Arab British Academy for Higher Education.
Price Elasticity of Demand
An important aspect of a product's demand curve is how much the quantity demanded
changes when the price changes. The economic measure of this response is the price
elasticity of demand.
Price elasticity of demand is calculated by dividing the proportionate change in quantity
demanded by the proportionate change in price. Proportionate (or percentage) changes
are used so that the elasticity is a unit-less value and does not depend on the types of
measures used (e.g. kilograms, pounds, etc).
As an example, if a 2% increase in price resulted in a 1% decrease in quantity demanded,
the price elasticity of demand would be equal to approximately 0.5. It is not exactly 0.5
because of the specific definition for elasticity uses the average of the initial and final
values when calculating percentage change. When the elasticity is calculated over a
certain arc or section of the demand curve, it is referred to as the arc elasticity and is
defined as the magnitude (absolute value) of the following:
Q2 - Q1
( Q1 + Q2 ) / 2
P2 - P1
( P1 + P2 ) / 2
where
Q1
Q2
P1
P2
=
=
=
=
Initial quantity
Final quantity
Initial price
Final price
The average values for quantity and price are used so that the elasticity will be the same
whether calculated going from lower price to higher price or from higher price to lower
price. For example, going from $8 to $10 is a 25% increase in price, but going from $10
to $8 is only a 20% decrease in price. This asymmetry is eliminated by using the average
price as the basis for the percentage change in both cases.
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For slightly easier calculations, the formula for arc elasticity can be rewritten as:
( Q2 - Q1 ) ( P2 + P1 )
( Q2 + Q1 ) ( P2 - P1 )
To better understand the price elasticity of demand, it is worthwhile to consider different
ranges of values.
Elasticity > 1
In this case, the change in quantity demanded is proportionately larger than the change in
price. This means that an increase in price would result in a decrease in revenue, and a
decrease in price would result in an increase in revenue. In the extreme case of near
infinite elasticity, the demand curve would be nearly horizontal, meaning than the
quantity demanded is extremely sensitive to changes in price. The case of infinite
elasticity is described as being perfectly elastic and is illustrated below:
Perfectly Elastic Demand Curve
From this demand curve it is easy to visualize how an extremely small change in price
would result in an infinitely large shift in quantity demanded.
Elasticity < 1
In this case, the change in quantity demanded is proportionately smaller than the change
in price. An increase in price would result in an increase in revenue, and a decrease in
price would result in a decrease in revenue. In the extreme case of elasticity near 0, the
demand curve would be nearly vertical, and the quantity demanded would be almost
independent of price. The case of zero elasticity is described as being perfectly inelastic.
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Perfectly Inelastic Demand Curve
From this demand curve, it is easy to visualize how even a very large change in price
would have no impact on quantity demanded.
Elasticity = 1
This case is referred to as unitary elasticity. The change in quantity demanded is in the
same proportion as the change in price. A change in price in either direction therefore
would result in no change in revenue.
Applications of Price Elasticity of Demand
The price elasticity of demand can be applied to a variety of problems in which one wants
to know the expected change in quantity demanded or revenue given a contemplated
change in price.
For example, a state automobile registration authority considers a price hike in
personalized "vanity" license plates. The current annual price is $35 per year, and the
registration office is considering increasing the price to $40 per year in an effort to
increase revenue. Suppose that the registration office knows that the price elasticity of
demand from $35 to $40 is 1.3.
Because the elasticity is greater than one over the price range of interest, we know that an
increase in price actually would decrease the revenue collected by the automobile
registration authority, so the price hike would be unwise.
Factors Influencing the Price Elasticity of Demand
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The price elasticity of demand for a particular demand curve is influenced by the
following factors:






Availability of substitutes: the greater the number of substitute products, the
greater the elasticity.
Degree of necessity or luxury: luxury products tend to have greater elasticity than
necessities. Some products that initially have a low degree of necessity are habit
forming and can become "necessities" to some consumers.
Proportion of income required by the item: products requiring a larger portion of
the consumer's income tend to have greater elasticity.
Time period considered: elasticity tends to be greater over the long run because
consumers have more time to adjust their behavoir to price changes.
Permanent or temporary price change: a one-day sale will result in a different
response than a permanent price decrease of the same magnitude.
Price points: decreasing the price from $2.00 to $1.99 may result in greater
increase in quantity demanded than decreasing it from $1.99 to $1.98.
Point Elasticity
It sometimes is useful to calculate the price elasticity of demand at a specific point on the
demand curve instead of over a range of it. This measure of elasticity is called the point
elasticity. Because point elasticity is for an infinitesimally small change in price and
quantity, it is defined using differentials, as follows:
dQ
Q
dP
P
and can be written as:
dQ P
dP Q
The point elasticity can be approximated by calculating the arc elasticity for a very short
arc, for example, a 0.01% change in price.
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