Takahashi, Harutaka
(2010):
*Global analysis of the growth and cycles of multi-sector economies with constant returns: A turnpike approach.*

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## Abstract

In Section 1, we explain the neoclassical optimal growth model, which includes multi capital goods, and is derived from neoclassical production functions; the transformations to the reduced model are also explained. Section 2 pertains to the explanation of the methods for proving the consumption turnpike theorem demonstrated by Scheinkman (1976) and McKenzie (1983). Also, the case in which the essentials of the von Neumann-McKenzie facet, which plays an important role in the next part, became a two-sector model and is explained using figures. In Section 3, we postulate a two-sector neoclassical optimal growth model, and the optimal path behavior in the vicinity of the optimal steady state path (modified golden rule path) are classified using the characteristics of von Neumann-McKenzie facet. Also, we will use these results to prove, based on a weaker hypothesis, that the theorem that the optimal path local stability and the optimal path attained by Benhabib and Nishimura（1985）becomes a two-term periodic solution. In Section 4, the generalization of the global asymptotic stability conclusion achieved with two divisions into a case that includes two or more types of capital goods. In Addendum, the important fundamental principles used in the main text will be defined, and a number of theorems will be proved.

Item Type: | MPRA Paper |
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Original Title: | Global analysis of the growth and cycles of multi-sector economies with constant returns: A turnpike approach |

Language: | English |

Keywords: | multi-sector model; turnpike theory; optimal growth; the Neumann-McKednzie facet |

Subjects: | O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity O - Economic Development, Innovation, Technological Change, and Growth > O2 - Development Planning and Policy > O21 - Planning Models ; Planning Policy |

