Consumer Math - Unit Cost

The Atlantic has a great article titled The 11 Ways That Consumers Are Hopeless at Math which will be the basis of my blogs this week.

Would you rather get a 33% discount off the price or 33% more product (more coffee, more cereal, etc)?

It turns out these are not the same. When you compare two products it's not enough just to say, product A is cheaper than B. What if B contains twice as much as A but only costs 50% more? Then B is the bargain. The trick to comparing different sizes of the same product is to use UNIT COST, that is dollars per quantity where quantity is some common unit of measurement like cups or pounds.

UNIT COST =  $cost / quantity

Now lets return to the original question. Which is better: a 33% discount or 33% more product?
The 33% discount reduces the top part of unit cost by 1/3 and new unit cost is 2/3 of the old.
The 33% more product  increases the bottom part of unit cost by 1 1/3,  or an increase of 4/3 in the denominator. We invert that number to find the new unit cost is 3/4.   And since fractions are difficult to compare let's convert everything back to percentages:
33% discount means a new unit cost 64% of the old
33% more product means a new unit cost that is 75% of the old
Discount wins!

"This is your brain on shopping, and it's not very smart" - The Atlantic