Total Revenue Test vs Marginal Revenue and Elasticity
Total Revenue Test and Marginal Revenue and Elasticity are two Elasticity concepts in AP Economics that students often mix up. The total revenue test uses how total revenue responds to a price change to tell whether demand is elastic or inelastic. Marginal revenue is positive when demand is elastic, zero at unit elasticity, and negative when demand is inelastic, so a price-maker never sells in the inelastic range. Here is how they compare side by side.
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.
Cutting price raises quantity but lowers revenue on existing units; which effect wins depends on elasticity. Where demand is elastic, the quantity gain dominates, so MR is positive and total revenue rises as price falls. At unit elasticity, MR equals zero and total revenue peaks. Where demand is inelastic, MR is negative. Because a monopolist would never operate where extra output reduces revenue, it always produces on the elastic portion of its demand curve.
Total Revenue Test vs Marginal Revenue: The Level and the Step
| Total Revenue Test | Marginal Revenue and Elasticity | |
|---|---|---|
| What you inspect | Whether total takings rose or fell after a price change | What the next unit sold adds to total takings |
| Reading for elastic demand | Revenue moves opposite to the price | Marginal revenue is positive |
| Reading for unit elastic demand | Revenue does not move | Marginal revenue is zero |
| Reading for inelastic demand | Revenue moves with the price | Marginal revenue is negative |
| Data required | Two price and quantity pairs | A full demand schedule, unit by unit |
| What it is used for | Classifying a stretch of demand quickly | Finding the profit maximising output, where marginal revenue meets marginal cost |
| What it says about a price maker | Nothing directly | It will never operate where demand is inelastic |
One schedule shows the total peaking exactly where the step crosses zero
Take a price maker facing demand where the price equals 12 minus the quantity sold, in illustrative dollars. Selling 4 units means a price of $8 and revenue of $32. Selling 5 means $7 and $35, so the fifth unit added $3. Selling 6 means $6 and $36, so the sixth added $1. Selling 7 means $5 and $35, so the seventh subtracted $1. Total revenue climbs, flattens at 6 units and then falls, while marginal revenue slides from $3 to $1 to negative $1 and crosses zero at the same place. Check the elasticity with the midpoint method and everything lines up. Between $8 and $7, quantity changes by 1 over the average of 4.5, which is 22.22 percent, while price changes by 1 over the average of 7.5, which is 13.33 percent, giving about 1.67 and marking that stretch elastic. Between $6 and $5, quantity changes by 1 over the average of 6.5, which is 15.38 percent, against a price change of 1 over 5.5, which is 18.18 percent, giving about 0.85 and marking that stretch inelastic. Elastic goes with rising revenue and positive marginal revenue, inelastic with falling revenue and negative marginal revenue.
Negative marginal revenue is why a price maker stays out of the inelastic stretch
Selling one more unit does two things at once. It brings in the price of that unit, and it forces the price down on every unit that was already being sold. When demand is inelastic the second effect dominates, so the extra sale actually reduces takings. Any firm doing that is paying production costs to earn less money, which no positive marginal cost can justify. Put marginal cost at $3 a unit in the schedule above. The fifth unit adds $3 of revenue and $3 of cost, so output stops there, at a price of $7. Revenue is $35, total cost is $15, and profit is $20. That output sits in the elastic stretch, and it always will, because marginal cost cannot be negative and the profit maximising rule sets marginal revenue equal to it. Push on to 7 units and revenue is no higher, still $35, while costs climb to $21 and profit drops to $14. This is the standard reason a monopolist is drawn producing on the upper half of its demand curve, which is worked through at /micro/monopoly. Practise the calculation at /calculate/marginal-revenue.
Frequently asked questions
What is the difference between the total revenue test and marginal revenue?
The total revenue test compares total takings before and after a price change to classify demand as elastic, inelastic or unit elastic, while marginal revenue measures what one extra unit adds to those takings. One looks at a level and the other at a step. They give the same verdict, since revenue can only rise while the next unit is still adding something.
Why is marginal revenue negative when demand is inelastic?
Because selling another unit requires cutting the price on every unit already being sold, and when demand is inelastic the quantity gained is too small to cover that loss. The revenue lost on existing sales outweighs the revenue gained on the new sale. Marginal revenue is therefore below zero even though the price itself is still positive.
Why does a monopoly never produce where demand is inelastic?
Because marginal revenue is negative there while marginal cost is positive, so cutting output would raise revenue and lower cost at the same time. A firm can always improve its profit by moving back into the elastic stretch. Profit maximisation sets marginal revenue equal to marginal cost, and that can only happen where marginal revenue is positive.
Live Elasticity graph. Drag the curves, or open the full version.
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