The lazy blogger rewrites his reply to interesting comments to an original post and claims that it is a new post. As a lazy blogger, hello, my name is John, here goes.
Suppose that OPEC decides to cut oil production. The initial market equilibrium is at point a where the demand (D1) and supply (S1) curves cross (click on the thumbnail to the right). The supply decrease leads to a new short run equilibrium where D1 and S2 cross at point b.
In the short run demand (D1) is constant yet the quantity demanded (points on the demand curve) falls from point a to point b (measured on the horizontal axis).
In the long run, with persistently high prices, people switch away from SUVs to more fuel efficient cars, move closer to their places of work, etc and the demand becomes more elastic (D1 rotates to D2).
This really isn't a change in demand or a change in quantity demanded, it is a third situation in which the original demand curve is more elastic.
Nevertheless, the only way for the price to fall relative to point a is for the long run demand to rotate so that it is upward sloping (i.e., people want to buy more gas when the price is high, relative to low), which doesn't happen.
Since quantity demanded is so clunky, here is how I think the economic journalists should describe this situation:
The OPEC production cut will lead to higher prices which will lead to a decrease in oil consumption (sales, etc, anything but demand).