Item ID: | 24860 |

Depositing User: | Harutaka Takahashi |

Date Deposited: | 10 Sep 2010 17:26 |

Last Modified: | 29 Sep 2019 07:01 |

References: | 1. Aghion, P. and P. Howitt (1998), Endogenous Growth Theory (Cambridge, Mass., MIT Press) 2. Atsumi, H. (1965),”Neoclassical growth and the efficient program of capital accumulation,” Review of Economic Studies 32,127-136. 3. Bartelsman, E. (1995),”Of empty boxes: Returns to scale revisited,” Economics Letters 49, 59-67. 4. Basu, S. and J. Fernald (1995),”Are apparent productive spillovers a figment of specificatin error?,” Journal of Monetary Economics 36, 165-188. 5. Basu, S. and J. Fernald (1997),”Returns to scale in U.S. production: Estimates and implications,” Journal of Political Economy 105, 249-283. 6. Becker, R. and J. Boyd (1997), Capital Theory, Equilibrium Analysis and Recursive Utility (Malden, Mass., Blackwell Publishers). 7. Benhabib, J. and K. Nishimura (1979a), “The Hopf bifurcation and the existence and stability of closed orbits in multi-sector models of optimal economic growth,” Journal of Economic Theory 21, 421-444. 8. Benhabib, J. and K. Nishimura (1979b), “On the uniqueness capital steady states in an economy with heterogeneous capital goods,” International Economic Review 20, 59-82 9. Benhabib, J. and K. Nishimura (1985),”Competetive equilibrium cycles,” Journal of Economic theory 35, 284-306. 10. Benhabib, J.,Q. Meng and K. Nishimura (2000),”Indeterminacy under constant returns to scale in multisector economies,” forthcoming in Econometrica. 11. Bond E., P. Wang and C. Yip (1996), “A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balance Growth and Transitional Dynamics,” Journal of Economic Theory 68, 149-173. 12. Brems, H. (1985), “Reality and neoclassical theory,” Journal of Economic Literature , 72-82. 13. Burmeister, E. and D. Graham (1975), “Price expectation and global stability in economic systems,“ Automatica 11, 487-497. 14. Burmeister, E. and R. Dobell (1970), Mathematical Theories of Economic Growth, (New York, Macmillan). 15. Burmeister, E. and K. Kuga (1970),”The factor-price frontier, duality and joint production,” Review of Economic Studies 37, 162-174. 16. Cass, D. and K. Shell (1983),”Do sunspots matter?,” Journal of Political Economy 91, 193-227. 17. Dolmas J. (1996),”Endogenous growth in multisector Ramsey model,” International Economic Review 37, 403-421. 18. Hall, R. (1988),”The relation between price and marginal cost in US industry,” Journal of Political Economy 96, 921-947. 19. Hall, R. (1990),”Invariance properties of Solow’s productivity residual,” in Peter Diamond ed., Growth, Productivity, Employment (Cambridge, Mass., MIT Press.). 20. Inada, K. (1971), “The production coefficient matrix and the Stolper-Samuelson condition,” Econometrica 39, 219-240. 21. Levhari, .D and N. Liviatan (1972), “On stability in the saddle-point sense, “ Journal of Economic theory 42, 68-95. 22. Lucas, R. E. (1988),”On the Mechanisms of Economic Development,” Journal of Monetary Economics 22, 3-42. 23. McKenzie, L. (1998),”Turnpikes,” American Economic Review Vol. 88 ,#2, 1-14. 24. McKenzie, L.(1990),”Turnpike theory ,” in J. Eatwell, M. Milgate and P. Newman eds, The New Palgrave (New York ,Elsevier Science Publishers B.V.). 25. McKenzie, L. (1984),”Optimal economic growth and turnpike theorems,” in Handbook in Mathematical Economics Vol.3, eds. K. Arrow and M. Intriligator (New York, North-Holland). 26. McKenzie, L. (1983),”Turnpike Theory ,discounted utility , and the von・Neumann facet,” Journal of Economic theory 30, 330-352. 27. McKenzie, L.(1963), “Turnpike theorems for a generalized Leontief model,” Econometrica 31, 165-180. 28. McKenzie, L. (1959),”Matrices with dominant diagonals and economic theory,” in K. Arrow, S. Karlin and P. Suppes eds. Mathematical Methods in the Social Sciences (Stanford, Stanford University Press). 29. Mino K. (1996), “Analysis of a Two-Sector Model of Endogenous Growth with Capital Income Taxation,” International Economic Review 37, 227-251. 30. Newman, P. (1961),” Approaches to stability analyis,” Economica 28, 12-29. 31. Palis J. and W. de Melo (1980), Geometry Theory of Dynamical Systems (New York, Springer-Verlag). 32. Ramsey, F. P.(1928),”A Mathematical theory of savings,” Economic Journal 38, 358-559. 33. Romer, P. M. (1986),”Increasing Returns and Long-Run Growth,” Journal of Political Economy 94, 1002-37. 34. Scheinkman, J. (1976),” An Optimal steady state of n-sector growth model when utility is discounted ,” Journal of Economic Theory 12, 11-20. 35. Srinivasan, T. (1964),”Optimal savings in a two-sector models of growth,” Econometrica 32, 358-373. 36. Takahashi, H. (1985), Characterizations of Optimal programs in Infinite Horizon Economies, Ph.D. Thesis submitted to the University of Rochester. 37. Takahashi, H. (1992),”The von Neumann facet and a global asymptotic stability,“ Annals of Operations Research 37, 273-282. 38. Takahashi, H. (2001),”Stable optimal cycles with small discounting in a two-sector discrete-time model: A non-bifurcation approach,” Japanese Economic Review Vol.52 #3, pp.328-38. 39. Takahashi, H. (2008), “Optimal Balanced Growth in a General Multi-sector Endogenous Growth Model with Constant Returns,” Economic Theory Vol.37 #1, pp31-49. 40. Yano, M. (1990),”Von Neumann facets and the dynamic stability of perfect foresight equilibrium paths in Neo-classical trade models,” Journal of Economics 51, 27-69. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/24860 |