My campus bookstore made a dramatic claim about reduced textbook pricing. Karen Natale, the “Bookstore & Licensing Program Manager” has this to say about the new bookstore and reduced prices:

In case you don’t have time to watch the video, here’s the relevant quote:

As you know, publishers set the prices, the bookstore doesn’t, on [new] textbooks. But bookstores add a margin, and the margin covers overhead, salaries, shipping and handling, all the things we need to do to stay in business. In the past, our margin was 23%, which is what the national average is. Many of the UNC campuses are at 25%. We are now, thanks to our new contract [with Barnes & Noble], at 18%. So that’s a significant savings that students are going to see staying in their pockets.

Wow! A margin of only 18%, when the national average is 23% and some UNC campuses are charging as much as 25%, according to her. Sounds great, right?

Suppose the publisher sells a book to the bookstore for the wholesale price of $105. With an advertised 18% margin, what do you think the shelf price should be? Pause for a moment and calculate this yourself. You probably came up with $123.90. You took $105 and multiplied it by 1.18, right?

Unfortunately, that’s not how it’s done. What you’ve done (and what advertisers are counting on) is to confuse margin with markup. There’s quite a difference.

To be brief, if you start with the sale price, the margin is percentage you *discount* to get the cost, whereas if you start with the cost, the markup is the percentage you *add* to determine the sale price. Thus markup and margin are “dual” to each other in some sense.

To be definite, suppose is the wholesale cost of the item to the reseller. Let represent the percent margin or markup desired, with . If represents *markup*, then the price of the item is . If represents *margin*, the formula is instead. To summarize,

.

So, back to our textbook example. Its wholesale cost to the bookstore was $105.00. Since they have an 18% *margin*, the price listed on the shelf will be . Did you notice? An 18% margin became a 22% markup!

In general, if the margin is then the markup is . Here’s a short table showing the relationship in increments of 10%.

0% margin = 0% markup

10% margin = 11.1% markup

20% margin = 25% markup

30% margin = 42.9% markup

40% margin = 66.7% markup

50% margin = 100% markup

60% margin = 150% markup

70% margin = 233% markup

80% margin = 400% markup

90% margin = 900% markup

Assuming , we may Taylor expand the margin factor as follows: . Thus we see that

So the markup formula is really just a first order Taylor approximation to the margin formula. In using the margin formula, they’re benefitting from keeping all those higher order terms, and they can really add up over many, many sales.

What’s worse, the difference between the markup formula and the margin formula becomes more dramatic as the margin goes up. The formulas are identical for , but the margin formula blows up to infinity as approaches 1 (i.e. 100%). Meanwhile, the honest markup formula remains “honest” no matter how high goes.

By the way, I don’t place any blame on Karen Natale. She’s been excellent in working with professors and publishers to get low prices and correct errors.

I’m guessing resellers advertise margin instead of markup since, for a fixed profit, the advertised margin will be smaller than the markup, making it sound like you’re getting a better deal than you really are. I suppose this tactic is par for the advertising world. Oh well. Now you know.