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

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.