Elasticity of Demand and Supply

Elasticity of Demand And Supply
The focus of this lecture is the elasticity. Students will learn about the price elasticity of
demand, price elasticity of supply, cross elasticity and income elasticity.
OBJECTIVES
1. Understand the definition of elasticity.
2. Be able to compute the elasticity coefficients.
3. Analyze the elasticity characteristics.
4. Illustrate the determinants of the elasticity.
5. Explain the total revenue test and understand the relationship between total
revenue and price elasticity of demand.
TOPICS
Please read all the following topics.
PRICE ELASTICITY OF DEMAND
DETERMINANTS OF Ed
TOTAL REVENUE TEST
PRICE ELASTICITY OF SUPPLY
CROSS ELASTICITY OF DEMAND
INCOME ELASTICITY OF DEMAND

Price Elasticity of Demand
Definition:
Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us
how much more. The degree of sensitivity of consumers to a change in price is measured by the concept of
price elasticity of demand.
Price elasticity formula: Ed = percentage change in Qd / percentage change in Price.
If the percentage change is not given in a problem, it can be computed using the following formula:
Percentage change in Qd = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd.
Percentage change in P = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price.
Putting the two above equations together:
Ed = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]}
Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative
number. But, we focus on the magnitude of the change by neglecting the minus sign and use absolute
value
Examples:
1. If the price of Product A increased by 10%, the quantity demanded decreased by 20%. Then the
coefficient for price elasticity of the demand of Product A is:
Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2
2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased
from $2 to $4 per unit, the coefficient for Ed is:
Ed = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} = {(900 - 1000) / 1/2(1000 + 900)} / {(4 - 2) / 1/2
(2+4)} = - 0.16
Take the absolute value of - 0.16, Ed = 0.16

Kinds Of Price Elasticity Of Demand
1) Perfectly elastic demand
2) Relatively elastic demand
3) Elasticity of demand equal to utility
4) Relatively inelastic demand
5) Perfectly inelastic demand

Cont.
Ed approaches infinity, demand is perfectly elastic. Consumers are very sensitive to
price change.
Ed > 1, demand is elastic. Consumers are relatively responsive to price changes.
Ed = 1, demand is unit elastic. Consumers’ response and price change are in same
proportion.
Ed < 1, demand is inelastic. Consumers are relatively unresponsive to price changes.
Ed approaches 0, demand is perfectly inelastic. Consumers are very insensitive to price
change.
Ed is usually greater in the higher price range than in lower price range. Demand is
more elastic in upper left portion of the demand curve than in the lower right portion of
the curve. However, it is impossible to judge elasticity of a demand curve by its flatness
or steepness. Along a linear demand curve, its elasticity changes. This relationship is
demonstrated in the following example:

An Example
DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE
Ed = PRICE ELASTICITY OF DEMAND
A B C D E F G H I J
Q: 0 50 100 150 200 250 300 350 400 450
P: 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
Ed: 17 5 2.6 1.57 1 0.64 0.38 0.2 0.06
ELASTICITY OF DEMAND;
FROM A TO E Ed >1
FROM E TO F Ed =1
FROM F TO J Ed <1

Perfectly elastic demand
P
R
I
C
E
y
0 x
Perfectly elastic
demand curve
D D
When the
demand for a
product
changes –
increases or
decreases
even when
there is no
change in
price, it is
known as

Relatively elastic demand
Relatively elastic
demand curve
P
R
I
C
E
demand0 x
y
D
D
When the
proportionate
change in
demand is
more than the
proportionate
changes in
price, it is
known as
relatively
elastic
demand.

