For example, inconsistent menu pricing drives me crazy (like on this Wendy’s Menu), and consistent menu pricing leaves me with a warm, fuzzy feeling (like on this Five Guys’ Menu). A recent example of this mathematical discomfort occurred at a studio where I often play music.
The owner of the studio is liquidating his library of VHS Tapes, which include a lot of rare concert videos. The tapes are nicely displayed in a glass case, and a sign displayed the prices:
I’m friendly with the staff, so I felt comfortable going off on a mathematical rant in front of them. I started in on their pricing structure.
“These prices don’t make sense,” I said. ”If someone buys 4 tapes, the cost is $2.50 per tape; for 8 tapes, it’s still $2.50 per tape. Shouldn’t you be offering a larger discount for 8 tapes?”
I continued. ”And look, if you buy 8 tapes, tapes 5, 6, 7,and 8 each cost $2.50, the same as tapes 1, 2, 3, and 4. But if you buy 12 tapes, tapes 9, 10, 11, and 12 each cost $1.25! The marginal cost of a tape should be strictly decreasing!”
The staff humored me by sharing a laugh over my mathematical discomfort, and that was the end of it. Until I returned to the studio.
As I was packing up and checking out of my session, a staffer approached me. ”I thought about what you said last time; it made a lot of sense.” I responded with a quizzical look, unsure of what he was talking about. ”The cost of the tapes,” he said. He pointed to the glass case. ”I changed the pricing system because of you.”
I slept a little easier that night, knowing that I had struck a blow for mathematical consistency.
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