Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or welfare economics.
Sometimes it seems as if there are more solutions than problems. On closer scrutiny, it turns out that many of today's problems are a result of yesterday's solutions.
It is hard to read a newspaper or watch a television newscast without encountering someone who has come up with a new 'solution' to society's 'problems.'
The anointed don't like to talk about painful trade-offs. They like to talk about happy "solutions” that get rid of the whole problem- at least in their imagination.