Friday, June 29, 2007

Volume Discounts: Pizza Mathematics, Part II

When we did the math, I was surprised to learn how rapidly the area of a pizza grows. A 12" pizza is 44% larger than a 10" pizza, and a 14" pizza is twice the size of a 10" pizza. That got me thinking about menu prices. By dividing the cost of a pizza by its area, I can determine the cost per square inch. Of course, pricing varies significantly from place to place. For the first example, I will use prices for Giordano's stuffed pizza with two toppings because that is what we ordered:

Size (inches)Area (square inches)PriceCost per square inch
1078.5$14.9519.04 cents
12113.1$18.9516.76 cents
14153.9$21.2513.81 cents

As I always suspected, ordering a larger size is a much better deal. What about their thin crust pizza?

Size (inches)Area (square inches)PriceCost per square inch
1078.5$10.9513.95 cents
12113.1$13.6512.07 cents
14153.9$16.7510.88 cents
16201.1$19.859.87 cents

Here is a great example of what a deal larger sizes are. A square inch of 10" thin crust is more expensive than a square inch of 14" stuffed, even though the stuffed pizza is about three times as thick.

For another example I will use Manzo's, a local Italian restaurant, because they offer a wider range of thin crust sizes. Again, prices are for a pizza with two toppings:

Size (inches)Area (square inches)PriceCost per square inch
1078.5$9.0011.46 cents
12113.1$10.509.28 cents
14153.9$11.757.63 cents
16201.1$13.006.46 cents
18254.3$14.755.80 cents

As long as you have a way to store the leftovers, a bigger pizza is a much better deal than a smaller one. There are numerous reasons for this. While a 14" pizza requires twice the ingredients of a 10", it doesn't require twice the labor. And restaurants probably account for fixed costs (rent, utilities, etc.) on a per-pizza basis rather than adjusting for size. Of course, one could argue that if ordering a bigger pizza just makes you eat more (i.e., if you don't save the extra food for another meal), then you are paying for it in different ways.

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