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


  • Gohin, Alex
  • Hertel, Thomas


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.

Suggested Citation

  • Gohin, Alex & Hertel, Thomas, 2003. "A Note on the CES Functional Form and Its Use in the GTAP Model," GTAP Research Memoranda 1370, Center for Global Trade Analysis, Department of Agricultural Economics, Purdue University.
  • Handle: RePEc:gta:resmem:1370
    Note: GTAP Research Memorandum No. 02

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    Cited by:

    1. Thomas W. Hertel & Uris L.C. Baldos & Keith O. Fuglie, 2020. "Trade in Technology: A Potential Solution to the Food Security Challenges of the 21st Century," NBER Working Papers 27148, National Bureau of Economic Research, Inc.
    2. De Lucia, Caterina & Bartlett, Mark, 2014. "Implementing a biofuel economy in the EU: Lessons from the SUSTOIL project and future perspectives for next generation biofuels," Renewable and Sustainable Energy Reviews, Elsevier, vol. 29(C), pages 22-30.

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