Cost Functions and the Estimation of Flexible Functional Forms
Lecture XVIII
I.
Flexible Functional Forms
A.
The crux of the dual approach is then to estimate a manifestation of behavior
that economist know something about.
1.
Thus, instead of estimating production functions that are purely
physical forms that economist have little expertise in developing, we
could estimate the cost function that represents cost minimizing
behavior.
2.
We then would be able to determine whether the properties of these
cost functions are consistent with our hypotheses about technology.
3.
However, it is often the direct implications of the cost minimizing
behavior that we are interested in:
a.
How will farmers react to changes in agricultural prices
through commodity programs?
(
)
;
C
y w
p
p
y
∂
=
+ Δ
∂
b.
What is the impact of a change in input prices (say in an
increase in fuel prices) on agricultural output?
(
)
;
C
y w
w
p
y
∂
+ Δ
=
∂
4.
Thus, the dual cost function results are usually sufficient for most
question facing agricultural economists.
B.
Given that we are interested in estimating the cost function directly, the next
question involves how to specify the cost function?
1.
One approach to the estimation of cost functions would then be to
hypothesize a primal production function and derive the theoretically
consistent specification for the cost function based on this primal.
For
example, if we started with a CobbDouglas production function, we
could specify a cost system consistent with that assumption.
2.
However, this approach would appear too restrictive.
Specifically, we
have shown that given that the cost function obeys certain properties
that a valid technology exists that would justify it.
3.
Thus, economists have typically turned to flexible functional forms
that allow for a wide variety of technologies.
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 Fall '09
 Staff
 Taylor Series, Analytic function, Charles Moss

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