IB DP Economics: Elasticity of demand

This guide follows the IB Diploma Programme Economics guide (first assessment 2022, published February 2020), the course examined from the 2022 session onwards. It covers sub-topic 2.5, Elasticity of demand. Price elasticity of demand (PED) and income elasticity of demand (YED) are SL and HL content. Material marked HL only applies to Higher Level students alone.

Use it with the revision notes and the practice questions. The course hub is IB DP Economics and the printable checklist tracks progress. For the demand and supply background, see demand, supply and equilibrium. If you want to find your weak spots first, try the free diagnostics.

What sub-topic 2.5 asks of you

Content	What you must be able to do	Level
Concept of elasticity	Explain responsiveness; draw relatively elastic and relatively inelastic demand	SL and HL
PED	Use the formula; describe the range of values; draw perfectly elastic, perfectly inelastic and unitary demand	SL and HL
PED along a straight line	Show PED changing along a downward-sloping straight demand curve	HL only
Determinants of PED	Explain substitutes, necessity, share of income, time	SL and HL
PED and total revenue	Draw and explain revenue changes after a price change	SL and HL
Importance of PED	Discuss its use in firms’ and governments’ decisions	SL and HL
Primary commodities	Explain why their PED is generally lower than for manufactures	HL only
YED	Use the formula; interpret sign and size; draw an Engel curve	SL and HL
Importance of YED	Firms, and changes in the sectoral structure of the economy	HL only

The guide lists calculations from data: PED, a change in price, a quantity demanded or total revenue, and YED, a change in income or a quantity demanded. “Calculate” means a numerical answer with the stages of working shown. The guide says calculators are not permitted in Paper 1, while a four function calculator or a GDC is allowed in Paper 2, so practise by hand and with a calculator.

The concept of elasticity

Elasticity measures how strongly one variable responds when another changes. Here the response is always the quantity demanded. It is a ratio of percentage changes, so it has no units.

Diagram: draw a relatively elastic demand curve flat and a relatively inelastic one steep, with price up the side and quantity demanded along the base. Apply the same price fall to both. The flatter curve shows a large rise in quantity and the steeper one a small rise. Steepness alone does not give PED, which also depends on where you are on the line.

Price elasticity of demand (PED)

PED = change in quantity demanded, in per cent
      -----------------------------------------
      change in price, in per cent

percentage change = (new - old) / old x 100

Demand slopes downwards, so the raw PED is negative. This page keeps the sign in the working and says “size” for the value ignoring the sign. Check which your teacher expects and state which you use.

Worked example one: a price rise (illustrative data)

In the fictional city of Corrick, a day pass for the buses costs 8 units. The operator raises the price to 10 and daily sales fall from 4,000 to 3,400 passes.

% change in price    = (10 - 8) / 8 x 100          = +25%
% change in quantity = (3,400 - 4,000) / 4,000 x 100 = -15%
PED = -15 / +25 = -0.6
Revenue before = 8 x 4,000  = 32,000
Revenue after  = 10 x 3,400 = 34,000

The size of PED is 0.6, so demand is price inelastic over this range. Revenue rose by 2,000.

Degrees of PED

Size of PED	Description	Meaning
0	Perfectly inelastic	No change in quantity whatever the price
Between 0 and 1	Relatively inelastic	Quantity moves proportionally less than price
Exactly 1	Unitary	Quantity moves proportionally the same as price
Between 1 and infinity	Relatively elastic	Quantity moves proportionally more than price
Infinity	Perfectly elastic	Any rise in price removes all demand

The theoretical range therefore runs from zero to infinity in size. The guide asks you to draw the three constant cases:

Perfectly inelastic     Perfectly elastic      Unitary PED
P |      |              P |                    P | \
  |      |                |________ D            |  \
  |      | D              |                      |   \  D
  +------ Q               +------------ Q        +------ Q
vertical line           horizontal line        rectangular hyperbola

A unitary demand curve is a curve along which price multiplied by quantity is constant, so total revenue is the same at every point. It is not a straight line.

HL only: PED changes along a straight demand curve

On a downward-sloping straight line the slope is constant but PED is not, because the same absolute change is a different percentage of price and of quantity at different points. Let demand be Q = 100 - 5P (a fictional market).

Price	Quantity	Total revenue	PED (percentage method)
14 to 16	30 to 20	420 to 320	-2.33
4 to 6	80 to 70	320 to 420	-0.25

Working for the first row: price rises from 14 to 16, +14.29%; quantity falls from 30 to 20, -33.33%; PED = -33.33 / 14.29 = -2.33. For the second: price rises from 4 to 6, +50%; quantity falls from 80 to 70, -12.5%; PED = -0.25.

The upper half of the line is price elastic, the midpoint is unitary (here at P = 10, Q = 50), and the lower half is price inelastic. At the vertical intercept demand is perfectly elastic in the limit and at the horizontal intercept it is perfectly inelastic in the limit. The midpoint, where PED is unitary, gives the largest total revenue; here it is 500.

Diagram (HL only): draw the straight line, mark the midpoint, and label the segment above it “elastic, size of PED above 1”, the midpoint “size of PED = 1” and the segment below “inelastic, size of PED below 1”.

