Economic Dynamics Model Using q-Laplace’s Transform

Abstract

Here, for the first time, we introduce the quantum Laplace transform as a tool to analyze dynamic models in economic theory. In order to do it, at first, we revisit some useful essential preliminaries of q-calculus as well as q-Laplace transform and then apply this framework to three important cases: the Walrasian price stability model, the measurement of input response in an inflationary setting, and the model of farm sponsored job training. The solutions derived through this approach are studied numerically that shows this method provides a clear and systematic way to interpret dynamic behavior in economics. A noteworthy feature of this framework is its consistency, and it is notable that as the parameter q→1, all the outcomes reduce smoothly to those obtained via the classical Laplace transform. This convergence highlights the robustness of the method that opens a promising pathway for deploying q-calculus in economic dynamics. In short, this approach opens new research opportunities for both theoretical and applied economics..