Transcript price elasticity of demand.

Lecture 5
Elasticity
Required Text:
Frank and Bernanke – Chapter 4
Market Demand Curve

For every single
consumer there is a
separate demand curve.
P
P1

If we have two
consumers in the
market, then we will
have two individual
demand curves, D1 and
D2.
P2
D2
D1
Q1
Q2
Q
Market Demand

Given the two demand curves
D1 and D2

Note that , at price=$2,
Consumer 1 buys 10 units
Consumer 2 buys 20 units
Thus the market demand at
P=$2 is 30 units

At price=$1,
Consumer 1 buys 22 units
Consumer 2 buys 30 units.
Thus the market demand is
52 units.
P
Market Demand
$2
$1
D2
D1
10

Thus, the aggregate or market
demand is obtained by the
horizontal summation of all
individual consumer’s demand
curves.
20 22
30
52 Q
Market Demand

Market Demand - a
schedule showing the
amounts of a good
consumers are willing and
able to purchase in the
market at different price
levels during a specified
period of time.
P
P1
P2
Market Demand

Change in its own price
results in a movement along
the demand curve.
Q1
Q2
Q
Factors that Shift the Market Demand Curve

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


Population
Tastes
Income
 Normal good
 Inferior good
Price of Related Goods
 Substitutes - increase in the price
of a substitute, the demand curve
for the related good shifts outward
(& vice versa)
 Complements - increase in the
price of a complement, the demand
curve for the related good shifts
inward (& vice versa)
Expectations
 Expectations about future prices,
product availability, and income
can affect demand.
P
D1
D2
D
Q
Responsiveness of the Quantity Demanded
to a Price Change

Earlier, we indicated that, ceteris paribus, the quantity
of a product demanded will vary inversely to the price
of that product. That is, the direction of change in
quantity demanded following a price change is clear.

What is not known is the extent by which quantity
demanded will respond to a price change.

To measure the responsiveness of the quantity demanded to
change in price, we use a measure called PRICE
ELASTICITY OF DEMAND.
Price Elasticity of Demand (ED)

Price Elasticity of demand for a good is defined as the
percentage change in the quantity demanded relative to
a percentage change in the good’s own price.
Q P
Q P
Ed 



Q
P
P Q
Algebraically:
Quantity
Q
∆Q =Q2-Q1
1
Price
P
∆P = P2-P1
Ed
125
2
1
100
-25
(1/-25)X(125/1) = - 0.04x125 = - 5
4
2
50
-50
(2/-50)x(100/2) = - 0.04x50 = - 2
5
1
10
-40
(1/-40)x(50/4) = - 0.025x12.5 = - 0.3
Classifications of Own-Price Elasticity
of Demand

Classifications:
 Inelastic demand ( |Ed| < 1 ): a change in price brings
about a relatively smaller change in quantity demanded (ex.
gasoline).
 Total Revenue = P×Q rises as a result of a price increase

Unitary elastic demand ( |Ed| = 1 ): a change in price
brings about an equivalent change in quantity demanded.


TR= P×Q remains the same as a result of a price increase
Elastic demand ( |Ed| > 1 ): a change in price brings about
a relatively larger change in quantity demanded (ex.
expensive wine).

TR = P×Q falls as a result of a price increase
Using Price Elasticity of Demand

Elasticity is a pure ratio independent of units.

Since price and quantity demanded generally
move in opposite direction, the sign of the
elasticity coefficient is generally negative.

Interpretation: If Ed = - 2.72: A one percent
increase in price results in a 2.72% decrease in
quantity demanded
Price Elasticity along
Linear Demand Curves

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Linear Demand Curve:
Q = a – bP
Price elasticity of this demand
Ed = (∂Q/ ∂P)(P/Q) = − b(P/Q)
Any downward sloping demand
curve has a corresponding
inverse demand curve.
Inverse linear Demand Curve:
P = a/b – (1/b)Q
P
a/b
a/2b
0
M
a/2
a
Q
At P= a/b, Ed = − ∞; at P = 0, Ed = 0; at P= a/2b, Ed = −1
In the region of the demand curve to the left of the mid-point M, demand is
elastic, that is − ∞ ≤ Ed < – 1
In the region to the right of the mid-point M, demand is inelastic, – 1 < Ed ≤ 0
Cross Price Elasticity of Demand



Shows the percentage change in the quantity demanded of
good Y in response to a change in the price of good X.
Edyx = % Change in Qdy / % change in Px
Algebraically:
Edyx 
Qy
Qy
Qy
Px
P


 x
Px
Px
Qy
Read as the cross-price elasticity of demand for commodity
Y with respect to commodity X.
Units of Y demanded
Price of X
60
$10
40
$12
Edyx
(-20/2)x(10/60) = - 1.66
Classification of
Cross-price elasticity of Demand

Interpretation:
 If Edyx = - 0.36: A one percent increase in price of chips results in
a 0.36% decrease in quantity demanded of beer

Classification:
 If (Edyx > 0): implies that as the price of good X increases, the
quantity demanded of Good Y also increases. Thus, Y and X are
substitutes in consumption (ex. chicken and pork).

If (Edyx < 0): implies that as the price of good X increases, the
quantity demanded of Good Y decreases. Thus Y & X are
complements in consumption (ex. bear and chips).

If (Edyx = 0): implies that the price of good X has no effect on
quantity demanded of Good Y. Thus, Y & X are Independent in
consumption (ex. bread and coke)
Income Elasticity of Demand (EI)
Shows the percentage change in the quantity demanded
of good Y in response to a percentage change in
Income.
 EI = % Change in QY / % change in I


Algebraically:
Units of Y demanded
Qy I
Qy
I
EI 



Qy
I
I
Qy
Income
100
$1200
150
$1600
EI
(50/400)x(1200/100) = 1.5
Income Elasticity of Demand (EI)


Interpretation:
 If EI = 2.27: A one percent increase income results in a
2.27% increase in quantity demanded of beer
Classification:
 If EI > 0, then the good is considered a normal good
(ex. beef).
 If EI < 0, then the good is considered an inferior good
(ex. ramen noodles)
 High income elasticity of demand for luxury goods
 Low income elasticity of demand for necessary goods
Price Elasticity of Supply (ED)

Price Elasticity of supply of a good is defined as the
percentage change in the quantity supplied relative to a
percentage change in the good’s own price.
Algebraically:


Qs
Qs
P
P
Es 



Qs
P
P Qs
Perfectly inelastic supple – A vertical supply curve
Perfectly elastic supply – a horizontal supply curve.