Price elasticity of demand
Key terms
Define each term.
Multiple choice
Circle the correct answer.
A 10% fall in the price of a good causes quantity demanded to rise by 25%. What is the PED?
Worked problems
Show your working.
Calculating PED. A café raises the price of a coffee from 10 to 12 riyals. Weekly sales fall from 500 cups to 400. Calculate PED.
Whether a price change raises revenue. A cinema cuts its ticket price from $8 to $6 and weekly attendance rises from 1,000 to 1,500. A bus company raises its fare from $2.00 to $2.50 and weekly passengers fall from 10,000 to 9,000. For each, calculate PED and the change in revenue.
Diagrams
Sketch two demand curves through the same point, one elastic and one inelastic, and show how the same price rise affects quantity differently on each.
Draw two demand curves, one steep (inelastic) and one flat (elastic). On each, show the same price rise and shade the revenue gained from the higher price on units still sold and the revenue lost from units no longer sold.
Answers
Price elasticity of demand: A measure of the responsiveness of quantity demanded to a change in price.
B. 25 ÷ 10 = 2.5, and the sign is negative because price and quantity moved in opposite directions. Demand is elastic.
Percentage change in price (12 − 10) ÷ 10 × 100 = +20%
Percentage change in quantity demanded (400 − 500) ÷ 500 × 100 = −20%
Apply the formula PED = −20 ÷ 20 = −1
Interpret A coefficient of −1 means demand is unit elastic. The percentage fall in quantity exactly matches the percentage rise in price.
Step 1. The cinema's PED. Price change = (6 - 8) / 8 x 100 = -25%. Quantity change = (1,500 - 1,000) / 1,000 x 100 = +50%. PED = 50 / -25 = -2. Demand is elastic.
Step 2. The cinema's revenue. Before: $8 x 1,000 = $8,000. After: $6 x 1,500 = $9,000. Revenue rises by $1,000, as expected when price is cut and demand is elastic.
Step 3. The bus company's PED. Price change = (2.50 - 2.00) / 2.00 x 100 = +25%. Quantity change = (9,000 - 10,000) / 10,000 x 100 = -10%. PED = -10 / 25 = -0.4. Demand is inelastic.
Step 4. The bus company's revenue. Before: $2.00 x 10,000 = $20,000. After: $2.50 x 9,000 = $22,500. Revenue rises by $2,500, as expected when price is raised and demand is inelastic.
Step 5. The general rule. To raise revenue, cut the price if demand is elastic and raise it if demand is inelastic. Both firms raised revenue, in opposite ways, because their demand had different elasticities.
Always show the revenue before and after as well as the PED. Questions on revenue usually give a mark for the calculation and another for linking the result to elasticity.
A steeper curve indicates more inelastic demand over that range. Label both axes and mark the quantity change on each.
Revenue rises when the gained rectangle is bigger than the lost one. On the inelastic curve it is; on the elastic curve it is not. The two rectangles are the whole argument in one picture.