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Two-Level CES Production Technology in the Solow and Diamond Growth Models

Abstract

The two-level CES aggregate production function-that nests a CES into another CES function-has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two-factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital-skill complementarity. Copyright © The editors of the "Scandinavian Journal of Economics" 2008 .

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Paper provided by Department of Economics, Louisiana State University in its series Departmental Working Papers with number 2005-07.

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Date of creation: Jul 2005
Handle: RePEc:lsu:lsuwpp:2005-07
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  1. Per Krusell & Lee E. Ohanian & JosÈ-Victor RÌos-Rull & Giovanni L. Violante, 2000. "Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis," Econometrica, Econometric Society, vol. 68(5), pages 1029-1054, September.
  2. Chris Papageorgiou & Kaz Miyagiwa, 2003. "The Elasticity of Substitution, Hicks' Conjectures, and Economic Growth," Departmental Working Papers 2003-08, Department of Economics, Louisiana State University.
  3. Daron Acemoglu, 1998. "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," The Quarterly Journal of Economics, Oxford University Press, vol. 113(4), pages 1055-1089.
  4. Fallon, P R & Layard, P R G, 1975. "Capital-Skill Complementarity, Income Distribution, and Output Accounting," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 279-301, April.
  5. John Duffy & Chris Papageorgiou & Fidel Perez-Sebastian, 2004. "Capital-Skill Complementarity? Evidence from a Panel of Countries," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 327-344, February.
  6. Claudia Goldin & Lawrence F. Katz, 1998. "The Origins of Technology-Skill Complementarity," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 693-732.
  7. Olivier de La Grandville & Rainer Klump, 2000. "Economic Growth and the Elasticity of Substitution: Two Theorems and Some Suggestions," American Economic Review, American Economic Association, vol. 90(1), pages 282-291, March.
  8. Claude Diebolt & Faustine Perrin, 2014. "Growth Theories," Working Papers 02-14, Association Française de Cliométrie (AFC).
  9. Griliches, Zvi, 1969. "Capital-Skill Complementarity," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 465-468, November.
  10. Francesco Caselli & Wilbur John Coleman II, 2006. "The World Technology Frontier," American Economic Review, American Economic Association, vol. 96(3), pages 499-522, June.
  11. Kaz Miyagiwa & Chris Papageorgiou, 2003. "Elasticity of substitution and growth: normalized CES in the Diamond model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 155-165, 01.
  12. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," Review of Economic Studies, Oxford University Press, vol. 34(2), pages 201-218.
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