β22 , β24 , andβ26 represent the harvesting cost per bushel for yields above 20, 48, 35, and 24
bu/ac for wheat, corn, grain sorghum, and soybeans, respectively. The “fertilizer operation
adjustment percent” coefficient, β38, represents the percent an estimated field operation
coefficient must be adjusted to take into account the simultaneous application of fertilizer with
that operation. One would expect this to be greater than 1 (100%), signifying that an operation
with fertilizer applied will cost more than the same operation without fertilizer applied, due to
the additional equipment and attachments needed to apply fertilizer, as well as the reduced field
efficiency of applying fertilizer (more time spent filling or switching fertilizer tanks, and less
time performing the desired operation). The intercept term of the linear scale factor adjustments
(β39) is expected to be positive while the slope term (β40) is expected to be negative. This will
allow for the scale factor (β39 +β40hai) to decrease as a farm increases harvested acres, resulting
in economies of size.
The empirical specification of the quadratic model (model 2) is the same as model 1
except that a term for harvested acres squared (ha2) is added to the scale adjustment. Model 2 is
specified as
(3) tcmci=[i]{β39+β40hai+β41hai2}+ei,
where the bracketed term [•] is the same as that specified in model 1. The signs on the estimated
scale coefficients (β39,β40,β41) are expected to be positive, negative, and positive, respectively.
This will allow for increasing returns to scale at a decreasing rate, an optimal farm size, and
ultimately decreasing returns to scale.
Model 3, a reciprocal model, uses one divided by harvested acres (1/ha) to allow an
asymptotic scale factor and is specified as