Lesson preview · Price elasticity of demand
Elasticity and total revenue
~7 min · Free to read
Imagine a small town with one cinema and one bakery. Nowhere else in town sells bread. Both cut their prices by 20%.
| Sales per day | Before the cut | After the cut |
|---|---|---|
| Cinema | 300 tickets at 10 dollars | 450 tickets at 8 dollars |
| Bakery | 500 loaves at 2 dollars | 525 loaves at 1.60 dollars |
The cinema’s takings rise from 3,000 to 3,600 dollars a day. The bakery’s takings fall from 1,000 to 840 dollars. Same cut, opposite results.
The money a seller takes in from a good is its total revenue (TR): the price (P) times the quantity sold (Q), or . Leaving taxes aside, it is also what buyers spend on the good.
A price cut pulls total revenue two ways at once:
- Each item sells for less, which lowers revenue.
- More items sell, which raises it.
Which pull wins depends on the price elasticity of demand (PED): the percentage change in quantity demanded divided by the percentage change in price.
Key Term
The total revenue test
The total revenue test tells you which way revenue moves when the price changes. Judge PED by its size, ignoring the minus sign.
- Elastic (bigger than 1): sales change by a bigger percentage than the price. Price and total revenue move in opposite directions. The cinema sold 50% more tickets (300 to 450), so its PED is +50% ÷ −20% = −2.5.
- Inelastic (smaller than 1): sales change by a smaller percentage than the price. Price and total revenue move together. The bakery sold 5% more loaves (500 to 525), so its PED is +5% ÷ −20% = −0.25.
- Unit elastic (exactly −1): the two pulls cancel out, and revenue stays about the same.
For small price changes, the test is almost exact. For big ones, it is exact only if you measure each percentage change from the midpoint: the average of the old and new values.
So elasticity decides which way revenue moves. Where demand is elastic, a lower price means buyers spend more in total. Where it is inelastic, they spend less. Revenue is highest where PED is exactly −1.
Trap · Common Misconception
"A higher price always brings in more money"
In the widget, raising the price from 13 to 15 dollars cuts revenue from 91 to 75 dollars. A higher price brings in more money only when demand is inelastic. When demand is elastic, for example because buyers have good substitutes, a price rise drives so many away that revenue falls.
Trap · Common Misconception
"More revenue means more profit"
Profit is total revenue minus costs. A price cut can raise revenue and still lower profit, because selling extra items can add to costs.
The cinema’s 150 extra viewers cost it little: the seats were empty anyway. A pizza shop that sells 150 more pizzas pays for more dough, cheese and staff hours. If its costs rise by more than its revenue, profit falls.
Why governments tax cigarettes. Many governments put extra taxes, often called sin taxes, on cigarettes and alcohol, partly to raise money. Demand for cigarettes is inelastic: nicotine is addictive, and there are few close substitutes apart from vapes and other tobacco.
In 2011, the World Health Organization’s cancer agency reviewed the research. Most estimates of the PED for cigarettes in rich countries fall between about −0.2 and −0.6, with an average of about −0.4. So if a tax pushes the price up 10%, smokers at first buy only about 4% less. Evidence: robust. Studies using different data and methods mostly agree.
Now imagine a tax that pushes up the price of one brand of crisps by 10%. Buyers can switch brands, so suppose its PED is −3: sales fall about 30%. For every 100 packs sold before the tax, smokers still buy 96 and pay the tax on each. Crisp buyers pay it on only 70 bags in 100. The same review found that raising tobacco taxes does bring in more tax money, and gave this finding its strongest rating.
Trap · Warning
The catch
A cigarette tax brings in steady money because most smokers keep buying. So raising money and cutting smoking pull against each other: at first, a 10% higher price cuts cigarette sales by only about 4%. Over the years the fall grows, because demand becomes more elastic with time.
Check yourself · no marks
A museum raises its entry price from 15 to 18 dollars, and its weekly ticket revenue falls. Is demand for visits elastic or inelastic?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 6
Demand for a food truck’s tacos is elastic. The owner lowers the price of a taco. What happens to the truck’s total revenue from tacos?
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