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How Do We Get Cobb-Douglas and Leontief Functions from CES Function: A Lecture Note on Discrete and Continuum Differentiated Object Models

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  • Saito Tetsuya

    (Lehigh University)

Abstract

Most lectures teach the relationship between the CES, Cobb-Douglas, and Leontief functions using the value of elasticity of substitution, namely, in the discrete object model. This lecture note aims at being a reference for algebraic computations of the Leontief and Cobb-Douglas functions by taking limits of CES functions both in discrete and continuum goods models. The argument on the discrete case uses l'H�pital's rule as usually done. The argument on the continuum case also uses l'H�pital's rule to show the convergence to the Cobb-Douglas function. To guarantee the convergence to the Leontief function, however, we rely on the squeeze principle.

Suggested Citation

  • Saito Tetsuya, 2012. "How Do We Get Cobb-Douglas and Leontief Functions from CES Function: A Lecture Note on Discrete and Continuum Differentiated Object Models," Journal of Industrial Organization Education, De Gruyter, vol. 6(1), pages 1-13, December.
    • Handle: RePEc:bpj:jioedu:v:6:y:2012:i:1:p:1-13:n:2
    DOI: 10.1515/1935-5041.1037
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    References listed on IDEAS

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    1. Michael Spence, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 217-235.
    2. Yoshinori Kurokawa, 2011. "Variety-skill complementarity: a simple resolution of the trade-wage inequality anomaly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 297-325, February.
    3. Laszlo Csontos & Subhash C. Ray, 1992. "The Leontief Production Function as a Limiting Case of the CES," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 27(2), pages 235-237, July.
    4. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    5. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.
    6. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    7. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 291-299.
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