A classic example of irrationality is mental accounting. Say you are going to the theater. You have a $100 ticket and a $100 bill, and on the way to the theater you lose the ticket. Would you spend your $100 to buy another one? Most people wouldn't, because they would be assigning a $200 cost to the theater department.

Now imagine that you only have a $100 bill with which you are going to pay the ticket, and you lose it on the way to the theater. Would you take out your credit card and pay for the ticket anyway? Most people would.

We know that if people were rational the two scenarios would be identical. But they differ, and this is interesting because we have a framework from which to look into it, and we can see it doesn't fit the framework, and therefore we can infer new and unexpected facts about the economic agents. Models inform in interesting ways how we go about trying to understand reality, even when they are poor predictors.