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Finite Lifetimes and Growth

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  • Larry E. Jones
  • Rodolfo E. Manuelli

Abstract

The recent literature an endogenous growth models has emphasized the effect that the rate of return has an the capital accumulation decisions and, consequently, on the growth rate of the economy. In most cases the basic model is a variant of the representative agent growth model. The key feature of the infinitely lived agent model is that "substitution effects" dominate, that is, in order to induce individuals to accumulate capital all that is required is a sufficiently high rate of return. In this paper we explore the long run behavior in a model with finite lifetimes -- a version of Diamond's overlapping generations model. Because individuals do not live forever (although the economy does) their level of income as well as the rate of return determine the rate of accumulation. Specifically, we show that for all one sector convex technologies the equilibrium limiting growth rate of the economy is zero. In this setting capital income taxation can have paradoxical effects; it is shown that if the proceeds are used to redistribute income to the young it is possible to have a positive long run growth rate. The effect of the tax rate on the growth rate is not monotonic: for small tax rates the effect is positive, while for sufficiently high rates it is negative. Additionally, income redistribution to the young will normally have positive effects upon the long run growth rate. We then study a two sector growth model and show conditions under which the laissez faire equilibrium displays long run growth. Intuitively, the key property is that the existence of a sector producing investment goods makes it possible that, along a growth path, the relative price of capital decreases sufficiently fast and allows the young to purchase ever increasing quantities of capital. Finally, we show that in an overlawing generations setting, a one sector model can generate growth if the technology displays a nonconvexity, as this is similar to the effect of a decrease in the price of capital: it prevents the ratio of the value of capital am the level of wealth of the young from exceeding one.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3469.

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Date of creation: Oct 1990
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Publication status: published as Journal of Economic Theory Volume 58 December 1992
Handle: RePEc:nbr:nberwo:3469

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  1. S. Rao Aiyagari, 1988. "Can there be short-period deterministic cycles when people are long lived?," Staff Report 114, Federal Reserve Bank of Minneapolis.
  2. Bencivenga, Valerie R & Smith, Bruce D, 1991. "Financial Intermediation and Endogenous Growth," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 195-209, April.
  3. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
  4. Nancy L Stokey, 1986. "Learning-by-Doing and the Introduction of New Goods," Discussion Papers 699, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised May 1987.
  5. William Easterly, 1989. "Policy Distortions, Size of Government, and Growth," NBER Working Papers 3214, National Bureau of Economic Research, Inc.
  6. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  7. King, Robert G & Rebelo, Sergio, 1990. "Public Policy and Economic Growth: Developing Neoclassical Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S126-50, October.
  8. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
  9. Blackorby, C. & Russell, R.R., 1992. ""On the Observational Equivalence of Models with Infinitely Lived Agents and Models with Overlaping Generations"," The A. Gary Anderson Graduate School of Management 92-15, The A. Gary Anderson Graduate School of Management. University of California Riverside.
  10. Atkinson, A B & Sandmo, A, 1980. "Welfare Implications of the Taxation of Savings," Economic Journal, Royal Economic Society, vol. 90(359), pages 529-49, September.
  11. Barro, Robert J., 1974. "Are Government Bonds Net Wealth?," Scholarly Articles 3451399, Harvard University Department of Economics.
  12. Azariadis, Costas & Drazen, Allan, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, MIT Press, vol. 105(2), pages 501-26, May.
  13. Rao Aiyagari, S., 1985. "Observational equivalence of the overlapping generations and the discounted dynamic programming frameworks for one-sector growth," Journal of Economic Theory, Elsevier, vol. 35(2), pages 201-221, August.
  14. Schmitz, James A, Jr, 1989. "Imitation, Entrepreneurship, and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 721-39, June.
  15. repec:fth:calaec:4-89 is not listed on IDEAS
  16. Karl Shell, 2010. "A Model of Inventive Activity and Capital Accumulation," Levine's Working Paper Archive 1409, David K. Levine.
  17. Freeman, Scott & Polasky, Stephen, 1992. "Knowledge-based growth," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 3-24, October.
  18. Larry E. Jones & Rodolfo Manuelli, 1990. "A Convex Model of Equilibrium Growth," NBER Working Papers 3241, National Bureau of Economic Research, Inc.
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