Quantity or price?


This little scrap of wisdom is about the price of coffee, hence the milky coffee background.

My favourite coffee shop usually sells q grams of coffee for £p, let's say. Sometimes they have sales, which come in two kinds. In one kind, you get 20% more coffee for your £p, in the other 20% less money buys you the usual amount q grams.

Why is there this distinction, I often used to wonder. Surely the two kinds of sale are equivalent, so why distinguish them? Finally I decided to apply a bit of arithmetic to the problem.

In an increased quantity sale, £p buys (q + q/5), or 6q/5 grams of coffee. In a reduced price sale, £(p - p/5), or £4/5, buys q grams, that is, £p will be spent on 5q/4 grams instead of the usual q.

So there is a difference! It looks as if you can obtain a bit more coffee at a reduced price sale, in fact (5q/4 - 6q/5) = (25 - 24)q/20 = q/20 grams more. To give an actual example, if £5 usually buys 100gm, then at a reduced price sale you will get 125gm while at an increased quantity sale just 120gm. A whole 5gm difference!

Maybe it hardly seems worth bothering about for the regular customer, but with a lot of regular customers there might be a reasonable difference in the shop's profits.