VRT is more profitable than URT if RVRT* - V1- V2 > 0, where V1 is the application
cost for VRT minus the application cost for URT and V2 is the cost of gathering spatial
information and using it to identify management zones and their yield response functions. If the
management zones and their response functions have already been identified, V2 is known and
the farmer will undertake VRT if RVRT* > V1, because V2 is a sunk cost in making the VRT
versus URT decision. If, on the other hand, V2 is not known, the farmer can use conservative,
educated guesses about the λi s, the corresponding yield response functions, and V1 to estimate
RVRT* - V1, which can be thought of as an education guess about the maximum amount a
farmer can invest in gathering spatial information and identifying the field’s management zones
and their yield response functions.
Equation (5) is concave inλi . Its concavity can easily be understood by considering
fields with three management zones; management zones 1, 2, and 3. For fields that are all in
management zone 1 ( λ1 = 1, λ2 = 0, and λ3 = 0), RVRT* = 0 because the weighted average
response function and the response function for management zone 1 are the same. Fields with a
positive λ2 and/or λ3 (0 <λ1 <1) have multiple management zones and farmers can consider
using VRT. Since optimization of input use with VRT is more suited to the site-specific yield
response functions than to the field-average response function, RVRT* now becomes positive
and continues to increase to a maximum as λ1 decreases over some range.
Spatial Break-even Variability Proportions (SBVPs) (English, Roberts, and
Mahajanashetti; Mahajanashetti; Roberts, English, and Mahajanashetti) are defined as the lower
and upper limits of λm-2 , λm-1 , and λm for given levels of λ1, λ2,..., λm-3, PY, Pj, and V1 such