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ELASTICITY: A MEASURE OF RESPONSE
Elasticity is the ratio of the percentage change in a dependent
variable to the percentage change in an independent variable
$100
90
-20
A
80
Price per unit
70
60
-10
+10
+20
B
50
40
Demand
30
20
10
190
Quantity per period
180
130
80
60
0
Calculating Elasticities
ep = percentage change in quantity demanded
percentage change in price
WRINKLE #1
ep =
=
60 - 40
ep = 40 - 60
60
70 - 80
80
60
80 - 70
70
50
=
14.3
-12.5
=
-4
-33.3
=
- 2.3
Calculating Elasticities
Arc elasticity is computed by calculating percentage changes
relative to the average value of each variable between two
points.
A to B
B to A
Q
20
-20
ep =
Q
P
=
(60+40)/2
=
-10
P
10
(80+70)/2
=
-3
(60+40)/2
(80+70)/2
=
-3
Price Elasticities Along the Demand Curve
WRINKLE #2
The price elasticity of demand varies between different pairs of points along a
linear demand curve. The higher the price and the lower the quantity demanded,
the greater the absolute value of the price elasticity of demand.
20
20
$100
90
80
ep =
Price per unit
50
40
ep =
= -3.0
A
= -1.0
-10
-10
(55+45)/2
(80+70)/2
70
60
(90+110)/2
(60+40)/2
20
B
(140+160)/2
C
ep =
= -0.3
D
-10
(30+20)/2
30
E
20
F
10
190
0
Quantity per period
Price Elasticity of Demand and Changes in Total Spending
• If the absolute value of the price elasticity of demand > 1 demand is price elastic.
• If the absolute value of the price elasticity of demand = 1 demand is unit price
elastic.
• If the absolute value of the price elasticity of demand < 1 demand is price inelastic.
Price Elastic
Price
Total Spending
Price
Total Spending
Price Inelastic
Price
Total Spending
Price
Total Spending
When the price of a good or service
changes, the quantity demanded changes
in the opposite direction (law of demand).
Total spending will move in the direction of
the variable that changes by the larger
percentage. If quantity demanded changes
by a larger percentage than price, total
spending will change in the direction of the
quantity change [demand is price elastic].
When a change in price results in a smaller
percentage change in quantity demanded
[demand is price inelastic], total spending
will move in the direction of the price
change.
Two Examples:
Gasoline:
Orange Juice:
Suppose that 1,000 gallons per day
are demanded at $1.25/gallon. Total
spending equals $1,250 per day.
But if the price increases to $1.40,
the quantity demanded decreases to
950 gallons. What is total spending?
Suppose that 1,000 cans of frozen
orange juice per month are
demanded at $1.00/can. Total
spending equals $1,000 per month.
But if the price increases to $1.10,
the quantity demanded decreases to
880 cans. What is total spending?
ep = -50
975
-5.13%
= 11.32% = -0.45
0.15
1.325
Price Inelastic
ep = -120
940
-12.77%
= 9.52% = -1.45
0.10
1.05
Price Elastic
Changes in Total Spending and a Linear Demand Curve
Elastic
region
$100
Moving from point s A to B implies a
reduction in price and an increase in
quantity demanded. Demand is elastic
between these two points. Total
spending, indicated by the red rectangle,
rises. When we move from points E to F,
which is the region of inelastic demand,
total spending falls.
80
70
A
Price per unit
B
C
Unit elastic
demand
Inelastic
region
30
E
20
F
190
60
0
Quantity per period
The demand curve below is given by the equation Q = 1-/P. The equation yields the
combinations of prices and quantities shown in the table. The price elasticity of
demand can be calculated between any two points on the demand curve. What can
you note about the price elasticity of demand in this example?
Point
A
B
C
D
E
F
G
H
I
J
Price
$10
9
8
7
6
5
4
3
2
1
Quantity
1.00
1.11
1.25
1.43
1.67
2.00
2.50
3.33
5.0
10
A
0.11
(1.11 + 1.00)/2
10
B
ep =
9
= -1.0
-1
8
Price per unit
7
C
0.33
(10 + 9)/2
(2.00+ 1.67)/2
D
ep =
= -1.0
6
-1
E
5
(6 + 5)/2
F
4
5
G
(10.00 + 5.00)/2
3
ep =
H
2
-1
I
1
0
J
1
2
3
4
= -1.0
5
6
7
8
9
10
(2 + 1)/2
Quantity per
period
Here elasticity of price demand is constant and is unit price elastic.
Notice that total spending (TS), as given by the red, green, and
magenta rectangles, is always the same. Indeed, the area of a
rectangle drawn from any point on this demand curve will equal
$10. A price change does not affect total spending when demand
is unit price elastic.
10
A
TS = $10
5
F
J
1
1
2
10
Determinants of the Price Elasticity of Demand
The greater the absolute value of the price elasticity of demand, the greater the
responsiveness of quantity demanded to changes in price. Depending on whether
demand is relatively elastic, unit elastic, or relatively inelastic, total spending may
fall, remain unchanged, or rise in response to a price change.
What determines whether demand is relatively more or
less elastic?
•Availablity of substitutes
•Importance in Household Budgets
•Time
CHANGES IN TOTAL SPENDING AS A
RESULT OF A SHIFT IN DEMAND
$100
The shift in demand depicted here by the change from D
to D’ results in the following changes in total spending:
From Point B to B’, TS = ($70 x 60) - ($70 x 20) = $2,800
80
From Point E to E’, TS = ($30 x 140) - ($30 x 100) = $1,200
A
70
B’
B
C
D
30
E’
D
E
F
D’
190
60
0
P
When the
percentage changes
in quantity
demanded are very
great relative to
percentage changes
in price, we may say
that demand is very
price elastic.
Q
Very Price Elastic Demand
P
When the
percentage changes
in quantity
demanded are very
small relative to
percentage changes
in price, we may say
that demand is very
price inelastic.
Q
Very Price Inelastic Demand
INCOME ELASTICITY OF DEMAND
ey =
percentage change in Q
percentage change in y
If ey is positive, then the demand for Good A rises as incomes rise or
decreases as incomes decrease [normal good];
If ey is negative, then the demand for Good A rises as incomes decrease
or decreases as incomes rise [inferior good].
CROSS PRICE ELASTICITY OF DEMAND
ecp =
percentage change in QA
percentage change in PB
If ecp is positive, then the quantity demanded of Good A rises as the
price of Good B rises or decreases as the price of Good B decreases
[substitutes];
If ecp is negative, then the quantity demanded of Good A falls as the
price of Good B rises or rises as the price of Good B decreases
[complements].