December 1982
Western Journal of Agricultural Economics
economies nor diseconomies of joint produc-
tion or that an aggregate output quantity and
price index exists. As it is well known the
separability restrictions implied by this latter
assumption are very severe. If on the other
hand, only one output of the multioutput
enterprise is considered then the very seri-
ous problem of separating input levels by
each of the outputs needs to be faced. For
this reason the use of a multi-output profit
function approach to agriculture appears to
be quite useful. This approach does not re-
quire any knowledge regarding the allocation
of the different inputs to each output.5
The only research located which estimates
a complete multioutput profit function ap-
plied to agriculture is reported in Lopez
[1981a]. This paper reports on the estimation
of a two output (animal and crop outputs),
four input (land, capital, hired labour and
operator labour) generalized Ieontief profit
function using cross-sectional Canadian cen-
sus data. Major distinctive features of this
study are the following: (a) a simple test for
existence of economies (or diseconomies) of
joint production is implemented. The hy-
pothesis of non-joint production of crop and
animal outputs was not rejected. This was not
unexpected given the high level of output
aggregation. It is likely that at more disag-
gregated levels this hypothesis may be re-
jected. (b) a procedure to separate substitu-
tion and expansion effects for both inputs and
outputs from the profit function estimates is
used. This amounts to deriving the output
trade-offs due to a change in one output price
for given input levels, and to measure the
input substitution stemming from a factor
price change for given output levels. That is,
5Incidentally, it lias been shown elsewhere [Lopez
1982b] that any flexible functional form specification for
a single ouput profit function necessarily implies that
the underlying production function is quasi-
homothetic. That is, that the production function is
homothetic although not necessarily with respect to the
origin. This implies that the associate cost function is of
the form c = ψ (у) c (w) + g (w), which is a very restric-
tive specification in the context of production theory.
An analogous result for the multi-output flexible func-
tional profit specification has not been shown.
the Marshallian elasticities are obtained as
directly provided by estimates of the profit
function and the trade-offs along the produc-
tion possibility frontier and isoquants are also
measured. This information is vital if one
desires to understand the structure or pro-
duction of the agricultural industry, (c) a
third feature is the consideration of hired and
operator (and family) labour as two distinct
inputs. In fact, these estimates indicate that
hired and operator labour respond very dif-
ferently to changes in input and output prices
which suggests that indeed they should be
regarded as different inputs. In general,
hired labour is much more responsive to
price changes than operator. Moreover, our
findings indicate that, surprisingly, operator
and hired labour behave as complements
rather than substitute inputs.
Finally, it is worthwhile to mention that
the use of the profit function concept has
allowed researchers to develop relatively
simple tests for the existence of allocative and
technical efficiency of farm production main-
ly in developing countries. Since the 1971
work of Lau and Yotopoulos who used a
Cobb-Douglas profit specification to test for
relative efficiency of Indian producers, sever-
al studies have used similar approaches.
Among these one may mention the work by
Sidhu and Baanante [1979] who using Punjab
data found that producers do obtaian alloca-
tive efficiency and that the profit function
seems to be an appropriate concept to be
used in the analysis of factor demand and
output supply responses.
Further Applications of Duality: Farm-
Household Supply and Demand Responses
The studies reviewed in the previous sec-
tions are mainly applications of linear duality.
Linear duality applies when the underlying
optimization problem is characterized by
having either a linear objective function or a
linear constraint function. The theory is
based on convex analysis. In this section an
application of generalized non-linear duality
is discussed [Epstein] in the context of the
farm-household model [Lopez 1981b]. Non-
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