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Managerial Economics
Demand Analysis
The Concept of Elasticity
and its Applications

Ch. 3
1
The concept of elasticity

The sensitivity (degree of
responsiveness) of sales (demand) to a
change in one of the demand-affecting
variables, say, price
2
The Importance of Elasticity
 The firm needs to know the effect of a
change in any of the determinants of demand
(price, advertising, income, competitors’
prices, etc.) that affects the demand for a
product in order to:
 Meet sales target
 Gain market share
 Maximize profit
3
The Price Elasticity of Demand
… measures the responsiveness of the
quantity demanded to a change in the
price of the product, holding constant the
values of all other variables in the demand
function. In mathematical term,
Ep =
%in Q
--------------- , ceteris paribus
%  in P
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The Arc Price Elasticity of
Demand
How can the percentage changes in Q and P be
calculated in order to derive the price elasticity of
demand?
Q
Ep =
--------------(Q1 + Q2)/2
-----------------P
-------------(P1 + P2)/2
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Drive the Demand Curve of the following
information:
(Q = 40,000,000 - 2,500P)
Price
16,000
P2=12,500
P1=12,000
B
A
Q
0
8,750,000
10,000,000
40,000,000
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How sensitive are consumers to a change
in the avg. price of automobiles?
We calculate the arc price elasticity of demand
between A and B as:
Ep =
10,000,000-8,750,000
-----------------------------[10,000,000+8,750,000]/2
-------------------------------- = - 3.267
12,000 - 12,500
----------------------[12,000 + 12,500]/2
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Interpretation
 Between points A and B (or between the
price range from $12,000 to $12,500), a
one-percent increase in the average price
of cars will bring about, on average, a
reduction of sales by 3.267%, ceteris
paribus.
 Because the price elasticity of demand is
calculated between two points on a given
demand curve, it is called the arc price
elasticity of demand.
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Classification of
The Price Elasticity of Demand
For decision-making purposes, three specific
ranges of price elasticity of demand have been
identified. Using the absolute value of the price
elasticity of demand, the three ranges are:
1) |Ep| > 1, the demand is said to be
elastic.
2) |Ep| < 1, the demand is said to be
inelastic.
3) |Ep| = 1, we have unitary elasticity.
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Caveat

Elasticity measure depends on the price
at which it is measured.

It is not generally a constant (because
the demand curve is not likely to be a
straight line).
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The Point Price Elasticity of Demand
It measures the price elasticity
of demand at a given price or a
particular point on the demand
curve.
Q P
ep = (-----)(----)
P Q
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Calculation of the point elasticity using
the demand for automobile equation
Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A
Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10, and A =
$300,000,000
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
The point price elasticity is:
Q P
ep = (-----) (---)
P Q
= (-2,500)(12,000/10,000,000)
=-3
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Point price elasticity (cont.)
What's the point elasticity of demand at
P2 = $12,500?
At this price, Q = 8,750,000.
Hence,
Q
P
ep = (-----) (---)
P Q
= (-2,500)(12,500/8,750,000)
= - 3.571
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Two versions of the elasticity
of demand – Point vs. Arc
Price
16,000
12,500
12,000
ep= -3.571
Ep= -3.267
ep= -3.0
8,750,000 10,000,000
Q
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From Concept to Applications
We began with a definition of the elasticity
of demand based on,
Ep
%in Q
= --------------%  in P
If we know the price elasticity of demand
(Ep), the formula will let us answer a
number of "what if" questions.
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Examples
(1) How great a price reduction is necessary
to increase sales by 10%?
(2) What will be the impact on sales of a 5%
price increase?
(3) Given marginal cost and price elasticity
information, what is the profit-maximizing
price?
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The price increase needed to reduce
gasoline consumption by 1%
Supposing that the elasticity of demand for
gasoline is -0.5, how much prices must go
up to reduce gasoline use by 1%?
- 0.01
- 0.5 = ---------- ,
%P
%P = (-0.01/-0.5) = + 0.02 or 2%
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Price elasticity of demand and Total
Revenue - Still Another Application
If |Ep | > 1, i.e., elastic demand,
P, TR decreases
If |Ep | < 1, i.e., inelastic demand,
P, TR increases
If |Ep | = 1, i.e., unitary elasticity,
P, TR remains
unchanged.
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Lessons:
(1) The first lessons in business: Never lower
your price in the inelastic range of the
demand curve. Such a price decrease would
reduce total revenue and might at the same
time increase average production cost.
(2) When the demand is inelastic, raise the
price to increase revenue and, possibly,
profit.
(3) When demand is elastic, price increases
should be avoided.
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Lessons
(4) But should we always cut price
when the demand is elastic?
Even over the range where demand is
elastic, a firm will not necessarily find it
profitable to cut prices; the profitability of
such an action depends on whether the
marginal revenues generated by the price
reduction exceed the marginal cost of the
added production.
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Another Example: Optimal Pricing
Step 1 – Using the relationship between MR and Ep
established in McGuigan/Moyer/Harris, Ch. 3, p. 90
Given, TR = PQ,
‫للفهم فقط‬
TR
 (PQ)
MR = ------- = --------Q
Q
Q
P
= P(-----) + Q (-----)
Q
Q
Q P
1
= P (1 + ----- -----) = P ( 1 + ----)
P Q
ep
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Optimal Pricing
Optimal Price is when MC = MR
i.e., MC = P (1 + 1/ep)
MC
P = ------------(1 + 1/ep)
That is, the profit-maximizing price is
determined by MC and ep
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Determinants of Price Elasticity of
Demand
Starter Questions :
(1) If the demand for gasoline is inelastic,
why is it that sales at a particular gas
station will drop off when it raises prices?
(2) What explains the fact that the demand
for some products is more sensitive to
price than the demand for other products?
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The determinants are:
1. The availability of substitute goods
2. The extent to which a good is considered
to be a necessity
3. The proportion of income spent on the
product
4. The cost of searching for lower prices
5. The degree to which price signals quality
6. Time
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Differentiation Strategy and
Elasticity


