APPLICATIONS OF DUALITY THEORY TO AGRICULTURE

provided by Research Papers in Economics

Applications of Duality Theory
to Agriculture

Ramon E. Lopez

Although a comprehensive framework for
most of the theoretical foundations of duality
has been available to economists since the
seminal work by Shephard in 1953, empirical
applications of duality have become popular
mainly during the last ten years. The first
empirical study which I am aware of that
exploited duality theory is the one by Ner-
Iove in 1963 which estimated a Cobb-
Douglas cost function as an indirect way of
measuring the parameters of the production
function of electric utilities.

The development of the concept of flexible
functional forms and its applications in the
derivation of plausible functional forms for
dual cost and profit functions in the early
seventies [Diewert 1971; Christensen, Jor-
gensen and Lau] was an important step
which led to the proliferation of empirical
applications of duality. Several of these stud-
ies have concerned the agricultural sector. Of
these, the study by Binswanger [1974a and
1974b] using U.S.A, data appears to be one
of the earliest.

A reason for the increasing popularity of
the use of duality in applied economic analy-
sis is that it allows greater flexibility in the
specification of factor demand and output
supply response equations and permits a
very close relationship between economic
theory and practice.

If a transformation function dependent on
factor quantities, a vector of output levels
and the production technology is specified
then empirical factor demand equations can
be derived from the first order conditions of
cost minimization. If profit maximization is

Ramon E. Lopez is an economist with Agriculture Cana-
da, Ottawa, Ontario.
assumed, the output supply response equa-
tions can also be derived from the first order
conditions. Unfortunately, unless very sim-
ple and hence restrictive functional forms for
the transformation function are assumed (i.e.
Cobb-Douglas) these conditions frequently
cannot be solved explicitly, and if that can be
done, the resulting equations may not be
feasible to estimate. The use of duality allows
us to side-step the problems of solving first
order conditions by directly specifying suit-
able minimum cost functions or maximum
profit functions rather than production or
transformation functions. From duality
theory we know the set of necessary prop-
erties of the cost and profit functions which
are implied by a “well behaved” production
technology and by the corresponding be-
havioural assumptions. It is the knowledge of
this set of minimum properties which has
allowed the development of suitable func-
tional forms for profit and cost functions. An
advantage of starting by specifying a cost or
profit function rather than the underlying
transformation function is that in order to
derive the estimating factor demand and out-
put supply responses there is no need to
solve any complex system of first order condi-
tions. The behavioural response equations
are obtained by simple differentiation of the
dual functions with respect to input and/or
output prices. The major advantage of this is
that it implies less algebraic manipulations
and, more importantly, it allows us to specify
more complex functional forms which impose
much less a priori restrictions on the estimat-
ing equations (i.e., we do not need to impose
restrictions on the values of the elasticities of
substitution, separability, Iiomotheticity etc.).

In what follows what has been done on the

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