Pricing Psychology: 33% more vs 33% discount

The Economist has an interesting article about the psychology of discounting.

The main claim of the article is
"Shoppers prefer getting something extra free to getting something cheaper."

which they "explain" with
"Most people are useless at fractions."

For example people don't realize that a 50% increase in quantity is the same as a 33% discount in price.

50% increase in quantity = 150% = 1.5
33% discount = 67% = 0.67
1 / 1.5 = 0.67 and thus 1 / 0.67 = 1.5

For those who still don't get it, we can also look at it the other way around:
a 33% discount on something that is 150% results in 100%

150% * (1-0.33) = 100%

and a 50% increase on something that is 67% also results in 100%

67% * (1+0.50) = 100%

Therefore if you're offered either a 33% extra for free or a 33% discount you should definitely go for the discount, since we already learned above, the 33% discount gives you a 50% extra for free.

Another marketing trick people often fall for is double discounting. So if a product has been reduced by 20% and then later on by another 25% percent, most people think 20% + 25% = 45% discount, while the truth is, it's only a 40% discount.

100% * (1-0.20) * (1-0.25) = 60% which is obviously a 40% discount

Note: values have been rounded to make them easier readable. If you perform the calculations yourself and you want precise results, use fractions instead of percentages, e.g. 1/3 instead of 33%.