Elasticity of demand equal to utility
Elasticity of
demand equal
to utility curve
y
x0 demand
P
R
I
C
E
D
D
When the
proportionate
change in
demand is
equal to
proportionate
changes in
price, it is
known as
unitary elastic
demand

Relatively inelastic demand
Relatively inelastic
demand curve
XO
Y
demand
D
D
P
R
I
C
E
When the
proportionate
change in
demand is less
than the
proportionate
changes in price,
it is known as
relatively inelastic
demand

Perfectly inelastic demand
demand
D
D
Perfectly inelastic
demand curve
0
Y
X
P
R
I
C
E
When a change in
price, howsover
large, change no
changes in quality
demand, it is
known as perfectly
inelastic demand

ALL KINDS OF DEMAND CAN BE SHOWN
IN ONE DIAGRAM AS FOLLOW
D
D1
D2
D3
D4
D5
Y
X0
DEMAND
P
R
I
C
E
WHERE
D1) Perfectly elastic
demand
D2)Relatively elastic
demand
D3)Elasticity of demand
equal to utility
D4)Relatively inelastic
demand
D5)Perfectly inelastic
demand

Determinants of Price Elasticity of Demand
Various factors influence the price elasticity of demand. Here are some of them:
1. Availability of Substitutes: If a product can be easily substituted, its demand is
elastic, like Gap's jeans. If a product cannot be substituted easily, its demand is
inelastic, like gasoline.
2. Luxury Vs Necessity: Necessity's demand is usually inelastic because there are
usually very few substitutes for necessities. Luxury product, such as leisure sail boats,
are not needed in a daily bases. There are usually many substitutes for these
products. So their demand is more elastic.
3. Price/Income Ratio: The larger the percentage of income spent on a good, the
more elastic is its demand. A change in these products' price will be highly noticeable
as they affect consumers' budget with a bigger magnitude. Consumers will respond
by cutting back more on these product when price increases. On the other hand, the
smaller the percentage of income spent on a good, the less elastic is its demand.
4. Time lag: The longer the time after the price change, the more elastic will be the
demand. It is because consumers are given more time to carry out their actions. A 1-
day sale usually generate less sales change per day as a sale lasted for 2 weeks.

Total Revenue Test
Total revenue (TR) is calculated by multiplying price (P) per unit and quantity (Q) of the good
sold.
TR = P x Q
The total revenue test is a method of estimating the price elasticity of demand. As Ed will
impact the total revenue, we can estimate the Ed by looking at the movement of the total
revenue.
Total Revenue Test
Ed > 1, total revenue will decrease as price increases. P and TR moves in opposite directions.
Producers can increase total revenue ( TR = Price x Quantity) by lowering the price. Therefore,
most department stores will have sales to attract customers. Apparel's demand is elastic.
Ed < 1, total revenue will increase as price increases. P and TR moves in the same direction.
Producers can increase total revenue by raising the price. Inelastic demand for agricultural
products helps to explain why bumper crops depress the prices and total revenues for
farmers.
You may look at the movement of TR in the example below. It demonstrated the relationship
described above.

TR Test Example
DEMAND FUNCTION FOR PRODUCT X: P = 2.5-0.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE
Ed = PRICE ELASTICITY OF DEMAND
A B C D E F G H I J
Q: 0 50 100 150 200 250 300 350 400 450
P: 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
TR: 0 200 350 450 500 500 450 350 200 0
Ed: 17 5 2.6 1.57 1 0.64 0.38 0.2 0.06
ELASTICITY OF DEMAND;
FROM A TO E Ed >1 TR increases
FROM E TO F Ed =1 TR remains same.
FROM F TO J Ed <1 TR decreases.

Cross Elasticity of DemandDefinition:
Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity
demand change of product X to a change in the price of product Y.
Formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y.
Percentage change in Qx = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 = new Qd of X.
Percentage change in Py = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y.
Exy = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]}
Characteristics:
Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes.
Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not related.
Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements.
Examples:
1. If the price of Product A increased by 10%, the quantity demanded of B increases by 15 %. Then the
coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating A and B are
substitutes.
2. If the price of Product A increased by 10%, the quantity demanded of B decreases by 15 %. Then the
coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = - 1.5 < 0, indicating A and B are
complements.

Income Elasticity of Demand
Definition:
Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's quantity
demanded and income. It measures the sensitivity of quantity demand change of product X to a change in
income.
Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in Income
Percentage change in Qx = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd.
Percentage change in Y = (Y2-Y1) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New income.
Ey = {(Q2-Q1) / [1/2 (Q1+Q2)] } / (Y2-Y1) / [1/2 (Y1 + Y2)]
Characteristics:
Ey > 1, Qd and income are directly related. This is a normal good and it is income elastic.
0< Ey<1, Qd and income are directly related. This is a normal good and it is income inelastic.
Ey < 0, Qd and income are inversely related. This is an inferior good.
Ey approaches 0, Qd stays the same as income changes, indicating a necessity.
Example:
If income increased by 10%, the quantity demanded of a product increases by 5 %. Then the coefficient
for the income elasticity of demand for this product is::
Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating this is a normal
good and it is income inelastic.

