Stability Analysis of a Bank Deposit-Loan Model with Reserve Requirement Policy

This study investigates the stability of a dynamic loan–deposit model within a single-bank system, incorporating the effects of reserve requirement policies. Unlike existing deposit–loan models, the proposed framework explicitly distinguishes between productive and consumptive loans, allowing a more detailed analysis of credit allocation under regulatory constraints. The model is represented by a system of nonlinear differential equations describing the interactions between deposit funds and the two types of loans. The analysis focuses on identifying equilibrium points and examining their local stability through Jacobian-based linearization. The results reveal five equilibrium points: the equilibrium without deposit and loan activities, the loan-free equilibrium, the productive loan-free equilibrium, the consumptive loan-free equilibrium, and the full-activity equilibrium. Under the stated parameter conditions, all equilibria are locally stable except the trivial equilibrium, which is unstable. Numerical simulations validate the analytical results and illustrate the influence of reserve requirements on deposit dynamics and loan composition. These findings suggest that reserve requirement policies play a crucial role as a regulatory tool in maintaining banking liquidity and promoting a stable balance between productive and consumptive lending.