Section 4

Worked Example and Exam Traps

Take a single price change — a $+25\%$ rise — and apply it to two goods: gasoline and restaurant burgers. The price move is identical. The revenue outcome is opposite. That contrast is not a coincidence; it is the entire concept of elasticity made visible.

Case 1: Gasoline (inelastic)

Both goods start at $P = \$ 4 $and$ Q = 100 $units, giving the same baseline total revenue of$ $400 $. For gasoline, the price rises from$ $4 $to$ $5$.

\%\,\Delta P = \frac{5 - 4}{4} \times 100 = +25\%

Because drivers have few short-run alternatives, quantity demanded falls only slightly — from 100 gallons to 95 gallons.

\%\,\Delta Q_d = \frac{95 - 100}{100} \times 100 = -5\%

The PED magnitude is the ratio of the two percentage changes. A 5% quantity drop in response to a 25% price rise gives a ratio well below 1 — the definition of inelastic demand.

|PED| = \frac{5\%}{25\%} = 0.2 < 1 \quad \text{(inelastic)}

Total revenue moves with the price rise: $100 \times \$ 4 = $400 $before,$ 95 \times $5 = $475$ after. Revenue went up when price rose. That upward movement in revenue is the inelastic signature.

TR: \quad 100 \times \$4 = \$400 \;\longrightarrow\; 95 \times \$5 = \$475 \quad (\text{revenue up})

Case 2: Restaurant burgers (elastic)

Now apply the same $+25\%$ price change to restaurant burgers, starting from the same $P = \$ 4 $,$ Q = 100$ baseline.

\%\,\Delta P = \frac{5 - 4}{4} \times 100 = +25\%

Burgers have many substitutes — other restaurants, home cooking, different fast-food options. A 25% price rise drives quantity demanded down sharply, from 100 burgers to 60 burgers.

\%\,\Delta Q_d = \frac{60 - 100}{100} \times 100 = -40\%

The PED magnitude is now greater than 1: the quantity response is proportionally larger than the price change, which is what elastic means.

|PED| = \frac{40\%}{25\%} = 1.6 > 1 \quad \text{(elastic)}

Total revenue falls: $100 \times \$ 4 = $400 $before,$ 60 \times $5 = $300$ after. Revenue went down when price rose. That is the elastic signature — the quantity loss more than offsets the higher price per unit.

TR: \quad 100 \times \$4 = \$400 \;\longrightarrow\; 60 \times \$5 = \$300 \quad (\text{revenue down})

Side-by-side summary

	Gasoline (inelastic)	Burgers (elastic)
Price change	$\$ 4 \to $5$ (+25%)	$\$ 4 \to $5$ (+25%)
Quantity change	$100 \to 95$ gallons ( $-5\%$ )	$100 \to 60$ burgers ( $-40\%$ )
$\|PED\|$	$0.2$	$1.6$
Verdict	Inelastic ( $\|PED\| < 1$ )	Elastic ( $\|PED\| > 1$ )
Total revenue before	$\$ 400$	$\$ 400$
Total revenue after	$\$ 475$	$\$ 300$
Revenue direction	Up (price rise + inelastic = more revenue)	Down (price rise + elastic = less revenue)

These calculations use the simple percentage method — dividing the change by the original value. Exam boards (particularly AP and IB) sometimes require the midpoint method, which divides by the average of the two values instead; the elastic/inelastic labels come out the same for these numbers. See the price elasticity of demand glossary page for the midpoint formula.

Common exam mistakes

Confusing slope with elasticity. A steeper demand curve is not automatically more inelastic. On a single straight-line demand curve,

|PED|

runs from elastic at the top (high price, low quantity) through unit elastic at the midpoint down to inelastic at the bottom (low price, high quantity) — the slope is constant throughout. Flipping the total-revenue test. A common wrong answer reads: 'demand is elastic, so raise the price to earn more revenue.' This is backwards. When demand is elastic, a price rise cuts total revenue because the quantity loss outweighs the higher price per unit. Dividing the raw change instead of the percentage change. PED is

\%\Delta Q_d \div \%\Delta P

, not

\Delta Q \div \Delta P

. Using the raw numbers gives a result that depends on the units chosen (gallons vs. litres, dollars vs. cents) and is not a meaningful elasticity. This error costs points on AP free-response questions. Forgetting the absolute value. PED is always negative because price and quantity move in opposite directions. You must compare

|PED|

— the magnitude — to 1, not the signed number. Reporting

PED = -1.6

and then writing '

-1.6 < 1

, therefore inelastic' is a sign error that will lose the mark.

To see the total-revenue effect in motion, open the supply and demand model and drag the demand curve — watch how the revenue rectangle changes shape as the curve steepens or flattens. For the complete definition, derivation, and determinants of elasticity, visit the price elasticity of demand glossary page.