Why bother with existence? Doubts on this score are too commonplace among economists to be dismissed out of hand. So let us face the issue squarely. What makes existence proofs unappealing? A typical reaction might be:

The problem with this reaction is that it fails to realize what proving existence is all about. If validation of standard operating procedure were the major contribution of existence proofs, then most of us would probably be more than happy to learn that our models pass the test and to leave the details to specialists. But in fact the conclusion reported in an existence proof is of secondary importance. What really matters is the understanding gained in proving the result.

The fact that insight is what we are after is why we are going to prove existence in several different ways, spread over two different chapters. It also explains why we will not strive for the most general results possible. The settings I have chosen for exploring existence are complex enough to bring out the important issues, but not so complex that they obscure what is going on.