Price Elasticity of Demand: Study Guide (Microeconomics 2.3)

What elasticity measures

The law of demand tells you the direction of a response: when the price of a good rises, people buy less of it. It does not tell you how much less. A 10% rise in the price of salt and a 10% rise in the price of one brand of trainers both cut the quantity demanded, but by very different amounts.

Elasticity measures the size of a response in percentage terms. Economists measure how the quantity demanded responds to a change in a good’s own price, to income, or to the prices of related goods. This topic covers the first of these. Topic 2.5 covers the others.

Price elasticity of demand (PED) measures how responsive the quantity demanded is to a change in the good’s own price:

PED = (percentage change in quantity demanded) ÷ (percentage change in price)

Because price and quantity demanded move in opposite directions, PED is negative. Economists usually quote its magnitude (its size without the sign), written |PED|. A PED of −2.5 and a |PED| of 2.5 say the same thing.

We use percentages, not raw changes, for two reasons. First, percentages have no units, so you can compare goods measured in kilograms, litres or tickets. Second, a $1 rise means a lot for a $2 bus fare and almost nothing for a $2,000 laptop.

Elastic, inelastic and unit elastic

The benchmark is a magnitude of 1, where the percentage change in quantity demanded is exactly as large as the percentage change in price.

Value	Description	Meaning
|PED| > 1	elastic	quantity demanded changes by a larger percentage than price
|PED| < 1	inelastic	quantity demanded changes by a smaller percentage than price
|PED| = 1	unit elastic	the two percentage changes are the same size
|PED| = 0	perfectly inelastic	quantity demanded does not change at all
|PED| infinite	perfectly elastic	any rise above one price makes quantity demanded fall to zero

A classification is always for a price range. The same demand curve can be elastic at high prices and inelastic at low ones, as you will see below.

Real goods lie between these extremes. The extremes are still useful limits: a good with no substitutes at all is close to the left graph, and one seller’s identical product in a market with many identical sellers is close to the right one.

The midpoint method

Suppose a price rises from $4 to $6. Measured from $4, that is a 50% rise. If the price falls from $6 back to $4, measured from $6, it is a 33% fall. The same change gives two different percentages, so it would give two different elasticities.

The midpoint method fixes this by dividing each change by the average of the two values:

• % change in Q = (Q₂ − Q₁) ÷ [(Q₁ + Q₂) ÷ 2] × 100
• % change in P = (P₂ − P₁) ÷ [(P₁ + P₂) ÷ 2] × 100
• PED = % change in Q ÷ % change in P

With the midpoint method you get the same answer whichever direction the price moves. The most common error on exams is to divide the change in quantity by the change in price. That gives the slope-type ratio, not the elasticity. Always convert both changes to percentages first.

If a question gives you the percentage changes directly (“price rises by 10% and quantity falls by 4%”), you do not need the midpoint method: PED = 4 ÷ 10 = 0.4.

Slope is not elasticity

Brightwater Aquarium is a fictional visitor attraction. Its daily demand for tickets is a straight line:

Price ($ per ticket)	2	4	6	8	10	12	14	16	18
Quantity (tickets per day)	180	160	140	120	100	80	60	40	20
Total revenue ($ per day)	360	640	840	960	1,000	960	840	640	360

Every $2 rise in price cuts quantity by 20 tickets. The slope is the same everywhere. But the percentage changes are not. At low prices, a $2 rise is a large percentage of the price and 20 tickets is a small percentage of a large quantity. At high prices, it is the other way round.

On any straight-line demand curve that meets both axes:

• demand is elastic above the midpoint (high price, small quantity);
• unit elastic at the midpoint, here $10 and 100 tickets;
• inelastic below the midpoint (low price, large quantity).

So you cannot judge elasticity just by how steep a curve looks. A steeper curve is less elastic than a flatter one only when you compare them at the same point (same price and quantity) on the same axes.

Elasticity and total revenue

Total revenue (TR) is what sellers receive: TR = price × quantity. It is also the total expenditure of buyers on the good. A price change pulls TR in two directions: each unit sold earns more (or less), but fewer (or more) units are sold. Elasticity tells you which effect wins.

Demand in the range	Price rises	Price falls
Elastic (|PED| > 1)	TR falls	TR rises
Inelastic (|PED| < 1)	TR rises	TR falls
Unit elastic (|PED| = 1)	TR unchanged	TR unchanged

This is the total revenue test. A short way to remember it: with inelastic demand, price and TR move in the same direction; with elastic demand, they move in opposite directions.

The test also works backwards. If a firm cuts its price and its total revenue falls, demand must have been inelastic over that range. With the midpoint method, the link is exact: |PED| is exactly 1 when TR does not change between the two prices.

