Arline companies are businesses. The function of a business is to make a profit. To make a profit they have to provide a service that people will use at a fare that people will pay. If a business fails to make a profit for a sufficiently long time it will fail.
Thus fares have to be at a level for people to be willing to make use of he product and for companies to make a profit. We've seen the results of lack of profitability in the airlines.
The above model works in a competetive environment. When iFly failed to make a
FLYi attempted to establish itself and attract customers by selling its product at a loss. If UA had not matched or approached their fare levels it would have lost a substantial number of customers and caused a large loss. It therefore lowered its fares to meet FLYi and minimize its loss. Now that FLYi is gone UA can raise their fares to a level where it may make a profit.
All of the above is of course grossly simplified.