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Growth and Slowdown of Nations: What Role for the Elasticity of Substitution?

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Although the importance of the elasticity of substitution between capital and labor (σ) has long been recognized in several branches of economics, it has received too little attention in the growth literature. This paper aims to partly rectify this omission by exploring the growth potentials with σ as a yardstick and studying how different values of σ impact upon the balanced growth paths in theoretical model. When σ is high, the incremental capital is easily substituted for labor, resulting in a nearly equiproportionate increase in both factors. Under constant returns to scale, diminishing returns sets-in very slowly, and the marginal and average products of capital can remain sufficiently large so that output can grow indefinitely. The theoretical model is built upon the work of de La Grandville and Solow (2004) who show that perpetual growth is possible in the Solow (1956) model even without technological progress, if value of σ exceeds a critical value that is greater than unity ( cH σ ). I extend the model to show that output level, capital stock and consumption follow perpetual decline if σ is less than another critical value ( cL σ ) that lies between zero and unity. The critical values depend on saving, population growth and depreciation rates, and the initial share of capital in total output; hence each country has at most one critical value. I show that the above results also carry into in a model of endogenous saving, and analytically prove that the balanced growth path exists only if σ lies between two critical values- cL σ and cH σ . I calibrate the critical value of σ from the data for each country. These values are then compared to σˆ ’s estimated from country time series data. A number of countries, mainly from Africa, have ˆ cL σ σ ).

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  • Debdulal Mallick, 2007. "Growth and Slowdown of Nations: What Role for the Elasticity of Substitution?," Economics Series 2007_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  • Handle: RePEc:dkn:econwp:eco_2007_02
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    File URL: http://www.deakin.edu.au/buslaw/aef/workingpapers/papers/2007_02eco.pdf
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    1. Susan Chun Zhu, 2004. "Trade, product cycles, and inequality within and between countries," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 1042-1060, November.
    2. Rudiger Dornbusch & Stanley Fischer & Paul A. Samuelson, 1980. "Heckscher-Ohlin Trade Theory with a Continuum of Goods," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 203-224.
    3. Peter K. Schott, 2008. "The relative sophistication of Chinese exports," Economic Policy, CEPR;CES;MSH, vol. 23, pages 5-49, January.
    4. Peter K. Schott, 2004. "Across-Product Versus Within-Product Specialization in International Trade," The Quarterly Journal of Economics, Oxford University Press, vol. 119(2), pages 647-678.
    5. Zhu, Susan Chun & Trefler, Daniel, 2005. "Trade and inequality in developing countries: a general equilibrium analysis," Journal of International Economics, Elsevier, vol. 65(1), pages 21-48, January.
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    JEL classification:

    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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