I don't think there is a simple trade off like this, nor do I think UA "chose" to give up yield, and such a thing would have been stupid.
Obviously if one has an under-performing route (low overall fares or low load overall) one can slightly increase your PRASM by cutting those. One can also cut the number of flights which will increase the load, sometimes dramatically. However this can also cause operational problems. UA has sometimes had these problems hub to hub where everything is oversold, and I am sure they loose fares at the edges as a result. My point is that cuts in capacity (leading to more load) impacts PRASM, but its not a one to one relationship.
What a good airline does is try to "right size" the airline for the profitable demand they think they can attract, and then try to sell those seats for MORE MONEY. Both UA and DL attracted .1% more passangers (this is in contrast with AS which increased its June 2012 traffic by
10%), both had cuts to capacity (more at Delta, less at UA). One must assume that had either cut capacity further they figured it would not help their overall revenue/cost profile or they would have cut further (cuts in flights only cut marginal costs by part of the % reduction, AC costs, debt, overhead remain the same).
So what can one draw out of all this? Delta, and AA, and US are doing a better job of attracting people who will pay MORE for their tickets than is UA. This "yield premium" is what UA is unable to get post 3/3, and it has been rapidly eroding.
Now keep in mind that this merger was sold to the street as one that due to NETWORK would be attractive to FFers and corporate accounts, and as such would provide a yield premium. So far this is not going as planned.
