Now that the Oscars are behind us and the “next big snowstorm” just missed NYC, I thought I would finally talk about pizza. But because of why you are here – I’ll make price per inch and price per square foot interchangeable.
One of my favorite podcasts, NPR Planet Money had a great segment called “74,476 Reasons You Should Always Get The Bigger Pizza “
The math of why bigger pizzas are such a good deal is simple: A pizza is a circle, and the area of a circle increases with the square of the radius. So, for example, a 16-inch pizza is actually four times as big as an 8-inch pizza. And when you look at thousands of pizza prices from around the U.S., you see that you almost always get a much, much better deal when you buy a bigger pizza.
Explanation of above math: 200.1 inches of pizza surface versus 50.2 inches of pizza surface (pi*r squared=surface area of a circle) And here’s an easy way to calculate the volume of a pizza  if you can’t help get enough pizza geometry.
Here’s the (pizza) logic
The premise of the piece is that it is much cheaper to buy a large pie than a small pie on a price per inch basis. Pricing for a large pie doesn’t expand as much as the surface area does so the price per inch drops precipitously. In the example above, the 16″ pizza wouldn’t be priced 4x as much as the 8″ pizza – probably more like 2x. Apparently pizza makers don’t take geometry seriously.
Buy the large and throw the unused portion in the fridge. Perhaps that is why people buy homes somewhat larger than what they actually need – they will grow into it.
In suburban real estate, after a certain point, larger the home is, generally the lower the price per square foot. There is a point of diminishing return on excess square footage. The total dollar price is higher, obviously, but the cost of additional space is usually less on a per square foot basis. Hence the pizza analogy applies.
Queen of Versailles, Florida
A well known example of diminishing return is the home featured in the documentary, Queen of Versailles . The 90,000 square foot home is so oversized for the Windmere, South Florida housing market that the vast majority of the living area likely has no value as a single family – other than to the current owners, of course.
In a market with one of the highest per capita population density for a US city, there is a premium for larger contiguous space so perhaps that is why we have so many pizza joints. Here is an price per square foot table by apartment size – you can see how ppsf expands with apartment size consistently over the decade (actually it has shown this pattern for the past 25 years). It’s expensive to get more living area in Manhattan.