Seems to me that managers at AS are trying to increase their profits the same as managers at AA, DAL, USAir, LUV, and all the other airlines who jumped on the "raise fares to match tax cuts" bandwagon. Or at least, they're utilizing their knowledge of basic Microeconomics

Total Revenue = Price x Quantity Demanded

The Law of Demand states that as price decreases, consumers demand more of the good. By implication, as price increases, consumers demand less, and as price remains the same, so does demand.

Therefore, if AS charges a lower fare relative to their competitors, or at least makes it appear as if they are, then the demand for their services increase. Conversely, services provided by other airlines who raise their fares will decrease. In either case, revenue could increase or decrease dependent on the market power of the airline and the magnitude of the price change.

Alaska probably passed the savings onto consumers because their demand is slightly more elastic than most of the other Legacy carriers. Plus, the loyalty they will gain from consumers for this seemingly altruistic act will likely secure an increased revenue stream in the future.