Comparative Asymptotic Analysis of Economic Modeling Techniques Under Tariff Perturbations: Demonstrating the Superiority of Delayed Differential Equations (DDEs)

Abstract

Economic modeling plays a crucial role in understanding the dynamics of policy shifts, such as tariff perturbations, on national and global economies. This paper provides a comparative analysis of four prevalent modeling techniques-Laplace Transform, Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), and Delayed Differential Equations (DDEs). The paper demonstrates that while traditional models like ODEs and PDEs are useful in certain contexts, DDEs are superior for modeling economic systems with time delays and feedback mechanisms, which are inherent in many real-world scenarios, particularly when assessing the effects of tariff changes.

Keywords: Economic Modeling, Tariff Perturbations, Laplace Transform, Ordinary Differential Equations, Partial Differential Equations, Delayed Differential Equations