This project develops a mathematical model to explore how capital and labor mobility influence the economic growth of two interconnected regions. By combining the Solow Growth Model and the Malthusian Population Model, the study captures the complex dynamics between capital accumulation, labor distribution, and regional disparities.
• Solow Model: Models capital accumulation using a Cobb-Douglas production function.
• Malthusian Model: Describes labor growth with crowding effects.
• Extended System: A system of four differential equations models the evolution of capital and labor in two regions, incorporating diffusion and capital-induced labor movement.
• No Capital-Induced Labor Movement (c = 0)
• Regions gradually reach a stable, symmetric economic equilibrium.
• Final states are independent of initial conditions.
• With Capital-Induced Labor Movement (c > 0)
• For small values of c, both regions still converge to equal capital and labor.
• For large c, asymmetric outcomes and inequalities arise, depending heavily on initial conditions.
• Moderate capital-labor interactions support convergence and balanced growth.
• Excessive capital-driven labor shifts can destabilize regional equality and reduce total capital and labor.
• Policy implications: encourage balanced openness to prevent uneven economic development.
• System modeled and solved using ordinary differential equations.
• Numerical simulations conducted to explore parameter sensitivity and equilibrium behavior.