Pondering proportional pizza prices

In my last post, I illustrated how much better a deal it is to get large pizzas rather than medium or small pizzas from Dewey’s. A friend pointed out that I hadn’t taken crust into account in that analysis. I dismissed the idea at first, thinking, incorrectly, that it wouldn’t matter. I dismissed it in part because I like to eat the crust, and so don’t tend to think of it as qualitatively different than the rest of the pizza.

As it happens, it matters for the analysis, since it actually makes small and medium pizzas even worse deals. A one inch crust is, proportionally, 33%, 28%, or 22% of the area of a small, medium, or large, respectively.

Here is a graph showing the square inches per dollar as a function of number of toppings, taking a one inch crust into account:
unit_per_dollar_cr1

 

And here’s a graph showing dollars per square inch as a function of number of toppings,  taking a one inch crust into account (see previous post for plots that don’t take the crust into account):

dollar_per_unit_cr1

By taking the crust into account, we see that the large is an even better deal than before. It’s also (very, very nearly) interesting to note that the crossover between smalls and mediums has shifted leftward a couple toppings. Without taking crust into account, smalls were a better deal than mediums for 0, 1, or 2 toppings, but with a one inch crust, small just barely beats medium, and then only if you get a plain cheese pizza.

In addition, here’s a plot showing square inches per dollar for small and medium pizzas relative to square inches per dollar for a large:

unit_per_dollar_cr1_ratio

For no toppings, you get ~60% as many square inches per dollar for either small or medium as you do for a large. This ratio stays fairly constant for mediums, but drops substantially for smalls, approaching 50% for 10 gourmet toppings.

And, finally, here’s a plot showing dollars per square inch for small and medium pizzas relative to dollars per square inch for a large:

dollar_per_unit_cr1_ratio

With respect to dollars per square inch, you spend ~150% for a no-topping small or medium relative to a large. The ratio stays more or less constant for mediums, while it increases quite a bit for smalls. If, for some reason, you decided to buy a 10-gourmet-topping small pizza, you’d be spending almost twice as much per square inch as you would if you bought a 10-gourmet-topping large.

I have way more real work to do than you might think.

 

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