Population dynamics and utilitarian criteria in the Lucas–Uzawa Model
This paper introduces population growth in the Uzawa–Lucas model, analyzing the implications of the choice of the welfare criterion on the model's outcome. Traditional growth theory assumes population growth to be exponential, but this is not a realistic assumption (see Brida and Accinelli, 2007). We model exogenous population change by a generic function of population size. We show that a unique non-trivial equilibrium exists and the economy converges towards it along a saddle path, independently of population dynamics. What is affected by the type of population dynamics is the dimension of the stable manifold, which can be one or two, and when the equilibrium is reached, which can happen in finite time or asymptotically. Moreover, we show that the choice of the utilitarian criterion will be irrelevant on the equilibrium of the model, if the steady state growth rate of population is null, as in the case of logistic population growth. Then, we show that a closed-form solution for the transitional dynamics of the economy (both in the case population dynamics is deterministic and stochastic) can be found for a certain parameter restriction.
If you experience problems downloading a file, check if you have the proper application to view it first. 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Holger Strulik, 2001.
"The Role of Human Capital and Population Growth in R&D-Based Models of Economic Growth,"
Quantitative Macroeconomics Working Papers
20109, Hamburg University, Department of Economics.
- Holger Strulik, 2005. "The Role of Human Capital and Population Growth in R&D-based Models of Economic Growth," Review of International Economics, Wiley Blackwell, vol. 13(1), pages 129-145, 02.
- Strulik, Holger, 2002. "The Role of Human Capital and Population Growth in R&D-Based Models of Economic Growth," Royal Economic Society Annual Conference 2002 170, Royal Economic Society.
- Marc Nerlove & Assaf Razin & Efraim Sadka, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, Oxford University Press, vol. 100(2), pages 321-334.
- Bucci Alberto & Guerrini Luca, 2009.
"Transitional Dynamics in the Solow-Swan Growth Model with AK Technology and Logistic Population Change,"
The B.E. Journal of Macroeconomics,
De Gruyter, vol. 9(1), pages 1-17, December.
- Alberto BUCCI & Luca GUERRINI, 2008. "Transitional dynamics in the Solow-Swan growth model with AK technology and logistic population change," Departmental Working Papers 2008-44, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Alberto Bucci & Luca Guerrini, 2009. "Transitional Dynamics in the Solow-Swan Growth Model with AK Technology and Logistic Population Change," DEGIT Conference Papers c014_020, DEGIT, Dynamics, Economic Growth, and International Trade.
- Maurice Obstfeld, 1992.
"Risk-taking, global diversification, and growth,"
Discussion Paper / Institute for Empirical Macroeconomics
61, Federal Reserve Bank of Minneapolis.
- Maurice Obstfeld., 1993. "Risk-Taking, Global Diversification, and Growth," Center for International and Development Economics Research (CIDER) Working Papers C93-016, University of California at Berkeley.
- Obstfeld, Maurice, 1993. "Risk-Taking, Global Diversification, and Growth," Center for International and Development Economics Research (CIDER) Working Papers 233197, University of California-Berkeley, Department of Economics.
- Obstfeld, Maurice, 1992. "Risk-Taking, Global Diversification, and Growth," CEPR Discussion Papers 688, C.E.P.R. Discussion Papers.
- Maurice Obstfeld, 1992. "Risk-Taking, Global Diversification, and Growth," NBER Working Papers 4093, National Bureau of Economic Research, Inc.
- Malthus, Thomas Robert, 1798. "An Essay on the Principle of Population," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number malthus1798.
- Barro, Robert J & Becker, Gary S, 1989.
"Fertility Choice in a Model of Economic Growth,"
Econometric Society, vol. 57(2), pages 481-501, March.
- Robert J. Barro & Gary S. Becker, . "Fertility Choice in a Model of Economic Growth," University of Chicago - Population Research Center 88-8, Chicago - Population Research Center.
- Barro, R.J. & Becker, G.S., 1988. "Fertility Choice In A Model Of Economic Growth," University of Chicago - Economics Research Center 88-8, Chicago - Economics Research Center.
- Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
- Smith William T, 2007. "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-33, August.
- Smith William T, 2006. "A Closed Form Solution to the Ramsey Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(1), pages 1-27, January.
- Guerrini, Luca, 2006. "The Solow-Swan model with a bounded population growth rate," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 14-21, February.
- Mehra, Rajnish & Prescott, Edward C., 1985.
"The equity premium: A puzzle,"
Journal of Monetary Economics,
Elsevier, vol. 15(2), pages 145-161, March.
- Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1982. "Population size and the social welfare functions of Bentham and Mill," Economics Letters, Elsevier, vol. 10(1-2), pages 61-64.
- repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
- repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
- La Torre, Davide & Marsiglio, Simone, 2010. "Endogenous technological progress in a multi-sector growth model," Economic Modelling, Elsevier, vol. 27(5), pages 1017-1028, September.
- Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
- Marsiglio, Simone, 2011. "On the relationship between population change and sustainable development," Research in Economics, Elsevier, vol. 65(4), pages 353-364, December.
- Simone Marsiglio, 2010.
"Endogenous Growth, Population Growth and the Repugnant Conclusion,"
UNIMI - Research Papers in Economics, Business, and Statistics
unimi-1103, Universitá degli Studi di Milano.
- Simone MARSIGLIO, 2010. "Endogenous growth, population growth and the repugnant conclusion," Departmental Working Papers 2010-14, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- A. Bucci & C. Colapinto & M. Forster & D. La Torre, 2011. "Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics," Journal of Economics, Springer, vol. 103(1), pages 83-99, May.
When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:29:y:2012:i:4:p:1197-1204. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.