John: Yes your condition hold for both the bag cost and coupon examples. Also I can see how it slides right into the proof I gave in Comment 6. I wrote,

> \\[f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y'). \\] \\(f\\) exactly preserves the tensor structure so, \\[f(x \otimes_X y) \leq_Y f(x' \otimes_X y') \\]

Just replace "\\(f\\) exactly preserves the tensor structure" with "by hypothesis"!

> \\[f(x) \otimes_Y f(y) \leq_Y f(x') \otimes_Y f(y'). \\] \\(f\\) exactly preserves the tensor structure so, \\[f(x \otimes_X y) \leq_Y f(x' \otimes_X y') \\]

Just replace "\\(f\\) exactly preserves the tensor structure" with "by hypothesis"!