demonstrate that shifts in growth rates and sectoral capacities correspond closely with historical inflection points, such as the Cold War and the War on Terror. Our findings offer compelling evidence of Lotka-Volterra-like oscillatory behavior in public budget allocation, underscoring the strategic dominance of military priorities over social investments. This dynamic modeling approach provides new insights into the systemic trade-offs embedded in fiscal policy and raises critical questions about the sustainability of militarized economic strategies.