Price Elasticity of Demand, Explained: How the Midpoint Formula Turns Price Tests Into Pricing Decisions

You are thinking about raising your price by 10 percent. Will your revenue rise by something close to 10 percent — or will enough customers walk away that you end up with less money than you started with? That question has a number for an answer, and it is called the price elasticity of demand. It measures how strongly your quantity sold responds to a price change, and once you know it, pricing stops being a guess. This guide explains the midpoint formula economists use to compute it, how to read the result, what makes demand flexible or rigid, and how to estimate the number from your own sales records.

What price elasticity of demand measures​

Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. In symbols:

elasticity = (percentage change in quantity) / (percentage change in price)

Because a higher price almost always means fewer units sold, the number is usually negative: price goes up, quantity goes down. Economists almost always talk about its absolute value — the size of the response with the minus sign dropped — and this guide follows that convention. When someone says "elasticity is 1.5," they mean negative 1.5: a 1 percent price increase cuts quantity by about 1.5 percent.

The intuition is simple. An elasticity near zero means customers barely react to price changes — think of prescription medication or gasoline in the short run. A large elasticity means even a small price move triggers a big swing in units sold — think of a restaurant meal in a neighborhood full of alternatives. Your pricing power lives in that number: the lower it is, the more room you have to raise prices.

The midpoint formula (and why economists insist on it)​

The naive way to compute a percentage change is "change divided by the starting value." But that creates an embarrassing problem: the answer depends on which direction you travel. Raise a price from $10 to $12 and the naive method reports a 20 percent increase; cut it from $12 back to $10 and it reports a 16.7 percent decrease. Same two prices, different percentages — so your elasticity would depend on whether you call the change a rise or a fall.

The midpoint formula fixes this by dividing every change by the average of the starting and ending values instead of by the starting value:

percentage change in quantity = (Q2 − Q1) / ((Q1 + Q2) / 2) × 100

percentage change in price = (P2 − P1) / ((P1 + P2) / 2) × 100

elasticity = (percentage change in quantity) / (percentage change in price)

Because the average is the same whichever point you start from, the midpoint method gives one answer regardless of direction. That symmetry is the whole point: an elasticity should describe the relationship between two points, not the trip you took between them.

A worked example, step by step​

Suppose you run a coffee cart. At $4.00 per latte you sell 200 lattes a day; after raising the price to $5.00 you sell 150 a day. Here is the midpoint calculation:

1. Change in quantity: 150 − 200 = −50. Average quantity: (200 + 150) / 2 = 175. Percentage change: −50 / 175 = −28.6 percent.
2. Change in price: $5.00 − $4.00 = $1.00. Average price: ($4.00 + $5.00) / 2 = $4.50. Percentage change: $1.00 / $4.50 = 22.2 percent.
3. Elasticity: −28.6 / 22.2 = −1.29, or 1.29 in absolute value.

Now check the revenue. Before: 200 × $4.00 = $800 per day. After: 150 × $5.00 = $750 per day. Revenue fell even though the price rose — exactly what an elasticity above 1 predicts, as the next two sections explain.

Try the same arithmetic in reverse, as if you were cutting the price from $5.00 to $4.00. The midpoint averages are identical ($4.50 and 175), so you get the same 1.29. The naive method would have given you two different answers; the midpoint method gives one.

Reading the number: elastic, unit elastic, inelastic​

The absolute value of elasticity falls into three regions, and the boundary that matters is 1:

• Elastic (above 1). Quantity responds more than proportionally. A 1 percent price increase cuts units by more than 1 percent. The coffee cart's 1.29 is elastic: customers had options, and many took them.
• Unit elastic (equal to 1). Quantity moves in exact proportion to price. A 1 percent price increase cuts units by exactly 1 percent, leaving total revenue unchanged.
• Inelastic (below 1). Quantity responds less than proportionally. A 1 percent price increase cuts units by less than 1 percent. Demand for necessities, addictive goods, and products with no close substitutes typically lands here.

Two extreme cases complete the picture. Perfectly inelastic demand (elasticity of zero) means quantity does not move at all when price changes — a vertical demand curve, approximated by life-saving drugs with no generic. Perfectly elastic demand (infinite elasticity) means any price increase above the going rate drops quantity to zero — a horizontal curve, approximated by a commodity seller in a crowded market where buyers can switch instantly.

The total revenue test: what elasticity says about your top line​

Total revenue is price times quantity, and a price change pushes those two factors in opposite directions. Elasticity tells you which push wins:

This table is the most practical thing in the article. If your demand is inelastic, price increases raise revenue and discounts destroy it. If your demand is elastic, it is the reverse: discounts pay for themselves in volume while increases bleed revenue — the coffee cart learned this the expensive way. Revenue peaks where elasticity equals exactly 1, which is why experienced pricers probe toward unit elasticity from either side.

One caution: revenue is not profit. A price cut that raises revenue can still cut profit if your margin per unit shrinks faster than volume grows. Always run the elasticity logic against contribution margin, not just the top line — if each extra unit barely covers its variable cost, volume gains are vanity.

What makes demand elastic or inelastic​

Elasticity is not a fixed property of a product; it comes from the customer's situation. Five determinants do most of the work:

1. Availability of close substitutes​

This is the dominant factor. The more good alternatives your customers have, the more elastic your demand. A cart selling lattes on a block with four coffee shops faces elastic demand; the only gas station for fifty miles faces inelastic demand. Branding, differentiation, and switching costs all work by making substitutes feel less close.

