Conservation farming on steep lands - USAid

ASSESSING ECONOMIC BENEFITS 10 1
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available. It would have been ideal if productior~ functions could have bcen
estimated fhr the intlividual crops and a niodel ccnstructed to optim~ze the
mix of labor, cheniicals. seeds, and land prior to and after adoption of thc:
niodel farni packsge. The data available, however, provided only the value
of prc)duction by sam@ plot, hours of labor employed, and value of purchased
inputs. At best, before and after revenuc functions could be estimated
from this information. Given these limitations, the optimum mix of chemical
and labor inputs were computed before and after the program.
Estitnation of tlle valrte jitnctiotrs. A Cobb-Douglas foi-m of value hnction
-;ras used to estimate the value functions as follow.,:
VALUE = exp(C) L"' IN:'?
where VALUE is the value of production in rupiah per hectare. C is the
constant from the regression equation. al is the coefticient attached to labor,
a2 is the coefficient attached to the other inputs, IN is the other inputs
measured in rclpiah per hectare, and L is labor hours divided by hectar-.
The value of production, labor inputs, and chemical inputs were divided
by plot area. This implies constant returns to scale for all three inputs,
a restriction we were willing to tolerate because the sample plot areas proved
to be less than a hectare in almost all instances. Generalizing from these
data in order to extrapolate to larger farms was considered too risky.
Ordinary least square regressions were 7erformed on the log transformations
of value, labor, and chemical inputs for both before and after the
program. The resulting two revenue functions were used to determine the
optimal combination of inputs and outputs, before and after implementing
the program. The difference in output value, given an economically efficient
mix of labor and chemical inputs, should provide a consistent measure
of the impact of the model farm program. This strdlegy is superior to siniply
comparing the before and after yields per hectare because it allows productivity
changes to be disaggregated between the different components
of the model farm package.
[I]
Detenninit~g efficicttt levels of inputs. The first derivatives of equation
1 with respect to L and IN provide the basis for determining how each
additional labor hour per hectare or rupiah of chemical input per hectare
influenced the value of production. The value of the marginal product of
labor is calculated as:
VMP, = a 1 exp(C) L(" '-I ) IN" ' [21
The value of the maeinal product of chemical inputs is calculated as: