An eigenvalue approach to the dynamics of supply-demand-price systems

This paper examines the oscillatory behavior of supply-demand-price dynamical systems using eigenvalue analysis. Unlike traditional stability assessments, our study reveals that the system does not exhibit asymptotic stability since all eigenvalues have zero real parts. This results in sustained harmonic oscillations rather than convergence to equilibrium. By formulating market dynamics through differential equations and analyzing the Jacobian matrix, we characterize the system’s long-term behavior based on its eigenvalues. Our findings provide mathematical formulations, theoretical insights, and numerical simulations that illustrate persistent price fluctuations and cyclical market behavior. The study enhances the understanding of market instability, hence emphasizing the role of linear algebra in economic dynamics and its implications for economic modeling and policy-making.