This file is part of IDEAS , which uses RePEc data
[ Papers |
Articles |
Software |
Books |
Chapters |
Authors |
Institutions |
JEL Classification |
NEP reports |
Search |
New papers by email |
Author registration |
Rankings |
Volunteers |
FAQ |
Blog |
Help! ]
A nonsmooth, nonconvex model of optimal growth Author info | Abstract | Publisher info | Download info | Related research | Statistics Takashi Kamihigashi (Research Institute for Economics and Business Administration, Kobe University)
Santanu Roy (Department of Economics, Southern Methodist University)
Additional information is available for the following
registered author(s):
This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to one, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches one, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page . Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number
173.
Download reference. The following formats are available: HTML
(with abstract ),
plain text
(with abstract ),
BibTeX ,
RIS (EndNote, RefMan, ProCite),
ReDIF
Length: 33 pages
Date of creation: Jul 2005Date of revision:
Handle: RePEc:kob:dpaper:173Contact details of provider: Postal: Nada-ku Rokkodai 2-1, Kobe 657-8501 Fax: 81-78-803-0386 Web page: http://www.rieb.kobe-u.ac.jp/ More information through EDIRC
For technical questions regarding this item, or to correct its listing, contact: (Research Assistant Room).
Keywords: Nonconvex ; nonsmooth ; and discontinuous technology ; optimal growth ; unbounded growth ; extinction ; neighborhood turnpike. ; Other versions of this item:
Article Paper Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
158, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
139, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Find related papers by JEL classification: C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis D90 - Microeconomics - - Intertemporal Choice and Growth - - - General O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.:
Joshi, Sumit, 1997.
"Turnpike Theorems in Nonconvex Nonstationary Environments ,"
International Economic Review ,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 225-48, February.
Kamihigashi, Takashi, 2003.
"Necessity of transversality conditions for stochastic problems ,"
Journal of Economic Theory ,
Elsevier, vol. 109(1), pages 140-149, March.
[Downloadable!] (restricted)
Jones, Larry E & Manuelli, Rodolfo E, 1990.
"A Convex Model of Equilibrium Growth: Theory and Policy Implications ,"
Journal of Political Economy ,
University of Chicago Press, vol. 98(5), pages 1008-38, October.
[Downloadable!] (restricted)
Guerrero-Luchtenberg, C.L., 2000.
"A uniform neighborhood turnpike theorem and applications ,"
Journal of Mathematical Economics ,
Elsevier, vol. 34(3), pages 329-357, November.
[Downloadable!] (restricted)
Montrucchio, Luigi, 1995.
"A New Turnpike Theorem for Discounted Programs ,"
Economic Theory ,
Springer, vol. 5(3), pages 371-82, May.
Azariadis, Costas & Drazen, Allan, 1990.
"Threshold Externalities in Economic Development ,"
The Quarterly Journal of Economics ,
MIT Press, vol. 105(2), pages 501-26, May.
[Downloadable!] (restricted)
de Hek, Paul & Roy, Santanu, 2001.
"On Sustained Growth under Uncertainty ,"
International Economic Review ,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 801-13, August.
Larry E. Jones & Rodolfo E. Manuelli, 1994.
"The Sources of Growth ,"
Macroeconomics
9411002, EconWPA, revised 05 Mar 1999.
[Downloadable!]
Other versions:
Larry E. Jones & Rodolfo E. Manuelli, 1994.
"The Sources of Growth ,"
GE, Growth, Math methods
9410002, EconWPA, revised 05 Mar 1999.
[Downloadable!] Jones, Larry E. & Manuelli, Rodolfo E., 1997.
"The sources of growth ,"
Journal of Economic Dynamics and Control ,
Elsevier, vol. 21(1), pages 75-114, January.
[Downloadable!] (restricted) Dolmas, Jim, 1996.
"Endogenous Growth in Multisector Ramsey Models ,"
International Economic Review ,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 403-21, May.
Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
158, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!]
Other versions:
Takashi Kamihigashi & Santanu Roy, 2005.
"A nonsmooth, nonconvex model of optimal growth ,"
Discussion Paper Series
173, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
139, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Kamihigashi, Takashi & Roy, Santanu, 2007.
"A nonsmooth, nonconvex model of optimal growth ,"
Journal of Economic Theory ,
Elsevier, vol. 132(1), pages 435-460, January.
[Downloadable!] (restricted) Dechert, W. Davis & Nishimura, Kazuo, 1983.
"A complete characterization of optimal growth paths in an aggregated model with a non-concave production function ,"
Journal of Economic Theory ,
Elsevier, vol. 31(2), pages 332-354, December.
