Speaker relative efficiency/sensitivity when using a high pass filter

I am using a second order high pass filter at 80 Hz yielding12dB down at 40Hz.  12dB is associated with a 16-fold power difference. This is my rationale for the inquiry.

Makes sense. I’m sure the numbers won’t be exact but it means I may be able to go from my 400 W amplifier down to a 100 W amplifier. The speaker manufacturer recommends 200.

@nymarty I am using a Devialet 400.  It has high and low pass filters along with time delay. I have a Dayton Audio SA1000 as my subwoofer amp with second order and fourth order high and low pass filters, respectively, at 80Hz but I am not currently using these. I would if I were to go with separates or an integrated with a tape monitor.  I'd lose the time delay feature of the Devialet but would hopefully make up for it with other attributes.  I could also use a miniDSP or equivalent which you might consider as well.

@lonemountain Do the small speakers you measured have considerable bass output? I would guess that a speaker that goes to 50Hz would yield less of a gain than one that goes to 35Hz. 

I am thinking tubes as well but did not want to go down that path and incur/incite the commentary about there being plenty of high output tube amplifiers. Thanks for broaching it. I also want to entertain lower power AB SS amps.

I have a fondness for class A from my Aleph 3 days. Again, just wanted to have a better sense of my options, which appear to have greatly increased.

200 W “peak unclipped program”

Understood, hence my calling it "relative efficiency".  I appreciate that your and Erik's replies are semantically more appropriate.

So it appears there is a decrement in the current/voltage required to drive a speaker to only 80Hz instead of 35 or so. I am wondering if there is a formula to determine what the quantity might be. My impetus is that requiring less power allows me to consider lower power amps, perhaps even making Class A available.