The Variable-Rate Decision for Multiple Inputs with Multiple Management Zones
Introduction
Economic analyses of the decision to use variable-rate technology (VRT) versus uniform-
rate technology (URT) to apply inputs within a farm field have concentrated on application of a
single input (eg., Lambert and Lowenberg-DeBoer; Swinton and Lowenberg-DeBoer; English,
Roberts, and Mahajanashetti). Unless inputs are independent of one another, a change in the
quantity of one input affects the marginal product of the other inputs as they interact in
producing output. Thus, for the multiple input VRT decision, the optimal quantities of the inputs
for each management zone must be determined by the simultaneous solution of the first order
conditions for profit maximization. This paper considers the profit-maximizing decision about
whether to use VRT or URT to apply multiple inputs within a field and evaluates this decision
for cases where nitrogen and water are applied to cotton fields with different proportions of their
acreage in three management zones.
Farmers are interested in knowing whether VRT is economically viable for their fields.
Profitability of VRT varies across fields with differences in spatial variability, where spatial
variability is defined as the distribution across a field of management zones with different crop
yield responses to inputs (Roberts, English, and Mahajanashetti). Within-field variability in soil
physical and chemical characteristics is a necessary condition for the economic viability of using
VRT (English, Roberts, and Mahajanashetti; Forcella; Hayes, Overton, and Price; Roberts,
English, and Mahajanashetti; Snyder). Relationships among crop yields, input levels, and soil
characteristics determine spatial variability within a field. These relationships also determine
yield response variability, where yield response variability is defined as the differences in
magnitudes of yield response among management zones (English, Roberts, and Mahajanashetti;