Increasing power required with altitude.. what's a good plain english explanation?

xerj writes:

I was trying to explain to a non-pilot why increased power is required with
altitude. She said "isn't the air thinner up there so there isn't as much
resistance?" I said "yes, but the plane needs to fly fast enough for the air
over the wings to feel like it does down low. So the speed required goes up
you get higher. More speed need more power."

Actually, she's right. You need higher speed at higher altitudes in
order to maintain a given amount of lift, because the air isn't as
dense. However, you don't necessarily need more power, because thin
air presents a lot less resistance to the aircraft. Airliners fly
high in part because it requires less power (and therefore consumes
less fuel). That's why they are eager to get up to high altitudes.

You may need a higher _throttle_ setting, because the engines produce
less power in thinner air. However, the amount of power required
still diminishes. To climb from altitude A to B in an aircraft, you
may have to increase the throttle from 60 to 75, but at the same time
the power produced by the engine at a given throttle setting
diminishes by 30%, so in fact you are flying with less power at
altitude B.

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