Which is better: A 33% discount on price or 33% more for the same cost?

At least I’m good enough at math to recognize this for the awesome deal that it is.

The answer to that question seems counter-intuitive to me, but then I’m not great at math. A problem that is shared by many other people it seems:

The Economist sums up the results of a new study published in the Journal of Marketing, which reveals that most consumers view these options as essentially the same proposition. But they’re not. The discount is by far the better deal. As the Economist puts it, because most shoppers are “useless at fractions,” they don’t realize that, for instance, a “50% increase in quantity is the same as a 33% discount in price.”

In one part of the study, Akshay Rao, the General Mills Chair in Marketing at the University of Minnesota’s Carlson School of Management, asked undergraduate students to evaluate two deals on loose coffee beans — one with 33% more beans for free, the other at 33% off the price. The students viewed the offers as six of one, half a dozen of the other.

But let’s do the math, using some easy round numbers for the sake of simplicity. Say the initial price is \$10 for 10 oz. of coffee beans. Hopefully, it’s obvious that the unit price is therefore \$1 per oz. An extra 33% more “free” beans would bring the total up to 13.3 oz. for \$10. That \$10 divided by 13.3 oz. give us a unit price of \$0.75 per oz. With a 33% discount off the initial offer, though, the proposition becomes \$6.67 for 10 oz., for a unit price of \$0.67 per oz.

Once it’s spelled out the difference becomes obvious. According to the article it’s not just that most of us are bad at math, but also the allure of the word “free” that leads us towards bad decision making. In my case, it certainly doesn’t help having things expressed as percentages which I’ve always had a hard time figuring out unless it’s multiples of 10, and even then I don’t tend to trust my calculative abilities.

Of course the marketers all know this which is why more often than not you’ll see products touted as offering some percentage more “for free!” than some sort of discount. In fact I can’t think of a single example of a product being offered either for X% discount or the same price with X% more at the same time. So I guess it’s a moot point. If you really only have one offer to consider then getting a bit more at the same price is still better than no deal at all.