I’ve seen people make estimates of what they thought was the right amount to pay for an e-book, but I can’t say I’ve seen one actually put it into an equation before. But Ramzi Amri, an MD/PhD candidate in Surgical Oncology, has. He wrote up an answer on Quora including the following mathematical formula for determining how much he was willing to pay for an e-book:

If an ebook has a price, in dollars, below the value of Beta, I’d consider buying it.

t= time (in minutes) it would take me to find the ebook on greyer areas of the internet.
f= fake-file multiplier: number of fake files I’d have to download to eventually find the real deal.
E= Elsevier Benchmark a.k.a. the relative level of evilness of the actual publisher. Elsevier is the benchmark and has a score of 100.
s= searchability. If, for any reason, the contents of the legal eBook in question are not searchable, this value is 0; else it is 1.

So if we assume it would take him two minutes to google up the book, he might have to download three fake files in the course of looking, the publisher is not evil (assume a rating of 1 since you can’t divide by zero), and the book is searchable, his Beta threshold would be 2 * 4 – 1 which works out to $7.

Of course, the equation would necessarily be subjective. You don’t actually know how long it’s going to take you to find the book, or how many false positives you’ll hit, until you try. How “evil” a publisher is obviously varies, though if the publisher is even slightly evil the price quickly drops to zero. Likewise, the exponent of “s” is just a fast way to say that if he can’t search the e-book (which, as a college student, is an ability he finds highly necessary), he won’t pay anything for it at all.

As a student, we can assume the formula is primarily meant to apply to textbooks, which see different types of use (and cost a lot more in general) than trade books—and tend to have more “evil” publishers. (Ones who try things like requiring textbooks be sent back at the end of the semester, for example. And, of course, we’ve covered the shenanigans of Elsevier itself a number of times.) So the whole equation might just be a fancy way of saying he rarely finds any textbooks worth paying for, unless they just can’t be found online.

And in a larger sense, that points out the problem that the textbook industry has. It’s hard to get students to pay those high prices for books they might not even be able to resell at semester’s end when they can find many of them online for free.

We all have our own internal calculus for how much trouble paying for something is worth, but it’s rare to see the formula actually articulated like that. I guess that’s what being a doctoral candidate can do.