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.
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- 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.
- 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.
- 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.
- 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.
- 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.
- Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
- 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, "undated". "Fertility Choice in a Model of Economic Growth," University of Chicago - Population Research Center 88-8, Chicago - Population Research Center.
- 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.
- 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.
- Obstfeld, Maurice, 1994.
"Risk-Taking, Global Diversification, and Growth,"
American Economic Review,
American Economic Association, vol. 84(5), pages 1310-1329, December.
- 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.
- Obstfeld, Maurice, 1992. "Risk-Taking, Global Diversification, and Growth," CEPR Discussion Papers 688, C.E.P.R. Discussion Papers.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. Mehra & E. Prescott, 2010.
"The equity premium: a puzzle,"
Levine's Working Paper Archive
1401, David K. Levine.
- 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.
- repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
- 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.
- repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
- Marsiglio, Simone, 2011. "On the relationship between population change and sustainable development," Research in Economics, Elsevier, vol. 65(4), pages 353-364, December.
- Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
- 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.
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