I have two points. One is that the interchange fee should not be related to costs. The second thing is economists do studies, empirical work, and we look to see what happens. We know we have a system. If your argument were correct and cash were cheaper and it was more expensive to use credit cards, we should find—because there's nothing stopping merchants—merchants saying, “You're coming with a credit card and it's costing me more; I'm going to give a discount for cash.” The fact that we don't see it is proof—it's not proof, but it goes towards validating the proposition that it must be more expensive. If it weren't more expensive, what you would do is simply give a discount.
Now, it's not true for all transactions. Different retailers may have different costs of cash and credit card, and some retailers may say, “We're not going to accept credit cards”, as Costco does. It has a very efficient model and it works. For other retailers, that doesn't work. So what you find is, let the system compete. If cash is dominant, it will; if credit cards are dominant, they will.