Download Arc and Point Measurement of Price Elasticity of Demand

Elasticity of Demand
This is the degree of responsiveness or sensitivity of the change in quantity demanded as a
result of the change in demand determinants.
Mathematically,
Elasticity of demand = Change in quantity demanded
Change in Demand determinants
Types of Elasticity of Demand
1. Price Elasticity of demand.
This refers to degree of responsiveness or sensitivity of the change in quantity demanded as a
result of the change in price of the commodity.
Mathematically,
Price Elasticity of Demand = Change in Quantity Demanded
Change in Price of the Commodity
Arc and Point Measurement of Price Elasticity of Demand
There are two methods of measuring price elasticity demand and they are as follows.

Point Method
The point method measures elasticity at one point on the demand curve or demand schedule
and it requires knowledge in differentiation.
The formula used to measure price elasticity of demand is:
Price elasticity of demand = Qd
P
Where,
x
P
Qd
Q = Differentiating quantity demanded with respect to price.
P
P= Price of the commodity
Q= Quantity Demanded
Problems 5.1
I.
Suppose the demand equation for a product is Q = 20 – 3P, what is the price elasticity
of demand at the price
a. D1? b. D2? c. D3?
II.
III.

If the demand equation for an item is Q  18  10 p - 3p 2 , calculate the price elasticity
of demand at the price of D1.
If the equation for an item is P  1500  45Q  5Q 2 , determine the price elasticity of
demand at Q= 12units
Arc Method
Arc method of measuring elasticity makes use of two points on the demand curve or demand
schedule.
Mathematically,
New Quantity – Old Quantity x 100
Old Quantity
Price Elasticity of Demand =
New Price – Old Price x100
Old Price
Measuring price elasticity of demand, using the above arc formula, would not provide the
same answers when calculating elasticity from A to B and B to A. To have the same answers
when measuring elasticity from A to B and B to A, the adjusted formula that follows could be
used.
New Quantity – Old Quantity x 100
Old Quantity + New Quantity
2
Price Elasticity of Demand =
New Quantity – Old Quantity x 100
Old Quantity + New Quantity
2
Problem 5.2
Suppose the quantity demanded at different prices by consumer in the Banjul area are
expressed in the demand schedule
Demand Schedule for Banjul Area
Price (D)
Quantity Demanded (kilo)
1
10
2 B
6
B
3 A
4
A
4
3
5
1
Calculate the price elasticity of demand when price
a) decreases from D3 toD2.
b) increases from D2 to D3.
2.Cross Elasticity of Demand
Cross elasticity of demand measures the degree of responsiveness or sensitivity of the change
in quantity demanded of X as result of the change in the price of YB, assuming products X
and Y are close substitutes.
Mathematically,
Change in Quantity Demanded of X
Cross Elasticity of Demand =
Change in the Price of Y
Point and Arc Measurement of Cross Elasticity of Demand
Point Method: The point method measures cross elasticity at one point.

Cross Elasticity of Demand = QX x
PY
Py
QX
Where,
QX
= Differentiating quantity demanded of product of X with respect
PY
to the price of product Y.
P y = Price of Product Y
Q X = Quantity Demanded of Product X
Problems 5.3
Given that the relationship between product A and product B is Q A = 95P B - 0.5P B 2 , where
Q A = units of product A demanded by consumers each day and P B = selling price of product
B.
Calculate the cross elasticity of demand for the two products when
i) the price of product B = D10.
ii) the price of product B = D 20.
Arc Method: The arc method measures cross elasticity at two points.
Mathematically,
New Quantity of X – Old Quantity of X x 100
Old Quantity of X
Cross Elasticity of Demand =
New Price of Y – Old Price of Y x 100
Old Price of Y
The adjusted formula is:
New Quantity of X – Old Quantity of X x 100
Old Quantity of X + New Quantity of X
2
Cross Elasticity of Demand =
New Price of Y – Old Price of Y x 100
Old Price of Y + New Price of Y
2
Problem 4.4
Given the demand schedule,
Price of Y (Dalasis)
5
4 A
3 B
2
1
Quantity Demanded of X (Units)
10
8 A
5 B
4
1
Calculate the cross elasticity of demand when the price of product Y
i). decreases from D4 to D3.
ii). increases from D3 to D4.
3. Income Elasticity of Demand
Income elasticity of demand refers to the degree of responsiveness or sensitivity of the
change in quantity demanded as a result of the change in income of the consumer.
Mathematically,
Change in Quantity Demanded
Income Elasticity of demand =
Change in Income of the Consumer
Point and Arc Measurement of Income Elasticity of Demand

Point Method: The point method measures income elasticity at one point on the
demand-income curve or demand-income schedule.
Mathematically,
Income Elasticity of Demand =
Q
I
x
I
Q
Where
Q
I
= Differentiation of the quantity with respect to the Income.
Q
= Quantity Demanded
I
= Income of the consumer
Problems 5.5
The Tropical Sea Food Company estimates that the demand-income relationships for its line
of frozen fish can be represented by the equation Q = 600 + 0.1, where Q = cartons of frozen
fish and I = average household income. Calculate the income elasticity of demand when
i). I = D25, 000.
ii). I = D30, 000.

