Midpoint Method vs Total Revenue Test
Midpoint Method and Total Revenue Test are two Elasticity concepts in AP Economics that students often mix up. The midpoint method calculates elasticity using the average of the two prices and quantities, so it gives the same value in either direction. The total revenue test uses how total revenue responds to a price change to tell whether demand is elastic or inelastic. Here is how they compare side by side.
It fixes the problem that ordinary percentage changes differ depending on the starting point. The change is divided by the midpoint (average) of the start and end values. The College Board uses it for AP elasticity calculations.
If cutting price raises total revenue, demand is elastic; if cutting price lowers total revenue, demand is inelastic. If total revenue is unchanged, demand is unit elastic. When demand is elastic, price and total revenue move in opposite directions.
Midpoint Method vs Total Revenue Test: One Gives a Number, One Gives a Verdict
| Midpoint Method | Total Revenue Test | |
|---|---|---|
| What you end up with | An elasticity coefficient, such as 1.75 | A category: elastic, inelastic or unit elastic |
| Data you need | Both prices and both quantities | Which way the price moved and which way revenue moved |
| Precision | The exact magnitude of the response | Only which side of 1 the answer falls on |
| How it is written | Change in quantity over average quantity, divided by change in price over average price | Compare price times quantity before and after |
| Effort involved | Several steps and a calculator | One comparison you can do in your head |
| Best used when | The question asks you to calculate or to compare two goods | The question asks what happens to a firm's revenue |
| Where it goes wrong | Nowhere, though the averages must be recalculated for each pair of points | Near unit elasticity, where revenue barely moves and the verdict looks ambiguous |
On the same data the two tools agree, and one of them shows its working
Suppose a cinema drops its ticket price from an illustrative $8 to $6 and weekday attendance rises from 30 to 50. The midpoint method takes the change in quantity, 20, over the average quantity, 40, which is 50 percent. It takes the change in price, 2, over the average price, 7, which is 28.57 percent. Dividing 50 by 28.57 gives 1.75, so demand over that stretch is elastic. The total revenue test needs far less. Revenue was 8 times 30, or $240, and is now 6 times 50, or $300. Revenue rose while price fell, so demand is elastic. Same conclusion, one step. The reason the shortcut works is arithmetic rather than a separate theory: revenue is price multiplied by quantity, so whichever percentage change is larger decides the direction of the product. When quantity moves more than price, quantity wins and revenue follows quantity. The averages in the midpoint formula exist for a different purpose, which is to make the answer identical whether the cinema cut its price or raised it back. Both routes are worked at /calculate/midpoint-method and /calculate/total-revenue-test.
The revenue test cannot answer a question that asks how much
Take a straight line demand curve where quantity equals 100 minus 10 times the price. At $5 the cinema sells 50 seats for $250. At $4 it sells 60 seats for $240, and at $6 it sells 40 seats for $240. Revenue moves by 10 either way, so the test reports only that $5 sits close to the peak. The midpoint method is far more informative on identical data. Between $5 and $4 quantity changes 10 over an average of 55, or 18.18 percent, while price changes 1 over an average of 4.50, or 22.22 percent, giving 0.82. Between $5 and $6 the same arithmetic gives 1.22. Below $5 demand is inelastic and above it demand is elastic, and elasticity is a different number at every point on a straight line. That last fact is what the revenue test hides. It also cannot be used at all when no price change has happened, when you need to compare the responsiveness of two different goods, or when a question supplies elasticity and asks you to predict the quantity change. Reach for the shortcut when the question is about revenue, and for the formula whenever a number is required.
Frequently asked questions
What is the difference between the midpoint method and the total revenue test?
The midpoint method calculates a numerical elasticity coefficient from two prices and two quantities, while the total revenue test simply reads the direction total revenue moved after a price change to classify demand as elastic, inelastic or unit elastic. One measures, the other classifies. Use the midpoint method when a question asks for a value and the revenue test when it asks about a firm's takings.
Why does the midpoint method give the same answer in both directions?
It divides each change by the average of the starting and ending values rather than by the starting value, and that average is identical whichever end you begin from. Using the starting value instead makes a price rise and the matching price cut produce different coefficients. This is the whole reason the midpoint version exists.
If total revenue does not change when the price changes, what is the elasticity?
Demand is unit elastic over that stretch, meaning the coefficient equals 1 in absolute value. The percentage fall in quantity exactly offsets the percentage rise in price, so price times quantity lands on the same figure. On a straight line demand curve this happens only at the midpoint.
Live Elasticity graph. Drag the curves, or open the full version.
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