A One-Penny Proof
By Bryan Caplan
In social science, the best arguments prove more than the best studies. Hands down.
Here’s one homely example of what I have in mind.
When economists explain marginalism, students often object, “But surely no one ever changes his behavior over a single penny.” However, they’re provably wrong. If “no one ever changes his behavior over a single penny,” raising your price by a penny automatically increases your profit. So does raising your price by another penny. And another penny. And another penny… Any firm could earn infinite profit by sequentially raising its price, one penny at a time. Since this absurd, the premise must be wrong. People can, do, and must occasionally change their behavior over a single penny.
Wait, there’s more. On the typical day, most firms don’t raise their prices. Given the plausible assumption that firms want to make as much money as possible, we can infer that every firm expects that raising any price by a penny would lead to lower profits. This is only possible if every firm expects that raising any price by a penny would change some customers’ behavior.
The lesson: Behavior that responds to a one-penny change isn’t just a theoretical curiosity; unless price-setters are deeply mistaken about their own markets, behavior that responds to a one-penny change is all around us, always has been, and always will be.
I don’t know who originated this one-penny proof. I suspect authorship is lost in the sands of time. No matter. The author, whoever he may be, created something great: A simple, timeless, and virtually bullet-proof argument about all human behavior and pricing decisions. How many papers in the latest AER can claim anything remotely comparable?