What makes demand more or less elastic

The most important factor is the availability of close substitutes. Here are the main ones:

Factor	More elastic when…	Example
Substitutes	there are many close substitutes	one brand of orange juice (other brands are easy to switch to)
Necessity or luxury	the good is a luxury rather than a necessity	holiday cruises compared with basic medicines
Share of income	the good takes a large share of the buyer’s budget	a new car compared with a box of matches
Time to adjust	buyers have longer to find alternatives	electricity over five years compared with over one week
How the market is defined	the market is narrowly defined	“Brand X bread” compared with “food”

Notice how many of these come back to substitutes. A narrow market has more substitutes than a broad one, and over time people discover or create substitutes.

Worked example 1: same slope, different elasticity

Question. Use the Brightwater table. (a) Calculate PED when the price rises from $4 to $6 (point A to point B). (b) Calculate PED when the price rises from $14 to $16 (point G to point H). (c) Classify each range and use the total revenue test to predict what happens to TR. Check with the table.

(a) From A ($4, 160 tickets) to B ($6, 140 tickets):

1. Change in Q = 140 − 160 = −20. Average Q = (160 + 140) ÷ 2 = 150. % change in Q = −20 ÷ 150 × 100 = −13.33%.
2. Change in P = 6 − 4 = 2. Average P = (4 + 6) ÷ 2 = 5. % change in P = 2 ÷ 5 × 100 = 40%.
3. PED = −13.33 ÷ 40 = −0.33, so |PED| = 0.33.

(b) From G ($14, 60 tickets) to H ($16, 40 tickets):

1. Change in Q = −20. Average Q = (60 + 40) ÷ 2 = 50. % change in Q = −20 ÷ 50 × 100 = −40%.
2. Change in P = 2. Average P = 15. % change in P = 2 ÷ 15 × 100 = 13.33%.
3. PED = −40 ÷ 13.33 = −3.0, so |PED| = 3.

(c) From $4 to $6, |PED| = 0.33 < 1: inelastic. A price rise should raise TR. Check: TR goes from 4 × 160 = $640 to 6 × 140 = $840, up $200.

From $14 to $16, |PED| = 3 > 1: elastic. A price rise should lower TR. Check: TR goes from 14 × 60 = $840 to 16 × 40 = $640, down $200.

Interpretation. Both moves are a $2 rise that loses 20 visitors, so the slope is identical. The elasticities differ by a factor of 9 because the percentages differ. That is why slope is not elasticity.

Worked example 2: working from percentages

Question. Tavira Mobile, a fictional phone company, has 2,000 subscribers on its $20 per month data plan. It cuts the price by 15% and the number of subscribers rises by 24%. (a) Calculate PED and classify demand. (b) Find total revenue before and after, and check it against the total revenue test. (c) Suppose instead that |PED| had been 0.5. By what percentage would subscribers have risen, and what would have happened to TR?

(a) The percentages are given, so no midpoint step is needed. PED = 24 ÷ (−15) = −1.6. |PED| = 1.6 > 1, so demand is elastic.

(b)

1. Before: TR = $20 × 2,000 = $40,000 per month.
2. New price = $20 × 0.85 = $17. New subscribers = 2,000 × 1.24 = 2,480.
3. After: TR = $17 × 2,480 = $42,160 per month, a rise of 5.4%.

Demand is elastic and the price fell, so the test predicts TR rises. It does.

(c) % change in Q = |PED| × % change in P = 0.5 × 15 = 7.5%. Subscribers = 2,000 × 1.075 = 2,150. TR = $17 × 2,150 = $36,550, a fall of $3,450 (about 8.6%). With inelastic demand, the price cut lowers TR.

Check. You can rearrange the formula: % change in Q = |PED| × % change in P. This lets you predict a response before it happens, which is how firms and governments use elasticity.

Common misconceptions

• “Elasticity is the slope of the demand curve.” Slope uses raw changes; elasticity uses percentage changes. Along a straight line, slope is constant but elasticity is not.
• “PED = change in quantity ÷ change in price.” This misses the percentage step. Convert both changes to percentages first.
• “A steep curve is always inelastic.” Steepness depends on the scale of the axes, and elasticity changes along a straight line. Compare curves only at a common point.
• “Inelastic demand means quantity does not change.” That is perfectly inelastic demand (|PED| = 0). Inelastic only means quantity changes by a smaller percentage than price.
• “A price rise always raises revenue.” Only when demand is inelastic. With elastic demand, a price rise lowers total revenue.
• “An elasticity of −2 is less than an elasticity of −0.5.” Compare magnitudes: |−2| = 2 is more elastic than |−0.5| = 0.5.
• “Elasticity is one number for a whole good.” It is measured for a price range and can be different in another range.

Where this leads

Next, Topic 2.4 applies the same percentage idea to sellers: the price elasticity of supply. Topic 2.5 then measures responses to income and to the prices of related goods, and later topics use elasticity to explain who bears a tax. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate. If the demand curve itself feels shaky, look back at the previous topic, supply, and at Topic 2.1 on demand.