2. Necessity versus luxury​

Necessities have inelastic demand — people buy roughly the same amount of insulin, salt, or electricity across a wide price range. Luxuries and postponable purchases are elastic: restaurant meals, vacations, and new furniture can wait for a sale. Note that the classification is about the buyer's perspective, not yours: your premium software tier is a luxury to a hobbyist and a necessity to the business built on it.

3. Share of the buyer's budget​

Small-ticket items feel inelastic because nobody rethinks a purchase over pennies — a 20 percent increase on a $2 item is 40 cents. Big-ticket items get scrutinized, compared, and delayed, which makes demand more elastic. This is why sellers of low-priced consumables can often pass through cost increases that would sink a durable-goods maker.

4. Time horizon​

Demand grows more elastic with time. In the short run, customers are locked into habits, contracts, and equipment; in the long run, they find substitutes, change routines, and renegotiate. Gasoline demand is famously inelastic this month and noticeably more elastic over five years, as commuters eventually carpool, move, or buy efficient cars. A price test that runs for a week measures short-run elasticity — do not assume the number still holds next year.

5. How narrowly the market is defined​

Broad categories are inelastic; narrow brands are elastic. Demand for "coffee" barely budges with price, but demand for your specific roast is far more sensitive, because the closest substitute is one shelf away. Small businesses almost always operate at the narrow end, which means your elasticity is higher than the category average cited in textbooks.

Estimating elasticity from your own sales data​

You do not need an economics degree — you need two price points and honest records. The simplest approach is a before-and-after price test:

1. Pick one product and hold everything else steady. No simultaneous promotions, packaging changes, or seasonality shifts if you can avoid them. The formula assumes only the price moved.
2. Record units sold per day or week at the old price for a long enough window to average out noise — at least two to four weeks for most small businesses.
3. Change the price once, by a meaningful amount. Five to fifteen percent is the usual range: large enough to produce a measurable response, small enough to reverse cheaply.
4. Record units at the new price over a comparable window, then apply the midpoint formula to the two averages.
5. Sanity-check the result. An elasticity above 5 or below 0.1 from a short test usually means something else moved — a competitor's sale, a holiday, a stockout — not that you discovered extreme sensitivity.

Keep a log of every test: product, dates, old and new price, average units, computed elasticity, and anything unusual during the window. A year of these entries is a pricing playbook no competitor can copy, because it is measured on your customers, not a textbook average.

For businesses with steady sales history but no deliberate tests, past involuntary price changes work too — a supplier cost increase you passed through, a marketplace fee change, a discount you ended. The math does not care why the price moved, only that you know the quantities on both sides.

Where your bookkeeping earns its keep​

Every elasticity estimate stands or falls on the quality of your quantity and revenue records. If your books lump all sales into one revenue account, you cannot reconstruct units per product per week — and without that, no formula can help you. The fix is to record sales with product-level detail from the start.

In a plain-text ledger, that means separate income accounts per product line rather than one undifferentiated sales account:

2026-09-01 * "Weekly sales - house latte" "POS summary week 35"
  Assets:Checking                          2800.00 USD
  Income:Sales:Lattes                     -2800.00 USD
 
2026-09-01 * "Weekly sales - cold brew" "POS summary week 35"
  Assets:Checking                          1470.00 USD
  Income:Sales:Cold-Brew                  -1470.00 USD

With quantities tracked alongside — as Beancount metadata, a linked spreadsheet, or your point-of-sale export — each price change becomes a measurable experiment: revenue per product comes straight from the ledger, units come from the POS, and the midpoint formula turns the pair into an elasticity. The Beancount documentation covers balance and transaction queries if you want to pull product-level revenue programmatically instead of by hand.

The habit compounds. Businesses that track revenue by product can also see which lines subsidize which, when a "best seller" is actually a margin loser, and whether a price increase lifted revenue or just moved units to a cheaper sibling product. Elasticity analysis is one payoff; cleaner decisions everywhere else are the rest.

Mistakes that produce a wrong number​

Four errors account for most bad elasticity estimates:

• Confusing slope with elasticity. On a straight-line demand curve, the slope is constant but elasticity is not — demand is elastic at high prices and inelastic at low prices along the same line. An estimate is only valid near the prices you measured.
• Letting other things move. A price increase during your busy season, or alongside a competitor's stockout, will understate elasticity. If you cannot isolate the price change, note the confound in your log and discount the result.
• Measuring list price instead of realized price. If discounts, coupons, and free shipping absorb half your increase, customers responded to the realized price, not the sticker. Compute average realized price (revenue divided by units) and use that as P.
• Treating one estimate as permanent. Competitors enter, substitutes appear, and your own brand equity shifts. Re-test your most important products at least yearly, and re-test immediately after any market shock.

Your next step​

Pick your highest-revenue product, pull its weekly units and realized prices for the last two months, and check whether any price change already happened in that window — most businesses will find one they never measured. Run the midpoint formula on it this week. Whatever number comes out, log it with its dates and context: you have just replaced your most consequential pricing guess with a measurement, and every future price decision on that product starts from evidence instead of instinct.