# Functional Forms

Here are some of the functional forms commonly used in CGE modeling. In general, all can be used to model either consumption or production, and in primal or dual form. See the Quick Reference Guide at the bottom of the page for examples of each one, including dual relationships and demand equations.
Leontief (L)
Key features include: zero elasticity of substitution; own-price elasticities are less than one; cross-price elasticities are negative; homothetic. Easy to parameterize but the implicit zero elasticity of substitution is unrealistically low in most situations.
Cobb-Douglas (CD)
Key features: unitary elasticity of substitution; own-price elasticities are equal to one; cross-price elasticities are zero; homothetic. Like Leontief, easy to parameterize. When used as a utility function, imposes unitary income elasticities.
Constant Elasticity of Substitution (CES)
Features: relaxes the imposed substitution elasticities in the Leontief and Cobb-Douglas; however, still homothetic.
Linear Expenditure System (LES)
Does not impose homotheticity. Can be derived from the Stone-Geary utility function. Straightforward to estimate.
Translog (TL)
Does not impose homotheticity. Flexible but more difficult to parameterize. Large number of parameters makes it difficult to estimate on short datasets. Also requires that the curvature restrictions in the integrability conditions be checked by hand after estimation.
Note that homotheticity (L, CD and CES) is highly undesirable in a utility function. It implies that expenditure shares do not vary with income, which has been consistently rejected in the empirical literature on demand.