I think to calculate the power curve you need to have a sequence of benchmark monsters. Or at least bundles of statistics (attack bonus, AC, damage per hit and hit points would be the minimum) that can stand in for a fully statted-out monster.
You'd want it to work out that 2 of monster A would be a match (50% chance of victory) against monster B, and 2 of monster B would be a match for monster C, and so on. You want to have some kind of linear progression on all 4 of the basic stats- attack, AC, damage and hp- so that the result is a "middle of the road" kind of creature.
Now is the tricky part: you have to decide what CRs to assign to these monsters. Suppose monster A is assigned a CR of 1. Then suppose that you decide that doubling the number of monsters increases the CR by +2. Then monster B has a CR of 3, monster C has a CR of 5, and so on. I'm handwaving some technical aspects of EL, but I think this is basically how 3.5 assigns CRs to critters. It's an exponential progression.
Here's another tricky part: ensuring that a party of PCs increase in power at the same rate as monsters. A party of 1st level characters shouldn't have much problem with monster A, and a party of 5th level characters should make similarly fast work with monster C. So the power curve of PCs is the same as that of monsters; it is also exponential.
Now how does this work, exactly? How do we have it so that monster B is a match for two of monster A? Let's take attack, hit points and AC off the table for the moment, and pretend the only difference lies in damage.
Suppose that if monster B were dazed it would take monster A exactly 8 rounds to kill it. Then two copies of monster A would take exactly 4 rounds. If monster B were fighting back and if the battle is going to be a tie, it would have to take monster B exactly 2 rounds to kill monster A. So B has to be four times as strong as A. (This is just Lanchester's square law, and it assumes that B is dividing its attacks equally between its two opponents.)
A similar analysis shows that it would also work if B had four times the hit points as A. If B had twice the hit points and did twice the damage, then that would also work. Hit points and damage have a nice property; if we know that C has twice as many hit points as B, and B has twice as many hit points as A, then we know that C has four times as many hit points as A. And similarly for damage. The knowledge is transitive.
If you add AC and attack rolls into the mix, then the numbers are also transitive, at least sometimes, and as long as the numbers aren't too extreme. Here's an example: If monster A hits monster B 30% of the time (and is hit 60% of the time), and monster B hits monster C 30% of the time (and is hit 60% of the time), how often does monster A hit monster C? (and how often is it hit?)
Let's make up some numbers. Monster A has an AC of 15 and an attack of +4. Monster B has an AC of 19 and an attack of +6. Monster C has an AC of 21 and an attack of +10. So monster A needs a 17 to hit monster C (20% chance) and is hit on a 5 or better (80% chance). So the hit ratios multiply out: A gets hit twice for every hit it gets on B, and B gets hit twice for every hit it gets on C. And it turns out that A gets hit four times for every hit it gets on C.
And although the percentage chance of hitting can never drop below 5% or go higher than 95%, there are mechanisms that can compensate. Maybe the big monsters get a little DR or fast healing; or perhaps they can use power attack (or cleave, or some kind of area attack) against weaker opponents. I don't see a way to make the numbers come out perfectly, but as an approximation it should be OK.
What's the point? Just this: its not too hard to achieve an exponential power curve in monsters by simultaneously increasing hit points, AC, damage per attack and hit points. And the game is designed to increase the power of a party at the same rate that monsters increase their power.
Now if there were only these 4 variables the game could be broken by exploiting a few loopholes. For instance, if you could increase your AC a few points, you would reap a disproportionate advantage over weaker opponents. If you could get a +5 AC advantage, then instead of hitting you 30% of the time, opponents would hit you only 5% of the time. It would be like increasing your hit points by a factor of 6. But that is why there are touch attacks, area attacks, and attacks that have nothing to do with hit points and AC; you can be an invincible tank, but if your will save is too low you could still get confused or dominated. Or if you have that covered, then direct damage (fireballs and the like) might be your Achilles heel. And while you might be able to afford items that give you a +5 AC advantage over what the game assumes you'll have, you won't be able to get a similar advantage against all vulnerabilities.
Anyway. I contend that the power curve is not quadratic; I say it is really exponential. I think (though I haven't argued this) that at high levels it is spellcasting that enables a party to increase its power fast enough to allow it to keep up with the monsters. Which means that the power curve is steeper for spellcasters than for fighter types.
