Dynamics of Solow-Spatial Model with Capital-Augmenting Technology and Human Capital
Keywords:
Solow model, capital augmenting-technology, human capital, reaction-diffusion, steady stateAbstract
This paper investigates the dynamics of a spatial Solow growth model incorporating capital-augmenting technology and human capital. We establish that the economically relevant steady state remains locally asymptotically stable under spatial diffusion. Furthermore, our stability and bifurcation analysis shows that the system does not exhibit Turing or Hopf bifurcations, as the determinant of the spatial Jacobian remains strictly positive for all wave numbers (p ≥0). Consequently, spatial diffusion consistently acts to smooth out regional disparities over time, driving the system towards a uniform steady state without being constrained by a specific diffusion-ratio threshold.
References
[1] F. Fabiao, "Solow Model, An Economic Dynamical System of Growth," Applied Mathematical Sciences, vol. 3, no. 58, pp. 2867-2880, 2009.
[2] R. M. Solow, "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, vol. 70, no. 1, pp. 65-94, 1956.
[3] T. W. Swan, "Economic Growth and Capital Accumulation," Economic Record, vol. 32, no. 2, pp. 334-361, 1956.
[4] L. Guerrini, "The Solow–Swan Model with a Bounded Population Growth Rate," Journal of Mathematical Economics, vol. 42, pp. 14-21, 2006.
[5] C. W. Cobb and P. H. Douglas, "A Theory of Production," The American Economic Review, vol. 18, pp. 139-165, 1928.
[6] R. Findlay, "Neutral Technical Progress and the Relative Stability of Two-Sector Growth," International Economic Review, vol. 8, no. 1, pp. 109-115, 1967.
[7] M. J. Boskin and L. J.-y. Lau, "Generalized Solow-Neutral Technical Progress and Postwar Economic Growth," National Bureau of Economic Research, 2000.
[8] J. Bluedorn, "The Human Capital Augmented Solow Model," Economics 101B-Macroeconomic, pp. 1-4, 2002.
[9] R. R. Nelson and E. S. Phelps, "Investment in Humans, Technological Diffusion, and Economic Growth," The American Economic Review, vol. 56, no. 1/2, pp. 69-75, 1966.
[10] R. E. Lucas, "On The Mechanics of Economic Development," Journal of Monetary Economics, vol. 22, no. 1, pp. 3-42, 1988.
[11] N. G. Mankiw, D. Romer and D. N. Weil, "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, vol. 107, pp. 407-437, 1992.
[12] W. Brock and A. Xepapadeas, "Diffusion-Induced Instability and Pattern Formation in Infinite Horizon Recursive Optimal Control," Journal of Economic Dynamics and Control, vol. 32, p. 2745–2787, 2008.
[13] V. Capasso, R. Engbers and D. La Torre, "On a Spatial Solow Model with Technological Diffusion and Nonconcave Production Function," Nonlinear Analysis: Real World Applications, vol. 11, p. 3858–3876, 2010.
[14] Y. Zhong and W. Huang, "Spatial Dynamics for a Generalized Solow Growth Model", Discrete Dynamics in Nature and Society, vol. 2018, no. 1, pp. 1-8, 2018.
[15] J. Neto, J. C. Claeyssen and S. P. Junior, "Returns to Scale in A Spatial Solow–Swan Economic Growth Model," Physica A: Statistical Mechanics and its Applications, vol. 533, p. 122055, 2019.
[16] N. Urena and A. Vargas, "Numerical Solution to a Parabolic-ODE Solow Model with Spatial Diffusion and Technology-Induced Motility," Journal of Computational and Applied Mathematics, vol. 447, p. 115913, 2024.
[17] C. Camacho and B. Zou, "The Spatial Solow Model," Economics Bulletin, vol. 18, no. 2, pp. 1-11, 2004.
[18] P. Brito, "Local Dynamics for Spatial Economic Growth Models," ISEG, Lisbon, 2001.
[19] R. Boucekkine, C. Camacho and G. Fabbri, "Spatial Dynamics and Convergence: The Spatial AK Model," Journal of Economic Theor, vol. 148, no. 6, pp. 2717-2736, 2013.
[20] S. Sutrima, R. Setiyowati and M. Mardiyana, "Lotka-Volterra System of Predator-Prey Type with Time-Dependent Diffusive," Results in Nonlinear Analysis, vol. 7, no. 2, pp. 27-42, 2024.
[21] S. Sutrima and R. Setiyowati, "Properties of Solutions and Stability of a Diffusive Wage-Employment System," Nonlinear Dynamics and Systems Theory, vol. 23, no. 4, p. 434–446, 2023.
[22] E. Danial and N. Warsiah, Metode Penulisan Karya Ilmiah, Bandung: Laboratorium Pendidikan Kewarganegaraan UPI, 2009.
[23] S. V. Hoover and R. F. Perry, Simulation: A Problem-Solving Approach, Reading: Addison-Wesley, 1989.
[24] M. Szydlowski and A. Krawiec, "On Capital Dependent Dynamics of Knowledge," Acta Physica Polonica B, vol. 37, p. 3161–3170, 2006.
[25] W. E. Boyce, R. C. Diprima and D. B. Meade, Elementary Differential Equations and Boundary Value Problems, Hoboken: John Wiley & Sons, Inc, 2017.
