The inventory-impact potential of liability: the marginal rate rises linearly from zero to max_rate over scale, then stays capped:
liability
max_rate
scale
phi(L) = r_max * L^2 / (2B) for L <= B phi(L) = phi(B) + r_max * (L - B) for L > B.
phi(L) = r_max * L^2 / (2B)
L <= B
phi(L) = phi(B) + r_max * (L - B)
L > B
Defined by this exact sequence of rounded integer operations, so charges and rebates, which always subtract two evaluations, telescope exactly.
The inventory-impact potential of
liability: the marginal rate rises linearly from zero tomax_rateoverscale, then stays capped:phi(L) = r_max * L^2 / (2B)forL <= Bphi(L) = phi(B) + r_max * (L - B)forL > B.Defined by this exact sequence of rounded integer operations, so charges and rebates, which always subtract two evaluations, telescope exactly.