Global endogenous growth and distributional dynamics

Brito, Paulo (2011): Global endogenous growth and distributional dynamics.

Abstract

In this paper we deal with the global distribution of capital and output across time. We supply empirical support to model it as a partial differential equation, if the support of the distribution is related to an initial ranking of the economies. If we consider a distributional extension of the AK model we prove that it displays both global endogenous growth and transitional convergence in a distributional sense. This property can also be shared by a distributional extension of the Ramsey model. We conduct a qualitative analysis of the distributional dynamics and prove that If the technology displays mild decreasing marginal returns we can have long run growth if a diffusion induced bifurcation is crossed. This means that global growth can exist even in the case in which the local production functions are homogeneous and display decreasing returns to scale.

• Item Type: MPRA Paper
• Language: English
• Keywords: optimal control of parabolic PDE, endogenous growth, diffusion induced bifurcation
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics; D - Microeconomics > D9 - Intertemporal Choice; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models

References

Acemoglu, D. (2009). Introduction to Modern Economic Growth. Princeton University Press.

Atkinson, A. B. and Stiglitz, J. E. (1980). Lectures on Public Economics. McGraw-Hill.

Barro, R. and Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100(2):223–51.

Bergson, A. (1938). A Reformulation of Certain Aspects of Welfare Economics. Quarterly Journal of Economics, 52(2):310–334.

Bertola, G. (2000). Macroeconomics of distribution and growth. In Atkinson, A. B. and Bourguignon, F., editors, Handbook of Income Distribution, volume 1 of Handbooks in Economics, pages 479–541. Elsevier.

Boucekkine, R., Camacho, C., and Fabbri, G. (2010). Spatial dynamics and convergence: the spatial ak models. Working Papers 2010/06, Department of Economics, University of Glasgow.

Boucekkine, R., Camacho, C., and Zou, B. (2009). Bridging the gap between growth theory and the new economic geography: the spatial Ramsey model. Macroeconomic Dynamics, 13:20–45.

Brito, P. (2004). The dynamics of growth and distribution in a spatially heterogeneous world. Working Papers of the Department of Economics, ISEG-UTL http://ideas.repec.org/p/ise/isegwp/wp142004.html.

Brock, W. and Xepapadeas, A. (2008). Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control. Journal of Economic Dynamics and Control, 32:2745–2787.

Butkovskiy, G. (1969). Distributed Control Systems. American Elsevier, New-York.

Carlson, D. A., Haurie, A. B., and Leizarowitz, A. (1996). Infinite Horizon Optimal Control. Springer-Verlag, 2nd edition edition.

Caselli, F. and Ventura, J. (2000). A representative consumer theory of distribution. Amer- ican Economic Review, 90(4):909–26.

Cass, D. (1965). Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies, 32:233–40.

Chatterjee, S. (1994). Transitional dynamics and the distribution of wealth in a Neoclassical model. Journal of Public Economics, 54(1):97–119.

Cross, M. and Greenside, H. (2009). Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge, Cambridge, UK.

Cross, M. C. and Hohenberg, P. C. (1993). Pattern formation outside of equilibrium. Rev. Mod. Phys., 65:851.

Derzko, N. A., Sethi, S. P., and Thompson, G. L. (1984). Necessary and sufficient conditions for optimal control of quasilinear partial differential equations systems. Journal of Optimization Theory and Applications, 43(1):89–101.

Desmet, K. and Rossi-Hansberg, E. (2010). On spatial dynamics. Journal of Regional Science, 50(1):43–63.

Fujita, M., Krugman, P., and Venables, A. (1999). The Spatial Economy. Cities, Regions and International Trade. MIT Press.

Fujita, M. and Thisse, J.-F. (2002). Economics of Agglomeration. Cambridge. Gelfand, I. M. and Fomin, S. V. (1963). Calculus of Variations. Dover.

Harsanyi, J. C. (1955). Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility. Journal of Political Economy, 63(4):309–321.

Henry, D. (1981). Geometric Theory of Semilinear Parabolic Equations. Number 840 in Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York. Hotelling, H. (1929). Stability in competition. Economic Journal, 39:41–57.

Isard, W. and Liossatos, P. (1979). Spatial Dynamics and Optimal Space-Time Development. North-Holland.

Kammler, D. W. (2000). A First Course in Fourier Analysis. Prentice-Hall.

Koopmans, T. (1965). On the concept of optimal economic growth. In The Econometric Approach to Development Planning. Pontificiae Acad. Sci., North-Holland.

Lions, J. L. (1971). Optimal Control of Systems Governed by Partial Differential Equations. Springer-verlag, New-York.

Lucas, R. E. (2009). Trade and the diffusion of the Industrial Revolution. American Eco- nomic Journal: Macroeconomics, 1(1):1–25.

Mueller, D. C. (2003). Public Choice III. Cambridge. Neittaanmaki, P. and Tiba, D. (1994). Optimal Control of Nonlinear Parabolic Systems. Marcel Dekker.

Quah, D. (2002). Spatial Agglomeration Dynamics. American Economic Review Papers and Proceedings, 92(2):247–52.

Ramsey, F. P. (1928). A mathematical theory of saving. Economic Journal, 38(Dec):543–59.

Samuelson, P. (1947). Foundations of Economic Analysis, volume 80 of Harvard Economic Studies. Harvard University Press. 1965, Atheneum.

Stiglitz, J. E. (1969). Distribution of Income and Wealth Among Individuals. Econometrica, 37(3):382–97.

T¨uring, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London B, 237:37–72.

Yaari, M. (1981). Rawls, Edgeworth, Shapley, Nash: theories of distributive justice reexamined. Journal of Economic Theory, 24:1–39.