st: Von Liebig Production Function

["Gauri Khanna" <gwkhanna@hotmail.com>]

Dear Stata listers,


I am resending this message as I did not receive it the first time that I 
posted it.

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 
water.

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.

Regards,

Gauri

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