Consumers Prefer to Get More Rather than Pay Less – Because They’re Bad at Math

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Is it better to get more or pay less? If you think they’re basically the same, you’re like most consumers. And, like most consumers, you’re wrong.

When offered the possibility of 33% off a product or the same product with 33% more quantity, which would you choose?

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.”

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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.

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Shoppers routinely bite on offers that are worse values because they do the math incorrectly, and also perhaps just because they’re infatuated with the idea of getting something extra for free. The prospect of receiving something for nothing has been demonstrated to make consumers do some pretty irrational things, including buying goods they otherwise wouldn’t have and being far more likely to order items online with free shipping, regardless of the overall expense.

It seems as if the psychology power of free may also make us worse at math. In another marketing experiment involving hand lotion in an actual store, researchers sold 73% more when it came in a bonus pack than when it was priced at a discount with the same exact unit price.

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Researchers have a term for the phenomenon in which shoppers pay little attention to unit price. They call it “base-value neglect.” Neglect at your own peril.

Tuttle is a reporter at TIME. Find him on Twitter at @bradrtuttle. You can also continue the discussion on TIME’s Facebook page and on Twitter at @TIME.