Population dynamics and utilitarian criteria in the Lucas–Uzawa Model
AbstractThis 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Economic Modelling.
Volume (Year): 29 (2012)
Issue (Month): 4 ()
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Web page: http://www.elsevier.com/locate/inca/30411
Population change; Utilitarian criteria; Uzawa–Lucas model; Transitional dynamics; Stochastic shocks; Closed-form solution;
Find related papers by JEL classification:
- O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
- J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth
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.:
- 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, 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," Discussion Paper / Institute for Empirical Macroeconomics 61, Federal Reserve Bank of Minneapolis.
- Maurice Obstfeld, 1992. "Risk-Taking, Global Diversification, and Growth," NBER Working Papers 4093, National Bureau of Economic Research, Inc.
- 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.
- Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, MIT Press, vol. 100(2), pages 321-34, May.
- 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.
- Mehra, Rajnish & Prescott, Edward C., 1985.
"The equity premium: A puzzle,"
Journal of Monetary Economics,
Elsevier, vol. 15(2), pages 145-161, March.
- repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- 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.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
- repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
- 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.
- 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, 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.
- 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.
- Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
- Marsiglio, Simone, 2011. "On the relationship between population change and sustainable development," Research in Economics, Elsevier, vol. 65(4), pages 353-364, December.
- 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.
- 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.
- 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.
- Simone Marsiglio & Davide La Torre, 2012. "A note on demographic shocks in a multi-sector growth model," Economics Bulletin, AccessEcon, vol. 32(3), pages 2293-2299.
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