CHAPTER 5: ELASTICITY
A general definition of elasticity
Elasticity: a measure of responsiveness or sensitivity.
In economics there are many cause-effect relationships which raise similar questions.
 How responsive is investment spending to changes in the interest rate?
 How responsive is government’s tax revenue to changes in taxpayers’ income?
 How responsive is the quantity of labour supplied to changes in the wage rate?
 How responsive is the demand for imports to changes in domestic income?
The list is almost endless. In each case we are interested in the responsiveness or sensitivity of one
variable to changes in another one. The measure of such responsiveness or sensitivity is called
elasticity.
Elasticity can formally be defined as the percentage change in a dependent variable (the one that
is affected) if the relevant independent variable (the one that causes the change) changes by one
per cent.
This is obtained by dividing the percentage change in the dependent variable by the percentage
change in the independent variable:
Elasticity =
percentage change in dependent variable
percentage change in independent variable
In this chapter we introduce four types of elasticity:
 The price elasticity of demand
 The income elasticity of demand
 The cross elasticity of demand
 The price elasticity of supply
Price elasticity of demand
In the previous section, we expressed the market demand curve as:
Qd = f(Px,Pg,Y,T,N,… )
Price elasticity of demand is concerned with the sensitivity of the quantity demanded to a change
in the price of the product. Thus, we examine the relationship Qd = f(Px) ceteris paribus.
In the case of a demand curve, the dependent variable is the quantity demanded and the
independent variable is the price of the product. The price elasticity of demand is the percentage
change in the quantity demanded if the price of the product changes by one per cent, ceteris
paribus.
Using the symbol ep for the price elasticity of demand, we therefore write:
ep =
percentage change in the quantity demanded of a product
percentage change in the price of the product
For example…
• if the price of the product changes by 5 per cent and this results in a 10 per cent change in
the quantity demanded, ceteris paribus, then…
• ep = 10 per cent ÷ 5 per cent = 2.
• This implies that a 1 per cent change in the price of the product will lead to a 2 per cent
change in the quantity demanded.
Looking at the diagrams below, we know that a rightward shift of the supply curve will lead to a
decrease in the price from P1 to P2, and an increase in the quantity demanded at equilibrium from
Q1 to Q2. But we also want to know by how much the price and the quantity will change.
To determine this, we need information about the price elasticity. With price elasticity of demand
we measure the percentage change in quantity demanded that results from a percentage change
in the price. In other words, how sensitive the quantity demanded is to a change in the price.
In Diagram (a)…
• original demand and supply curves are DD
and SS respectively.
• original equilibrium is at E1, indicating a
price P1, and a quantity Q1.
• If supply increases to S'S', the equilibrium
changes to E2,
In Diagram (b)…
• the original equilibrium is the same as in
(a), but the demand curve is steeper
• if the supply curve shifts by the same
magnitude as in (a), the new equilibrium
E3 differs from E2 in (a).
• in (b) the reduction in price is greater and
the increase in quantity is smaller than in
(a).
The price elasticity of demand is very important for businesses.
• For example, if they decrease the price of a product or service, they know the quantity
demanded will tend to increase, as stipulated in the law of demand, but by how much will
the quantity demanded increase?
• Likewise, if they increase the price, the quantity demanded will tend to decrease. But by
how much?
Some important aspects and implications of the definition of price elasticity of demand must be
emphasised…
• Elasticity is calculated by using percentage changes, which are relative changes, not
absolute changes. If we use percentage changes, the units in which prices and quantities
are measured do not affect the result.
• Strictly speaking, the measured price elasticity of demand has a negative sign, since the
change in the price of a product and the change in the quantity demanded move in
opposite directions. However, we ignore the negative sign and simply concentrate on the
absolute value of the price elasticity of demand.
Calculating price elasticity of demand
To calculate the price elasticity of demand, we have to calculate the percentage change in the
quantity demanded and divide it by the percentage change in the price of the product. If we
denote the quantity demanded by Q, the change in quantity demanded by ∆Q, price of the
product by P and the change in price by ∆P, we can calculate the price elasticity of demand as:
The formula above is known as the point elasticity formula and is used to calculate the price
elasticity of demand if the price changes are relatively small. However, sometimes there are large
fluctuations in the price and then we need to use a special formula, called the arc elasticity
formula. We do not cover arc elasticity in the Grade 10 syllabus.
Price elasticity of demand and total revenue (or total expenditure)
price elasticity of demand can be used to determine by how much the total expenditure by
consumers on a product (which is also the total revenue of the firms producing that product)
changes when the price of the product changes.
The total revenue (TR) = price (P) of the good or service x quantity (Q) sold.
We know that any change in price leads to a change in the quantity demanded in the opposite
direction to the change in price. The effect of a price change on total revenue will thus depend on
the relative sizes of the price change and the change in the quantity demanded.
• If change in price P > change in quantity demanded Q (eP > 1)…
o total revenue will change in the opposite direction to the price change.
• If change in price = change in the quantity demanded Q (eP = 1)
o total revenue will remain unchanged.
• If change in price < change in the quantity demanded (eP < 1)
o total revenue will change in the same direction as the price change.
A numerical example
The demand curve corresponding to the demand schedule of Table 5-1 is shown below.
Figure 5.1 (a)…
• The price elasticity of demand will be equal to one at the point on the demand curve that is
exactly midway between the intersections with the price and quantity axes.
• At any point on the demand curve above the midpoint the price elasticity of demand will
be greater than one, and at any point below the midpoint it will be smaller than one.
• (You can verify these statements by calculating the point elasticity of demand at various
points along the demand curve using the information in Table 5-1.)
Figure 5.1 (a)…
As the price of cappuccinos falls, and the quantity of cappuccinos demanded (and sold) increases…
• the total revenue (TR) rises at first,
• then reaches a maximum
• and then declines.
Table 5-1 and Figure 5-2 illustrate three important results…
 If ep of > 1 (elastic), total revenue increases as the quantity sold increases.
 Total revenue reaches a maximum when ep = 1.
 If ep of < 1 (inelastic), TR falls as the quantity sold increases.
Different categories of price elasticity of demand
The following five categories of price elasticity of demand can be distinguished:
• Perfectly inelastic demand (ep = 0)
• Inelastic demand (ep lies between 0 and 1)
• Unitarily elastic demand or unitary elasticity of demand (ep = 1)
• Elastic demand (ep lies between 1 and ∞)
• Perfectly elastic demand (ep = ∞)