Price elasticity, income elasticity and cross elasticity of demand

Economics AS · The price system and the microeconomy. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Elasticity measures how strongly quantity demanded responds to a change in something else. All three measures have the percentage change in quantity demanded on top. PED uses the good's own price underneath, YED uses income, and XED uses the price of another good.

Read each answer in two parts. The sign tells you the type of relationship: YED is positive for normal goods and negative for inferior goods; XED is positive for substitutes and negative for complements. The size tells you the strength: above 1 is elastic, below 1 is inelastic (ignoring the sign).

PED also decides what happens to total spending when price changes, which is why firms and governments use it.

Rules to remember

PED = % change in quantity demanded ÷ % change in price. It is normally negative.
YED = % change in quantity demanded ÷ % change in income. Positive: normal good (above 1 luxury, between 0 and 1 necessity). Negative: inferior good.
XED = % change in quantity demanded of X ÷ % change in price of Y. Positive: substitutes. Negative: complements. Zero: unrelated.
PED size (ignore the sign): 0 perfectly inelastic (vertical curve); 0 to 1 inelastic; 1 unitary; above 1 elastic; infinity perfectly elastic (horizontal curve).
Straight-line demand curve: elastic above the midpoint, unitary at the midpoint, inelastic below it.
Elastic demand: price and total revenue move in opposite directions. Inelastic: they move in the same direction. Unitary: revenue does not change.
Demand is more price elastic with more close substitutes, a larger share of income, a longer time period, and when the good is a luxury rather than a necessity or habit.

Common mistake

Students put the percentage change in price on top, or use the change in units instead of the percentage change. Quantity is always on top, and both changes must be percentages of the original values.

Worked example

A shop cuts the price of a jacket from $50 to $45. Weekly sales rise from 200 to 250. Find the PED, using the original values as the base, and the change in weekly revenue.

% change in quantity = (50 ÷ 200) × 100 = +25%.
% change in price = (−5 ÷ 50) × 100 = −10%.
PED = +25 ÷ −10 = −2.5, so demand is elastic.
Revenue before = $50 × 200 = $10,000; after = $45 × 250 = $11,250.

Answer: PED = −2.5 (elastic); weekly revenue rises by $1,250.

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