"Comparative Asymptotic Analysis of Economic ModelingFrameworks Under Tariff Perturbations: Establishing the Superiority of Delayed Differential Equations"

Purpose – This study compares four dynamic modeling frameworks—Laplace Transforms, Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), and Delayed Differential Equations (DDEs)—to assess their relative effectiveness in capturing the macroeconomic impacts of tariff-induced policy shocks. The central aim is to determine which modeling approach most accurately reflects delayed feedback mechanisms, nonlinear adjustment dynamics, and policy lags inherent in real-world economies. Design/methodology/approach – We develop a stylized two-sector trade-economy model incorporating domestic and imported output, the consumer price index, and government subsidies. Each model—Laplace, ODE, PDE, and DDE—is subjected to an equivalent tariff shock scenario. We utilize asymptotic expansions, delay differential simulations, and numerical solvers to explore dynamic behavior under both instantaneous and lagged policy responses. In particular, the DDE framework incorporates a dual-delay structure to reflect both endogenous market inertia and exogenous policy implementation lags. Supplementary analyses using bifurcation diagrams, cobweb plots, and Lyapunov exponents provide insight into system stability, oscillations, and potential chaotic dynamics. Findings – The comparative analysis reveals that while ODEs and PDEs can model smooth or spatially diffused dynamics, they fail to capture the effects of feedback delays and memory-dependent behavior. Laplace transform methods, although analytically concise, are inadequate in time-domain interpretation. In contrast, Delayed Differential Equations (DDEs) offer superior capability in modeling the nonlinear, lagged, and oscillatory features of policy shocks. The dual-delay DDE system uniquely reflects how economic and policy-driven delays interact to shape inflation, output volatility, and long-term equilibrium shifts. Originality/value – This paper provides one of the first comprehensive comparisons of classical and advanced time-evolution models under a unified economic context with explicit focus on policy-induced delays. By highlighting the importance of dual-delay DDEs in modern macroeconomic modeling, it contributes a robust framework for evaluating trade interventions, inflationary impacts, and policy design under delayed feedback conditions—critical for real-time economic forecasting and decision-making in policy environments where timing is pivotal. To further the analysis results, we also employed advanced mathematical tools such as: • Lyapunov exponent analysis }, to assess the system’s sensitivity to initial conditions and detect chaotic regimes. • Bifurcation diagrams , to explore stability boundaries and transition behaviors under varying delay parameters; • Cobweb plots and discrete economic maps , to simulate adjustment dynamics in consumer and producer behavior; • Time-evolving simulations , to evaluate policy impacts under realistic, non-instantaneous conditions. JEL Classification – C61, C62, C63, C65, F13