1.1 Elasticity
** This note is summarized by Hui Wang.
Important reference Study Guides of Stalla Review for CFA Exams
Learning Outcomes
The candidate should be able to:
a. Calculate and interpret the elasticities of demand (price elasticity, cross elasticity,
income elasticity) and the elasticity of supply, and discuss the factors that influence
each measure;
b. Calculate elasticities on a straight-line demand curve, differentiate among elastic,
inelastic, and unit elastic demand, and describe the relation between price elasticity
of demand and total revenue.
Generally speaking, elasticity measures the percentage change in the dependent
variable in response to one percent change in an independent variable.
Mathematically, elasticity is calculated as:
Elasticity=
The price elasticity of demand
A market demand curve is a function in which quantity demanded is dependent on a
product’s price. The price elasticity of demand is defined as the percentage change in
quantity demanded resulting from a one percent change in price,
η=
When comparing price elasticities of demand, we can use the absolute values of the
elasticity and ignore the minus sign. Price elasticity of demand is a units-free measure
in that the percentage change in either variable is independent of the units in which
the variable is measured.
Inelastic and elastic demand
Value
η=0
-1<η<0
η=-1
-∞<η<-1
η=-∞
Meaning
Perfectly inelastic
Inelastic
Unit (or unitary) elastic
Elastic
Perfectly elastic
Elasticity along a straight-line demand curve
Note that for a straight-line demand curve
is the slope of the demand curve,
combined with a point on the demand curve we can calculate the price elasticity of
demand at that point. So when we move down the demand curve, the demand is
getting more and more inelastic; when we move up the demand curve, the demand is
getting more and more elastic.
Point and arc elasticities
If price only changes a very small amount, we can compute the point elasticity of
demand:
η=
But when there are large changes in price, it is more appropriate to use the arc
elasticity of demand:
η=
÷
Total revenue and elasticity
The total revenue is calculated as the price of the good multiplied by the quantity sold.
The relationship between the total revenue change in response to price change and
price elasticity of demand is that:
Price elasticity of demand
Elastic
Inelastic
Unit elastic
Relationship between price change and total revenue
a 1% price cut increases the quantity sold by more
than 1% and total revenue increases
a 1% price cut increases the quantity sold by less
than 1% and total revenue decreases
a 1% price cut increases the quantity sold by 1% and
total revenue does not change
We can also use this relationship to estimate the price elasticity of demand. The
method used is called total revenue test:
Change in TR that results from a change in the price
a price cut increases total revenue
a price cut decreases total revenue
a price cut leaves total revenue unchanged
Price elasticity of demand
elastic
inelastic
unit elastic
Similarly, the change in a consumer’s expenditure on a certain good depends on her
elasticity of demand. If a consumer’s demand for a good is elastic, a price cut will
increase the quantity she buys and thus increase her expenditure on the good and vice
versa.
The factors that influence the elasticity of demand:
(1) Closeness of substitutes: the closer the substitutes for a good or service, the more
elastic is the demand for it.
(2) Product’s price relative to a consumer’s total budget: products that command a
larger percentage of a consumer’s total budget tend to be more price elastic.
(3) Time elapsed since price change: demand is likely to be more elastic over a long
period relative to a short period.
Cross elasticity of demand
The cross elasticity of demand measures the responsiveness in the quantity demand of
one good when a change in price takes place in another good:
Cross elasticity of demand=
The cross elasticity of demand for substitute goods are positive; the cross elasticity of
demand for complements are negative. If the cross elasticity of demand for two goods
is zero, then the two goods are not related.
Income elasticity of demand
The income elasticity of demand for a particular good is defined as the percentage
change in quantity demanded resulting from a one percent change in consumers’
income. Mathematically, it equals:
η=
*
For most products, the income elasticity of demand is positive. Such goods are called
normal goods. For some other goods, however, the income elasticity of demand is
negative. We call the goods with a negative income elasticity of demand inferior
goods.
Elasticity of supply
The price elasticity of supply measures the rate of response of quantity supplied to a
change in price. It is calculated as:
Elasticity of supply=
As with price elasticity of demand, when price changes are large, it is more
appropriate to use arc elasticity and when price changes are very small, it is more
appropriate to use point elasticity.
If the quantity supplied is fixed, regardless of the price, the supply is perfectly
inelastic. When the percentage change in quantity supplied is equal to the percentage
change in price, the supply is unit elastic. If there is a price at which sellers are wiling
to offer any quantity for sale, the supply is perfectly elastic.
One special case is that for any linear supply curve that passes through origin, the
elasticity of supply is 1, that is, the supply is unit elastic.
Factors that influence the elasticity of supply
(1) Spare production capacity: if there is plenty of spare capacity then a firm is able to
increase its output without a rise in costs and therefore supply will be more elastic.
(2) Ease and cost of factor substitution: if resources used to produce a good are
occupationally mobile then the elasticity of supply for the good is higher than if
resources cannot easily and quickly be switched.
(3) Time period involved in the production process: supply is more price elastic the
longer the time period that a firm is allowed to adjust its production levels.
Stocks of finished products and components: if stocks of raw materials and finished
products are at a high level then a firm is able to respond to a change in demand more
quickly by supplying the goods in stock to the market.
Exercise Problems: (provided by Stalla PassMaster for CFA Exams.)
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EXPLANATION
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