Price elasticity of demand: WASSCE Economics

If the price of salt doubled, would your family stop buying it? Probably not. If the price of one brand of biscuit doubled, you would switch at once. Elasticity measures that difference, and it decides who pays taxes, what firms charge and how farm incomes behave.

Learning objectives

By the end of this lesson you should be able to:

define price elasticity of demand and calculate it
interpret elasticity values: elastic, inelastic, unitary, perfectly elastic and perfectly inelastic
explain the factors that determine price elasticity of demand and the total revenue test

What elasticity measures

The law of demand tells us that quantity demanded falls when price rises. It does not tell us by how much. Elasticity answers that question.

Definition

Price elasticity of demand (PED) measures the degree of responsiveness of the quantity demanded of a good to a change in its own price.

\text{PED} = \dfrac{\%\ \text{change in qty demanded}}{\%\ \text{change in price}}

\begin{aligned}\text{PED} &= \dfrac{\%\ \text{change in qty demanded}}{\%\ \text{change in price}}\end{aligned}

(qty is short for quantity.)

An equivalent form, using the original price $P$ and original quantity $Q$ :

\text{PED} = \dfrac{\Delta Q}{\Delta P} \times \dfrac{P}{Q}

Because price and quantity demanded move in opposite directions, the answer is negative. In practice we ignore the minus sign and look at the size of the number.

Two worked examples

Worked example

Sugar. The price of a bag of sugar rises from NLe 20 to NLe 25. The quantity demanded falls from 100 bags to 90 bags a week.

% change in price $= \dfrac{5}{20} \times 100 = 25\%$
% change in quantity $= \dfrac{-10}{100} \times 100 = -10\%$
$\text{PED} = \dfrac{-10}{25} = -0.4$ , so the coefficient is 0.4

Since 0.4 is less than 1, demand for sugar is inelastic: buyers hardly cut back.

Worked example

A soft drink. The price of a bottle falls from NLe 10 to NLe 8. The quantity demanded rises from 50 to 70 bottles a day.

% change in price $= \dfrac{-2}{10} \times 100 = -20\%$
% change in quantity $= \dfrac{20}{50} \times 100 = 40\%$
$\text{PED} = \dfrac{40}{-20} = -2$ , so the coefficient is 2

Since 2 is greater than 1, demand is elastic: buyers respond strongly.

Interpreting the number

Coefficient	Name	Meaning	Shape of demand curve
0	Perfectly inelastic	Quantity does not change at all when price changes	Vertical
Between 0 and 1	Inelastic	Quantity changes by a smaller % than price	Steep
Exactly 1	Unitary	Quantity changes by the same % as price	A rectangular hyperbola
Greater than 1	Elastic	Quantity changes by a larger % than price	Flat
Infinity ( $\infty$ )	Perfectly elastic	Any rise in price makes quantity demanded fall to zero	Horizontal

Five small demand graphs: a vertical line for perfectly inelastic demand, a steep line for inelastic, a curved rectangular hyperbola for unitary, a flat line for elastic and a horizontal line for perfectly elastic demand

Figure 1. The five degrees of price elasticity of demand. WASSCE Tutor diagram.

Common mistake

Do not judge elasticity from the slope of a curve drawn on a page. A curve can look steep or flat depending on the scale of the axes. Calculate the coefficient from the figures.

Determinants of price elasticity of demand

Availability of substitutes. Goods with many close substitutes have elastic demand. If one brand of soap becomes dearer, buyers switch to another.
Necessities versus luxuries. Necessities such as salt, rice and medicine have inelastic demand. Luxuries such as jewellery are more elastic.
Proportion of income spent. Goods that take a tiny part of income (matches, salt) have inelastic demand; expensive items (cars, fridges) are more elastic.
Habit and addiction. Cigarettes and alcohol have inelastic demand.
Number of uses. A good with many uses (palm oil) tends to be more elastic: a lower price brings in new uses.
Time. Demand becomes more elastic in the long run as buyers find substitutes.
Durability. Purchases of durable goods can be postponed when prices rise, so demand is more elastic.

In Sierra Leone

When fuel prices rise, okada riders and keke drivers must still buy fuel to work, so demand for fuel is inelastic in the short run. Over a longer period some people may switch to buses or walk shorter journeys, so demand becomes a little more elastic.

The total revenue test

Total revenue (what sellers receive) is price × quantity. Elasticity tells a seller what will happen to revenue when price changes.

Demand is	Raise the price	Lower the price
Inelastic	Total revenue rises	Total revenue falls
Elastic	Total revenue falls	Total revenue rises
Unitary	Total revenue unchanged	Total revenue unchanged

Check it with the examples:

Sugar (inelastic): revenue rises from $20 \times 100 = \text{NLe } 2{,}000$ to $25 \times 90 = \text{NLe } 2{,}250$ when the price rises.
Soft drink (elastic): revenue rises from $10 \times 50 = \text{NLe } 500$ to $8 \times 70 = \text{NLe } 560$ when the price falls.

Key points

PED = % change in quantity demanded ÷ % change in price; ignore the minus sign.
Greater than 1: elastic. Less than 1: inelastic. Equal to 1: unitary.
Determinants: substitutes, necessity, share of income, habit, uses, time, durability.
If demand is inelastic, a price rise raises total revenue; if elastic, it lowers it.

WASSCE examination focus

WAEC tests this

Expect a calculation (often from a short table) followed by "Is demand elastic or inelastic? Give a reason." Show the formula, the percentage changes and the final coefficient, then interpret it in words. Essay questions ask for five determinants of elasticity of demand, each with an example.

Quick check

Price rises by 10% and quantity demanded falls by 30%. What is the PED, and is demand elastic or inelastic?
Give two reasons why demand for salt is inelastic.
A seller faces inelastic demand. Should she raise or lower her price to increase revenue?

Answers: 1. $30 \div 10 = 3$ : elastic. 2. It is a necessity, it takes a very small share of income, and it has no close substitute. 3. Raise it: with inelastic demand, a higher price increases total revenue.

Price elasticity of demand