Determinants of PED

1. Number and closeness of substitutes. More and closer substitutes mean a larger quantity response to a price rise, so demand is more elastic. A branded snack with many similar rivals is elastic; a lifesaving medicine with no rival is not.
2. Degree of necessity. Necessities such as basic food and fuel for essential travel are inelastic. Luxuries can be postponed, so demand is more elastic.
3. Proportion of income spent on the good. A tiny share of income (a box of matches) is hardly noticed when the price rises. A large share (a car) is scrutinised, so demand is more elastic.
4. Time. Over a short period consumers cannot change habits, find substitutes or replace equipment, so demand is more inelastic. Over a longer period it becomes more elastic.

These factors interact, so say which dominates in the case given.

PED and total revenue

Total revenue (TR) = price x quantity. A price change moves TR in a direction fixed by PED.

Demand is	Price rises	Price falls
Price elastic (size above 1)	Revenue falls	Revenue rises
Unitary (size equal to 1)	No change	No change
Price inelastic (size below 1)	Revenue rises	Revenue falls

Reason: a price rise gains revenue on units still sold and loses it on units no longer sold. If the quantity response is proportionally larger, the loss wins.

Worked example two: a price cut (illustrative data)

A cinema in the fictional town of Tarnby cuts its ticket price from 12 to 10 and weekly attendance rises from 600 to 780.

% change in price    = (10 - 12) / 12 x 100 = -16.67%
% change in quantity = (780 - 600) / 600 x 100 = +30%
PED = +30 / -16.67 = -1.8      (size 1.8: price elastic)
Revenue before = 12 x 600 = 7,200
Revenue after  = 10 x 780 = 7,800

Revenue rose by 600 because demand is elastic.

Diagram: draw a demand curve with price and quantity axes. Mark the original price P1 and quantity Q1, then draw the revenue rectangle with corners at the origin and the point (Q1, P1). Mark the lower price and larger quantity and draw the second rectangle. In the elastic case the second rectangle has the larger area; in the inelastic case it has the smaller area. Shade the area lost and the area gained. Do the same for a price rise to show the opposite result.

Rearranging the formula

To find a missing quantity, price or revenue, rearrange: percentage change in quantity = PED x percentage change in price. If PED is -0.4 and price rises 5%, quantity falls by 0.4 x 5 = 2%.

Why PED matters to firms and governments

Firms. PED guides pricing. A firm facing elastic demand may raise revenue by cutting price; one facing inelastic demand may raise revenue by raising price. Revenue is not profit, however: extra output raises costs, and a rival may match a price cut.

Governments. A tax on a good with inelastic demand brings in more, because buyers cut back only slightly. The same fact limits a tax meant to cut consumption of a harmful good, so other measures may be needed. Weigh the burden on households that spend a large share of income on the good.

The guide marks this as evaluation (AO3), so reach a conclusion and say what would change it, such as the time period or the accuracy of the PED estimate.

HL only: why PED is lower for primary commodities

Primary commodities (agricultural and mineral raw materials) generally have a lower PED than manufactured products. Typical reasons:

• Many primary goods are necessities or essential inputs with few substitutes in the short run. A manufactured good usually faces many close brand rivals.
• A primary good is often a small share of the cost of the final product, so a price change barely alters the buyer’s decision.
• Demand for a commodity is often derived from demand for the final good, so buyers cannot cut back much unless final demand falls.

State the contrast clearly and note that “generally” allows exceptions, such as a commodity with a close substitute.

Income elasticity of demand (YED)

YED = change in quantity demanded, in per cent
      ----------------------------------------
      change in income, in per cent

Worked example three (illustrative data)

Households in the fictional country of Wexmoor see income rise from 2,000 to 2,200 per month (+10%).

Good	Quantity change	Percentage	YED
Restaurant meals	20 to 26	+30%	+3.0
Rice	50 to 51	+2%	+0.2
Instant noodles	30 to 27	-10%	-1.0

Reading the sign and size

• Positive YED: normal goods. Demand rises with income.
• Negative YED: inferior goods. Demand falls as income rises, because consumers switch to something better.
• Between 0 and 1: income inelastic, typical of necessities. Quantity rises by a smaller percentage than income.
• Above 1: income elastic, typical of services and luxury goods. Quantity rises by a larger percentage than income.

Engel curve

An Engel curve shows how the quantity demanded of one good changes with income. Put income up the side and quantity demanded along the base (label the axes, because some books swap them). For an income elastic good the curve is flatter than a straight line from the origin to the same point, since quantity rises faster than income. An income inelastic normal good is steeper than that line. An inferior good slopes backwards, bending back towards the vertical axis as income rises.

HL only: why YED matters

For firms. A firm selling income elastic goods expects sales to rise faster than incomes in a boom and fall faster in a recession; a seller of necessities has steadier sales. Firms use YED to forecast demand and to shift towards higher-YED products as incomes rise.

Sectoral structure. As incomes grow, demand for agricultural goods (low YED) grows more slowly than income, manufactured goods roughly in line or faster, and services (high YED) fastest. This helps explain why the share of agriculture in output tends to fall and the share of services tends to rise as an economy develops.

Common errors

• Putting the price change on top of the fraction instead of the quantity change.
• Taking the percentage of the new value instead of the starting value.
• Calling a steep straight line inelastic everywhere (HL: PED varies along it).
• Claiming a price rise always raises revenue, without checking PED.
• Treating revenue as profit.
• Drawing a unitary demand curve as a straight line.

Official syllabus

IB Diploma Programme Economics guide, first assessment 2022, published February 2020, International Baccalaureate Organization. Sub-topic 2.5 Elasticity of demand, within Unit 2: Microeconomics.