Arc Method: It measures income elasticity at two points on the demand-income curve
or demand income schedule.
Mathematically,
New Quantity – Old Quantity x 100
Old Quantity
Income Elasticity of Demand =
New Price – Old Price x 100
Old Price
The adjusted formula is:
Income Elasticity of Demand =
New Quantity – Old Quantity x 100
Old Quantity + New Quantity
2
New Income – Old Income x 100
Old Income + New Income
2
Problems 5.6
Given the demand-income schedule
Income (Dalasis )
1, 000
2, 000 A
3, 000 B
4, 000
5, 000
Quantity Demanded (Units )
100
125 A
157 B
225
300
Calculate the income elasticity of demand when income
i). increases from D2, 000 to D3, 000.
ii). decreases from D3, 000 to D2, 000.
Important Notations
1. Price Elasticity of Demand:
a. Inelastic Demand. Demand is said to be inelastic when the price elasticity of demand (or
price elasticity coefficient) is less than one, regardless of its negative sign (the value is always
negative because price and quantity demanded move in opposite direction). The change in
quantity demanded is less than the change in price of the commodity. Figure
5.1 shows an inelastic demand.
Price
D
P1
P0
D
Q1 Q 0
Figure 5.1: Inelastic Demand
Quantity Demanded
b. Unitary Demand. Demand is said to be unitary when the price elasticity of demand is equal
to one, regardless of the sign. The change in quantity demanded is equal to the change in
price. The diagram that represents this is shown in figure 5.2.
Price
D
P1
P0
D
Q1 Q 0
Figure 4.2: Unitary Demand
Quantity Demanded
c. Elastic Demand. Demand is said to be elastic when the price elasticity of demand is greater
than one, regardless of sign. The change in quantity demanded is more than the change in
price of the product. Figure 4.3 represents an elastic demand.
Price
D
P1
P0
D
Quantity Demanded
1
Q
Q0
Figure 4.3: Elastic Demand
d. Perfectly Elastic Demand. Demand is said to be perfectly elastic when the price elasticity
of demand is infinite, regardless of the sign. The demand curve is horizontal and price. The
price is the same no matter the quantity demanded. Figure 4.4 depicts perfectly elastic
demand.
Price
P
D
Quantity Demanded
0
1
2
Q Q
Q
Figure 4.4: Perfectly Elastic Demand
e. Perfectly Inelastic Demand. Demand is said to be perfectly inelastic when the price
elasticity of demand is equal to zero. The demand curve is vertical. Quantity demanded is the
same no matter the price of the product (quantity is fixed but price varies). Figure 4.5 visual
explains perfectly inelastic demand.
Price
D
P2
P1
P0
0
Quantity Demanded
Q
Figure 4.5: Perfectly Inelastic Demand
2. Cross Elasticity of Demand
a. Substitute Products. The cross elasticity of demand is positive.
b. Complementary Products. The cross elasticity of Demand is negative.
c. Independent Products. The cross elasticity of demand is zero.
3. Income Elasticity of Demand
a. Income Inelastic Demand. Demand is income elastic when the income elasticity of demand
is less than one (the sign is always positive for normal goods because income and quantity
demanded move in the same direction or they are directly related). The change in quantity
demanded is less than the change in income.
b. Income Unitary Demand. The income elasticity of demand is equal to one. The change in
quantity demanded is equal to the change in income.
c. Income Elastic Demand. The income elasticity of demand is greater than one. The change
in quantity demanded is more than the change in income.
d. Income Perfectly Elastic Demand. The income elasticity of demand is infinite. The income
is fixed but quantity demanded varies.
e. Income Perfectly Inelastic Demand. The income elasticity of demand is equal to zero.
Income varies but quantity demanded is fixed.
Factors Influencing Price Elasticity of Demand
a. Importance of the Product. Consumers would become insensitive where a product is
necessary to their daily living and lifestyles (toothpaste, tea). On the other hand, items
considered luxury tend to show high degree of price sensitivity.
b. Degree of Market Satiation. Products that are available to all households would force the
selling price to reduce. If almost all households have television, producers will have no
option but to decrease their selling price.
c. Income Profile of Consumers. The demand for luxury products that are meant purely for
those that are ostentatious or class conscious may be price inelastic. The demand for the
product will increase with a large increase in price. The sell price of the product may be small
in relation to the consumer’s income. Consumers will become price conscious when the
selling price of a product is larger in relation to their income.
d. Availability of Substitutes. The presence of close substitute products makes consumers
more responsive to price changes. From another front, the absence of close substitutes makes
consumers less price sensitive.
