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st: re: von Liebig production functions

From   Kit Baum <>
Subject   st: re: von Liebig production functions
Date   Mon, 6 Aug 2007 10:41:35 -0400

Gauri said

I was wondering if any one knew whether it is possible to use a Von Liebig
(VL) production function using Stata code? The VL production function is
such that inputs are used in fixed proportions and the isoquants are L
shaped. Hence, if one of the inputs increase, there is no corresponding
increase in output.

More succintly, for two inputs, Water (W) and Nitrogen (N) the production
function is described as

Y(output)=min(fn(N, n), fw(W, w))+u

where the 's are the associated parameters to be estimated.

It can be restated as

Y(output)=min(n + n.N, w + w.W, m) +u

where N amd W are applied quanitites of Nitrogen and Water with their
associated parameters , and parameter m is a measure of the potential
maximum yield imporsed by the scarcity of nutrients other than nitrogen and

For those interested, a description can be found in - Paris and Knapp,
1989,"Estimation of von Liebig Response Functions", American Journal of
Agricultural Economics, pp 178-186.

The article shows that there are routines but I just wondered if it was
possible in Stata.

I don't know how this may be feasible in Stata (other than estimating a CES function subject to the constraint that \rho -> \infty), but I would note that the functions described are much better known to economists as Leontief production functions, after Wassily Leontief, Nobel prize winner 1973, now deceased. According to IDEAS, this author has chosen not to make the email address public.

Kit Baum, Boston College Economics and DIW Berlin
An Introduction to Modern Econometrics Using Stata:

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