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?
A good has an income elasticity of demand of -0.6. If incomes rise by 5%, what happens to quantity demanded?
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.
Revenue effect of a price rise. Return to the café. Did raising the price from 10 to 12 riyals increase revenue?
Calculating and classifying YED and XED. Average household income rises from $40,000 to $44,000. Over the same period, weekly sales of good A rise from 200 to 230, of good B from 500 to 520, and of good C fall from 300 to 270. Separately, the price of coffee rises by 20%, after which demand for tea rises by 10% and demand for sugar falls by 6%. Calculate YED for A, B and C and XED for tea and sugar, and classify each.
Chains of reasoning
The steps are in the wrong order. Write the letters in the order that makes a linked chain.
Why a price cut can raise revenue
- A The quantity gain outweighs the price loss.
- B If PED is greater than 1, the percentage rise in quantity exceeds the percentage fall in price.
- C The reverse holds where PED is less than 1, so a firm facing inelastic demand raises revenue by raising price instead.
- D The lower price attracts buyers who were previously priced out and encourages existing buyers to purchase more.
- E Total revenue rises, since TR = P × Q and Q has grown proportionately more than P has fallen.
- F Quantity demanded therefore rises.
- G A firm lowers price, so revenue per unit sold falls.
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.
Draw a straight-line demand curve with the corresponding total revenue curve beneath it. Mark the elastic range, the unit elastic point and the inelastic range.
Answers
Price elasticity of demand: A measure of the responsiveness of quantity demanded to a change in price.
Income elasticity of demand (YED): A measure of the responsiveness of quantity demanded to a change in income.
Cross elasticity of demand (XED): A measure of the responsiveness of quantity demanded of one good to a change in the price of another good.
B. 25 ÷ 10 = 2.5, and the sign is negative because price and quantity moved in opposite directions. Demand is elastic.
B. % change in quantity = YED x % change in income = -0.6 x 5 = -3%. The negative YED makes it an inferior good, so a rise in income reduces demand for it.
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.
Revenue before 10 × 500 = 5,000 riyals
Revenue after 12 × 400 = 4,800 riyals
Conclusion Revenue fell by 200 riyals. With PED at exactly −1 the two effects should offset, but the arc method gives slightly different results depending on the direction of the change, which is why revenue moves a little rather than staying flat.
Step 1. Percentage change in income. (44,000 - 40,000) / 40,000 x 100 = +10%.
Step 2. YED for good A. Quantity change = (230 - 200) / 200 x 100 = +15%. YED = 15 / 10 = +1.5. Positive and above 1, so A is a luxury (income elastic normal good).
Step 3. YED for good B. Quantity change = (520 - 500) / 500 x 100 = +4%. YED = 4 / 10 = +0.4. Positive but below 1, so B is a necessity (income inelastic normal good).
Step 4. YED for good C. Quantity change = (270 - 300) / 300 x 100 = -10%. YED = -10 / 10 = -1.0. Negative, so C is an inferior good.
Step 5. XED of tea with respect to the price of coffee. XED = +10 / +20 = +0.5. Positive, so tea and coffee are substitutes: dearer coffee sends buyers to tea. At 0.5 they are fairly weak substitutes.
Step 6. XED of sugar with respect to the price of coffee. XED = -6 / +20 = -0.3. Negative, so sugar and coffee are complements: less coffee bought means less sugar to go in it.
Write the sign every time and use it in the classification. An answer that calculates 0.3 for sugar and calls it a substitute has lost both the calculation and the interpretation marks.
G, D, F, B, A, E, C
- A firm lowers price, so revenue per unit sold falls.
- The lower price attracts buyers who were previously priced out and encourages existing buyers to purchase more.
- Quantity demanded therefore rises.
- If PED is greater than 1, the percentage rise in quantity exceeds the percentage fall in price.
- The quantity gain outweighs the price loss.
- Total revenue rises, since TR = P × Q and Q has grown proportionately more than P has fallen.
- The reverse holds where PED is less than 1, so a firm facing inelastic demand raises revenue by raising price instead.
AO2 analysis is 40% of the marks. Examiners credit the linking between steps rather than the conclusion. Never jump from 'price fell' to 'revenue rose'.
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.
Total revenue peaks exactly where PED equals −1, at the midpoint of the demand curve. Line the two diagrams up vertically so the quantity axes match.