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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?
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220
TR 0 = 220 x 120 = 26,400
TR1 = 180 x 140 = 25,200
TR2 = 180 x 200 = 36,000
120
180
0 Q
D 2
D 1
140 200video.edhole.com
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.
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Determining Price Elasticity
Percentage Change in Quantity
Ep =
Percentage Change in Price
Change in Quantity
Quantity
Ep =
Change in Price
Price video.edhole.com
Ep (a --- b) = (10/8)/(-2/10) = -6.25
Ep (c ---d ) = (10/80)/(-2/4) = -.25
P
Q
D
ab
cd2
4
8
10
8 18 80 90
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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.
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Arc (Price) Elasticity
P
Q
D24
Note that if we increased the price,
(from 8 to 10 or 2 to 4)
the original P and Q would be 2 and 8 and 18 and 90, respectively.
Ep = (-10/18)/(2/8) = -2.22
Ep = (-10/90)/(2/2) = -.11
810
8 18 80 90
a
b
c
d
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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 -2
(P1+P2) 10+8
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Elasticity and the Price Level
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.
P
D
8 18 80 90
a
b
c
d24
810
| Ep | > 1 : Elastic
| Ep | < 1 : Inelastic
| Ep | = 1 : Unit-elastic
E =-3.49
E = -.17
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Point Elasticity Q
---------
Q1+Q2 Q P1+P2 Q P
E = ------------ = ------- . ------- = ------- . ------
P P Q1+Q2 P Q
---------
P1+P2
dQ P
Or, = ------ . -----
dP Qvideo.edhole.com
P,MR
Q
Q
TR
0
0
| E | = 1
Q = C - b P
C 1P = ----- - ----- Q b b
C 2MR = ------ - ------ Q b b
C
DMR
Note: In the demand equation dQ/dP = -b
That means
PE p = -b ----- Q
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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 d Q
MR = ------ = -------- = ------ .Q + ------ .P
Q Q d Q d Q
d P Q P 1
= ( -----. ----- + ------ ).P = P. ( ------- + 1 )
d Q P P Evideo.edhole.com
0 Q
Q = C - b P
Slope= -1/b
Slope=-2/bD
MR
C
P, MR
dQ ---- = - bd p
dQ P PE = ----- . ----- = -b . ------ d p Q Q
1MR = P. ( 1 + ---- ) E
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Special Cases
P
D
D
Q0 0 Q
Infinitely (price) elastic Infinitely price inelastic
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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).video.edhole.com
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 timevideo.edhole.com
Elasticity and Passage of Time
DoD1D2D3
QoQ’oQ1Q2Q3
Q
P
O
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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
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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 d Q I
EI = = or = ------ . ------
I2-I1 d I Q
I1+I2
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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 d Qx Py
Ec = or = ----------- . -------
Py2- Py1 d Py Qx
Py1+Py2video.edhole.com