[Principled]

Actually, I have no idea what you are talking about.

If each stage saves 9%, the total savings will be more than 9% of the pre-saving-on-each-stage price.

This is easy to model. Have you tried?

[Principled]

Correction:

If each stage saves 9%, the total savings can be more than 9% of the pre-saving-on-each-stage price.

[RobFromGa]

I'm not sure what point you are trying to make, my statement was that if the most any input component of price was reduced was 9%, then the most the total cost could be reduced would be 9% (that would be in the case where all the cost of the good was in that single most reduced component).

If you are trying to prove that is false, knock yourself out. I'm heading out for a while, have fun...