Price Elasticity of Supply
Definition:
Law of supply tells us that producers will respond to a price drop by producing less, but it does not tell us
how much less. The degree of sensitivity of producers to a change in price is measured by the concept of
price elasticity of supply.
Price elasticity formula: Es = percentage change in Qs / percentage change in Price.
Percentage change in Qs = (Q2-Q1) / [1/2 (Q1+Q2)] where Q1 = initial Qs, and Q2 = new Qs.
Percentage change in P = (P2-P1) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price.
Es = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]}
Because of the direct relationship between Qs and Price, the Es coefficient will always be a positive number.
Examples:
1. If the price of Product A increased by 10%, the quantity supplied increases by 5%. Then the coefficient
for price elasticity of the supply of Product A is:
Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = 0.5
2. If the quantity supplied of Product B has decreased from 1000 units to 200 units as price decreases from
$4 to $2 per unit, the coefficient for Es is:
Es = {(Q2-Q1) / [1/2 (Q1+Q2)] } / {(P2-P1) / [1/2 (P1 + P2)]} = {(200 - 1000) / 1/2(1000 + 200)} / {(2-4) / 1/2
(4+2)} = 2

Ranges of Elasticity
© iTutor. 2000-2013. All Rights Reserved

A Variety of Supply Curves
Perfectly Inelastic Supply - Elasticity equals 0
Inelastic Supply- Elasticity is less than 1
Price
Quantity100
$10
$5
1. An increase in price...
2. ...leaves the quantity supplied
unchanged.
Price
Quantity100
$5
$4
1. A 22 % increase in price...
2. ...leads to 10% increase in
Quantity.
110
Supply
Supply

Unit Elastic Supply - Elasticity equals 1
Elastic Supply - - Elasticity is greater than 1
A Variety of Supply Curves
Price
Quantity
$5
$4
2. ...leads to a 25% increase in
Quantity.
100
Price
Quantity100
$5
$4
2. …leads to a 67% increase in
Quantity.
167
125

Quantity
Price
Supply$4
1. At any price
above $4, quantity
supplied is infinite.
2. At exactly $4,
producers will
supply any quantity.
3. At a price below $4,
Quantity supplied is zero.
Perfectly Elastic Supply - Elasticity equals infinity

Determinants of supply elasticity
 The following list contains the main determinants of supply elasticity.
1. Product Type
2. Time
3. Production Capacity
4. Input substitution -- Flexibility and Mobility
 Product Type - The type of product impacts how quickly a producer is able to
respond to a change in price. A manufacturing firm may be able to quickly
adjust production levels with only minor adjustments in the equipment while
other products such as apples require several years to establish a new
orchard. Since child care services requires relatively few skills compared to the
those of a physician, the supply elasticity of child care services is more elastic
than that of physician services.
 Time - Time is a key determinant of supply. In the case of apples and some
other agriculture products, the immediate elasticity of supply is very inelastic,
i.e., there are only so many apples available for sale today. However, with time
producers are able to respond to the increase in price, manufacturing firms can
build new facilities, farmers can plant additional acres to the particular crop.
Thus in time, the elasticity of supply becomes more elastic.

 Production Capacity - If a firm is already operating at full capacity, then to
increase supply would require building additional facilities and purchasing new
equipments. A firm that is operating at below full capacity, can respond to a
price increase quicker than a firm that is already at full capacity.
 Input substitution -- Flexibility and Mobility
 Another determinant in the elasticity of supply is input substitution. As the
price of a good increases, how easily can inputs that were used in the
production of another good be switched over to producing the good with
the higher price?
P
Q
Short run
Intermediate run
Long run

Oil and elasticity of supply
 World supply of oil following a
large rise in world demand
Variable amount of spare
capacity among the major oil
producers
Can oil stocks be put onto the
market to meet the rise in
demand?
Oil supply might be inelastic if
current output is close to
capacity

Point elasticity of demand
Meaning
Point elasticity is the price elasticity of demand at
a specific point on the demand curve instead of
over a range of it.
It uses the same formula as the general price
elasticity of demand measure, but we can take
information from the demand equation to solve
for the “change in” values instead of actually
calculating a change given two points.

