The Dynamics of Household Indebtedness with Financial Intermediation and Resource Constraints in a Neoclassical Growth Model

Our study examines the dynamics of household indebtedness within a neoclassical growth model, assuming a single representative household with quasi-hyperbolic discounting, an explicit financial sector, and resource constraints. The household’s utility depends on its consumption and the sustainability of the resource stock, with time-inconsistent preferences, while the financial sector intermediates interest-bearing loans. The production function models the depletion of natural resources, emphasizing sustainability. Our results indicate that equilibrium solutions exist, and their stability depends on interest rates, savings rates, and resource utilization. Numerical simulations show that low interest rates and moderate present bias can stabilize the system, while high interest rates may generate debt cycles. Increasing the tax rate reduces equilibrium variables but promotes long-term stability through sustainable resource management.