by Paul Dancstep • October 17, 2015
George Banks makes an interesting point. No one likes to waste food. So if you're shopping for hotdogs and you don't want to have any excess buns or wieners you're going to have to buy supplies for at least 24 hotdogs, even if you originally wanted fewer. The package quantities for these products appear to be chosen in such a way that hotdog eaters are forced to overconsume.
But how credible is this conspiracy theory? If I were a bigshot from the bun company and you were a bigshot from the wiener company, are these the disparate package quantities that we would naturally come up with? Consider what would happen if instead of eight wieners per package there were only seven. Under these circumstances one has to buy supplies for 84 hotdogs in order to achieve parity.
It is unlikely that a rational consumer would buy that many hotdogs, especially if we assume that their motive is to not waste food. What this tells us it that for our conspiracy to work the least common multiple of our two package sizes must be a reasonably small.
Now consider what would happen if there were only three wieners in a package. After buying a package of buns and a package of wieners, the consumer must buy three additional packages of wieners to eliminate the bun surplus. Since all of these extra purchases accrue only to the wiener maker, the bun maker ends up taking all of the risks of collusion without getting any of the benefits.
In order to be fair to both conspirators, the quantity in one package cannot be a multiple of the quantity in the other package.
With these constraints in mind, eight and twelve begin to look like suspiciously convenient numbers for the hotdog industry to have settled on. But can we do better? The following interactive lets us explore the outcomes of other package disparity scenarios. We can use this tool to help find the optimal product discrepancy for us to benefit equally from the excess purchases of all those trusting nitwits.
Interactive created by Anita Lillie.
Clip from Father of the Bride by Touchstone Pictures.