What does it cost when you buy a 300-page paperback from Amazon? The price of the book is only the initial cost. When you store it on your bookshelf, it takes space and renting a space costs money. The price of the book might be only $10; the storage cost for 15 years is probably higher than $5.5.
A 1000 square feet apartment costs around $2100/month in the US. Roughly $300 of the cost is fixed cost independent of the size of usable area, including the cost of transaction, management cost, stairs, mechanical rooms, and partly the costs of outdoor areas, utility bills, and property tax. The rest of the rent should grow linearly with area. This leaves $1800/month for 1000 sq ft, or $1.8/month/sq ft, or $0.0125/month/sq inches.
In the short run, buying a book will not increase your rent, but in the long run you are mobile and you will pick a house that’s about the right size by equating your marginal benefit per sq ft per month to around $1.8.
Assume that a book is 8’’ × 5.5’’ × 1’’, and your bookshelf is 29’’ × 12’’ × 72’’ with 6 shelves plus the top. To calculate the minimal needed space, we squeeze as many bookshelves as possible in a library pattern, with aisles that are only 24’’ wide. Half of the area will be bookshelves and half will be aisles since 2 × bookshelf depth = aisle width. A book would cost 1’’ (width) × 12’’ (depth) of space on one of seven shelves (including the top) and an equal share of aisle space. Therefore, one book occupies 1” × 12” ÷ 7 shelves × 2 = 3.42 square inches of space.
Now the cost of storing one book a month is 0.0125 × 3.42 = $0.04286; or $0.5143 a year. Fifteen years? Let’s use a realistic annual discount rate of 4.5% to calculate the present value: $0.5143 / 0.045 × (1 – 1 / 0.045^15) = $ 5.5232. To store a book forever, the cost is: $0.5143 / 0.045 = $11.4286. Next time you bring home a free book from library, beware that you are signing a contract to pay 51 cents each year (adjust for inflation) until you get rid of the book.