20 July 2007

pizza pie are square(d)

Geometry Saved Me Money, from Binary Dollar, via Grey Matters. Which is more: a twelve-inch pizza or two eight-inch pizzas?

The twelve-inch pizza, of course; it is more square inches of pizza. (I'm assuming all pizzas are equally thick.)

However, if you really like crust, the two eight-inch pizzas might actually be the better deal. One twelve-inch pizza contains 36π square inches of interior and 12π inches of crust; two eight-inch pizzas contain 32π square inches of interior and 16π inches of crust. So if you're willing to trade 4π square inches of interior for 4π inches of crust, take the smaller pizzas. That is, if you'd rather have a third of the crust of the pizza than a ninth of the interior, or if you'd prefer three crusts to one crustless slice.

I like the crust, so I might.

(This analysis assumes, of course, that the thickness of the crust is negligible, so that "an inch of crust" actually means something.)

The waitress in the restaurant where this question came up thought the customers would prefer the two eight-inch pizzas because it was more "slices of pizza". Maybe it's just me, but a "slice of pizza" is a meaningless unit, because it's not standard. I would have at least expected the argument that eight plus eight is more than twelve.

I suspect that pizza is the food that is most often "illogically" priced. I've seen, say, chicken wings sold at "10 for $5, 15 for $8" but you don't see that too often, because most people can do the math and realize that buying 15 is a bad deal. (Think of it this way: what if I want thirty? I can get three 10-packs for $15, or two 15-packs for $16.) But with pizza people will throw up their hands. Also, I have seen places where a larger size of pizza costs more per square inch than a smaller pizza (I can't find any right now); I was once told that this was because for whatever reason the large size was more inconvenient to make (it fit in the oven funny, for example). That at least seems like a plausible economic reason; it's clearly not the cost of the ingredients and almost certainly not the labor.


John Armstrong said...

And this whole thing is predicated on your assumption that (a) people are rational actors who (b) subdivide pizza by the square inch instead of by the slice.

I think the waitress was spot-on, because people really do think in terms of slices long before they think of square inches. Yes, it's irrational, but yes, that's how people actually think.

And now we know why you're the probabilist rather than the economist.

Melanie said...

I think the most irrationally priced drink is soda. Generally a 1 liter bottle will cost equal to/more than a 2 liter bottle. Presumably you're paying for the ability to be able to drink the soda easily without using a cup? Also, I've been to restaurants with free soda refills where it'll be, say, $1 for a small, $1.25 for a medium, $1.50 for a large, and I'll be the only person who doesn't order a large. I always assumed that was meant for takeout customers. When I asked why people ordered a large, they said "Well it's only 50 cents more." I suppose they're paying to not have to get up as often?

One of the things I liked about Japan that inevitably baffled the foreigners was that vending machines would sell different sizes of drinks for the same price, and generally the smaller sizes would be more popular, because why would you want to wastefully buy more than you wanted to drink?

The Probabilist said...


maybe people don't think in terms of square inches instead of slices. But I think people do realize that not all slices of pizza are created equal. Otherwise, pizzerias could cut their pizzas into sixteen slices instead of the standard eight and convince people that they were getting twice as much pizza.

The Probabilist said...


one thing I've noticed about the 1 liter vs. 2 liter issue is that often the 1-liter soda bottle will be stored in a refrigerated container, while the 2-liter is stored out on the shelf where it can get warm. So perhaps you are paying for having the store refrigerate the soda for you.

Another place where the pricing is irrational-seeming is movie theater popcorn. My local movie theater has three sizes of popcorn, priced at something like $3.50, $3.75, and $4 -- I don't recall the exact prices but the increments between them were definitely 25 cents. The large is perhaps twice the size of the small.