A spatial Solow model with transport cost

Juchem Neto, Joao Plinio and Claeyssen, Julio Cesar Ruiz and Porto Junior, Sabino da Silva (2014): A spatial Solow model with transport cost.

Abstract

In this paper we introduce capital transport cost in an unidimensional unbounded economy described by a spatial Solow model with capital-induced labor migration. Proceeding with a linear stability analysis of its spatially homogeneous equilibrium solution, we show that exists a critical value for the capital transport cost where the dynamic behavior of the economy changes, provided the capital-induced labor migration intensity is big enough. On one hand, if capital transport cost is bigger than this critical value, the homogeneous equilibrium of the model is stable, and the economy converges to this spatially homogeneous state in the long run; on the other hand, if transport cost is smaller than this critical value, the equilibrium is unstable, and the economy may develop distinct spatio-temporal dynamics, including the formation of stable economic clusters and spatio-temporal economic cycles, depending on the other parameters of the model. This result, though obtained using a different formalism, is consistent with the main results of the standard core-periphery model used in the New Economic Geography literature, where a small transport cost is essencial to the formation of spatial economic agglomeration. Finally, we close this work validating the linear stability analysis results through numerical simulations, and verifying that the introduction of a positive transport cost in the model causes a break in the symmetry of the spatial economic agglomerations generated.

• Item Type: MPRA Paper
• Language: English
• Keywords: Spatial Solow Model, Regional Science, Economic Agglomeration, Economic Geography.
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O40 - General; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

References

Boucekkine, R., Camacho, C., and Fabbri, G. (2013). Spatial dynamics and convergence: the spatial ak model. Journal of Economic Theory, 148:2719–2736.

Brakman, S., Garretsen, H., and van Marrewijk, C. (2009). The New Introduction to Geographical Economics. Cambridge University Press, UK.

Brito, P. (2004). The dynamics of growth and distribution in a spatially heterogeneous world. Working Paper, ISEG, WP13/2004/DE/UECE.

Brito, P. (2005). Essays in Honour of Antonio Simoes Lopes, chapter A Spatial Solow Model with Unbounded Growth, pages 277–298. ISEG/UTL.

Camacho, C. and Zou, B. (2004). The spatial solow model. Econ. Bull., 18(2):1–11.

Camacho, C., Zou, B., and Briani, M. (2008). On the dynamics of capital accumulation across space. Eur. J. Oper. Res., (186):451–465.

Capasso, V., Engbers, R., and La Torre, D. (2010). On a spatial solow model with technological diffusion and nonconcave production function. Nonlinear Anal-Real, (11):3858–3876.

Capasso, V., Engbers, R., and La Torre, D. (2012). Population dynamics in a spatial Solow model with a convex-concave production function, pages 61–68. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer-Verlag, Milano, Italy.

Combes, P.-P., Mayer, T., and Thisse, J.-F. (2008). Economic Geography - The Integration of Regions and Nations. Princenton University Press, UK.

Edelstein-Keshet, L. (2005). Mathematical Models in Biology. Classics in Applied Mathematics. SIAM, Philadelphia, US.

Engbers, R. (2009). Spatial Structures in Geographical Economics - Mathematical Modeling, Simulation and Inverse Problems. PhD thesis, Westfalische Wilhems-Universitat, Munster.

Fujita, M., Krugman, P., and Venables, A. J. (1999). The Spatial Economy. MIT Press.

Fujita, M. and Thisse, J.-F. (2002). Economics of Agglomeration: Cities, Industrial Location, and Regional Growth. Cambridge University Press, UK.

Isard, W. (1956). Location and Space Economy: A General Theory Relationg to Industrial Location, Market Areas, Land Use, Trade and Urban Structure. MIT Press, Cambridge.

Isard, W. (2003). History of Regional Science and the Regional Science Association International - The Beginnings and Early History. Spring-Verlag, Berlin.

Isard, W. and Liossatos, P. (1975a). Parallels from physics for space-time development models: Part i. Reg Sci Urban Econ, 1(1):5–40.

Isard, W. and Liossatos, P. (1975b). Parallels from physics for space-time development models: Part ii - interpretation and extensions of the basic model. Regional Science Association, 35:43–66.

Isard, W. and Liossatos, P. (1979). Spatial Dynamics and Optimal Space-Time Development, volume 4 of Studies in Regional and Urban Economics. North-Holland, New York, US.

Juchem Neto, J. P. and Claeyssen, J. C. R. (2014). Capital-induced labor migration in a spatial solow model. Journal of Economics, 112(2):1–23.

Krugman, P. (1979). Increasing returns, monopolistic competition and international trade. Journal of International Economics, 9:469–479.

Krugman, P. (1991). Increasing returns and economic geography. J Polit Econ, (99):483–499.

Murray, J. D. (2003). Mathematical Biology - II: Spatial Models and Biomedical Applications. Springer-Verlag, New York, US, third edition edition.

Quigley, J. M. (2001). The renaissance in regional research. The Annals of Regional Science, 35:167–178.

Tveito, A. and Winther, R. (1998). Introduction to Partial Differential Equations - A Computational Approach. Springer-Verlag, New York. 11. Reaction-Diffusion Equations: pp. 337-360.

Zhu, M. and Murray, J. D. (1995). Parameter domains for generating spatial pattern: A comparison of reaction-diffusion and cell-chemotaxis models. Internat. J. Bifur. Chaos, 5(6):1503–1524.