DTM.9:5.1 - A broad response releases the variant it was meant to limit

Continue the illustrative activity model of DTM.6. A is useful execution and B is execution producing specified errors inside a group. Both occupy limited execution capacity. Suppose the checking response is generated more strongly by visible A activity and also by B:

a = 2A + 0.5B + u
A' = A[2(1−A−B) − 0.2 − a]
B' = B[(1−A−B) − 0.3 − 0.2a − v].

Here u is additional broad checking and v selectively stops established B activity. A, B and remaining capacity are nonnegative. Time and activity are normalized; coefficients are chosen for this example. The equation for a assumes fast adjustment with no consequential memory.

With positive initial presence and the stated model, the stable stationary comparisons are:

Increasing broad checking removes the more sensitive A and releases capacity for B. The larger response therefore leaves more B. This conclusion follows from the stipulated resource and sensitivity relations; it is not an empirical claim about procedure catalogues or a general argument against checking.

Selective action succeeds here only if B can actually be distinguished and stopped at the assumed cost. It cannot be presented as an available improvement before that capability is established.