I saw this post from Bryan Caplan when I was jet-setting to Vegas, and thought something was really wrong with it. But I haven’t had time until now to write it up. Here’s Bryan:
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?
Sorry Bryan, but not only am I not impressed by the rigor of this demonstration…I don’t even think it’s right.
Bryan is assuming his conclusion, without apparently realizing it: Critics challenge the notion that people (they have in mind consumers) might care about changes of one penny, and Bryan responds with an argument that assumes people (he has in mind producers) care about changes of one penny.
Look, the quickest way for me to make my point is to replace every occurrence of “one penny” in Bryan’s argument with “one-quadrillionth of a penny.” Did I just prove to you that everyone in the economy is acutely sensitive to price, down to the one-quadrillionth of a penny? Are market prices what they are right now, and not one-quadrillionth of a penny higher, because there is at least one person who would lower his purchases at that higher price?
If my point above seems too cute for you, switch to a more straightforward claim: I personally round off to the nearest dollar when I fill in the tip at a restaurant. In other words, I will calibrate the tip such that the final tally is a whole dollar amount. It’s definitely not the case that I would have ordered more or less food, depending on if the price of the entree is $12.99 versus $12.98.
In some markets, pennies matter. For example, when people are shopping for gasoline, they definitely pay attention to the posted price per gallon, down to the penny. But when someone is in the market for a new SUV, I don’t think pennies come into play at all.
Note that I’m not challenging Bryan’s basic conclusion; I’m not making an argument against marginalism per se. I’m just saying I don’t find Bryan’s “one-penny proof” very compelling.
UPDATE: Kavram in the comments write:
Skylien got it right. If marginal pennies were truly inconsequential the fact that so many market prices (notably installment payments for infomercial products) end with .99 would be one of the greatest coincidences known to mankind.
Actually, this is evidence in my favor, and massive evidence against Bryan. If prices were set by “rational” forces of supply and demand, you would expect an uniform distribution of trailing digits. In other words, 1% of the goods and services should end with a price of .00, another 1% should end with .01, etc.
The fact that in some markets, prices end with .99 means that something besides Caplan’s mechanism is at work. Yes, in a tautologous sense, the producers of infomercial products charge $19.99 because they think that if they charge $20.00 their sales will go down. But, if they charged $19.98 their sales would go down too! Worse yet, if they charged $19.72666 (and they expressed it like that, in the ad), then they would probably sell zero units because the average late-night viewer would be freaked out by that.
So, did I just prove that demand curves slope upward? Is this a Giffin good, perhaps? I mean, here we have a case where the seller makes more profit, by charging a higher price.
To reiterate, I am not claiming that market prices are random. Yes, they are what they are for a reason; human beings consciously agree to terms, and so market prices must “come from” humans somehow. What I am claiming is that these prices aren’t the simple product of intro-level profit and utility maximization, in the way Caplan believes. If he tells his students, “All prices in a market economy are set at that exact level, such that a one-penny increase in price would cause at least one buyer to fall out of the market and thus lower profits,” then I agree with any student who says, “Are you nuts?!”