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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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    2. Hu, Chunhua & Lai, Shaoyong & Lai, Chong, 2020. "Investigations to the price evolutions of goods exchange with CES utility functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).

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