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

Saito Tetsuya
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Saito Tetsuya: Lehigh University

Journal of Industrial Organization Education, 2012, vol. 6, issue 1, 13

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.

Keywords: Convergence of functions; CES; Linear; Cobb-Douglas; Leontief (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jioedu:v:6:y:2012:i:1:p:1-13:n:2

DOI: 10.1515/1935-5041.1037

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