If your strategy is to differentiate your
product (a costly activity), you need low
elasticity (inelastic demand) to enable the
higher price.
If you are attempting a low-cost/price
leadership strategy, high elasticity is the
key. (You need to convince customers that
your products are good substitutes for the
leading brands.)
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Other Elasticities
The income elasticity of demand provides a
measure of the responsiveness of demand to
changes in income, holding constant the effect of
all other variables.
The "arc" income elasticity is:
Q
-----------Q1 + Q2
EI = --------------I
---------I1 + I 2
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Arc Income Elasticity Illustrated
The Demand for Automobiles:
Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A
Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10,
and A = $300,000,000
Then, Q1 = 10,000,000.
But if income rises to I2 = $24,000, sales forecast is raised by 500,000
to Q2 =10,500,000.
This implies an income elasticity of:
500,000
-------------------------------10,000,000+10,500,000
EI =
----------------------------------- = 2.317
500
------------------------------23,500+24,000
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Point income elasticity:
Q
eI =
I
----- ----I
Q
At I1 = $23,500,
23,500
eI = (1,000) ( ----------------) = 2.35
10,000,000
and at I2 = $24,000,
24,000
eI = (1,000) ( ---------------) = 2.29
10,500,000
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Examples of Income Elasticities
Description
Income Elasticity
Examples
----------------------------------------------------------------------------------Inferior goods
EI < 0
Basic foodstuffs,
(Countercyclical)
generic products, bus
rides, etc.
Noncyclical normal 0 < EI < 1
Cigarettes, liquor, goods
soaps, movies, health care
etc.
Cyclical normal
EI > 1
New cars, houses, goods
travel,capital
equipment, etc.
------------------------------------------------------------------------------------------
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Cross-Price Elasticity of Demand
A change in the price of Coca Cola influences
the sales of Pepsi. We use the concept of
cross-price elasticity of demand to measure
the relationship between the price of Coca
Cola and the volume of sales of Pepsi.
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The Arc Cross Elasticity of Demand
Supposing that product x and y are
related, and that,
Qx = a0 + a1Px + a2I + a3Py
The arc cross-price elasticity is:
Qx
-------------Qx1 + Qx2
EPy = ------------------Py
------------Py1 + Py2
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The point cross-price elasticity
Qx Py
e py = ( -----)(----)
Py Qx
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Some Uses of Cross-Price Elasticity


According to an FTC Report by Michael
Ward, AT&T’s cross price elasticity of
demand for long distance services is 9.06
If MCI and other competitors reduced their
prices by 4 percent, what would happen to
the demand for AT&T services?
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Answer
AT&T’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
d
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
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Antitrust and Cross Elasticities of
Demand

Cross elasticity of demand is used in
industrial organization to measure the
interrelations among industries. The case
of DuPont and its Cellophane.
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