e. The Number of Uses for a Product. Demand would become more price elastic where there
are wide ranges of uses for a product. The number of uses for a product will create more
opportunity for variation in quantity sold as price changes. A rise in price will decrease the
number of economical uses of a product. The reduction in price will increase the range of
economical feasible uses for the product. This particular part of demand is concerned with
products such as aluminium, steel and other primary metals, plastics, wool, and paper
products.
f. The durability of the product. Price elasticity can partly depend on product durability
because of the possibility of replacement delays. Differing the purchase of a new durable
good by making provision for maintenance may be an effective, though temporary, substitute
for the replacing good whose prices are increasing.
g. Time Period. In the long run the market demand for a product tends to be more elastic. In
the short run, the market demand for a product tends to be inelastic
Elasticity and Total Revenue
For elastic products, a fall in price will increase total revenue. An increase in price can reduce
total revenue.
A product with an inelastic demand will raise more total revenue when price increases. A fall
in price for an inelastic product will reduce the revenue.
The table below can provide further understanding.
P
Elastic Demand
TR
Inelastic Demand
TR
P
TR
TR
Where
P= Price of the product
TR=Total Revenue= Price x Quantity
Importance of Elasticity of Demand
1. Individual (consumer): The consumer is concerned about elasticity to determine the effect
of a price change upon the total amount of money he/she is willing and able to spend on a
given product.
2. Firm (producer): The firm is interested in elasticity concept to determine the effect of
price changes on sales volume.
3. Elasticity also enable us to know whether products are substitutes or complementary or
independents.
Elasticity of Supply
Elasticity of supply measures the degree of responsiveness or sensitivity of the change in
quantity supplied as a result of the change in supply determinants, specifically price of the
commodity and the price of other commodity.
Mathematically,
Elasticity of Supply = Change in Quantity Supplied
Change in Supply Determinants
Types of Elasticity of Supply
a) Price elasticity of supply: This is the degree of responsiveness of the change in quantity
supplied of a commodity as a result of change in price of the commodity. The point and
arc measurement can be used to calculate price elasticity of supply.
i) Point Measurement. It measures elasticity at one point on the supply curve or schedule.
Mathematically,
Price Elasticity of Supply =
 Qs
P
x P
Qs
ii). Arc Measurement. This measures elasticity at two points on the supply curve or supply
schedule.
Mathematically,
New Quantity Supplied – Old Quantity Supplied x 100
Old Quantity Supplied
Price Elasticity of Supply =
New Price – Old Price x 100
Old Price
The adjusted Formula is:
New Quantity Supplied – Old Quantity Supplied x100
Old Quantity Supplied + New Quantity Supplied
2
Price Elasticity of Supply =
New Price – Old Price x 100
Old Price + New Price
2
b). Cross Elasticity of supply: It measures the degree of responsiveness of the change in
quantity supplied of product Y as a result of the change in the price of product X, assuming
products X and Y are close substitutes. The Point and Arc Measurement can be used to
calculate cross elasticity of supply.
i). Point Measurement: It measures elasticity at point on the supply curve or supply schedule.
Cross Elasticity of Supply = Qsx x
 Py
Py
Qsx
ii). Arc Measurement. It measures cross elasticity at two points.
New Supply of Y- Old Supply of Y x 100
Old Supply of Y
Cross Elasticity of Supply=
New Price of X- Old Price of X x 100
Old Price of X
The adjusted formula is:
New Supply of Y- Old Supply of Y x 100
Old Supply of Y + New Supply of Y
2
Cross Elasticity of Supply=
New Price of X- Old Price of X x 100
Old Price of X + New Price of X
2
Elasticity of Supply and Time
1. Market Period: In the market period, there is a perfectly inelastic supply. This means that
quantity supplied remains fixed no matter the price levied on the product. The market
period is represented by the supply curve So.
2. Short run: The short run would exist where a supplier cannot vary its fixed costs. In this
case supply is inelastic. Inelastic supply refers to a situation where suppliers are less
sensitive or less responsive to price changes. The diagram S1 represents short run supply.
3. Long run: A long run will exist where both fixed and variable cost varies .The elasticity
of supply is elastic. It is elastic because suppliers are more responsive or more sensitive to
price changes. Long run supply is represented by the supply curve S2.
Price
So
S1
S2
Quantity Supplied