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

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  • Gohin, Alex
  • Hertel, Thomas

Abstract

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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    File URL: https://www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=1370
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    Cited by:

    1. Jason F.L. Koopman & Onno Kuik & Richard S.J. Tol & Roy Brouwer, 2015. "Water Scarcity From Climate Change And Adaptation Response In An International River Basin Context," Climate Change Economics (CCE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22.
    2. Paul E. Brockway & Matthew K. Heun & João Santos & John R. Barrett, 2017. "Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation," Energies, MDPI, vol. 10(2), pages 1-23, February.
    3. Hertel, Thomas & Baldos, Uris Lantz & Fuglie, Keith O., 2019. "Trade in Technology: A Potential Solution to the Food Security Challenge of the 21st Century," Conference papers 333121, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    4. Abdulla Kaya & Denes Csala & Sgouris Sgouridis, 2017. "Constant elasticity of substitution functions for energy modeling in general equilibrium integrated assessment models: a critical review and recommendations," Climatic Change, Springer, vol. 145(1), pages 27-40, November.
    5. 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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