How price elasticity works
Every business owner eventually asks the same question in the same worried tone: if I put the price up, how many customers walk? Elasticity is just that question written as a ratio. Take the percentage change in how much you sold, divide it by the percentage change in price, and you have a single number describing how twitchy your buyers are.
An elasticity of 2 says a 1 percent price rise costs you 2 percent of your volume, which is a skittish market. An elasticity of 0.3 says the same rise costs you three tenths of a percent, which is a market barely paying attention. The dividing line sits at 1, and it matters more than it looks, because it is exactly the point where a price change leaves your total revenue completely unmoved.
The formula
Where ΔQ is the change in quantity, ΔP is the change in price, and each is divided by the average of the old and new values rather than by the starting value. That averaging is what makes this the midpoint method, and it exists to fix a real irritation, covered below.
Worked example
A coffee shop raises a $4.00 cup to $4.50. Weekly sales slip from 900 cups to 800. Contribution margin is 60 percent, so each cup costs $1.60 to make.
Quantity: −100 ÷ 850 = −11.76%
Price: +$0.50 ÷ $4.25 = +11.76%
Elasticity = −11.76% ÷ 11.76% = −1.00
Dead on unit elastic, which means revenue should not have moved at all. It did not:
Before: 900 × $4.00 = $3,600
After: 800 × $4.50 = $3,600
Now the part that decides whether this was a good week. Profit before was 900 × $2.40 = $2,160. Profit after was 800 × $2.90 = $2,320. Identical revenue, and $160 more profit, because 100 cups that were never sold were also 100 cups that never had to be bought, brewed, lidded or poured.
Revenue peaks at unit elasticity. Profit does not.
This is the most expensive thing on this page, so it is worth slowing down for.
The textbook result is true: revenue is maximised where elasticity equals 1. Below that line a price rise adds revenue, above it a price cut adds revenue, and at exactly 1 you are standing on the summit. Nothing wrong with any of that.
But revenue is not what you keep. Every unit you sell carries a cost, and every unit you stop selling hands that cost back to you. So the price that maximises profit always sits above the price that maximises revenue, and the gap between them widens as your variable costs grow. The coffee shop above landed exactly on the revenue summit and still made $160 more, which is the whole argument in one week's trading.
The practical version of this is a question you can answer before you change anything: how much volume can I afford to lose? At a contribution margin m, a price rise to P2 breaks even on profit when volume falls to:
Run it for a 10 percent price change at a 40 percent margin and you get two numbers that ought to be taped above every pricing meeting:
- Raise the price 10 percent: you can lose 20 percent of your customers and profit is unchanged.
- Cut the price 10 percent: you need 33 percent more volume just to get back to where you started.
Discounts are not the mirror image of price rises. They are considerably harder work, and the thinner your margin the harder they get. A 10 percent discount at a 20 percent margin needs your volume to double.
Why the midpoint formula, and not the obvious one
The obvious way to work out a percentage change is to divide by where you started. It is also the way that gives you two different answers for the same pair of numbers.
Take the coffee shop again. Going up, $4.00 to $4.50 is a 12.5 percent rise and 900 to 800 cups is an 11.1 percent fall, giving an elasticity of 0.89. Now walk the same two points backwards: $4.50 to $4.00 is an 11.1 percent cut and 800 to 900 cups is a 12.5 percent gain, giving 1.13.
Same shop, same week, same two data points, and the two answers land on opposite sides of 1. One says demand is inelastic and you should charge more; the other says it is elastic and you should be careful. The midpoint formula divides by the average of the two prices and the average of the two quantities, so the arithmetic no longer cares which end you call the beginning, and the answer comes out at exactly 1.00 whichever way you walk.
That is the only reason the midpoint version exists, and it is a good one. This calculator shows you both so you can see the gap for yourself.
What elasticity quietly assumes
The formula holds one enormous thing fixed: that nothing except your price changed between the two measurements. In a real quarter, plenty did. A competitor ran a promotion, the weather turned, payday landed, a review went up, you were out of stock on a Tuesday.
So treat a single before-and-after as a direction rather than a measurement. It is genuinely useful for that, and anyone who has priced anything under real conditions has done exactly this with worse tools and less time. If the number surprises you, the most likely explanation is not that your customers are strange but that something else moved at the same time. And if elasticity comes out positive, meaning volume rose when you raised the price, something else almost certainly did move: that pattern is real in a few luxury markets and much more commonly a sign that your two weeks were not comparable.
Once you know roughly how elastic your demand is, the next questions are what your margin actually is at the new price, and how many units you now need to cover your fixed costs. The margin calculator handles the first and the break-even calculator handles the second.