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Other supply specifications

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IV.II.2 Other supply specifications

In econometric practice many specifications are used. Here some frequently used models are shortly described as illustrations.

A simple production function may be formulated by the Cobb-Douglas specification

Other supply specifications


where Y denotes output, K is capital, and L is labor. Eq. (IV.II.2-1) can be written in log-linear form as



This specification can be related to input demand systems by the use elasticities of substitution between input factors defined as



From this result it also possible to deduce some simple factor demand equations




Now consider the generalized Leontief cost function which states formally that




where dii is obviously a constant term in the equations.

The general Hicks-Allen partial elasticity of substitution is defined by


where C is a cost function.

Now (IV.II.2-11) can be applied to the generalized Leontief model which can be shown to yield




Even cross-price elasticities can be obtained for the generalized Leontief cost function by






A general form of production functions which are nonhomothetic, is defined by the nonhomothetic translog cost function



which are the so-called homogeneity conditions.

The nonhomothetic translog model can be transformed into a homothetic translog equation if the following restrictions are imposed


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