In statistical inference, the shadow price of health, lambda, is a nuisance parameter. The wedge-shaped confidence regions resulting from either the “count outwards” bootstrap approach or from Fieller’s theorem are equivariant (commutative) under changes in lambda. Every outcome within the ICE uncertainty scatter thus remains inside of, right on or else outside of the resulting ICE ray confidence limits. Unfortunately, widely practiced economic approaches, such as Net Benefit and acceptability curves, are highly dependent upon variation in lambda. These economic evaluations are actually quite subjective in the sense that they incorporate uncertainty about lambda inconsistent with the statistical uncertainty in patient level data on the relative cost and effectiveness of treatments. These concepts are illustrated graphically using functions from my R-package “ICEinfer.”