How is the power range determined?

Let's say that you have a floor standing speaker with the freq. resp. 30-20KHz, 8 ohm impedance, and 90dB sensitivity.
How would you (or the manufacturer) determine the power range of the speaker?
Is there a way to determine the optimum amp power for the speaker?
If the speaker manufacturer states the power range as 50~300 Watts, if price and size don't matter and everything else equals, would you rather go for as much power as possible, or would you still try different amps with different wattage to determine which amp would be best for the speakers in your room?
The manufacturer determines the maximum power rating based on how much power the low frequency driver elements (the woofer or woofers) are rated to handle. The high frequency drivers will invariably have much lower power ratings, but music typically contains much less energy at high frequencies than at low frequencies.

The manufacturer's recommended minimum power rating is based on a rough guess as to how much power would be required to play music at reasonable volume in a relatively small room, at a relatively small listening distance.

As a goal, it's generally a good idea to have the power rating of the amplifier around the same as the speaker's recommended maximum power, especially as here if price and size don't matter, and we assume that "everything else equals" (meaning sound quality in particular).

You can get away with less power if your room is not particularly big, your listening distance is not particularly great, and the music you listen to does not have wide dynamic range. Recordings of classical symphony orchestra tend to have the widest dynamic range, meaning that they have the greatest difference in volume between loud and soft passages. Setting the volume level for good reproduction of the soft passages on that kind of material leads to very high power levels being required when the occasional orchestral peaks, bass drum beats, etc., occur.

-- Al
Many manufacturers of high end equipment don't give power ratings. The reason is simple...there are many different ways to calculate the power rating so it is a meaningless number to most people. Unless you drive the amp into clipping it is unlikely you will damage the speaker before you reach an uncomfortable volume level. It is far easier to damage a driver with a low power amp driven into clipping than it is with a much higher power amp that only occasionally hits peaks beyond the average rating of the speaker. For this reason you should choose an amp that exceeds, not equals the maximum rating if it is known.

There are different methods to get an idea of how much power you need which depend on a lot of factors, but here is one. It is an oversimplification of the complete picture but gives you a starting point. First estimate how loudly you want to listen to your 90dB speakers and double the 90/dB at 1W for every 3dB. Say you are a metal head who wants to hit 105dB peaks. You need to double it 5 times so 1x2x2x2x2x2 = 32W. That is at 1 meter but you need to quadruple the power every time you double the distance so if you are sitting 4 meters away you need 32x4x4= 512W.

You should go even higher because you don't want the amp to clip. Of course if you sit closer or don't need to hit 105dB peaks your needs go way down.

While it is true that there is generally less energy at higher frequencies UNCLIPPED that is radically changed when the amp clips as it produces distortions and energy at much higher frequencies than the fundamental. Having repaired a large number of PA and sound reinforcement speakers I guarantee you it is almost always the tweeter that is blown and very seldom a woofer.

The bottom line is this....too little is far worse than more than enough.

Go for the amp whose sound you like the best and still has sufficient power. Herman is right about erring on the high side. Al has given you good advice also. Just remember that because 2 amps have the same power rating does not mean that they will sound the same. Try as many amps as you can, you will be surprised at the differences.
For the full range speaker forget about sensitivity at all since it's being only measured @1000hz. Other frequency ranges will have certainly different parameters. The only thing to look for is the minimal power rating where more-likely your amp will clip at desirable volume so in your case I'd look first for the amps >50W and than depending on your listening tastes and room I would adjust it further and finally I will choose the one with sufficient power, affordable price and good sound to my ears.
For the full range speaker forget about sensitivity at all since it's being only measured @1000hz.

While the last part may be true (it is only measured at a certain frequency) I must disagree with the advice to ignore the sensitivity rating. It is true that sensitivity varies with frequency but if it is so grossly different that it renders nominal sensitivity irrelevant then you should be looking for a speaker with a flatter frequency response.
My rule of thumb with "normal" speakers (6 to 8 ohms, 86dB to 91dB)is to use an amp with 30% more watts over what the mnfc recommends. Dali recommends a max of 150w for my Ikon6 towers. I drive them with a 2 x 200w Aragon 4004 MKII. There is no doubt in my mind that the Ikons could easily take 300wpc if played at reasonable volume.
I agree with the good comments by Stan, Herman, and Mmarvin19. But I'd add the slight qualification that in the case of speakers such as the original poster described (300W power handling, 90db sensitivity), going to a 400W or so amp (that provides good sound quality) will result in a very limited set of choices, which will also be very expensive (apart possibly for some Class D amps).

300W into a 90db speaker represents a sound pressure level of 115db at 1 meter, from each speaker, a situation which is unlikely to lead to clipping. The 30% over mfr. rating rule of thumb strikes me as a good guideline for speakers that have more ordinary (lower) combinations of power handling and sensitivity, and perhaps situations where the room is exceptionally large.

-- Al
Good topic. I am of the mindset that, in general, people tend to underpower their systems. Although a certain decibal level may be produced by a speaker, it does not guarantee that it will be able to properly delineate the details. The hallmark of underpowering is not clipping, but a lack of focus when things get congested or trouble with huge dynamic contrasts. These things, to get do them correctly, need a certain power reserve. Perhaps the ratings for lower power on speakers are as much a nod to the market constraints.

With that said, there may be some great amps of lower power that do many things quite well, with certain types of music, in smaller rooms. However, having absolute control of the bass, clarity and soundstaging during congested passages, and the proper speed for dynamic shifts may be the downsides.
You guys are FANTASTIC.
Many thanks for wonderful tips.
Recommended amplification for my current 91db speakers was 25-150W. I figured that 70 tube watts would be plenty; and it was, until I through 200 watts at them. I couldn't believe how much music I was missing. Another benefit is that my system became musically satisfying at much lower volumes than it used to.

From a marketing point of view, it's in the best interest of a manufacturer to claim that his speakers are compatible with the widest range of supporting products possible. If this makes sense, then that low recommended figure will nearly always be a stretch.