Transcript Demand and Elasticity Consider the following cases:  Making Sales Targets  A Public Transportation Problem: Can the daily ridership fluctuations be controlled through.

Demand and Elasticity
Consider the following cases:
 Making Sales Targets
 A Public Transportation Problem:
Can the daily ridership fluctuations be controlled
through a pricing strategy?
 The Airliners’ Pricing Problem:
How can an airliner fill its plains while
maximizing its profit?
TR 0 = 220 x 120 = 26,400
TR1 = 180 x 140 = 25,200
D2
TR2 = 180 x 200 = 36,000
D1
220
180
0
Q
120
140
200
Note: Slope and Scale
o
o
A
B
Elasticity
A general definition:
“Elasticity” is a (standard) measure of the
degree of sensitivity ( or responsiveness) of one
variable to changes in another variable.
The price elasticity of Demand
The (self) price elasticity of demand is a
measure of the degree of sensitivity of demand
to changes in the (self) price, ceteris paribus.
Determining Price Elasticity
Percentage Change in Quantity
Ep =
Percentage Change in Price
Change in Quantity
Quantity
Ep =
Change in Price
Price
P
a
10
b
8
c
4
2
d
8
18
80
D
90
Ep (a --- b) = (10/8)/(-2/10) = -6.25
Ep (c ---d ) = (10/80)/(-2/4) = -.25
Q
What does the elasticity
“measure” really measure?
 The elasticity measure is a ratio between
two percentage measures: the percentage
change in one variable over the percentage
change in another variable
 A price elasticity of -6.25 means that for
each one percent change in price the
quantity demanded will change by 6.25
percent.
Arc (Price) Elasticity
Note that if we increased
P
the price,
(from 8 to 10 or 2 to 4)
the original P and Q would 10
8
be 2 and 8 and 18 and
90, respectively.
Ep = (-10/18)/(2/8) = -2.22
a
b
c
4
d
2
Ep = (-10/90)/(2/2) = -.11
8
18
80 90
D
Q
Arc Elasticity
To get the average elasticity between two
points on a demand curve we take the
average of the two end points (for both
price and quantity) and use it as the initial
value:
Q2-Q1
10
(Q1+Q2)
8+18
Ea =
= -3.49
P2-P1
(P1+P2)
-2
10+8
Elasticity and the Price Level
P
Along a linear demand curve as
the price goes up, |elasticity |
increases.
Note that between points "a" and
"b" the (arc) elasticity of the
above demand curve is -3.49,
whereas between "c" and "d" it is
-.17.
10
8
| Ep | > 1 :
Elastic
| Ep | < 1 :
Inelastic
| Ep | = 1 :
Unit-elastic
a E =-3.49
b
c E = -.17
d
4
2
D
8
18
80 90
Point Elasticity
Q
--------Q1+Q2
Q
P1+P2
Q
P
E = ------------ = ------- . ------- = ------- . -----P
P Q1+Q2
P
Q
--------P1+P2
dQ
P
Or,
= ------ . ----dP
Q
P,MR
Q = C - b P
|E|=1
C
1
P = ----- - ----- Q
b
b
D
MR
Q
0
TR
C
2
MR = ------ - ------ Q
b
b
C
Note:
In the demand equation
dQ/dP = -b
That means
Q
0
P
E p = -b ----Q
A note about marginal revenue:
Recall: TR = P.Q ;
P = f (Q )
 Marginal Revenue = Change in TR resulting from
producing (selling) one additional unit of output.
TR
(P.Q) d P
dQ
MR = ------ = -------- = ------ .Q + ------ .P
Q
Q
dQ
dQ
dP Q
P
1
= ( -----. ----- + ------ ).P = P. ( ------- + 1 )
dQ P
P
E
dQ P
P
E = ----- . ----- = -b . -----dp
Q
Q
Q = C - b P
dQ
---- = - b
dp
P, MR
1
MR = P. ( 1 + ---- )
E
Slope= -1/b
Slope=-2/b
MR
0
D
Q
C
Special Cases
P
D
D
0
Q
Infinitely (price) elastic
0
Infinitely price inelastic
Q
Important Observations
•When demand is elastic, a decrease in price
will result is an increase in the revenue
(sales).
•When demand is inelastic, a decrease in
price will result is a decrease in the revenue
(sales).
•When demand is unit-elastic, an increase
(or a decrease) in price will not change the
revenue (sales).
What Determines Elasticity
 Necessities versus luxuries
Eating at restaurants
Groceries
 Availability of substitutes
Chicken versus beef
 How much of our income a good takes
Salt versus Nike sneakers
 The passage of time
Elasticity and Passage of Time
P
D3
D2
Do
D1
Q
O
Q3
Q2
Q1 Q’o Qo
Other Elasticity Measures
Recall: “Elasticity” is a (standard) measure of
the degree of sensitivity ( or responsiveness) of
one variable to changes in another variable.
 Income Elasticity: a measure of the degree of
sensitivity of demand for a good (or service) to
changes in consumers’ (buyers’) income
 Cross Price Elasticity: a measure of the degree
of sensitivity of demand for a good (or service)
to changes in the price of another good or
service
Income Elasticity of Demand
A measure of the degree of responsiveness of
demand (for a good) to a change in income,
ceteris paribus.
(Shift of the demand curve)
Q2-Q1
Q2+Q1
EI =
I2-I1
I1+I2
d Q
I
= or = ------ . -----d I
Q
Cross (Price) Elasticity
A measure of the degree of responsiveness of
the demand for one good (X) to a change in
the price of another good (Y):
(Shift of demand curve)
Qx2- Qx1
Qx2+Qx1
Ec =
or =
Py2- Py1
Py1+Py2
d Qx
Py
----------- . ------d Py
Qx