Research ArticleOpen AccessGoogle Scholar indexed
Asymptotic Behaviors Analysis of the Spatial AK Model with Trade Costs
Southwest Jiaotong University, Chengdu, China
- 1 Southwest Jiaotong University, Chengdu, China
Theoretical Economics Letters·Volume 11 (2021)·Pages 603–614·Published 8 May 2021·DOI10.4236/tel.2021.113040
Copy link · social · email
Abstract
We consider a spatial economic growth model with trade costs whose spatial-temporal dynamics of the capital stock are governed by a parabolic partial differential equation and analyze the effects of the trade costs on the asymptotic behaviors of the capital in the framework of spatial AK model, where the technology is time-varying. Taking advantage of the good properties of the Green function, we formulate an explicit solution to the auxiliary partial differential equation of the original problem and derive the sufficient conditions on the consumption function that guarantee the existence and the uniqueness of the solution and obtain the convergence properties of the capital in the long run for the spatial AK model with trade costs.
KeywordsSpatial AK ModelTrade CostsAsymptotic Behaviors
- Aldashev, G., Aldashev, S., & Carletti, T. (2014). On Convergence in the Spatial AK Growth Models (pp. 1-18). https://arxiv.org/abs/1401.4887
- Ballestra, L. V. (2016). The Spatial AK Model and the Pontryagin Maximum Principle. Journal of Mathematical Economics, 67, 87-94. https://doi.org/10.1016/j.jmateco.2016.09.012
- Behrens, K., & Picard, P. M. (2011). Transportation, Freight Rates, and Economic Geography. Journal of International Economics, 85, 280-291. https://doi.org/10.1016/j.jinteco.2011.06.003
- Boucekkine, R., Camacho, C., & Fabbri, G. (2013). Spatial Dynamics and Convergence: The Spatial AK Model. Journal of Economic Theory, 148, 2719-2736. https://doi.org/10.1016/j.jet.2013.09.013
- Boucekkine, R., Camacho, C., & Zou, B. (2009). Bridging the Gap between Growth Theory and the New Economic Geography: The spatial Ramsey Model. Macroeconomic Dynamics, 13, 20-45. https://doi.org/10.1017/S1365100508070442
- Brito, P. (2004). The Dynamics of Growth and Distribution in a Spatially Heterogeneous World (pp. 1-45). https://core.ac.uk/download/pdf/7027939.pdf
- Camacho, C., Zou, B., & Briani, M. (2008). On the Dynamics of Capital Accumulation Across Space. European Journal of Operational Research, 186, 451-465. https://doi.org/10.1016/j.ejor.2007.02.031
- Desmet, K., & Rossi-Hansberg, E. (2010). On Spatial Dynamics. Journal of Regional Science, 50, 43-63. https://doi.org/10.1111/j.1467-9787.2009.00648.x
- Fabbri, G. (2016). Geographical Structure and Convergence: A Note on Geometry in Spatial Growth Models. Journal of Economic Theory, 162, 114-136. https://doi.org/10.1016/j.jet.2015.12.004
- Isard, W., & Liossatos, P. (1979). Spatial Dynamics and Optimal Space-Time Development. Amsterdam: North-Holland.
- Juchem Neto, J., Claeyssen, J., & Prto Jnior, S. (2018). Economic Agglomerations and Spatio-Temporal Cycles in a Spatial Growth Model with Capital Transport Cost. Physica A: Statistical Mechanics and its Applications, 494, 76-86. https://doi.org/10.1016/j.physa.2017.12.036
- Juchem Neto, J. P., & Claeyssen, J. C. R. (2015). Capital-Induced Labor Migration in a Spatial Solow Model. Journal of Economics, 115, 25-47. https://doi.org/10.1007/s00712-014-0404-6
- Thisse, J., & Fujita, M. (2002). Economics of Agglomeration. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511805660