A Note on the CES Functional Form and Its Use in the GTAP Model

The purpose of this note is to provide an exhaustive reference for those interested in learning more about the Constant Elasticity of Substitution (CES) function and its use in the representation of producer behavior in the GTAP Model. Particular attention is paid to the role of technical change variables and their effect on cost minimizing demands and input shares. This note is divided into three sections. In the first section, the basic cost minimization problem is laid out and conditional factor demands, as well as the unit cost function, are derived. In section two, this system of equations is expressed in terms of proportional changes, as currently specified in GTAP. This greatly facilitates decomposition of predicted changes in demands and costs between three effects, namely expansion, substitution, and technical change effects. Section two also shows the relationship between changes in cost shares and changes in prices and factor-biased technical change variables. Finally, section three relates these derivations to the notation employed in GTAP.