APPLICATIONS OF DUALITY THEORY TO AGRICULTURE

December 1982

Western Journal of Agricultural Economics

TABLE 1. Hicksian Input Demand Elasticities Obtained in Various Studies.

^aIncludes fertilizers, chemicals and other intermediate inputs.

prices; (2) there exist sizeable substitution
possibilities among several input pairs of
which energy-based inputs and land appear
to exhibit the greatest potential; (3) the
aggregate agricultural technology is not
homothetic and (4) the more simple produc-
tion function specifications such as the Cobb-
Douglas or Leontief⁴ are not appropriate
specifications as shown by the studies by
Binswanger and Lopez, respectively.

It was indicated at the outset that a nice
feature of dualilty is that knowledge of the
properties of the dual behavioural functions
(cost or profit functions) permit a close re-
lationship between economic theory and em-
pirical analysis. In particular, cost minimiza-
tion behaviour implies that the functions (1)
and (3) should be increasing, linear
homogeneous and concave functions of
prices. Moreover, its Hessian matrix must be
symmetric which implies that the factor de-
mands satisfy the well-known reciprocity
conditions. The empirical results are used to
either test of impose the above restrictions
on the estimating demand equations. The
various empirical tests of the required prop-
erties of the cost function implemented by
Binswanger [1974a] and Lopez [1980]
showed that in general the empirical evi-
dence in North America does not allow one
to statistically reject the parametric restric-
tions implied by those properties. The im-

⁴This function is widely assumed mainly in linear pro-
gramming studies.

356

portant implication of this is that cost
minimizing behaviour is an appropriate hy-
pothesis for North American agriculture even
at the aggregate industry level.

The Profit Function Approach

A common feature of the empirical studies
reviewed in the previous section is that they
consider a single output technology. Addi-
tionally, a serious limitation of the cost ap-
proach in general is that it assumes that
output levels are not affected by factor price
changes and, thus, the indirect effect of fac-
tor price changes (via output levels) on factor
demands are ignored.

Moreover, the inclusion of output levels as
explanatory variables may lead to simultane-
ous equation biases if output levels are not
indeed exogeneous. This problem is certainly
compounded if a multi-output cost function is
estimated. In this case the input shares or
input-output ratios normally used to estimate
the factor demands are dependent on each of
the outputs even if constant returns to scale
are assumed [Hall] and, moreover, these
share equations are non-linear in the various
outputs. This makes it very difficult to use
econometric techniques designed to tackle
simultaneity problems.

The profit function approach allows one to
overcome most of these problems although at
the cost of requiring a stronger behavioural
assumption. The profit maximization as-
sumption may be substantially more difficult

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