Continue
Here is the process to find the point elasticity
of demand formula:
• Point Price Elasticity of Demand =
(% change in Quantity)/(% change in Price)
• Point Price Elasticity of Demand =
(∆Q/Q)/(∆P/P)
• Point Price Elasticity of Demand = (P/Q)
(∆Q/∆P)

Continue
• Where (∆Q/∆P) is the derivative of the
demand function with respect to P.
• You don’t really need to take the derivative of
the demand function, just find the coefficient
(the number) next to Price (P) in the demand
function and that will give you the value for
∆Q/∆P because it is showing you how much Q
is going to change given a 1 unit change in P.

Example 1:
• Demand curve: Q = 15,000 - 50P
Given this demand curve we have to figure out
what the point price elasticity of demand is at P =
100 and P = 10.
• First we need to obtain the derivative of the
demand function when it's expressed with Q as a
function of P. Since quantity goes down by 50
each time price goes up by 1,
This gives us (∆Q/∆P)= -50

Continue
• Next we need to find the quantity demanded at
each associated price and pair it together with the
price:
(100, 10,000), (10, 14,500)
e = -50(100/10,000) = -.5
e = -50(10/14,500) = -.034
And these results make sense, first, because they
are negative (downward sloping demand) and
second, because the higher level results in a
relatively more price elasticity of demand measure.

Example 2
• How to find the point price elasticity of
demand with the following demand function:
Q = 4,000 – 400P
• We know that ∆Q/∆P in this problem is -400,
and we need to find the point price elasticity
of demand at a price of 10 and 8.

Continue
• At a price of 10, we demand 0 of the good, so
the measure is undefined. At a price of 8
demand will be 400 of the good, so the
associated measure is:
e = -400(8/400) = -8

Continue
What about a demand function of:
Q = 8,800 – 1,000P
• find the associated measure at prices of 0, 2,
4, and 6.
• e = -1,000(0/8,800) = 0
• e = -1,000(2/6,800) = -0.294
• e = -1,000(4/4,800) = -0.8333
• e = -1,000(6/2,800) = -2.14

Point elasticity of Supply
Here is the process to find the point elasticity of
supply formula:
• Point Price Elasticity of Supply =
(% change in Quantity)/(% change in Price)
(∆Q/Q)/(∆P/P)
(P/Q)(∆Q/∆P)

Example 1
Supply: Q = 2000 + 20P
By using this supply function calculate price
elasticity of supply at price 40,60 and 80?
Es = Slope (P/Q)
Es = 20 (40/2800) = 0.28
Es = 20 (60/3200) = 0.37
Es = 20 (80/3600) = 0.44

Question 1
Consider the ice cream market in Madison. In
July, the ice cream market demand and supply
curves are given by the following equations
where Q is the quantity to ice cream units and
P is the price in dollars per unit of ice cream:
• Demand: Q = 14000 – 10P
• Supply: Q = 2000 + 20P

a) Find the equilibrium price and quantity of ice
cream in July.
b) Calculate the price elasticity of demand and
supply at the equilibrium price in July. Use the
point elasticity formula to compute these two
values of these elasticities.
In October, ice cream demand in Madison
decreases. So, the new demand curve is given
by
Demand: Q = 7000 – 30P
Assume the supply curve doesn’t change.

c) Find the equilibrium price and equilibrium
quantity in October, and calculate the price
elasticity of demand and supply at this new
equilibrium price. Use the point elasticity
formula in calculating these values.

Elasticity of Demand and Supply

Elasticity of Demand and Supply

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Elasticity of Demand and Supply

Similar to Elasticity of Demand and Supply (20)

More from Dr. Shweta Uppadhyay

More from Dr. Shweta Uppadhyay (20)

Recently uploaded

Recently uploaded (20)

Elasticity of Demand and Supply