[Downloadable!] (restricted)
Kaganovich, Michael, 1998.
"Sustained endogenous growth with decreasing returns and heterogeneous capital ,"
Journal of Economic Dynamics and Control ,
Elsevier, vol. 22(10), pages 1575-1603, August.
[Downloadable!] (restricted)
Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991.
"One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics ,"
International Economic Review ,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
[Downloadable!] (restricted)
Montrucchio, Luigi, 1994.
"The neighbourhood turnpike property for continuous-time optimal growth models ,"
Ricerche Economiche ,
Elsevier, vol. 48(3), pages 213-224, September.
[Downloadable!] (restricted)
Takashi Kamihigashi & Santanu Roy, 2005.
"Dynamic optimization with a nonsmooth, nonconvex technology: The case of a linear objective function ,"
Discussion Paper Series
175, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!]
Other versions:
Takashi Kamihigashi & Santanu Roy, 2004.
"Dynamic Optimization with a Nonsmooth, Nonconvex Technology: The Case of a Linear Objective Function ,"
Discussion Paper Series
161, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Takashi Kamihigashi & Santanu Roy, 2006.
"Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function ,"
Economic Theory ,
Springer, vol. 29(2), pages 325-340, October.
[Downloadable!] (restricted) Alexandre Scheinkman, Jose, 1976.
"On optimal steady states of n-sector growth models when utility is discounted ,"
Journal of Economic Theory ,
Elsevier, vol. 12(1), pages 11-30, February.
[Downloadable!] (restricted)
Olson, Lars J. & Roy, Santanu, 1996.
"On Conservation of Renewable Resources with Stock-Dependent Return and Nonconcave Production ,"
Journal of Economic Theory ,
Elsevier, vol. 70(1), pages 133-157, July.
[Downloadable!] (restricted)
Other versions:
Full
references Cited by : (explanations , Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.)
Nguyen Manh Hung & Cuong Le Van & Philippe Michel, 2008.
"Non-convex Aggregate Technology and Optimal Economic Growth ,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
halshs-00267100_v1, HAL.
[Downloadable!]
Other versions:
N. M. Hung & Cuong Le Van & P. Michel, 2008.
"Non-convex Aggregate Technology and Optimal Economic Growth ,"
Working Papers
05, Development and Policies Research Center (DEPOCEN), Vietnam.
[Downloadable!] N.M. Hung & C. Le Van & P. Michel, 2006.
"Non-Convex Aggregate Technology and Optimal Economic Growth ,"
Cahiers de recherche
0603, Université Laval - Département d'économique.
[Downloadable!] Manh Nguyen Hung & Cuong Le Van & Philippe Michel, 2005.
"Non-convex aggregative technology and optimal economic growth ,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
halshs-00197556_v1, HAL.
[Downloadable!] Manh Hung Nguyen & Cuong Le Van & Philippe Michel, 2005.
"Non-convex aggregative technology and optimal economic growth ,"
Cahiers de la Maison des Sciences Economiques
b05095, Université Panthéon-Sorbonne (Paris 1).
[Downloadable!] N. Hung & C. Le Van & P. Michel, 2009.
"Non-convex aggregate technology and optimal economic growth ,"
Economic Theory ,
Springer, vol. 40(3), pages 457-471, September.
[Downloadable!] (restricted) Takashi Kamihigashi & Santanu Roy, 2005.
"A nonsmooth, nonconvex model of optimal growth ,"
Discussion Paper Series
173, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!]
Other versions:
Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
158, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Takashi Kamihigashi & Santanu Roy, 2003.
"A Nonsmooth, Nonconvex Model of Optimal Growth ,"
Discussion Paper Series
139, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!] Kamihigashi, Takashi & Roy, Santanu, 2007.
"A nonsmooth, nonconvex model of optimal growth ,"
Journal of Economic Theory ,
Elsevier, vol. 132(1), pages 435-460, January.
[Downloadable!] (restricted) Olivier Bruno & Cuong Le Van & Benoit Masquin, 2008.
"When Does a Developing Country Use New Technologies? ,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
halshs-00101361_v2, HAL.
[Downloadable!]
Takashi Kamihigashi, 2006.
"Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks ,"
Discussion Paper Series
189, Research Institute for Economics & Business Administration, Kobe University.
[Downloadable!]
Access and
download statistics Did you know? All bibliographic data on IDEAS has been put in the public domain by the publishers.
This page was last updated on 2009-11-22.
This information is provided to you by IDEAS at the Department of Economics , College of Liberal Arts and Sciences , University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics .