Discrete Dynamic Systems in Economics: A Study of Linear Difference Equations and Nonlinear Models with Naive and Adaptive Expectations

This study investigates market dynamics using a discrete economic model of supply and demand. Initially, the linear case with naïve or static expectations is analyzed, and the stability conditions that lead to different system behaviors, such as convergence to equilibrium, periodic oscillations, or divergence, are determined analytically through the study of fixed points and cobweb dynamics. Subsequently, the analysis is extended to the nonlinear case with adaptive expectations, where the interaction between supply nonlinearity and the expectation formation process is found to generate complex behaviors. The results show how variations in the nonlinearity parameter induce bifurcations observable in time series. The study provides a comprehensive analytical framework that links mathematical properties with observable economic phenomena, offering tools to predict and manage stability in real markets, with direct applications in economic policy and financial risk management.