Study of Walrasian Model Using Quantum Calculus

Abstract

In this work, for the first time, we present the Walrasian Model in view of q-calculus as a novel perspective of economic dynamics. Though q-methods have been widely applied in mathematical physics, their use in microeconomic theory remains unexplored. In order to study this model, at first, we begin by outlining the foundational concepts of q-calculus, and then reformulate the Walrasian framework within this q-calculus set up. This approach is not only applied to solve the one-dimensional dynamic equation that illustrates the effectiveness through a classic example of microeconomics but also the numerical validation against classical datasets confirms the robustness of this method. Most importantly, we show, if the deformation parameter q tends to 1, the results converge seamlessly to those obtained via the classical calculus that bridges the new formulation with established theory. This study also highlights the potential of q-calculus as a powerful tool for advance research in economic dynamics and opens new directions for theoretical as well as applied economics.