Stability of the Solow Model with Hicks-Neutral Technology under Capital and Human Capital Diffusion
Keywords:
Solow model, reaction-diffusion system, steady state, stability analysis, bifurcationAbstract
Differences in economic growth across regions indicate that spatial interactions between physical capital and human capital may influence long-run economic dynamics. To investigate these spatial interactions, this study develops a reaction-diffusion-based Solow model incorporating Hicks-neutral technology and human capital to analyze the stability of its dynamic system. Through a detrending process, the system becomes autonomous and is expressed in terms variables per effective worker, thereby enabling a steady-state stability analysis related to a balanced growth path. Analysis results show that without diffusion, the steady state is locally stable as long as conditions of decreasing returns to scale hold. When spatial diffusion with homogeneous Neumann boundary conditions is introduced, results from linearity and eigenvalue analysis indicate that the real part of all eigenvalues remains negative for all spatial modes. This implies that diffusion does not trigger either Hopf or Turing bifurcations, so no persistent spatial patterns form. Numerical simulations confirm the analytical results and illustrate the exponential decay of deviations toward the balanced growth path. These results suggest that the system remains stable despite modal diffusion and highlight the application of reaction–diffusion modeling and dynamical systems analysis as mathematical tools for studying spatial economic growth.
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