How to Price an eBook

Guest Post by Tahir Yaqoob

First of all, thanks to Jennifer for the invitation to present this article on her blog and help with this article. As the eBook revolution continues to gain momentum, the question of eBook pricing strategy and models comes up frequently. The ultimate goal being to discover the optimal retail price for maximum eBook revenue.

On the one hand revenue is proportional to the retail price and number of books sold in a given amount of time, but on the other hand, the number of eBooks sold in a given amount of time drops as the price increases. There is a trade-off such that there is some optimal price that gives the maximum revenue.

This is actually a standard calculus problem and what I'm going to show you is a remarkably simple result. However, there are caveats, and ultimately, nothing can beat real measurements and data.

In an ideal world you would do a controlled experiment over a sufficiently long period of time to eliminate statistical fluctuations. You would measure the revenue as you change the price and thereby estimate the optimal price.

However, in practice, you very likely don’t have the time to do that, and even if you did, there are so many factors that affect sales that it would be extremely hard to account and correct for those factors.

Still, I think the result I'm going to show you serves as a baseline guesstimate for orientation purposes. I would not recommend basing your marketing plan on this alone! Every book is unique and every book's situation is unique.

I'm only going to deal with the case of Kindle books priced between 2.99 and 9.99, otherwise this article would be way too long and complicated.

Sales vs. Price: Five Cases

Let's take a look at Fig. 1, which shows 5 possible different ways the number of books sold per month could change with retail price.

Figure 1

Case A: The horizontal dotted line is a no-brainer: sales are flat, so the optimal price is the highest price.

Case B: You may think this is strange but here the number of books sold goes up before it goes down: this is appropriate when the book's quality is perceived to be low if the price is too low.

Case C: Here the number of books sold stays fairly flat until some critical value, after which it drops. This is probably the case relevant for the majority of eBooks.

Case D: Here the number of books sold drops continuously in a straight-line fashion between 2.99 and 9.99.

Case E: Here the number of books sold plummets dramatically when you raise the price above 2.99, but then the rate of plummeting slows down.

The Main Result

What is interesting is case D, because some basic mathematics leads to a remarkably simple result. I am going to tell you what that result is and then I'm going to show you why it is true without using equations, but rather, I will show you how the result can be understood intuitively. Then I will illustrate with a specific example with some numbers. So, here is the result:

If you can estimate (or establish) the price at which your sales drop to zero, all other factors being equal, the price that will return the maximum revenue is precisely half of that value.

In other words if case D applies, and if, for example you estimate that your sales would first drop to zero at $15, your optimal price is $7.50.

What is remarkable is what this result does not depend on. It does not depend on any actual sales numbers at any price; and it does not depend on the royalty rate, as long as it is the same from 2.99 to 9.99. It actually depends on one thing only and nothing else, and that is, the price at which your sales first drop to zero.

How to Apply the Result

You probably have a fairly good idea of what that price would be without doing the experiment. You could also estimate it as some percentage above the highest price of your book's closest competitor. (If you think that your book has no competitor, think again: what is relevant is perceived competition, and every book has that, otherwise people would be lining up outside your house with their check books!)

If it is a Kindle book your estimate can be up to $20. If it is more than that, then you have to choose $9.99 as the price of your book, unless you want to drop your royalty rate to 35 percent, which would not make sense.

Why It’s So

So, what is the fundamental reason for the simple “rule of thumb?” Well, your net revenue is the product of something that depends on the retail price (royalty times price), and something else that depends on price (i.e., the number of books sold drops with price). Therefore, you get a “price squared” in the net revenue equation.

Now, the graph of anything squared (for which the variable has no higher power than a square) is a parabola, or upside-down “U.” But we know that the parabola must go through zero at a retail price of zero (i.e., at zero revenue), and it must go through zero at the price we estimated the number of books sold to drop to zero (by definition, obviously).

But hang on, a parabola is symmetric around the peak or hump! So the peak must lie precisely halfway between the two zeros! Remember that this only applies to “case D” and it does not apply to paperbacks, which have a completely different pricing and revenue structure.

Caveats

There are many caveats but a major one that the above does not take into account is the exponential effect of the Amazon ranking machinery, which will directly affect results.

Basically, the more units you can move in the shortest time, the more Amazon rewards you with increased exposure, regardless of price. This effect will skew the optimal price below the baseline.

An Example with Numbers

Now, to pull all this together, here is an example with some numbers. Fig. 2 shows a line corresponding to revenue versus retail price per book (this is just the royalty rate times the retail price; I have used 70 percent royalty here but it doesn't matter).

Figure 2

In Fig. 3 is a made-up example of number of books sold versus retail price (assuming "case D"). In this example we estimate the sales to drop to zero at $15.

Figure 3

Now we multiply the graphs in Fig. 2 and Fig. 3 together to get the net revenue versus retail price and this is shown in Fig. 4.

Figure 4

You can see that the maximum revenue occurs at a retail price of precisely half of $15, as expected. You can then use this baseline as a guide to figure out what the ideal price might be for your unique situation.

Summary and Take-Away

The main thing is, don’t take this too literally: the optimal price problem is extremely complex. However, I have shown that you can calculate a baseline number to work with by estimating the price at which your sales would drop to zero: half of that price is the optimal baseline.

Good luck with your publishing adventures: remember that the main goal is to enjoy what you’re doing day-to-day, not just the end result, because you are in it for the long haul!

"Tahir Yaqoob is an astrophysicist & educator with over 25 years of experience. He obtained a B.A. in physics from the university of Oxford, England, and a Ph.D. in astrophysics from the University of Leicester, England. He has authored or co-authored over 120 research papers in peer-reviewed journals and is the author of two books, What Can I Do to Help My Child with Math When I Don't Know Any Myself?, and Exoplanets and Alien Solar Systems, which makes the exciting new science of planets beyond our solar system easily accessible to the layperson. Both books are available in eBook and paperback formats."