EC611--Managerial Economics
Demand Elasticity
Dr. Savvas C Savvides, European University Cyprus
Determinants of Demand for a
Product
QX = f (PX, AX ,OX , FX … Yc , Tc , Ec ….
Strategic vbls.
Controlled vbls.
Consumer vbls.
Uncontrolled vbls.
… PY, AY ,OY , FY … G, N, FX, W…)
Competitor vbls.
Uncontrolled
Environmental vbls.
Variables
1
Linear Demand Function
QX = f(PX, N, I, PY, T)
QX = a0 + a1PX + a2N + a3I + a4PY + a5T
PX
Intercept:
a0 + a2N + a3I + a4PY + a5T
Slope:
∆QX/∆PX = a1
QX
2
The price elasticity of demand
…measures the sensitivity of the quantity
demanded of a good to a change in its price
It is defined as:
% change in quantity demanded
% change in price
3
Price Elasticity of Demand
Point Definition
∆Q / Q ∆Q P
=
⋅
EP =
∆P / P ∆P Q
Linear Function
P
= a1 ⋅
Q
E
P
4
Price Elasticity –Example 1
Assume that the demand function for a commodity is:
Q = 245 – 3.5P
Recall that
E
P
= a1 ⋅
Î What is Ep if P = 10?
P
Q
To find Ep we need to find values for P, Q and α1 (or
dQ/dP)
At P=10, Q = 245 –3.5 (10) = 210
dQ/dP is found by the first derivative of the demand eq.
Î dQ/dP = -3.5 Substituting in the elasticity eq. we get:
Î Ep = (dQ/dP) (P/Q) = -3.5 (10/210) = -1/6 = - 0.167
Therefore, if P changes by 10%, Q will fall by 1.67%.
Î The demand for this product is inelastic
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Price Elasticity–Example 2
Assume the following demand equation:
P = 125 –5Q
Î What is Ep if Q = 10 units?
To find Ep we must first invert the eq. in terms of P:
Î -5Q = P – 125
At Q= 10
Î 5Q =125 –P
Î 10 = 25 –0.2 P
Î Q = 25 –0.2P
Î 0.2P = 15
Î P =75
Substituting in the Ep expression we get:
Î Ep = (dQ/dP) (P/Q) = -0.2 (75/10) = -1.5
Therefore, if P changes by 10%, Q will fall by 15%.
Î The demand for this product is elastic
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Relationship between Demand Curve and
Marginal Revenue Curve
The slope of MR is twice the slope of Demand curve
AR = P = a – bQ
TR = P * Q = Q (a – bQ ) = aQ – bQ2
MR = dTR / dQ = a –2bQ
Îslope of demand curve (or AR) = - b
ÎSlope of Marginal Revenue = -2b
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Marginal Revenue, Total Revenue,
and Price Elasticity
TR
MR>0
EP > 1
MR<0
EP < 1
EP = 1 MR=0
TR
QX
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Elasticity and Total Revenue
Assume a price reduction
(1) Elastic demand:
Increase in revenue (due to
more sales, Q) will exceed
the fall in revenue (due to
fall in P)
Î MR is positive
Î Total Revenue will rise.
(+)TR > (-)TR
(+)TR < (-)TR
TR
(2) Inelastic demand:
Increase in revenue (due to
more sales, Q) will be less
than the fall in revenue
(due to fall in P)
Î MR is negative
Î Total Revenue will fall.
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Relationship Between Price Elasticity
& Revenue
Price Elastic
Demand
Unitary Elastic Price Inelastic
Demand
Demand
Price
Increase
P X Q = TR
P X Q = TR
P X Q = TR
Price
Decrease
P X Q = TR
P X Q = TR
P X Q = TR
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Marginal Revenue and Price
Elasticity of Demand
PX
EP > 1
⎛
1 ⎞
MR = P ⎜1 +
⎟
⎝ EP ⎠
EP = 1
EP < 1
QX
MRX
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Application of Elasticity —
Relationship between MR, P and Elasticity
We know that TR =P*Q
MR = dTR/dQ = d(P*Q)/dQ
Using the Product Rule: Î
P (dQ/dQ) + Q (dP/dQ)
Multiplying and dividing through by P, we get:
MR = P [ 1 + Q/P(dP/dQ)]
Recall that Ep = (dQ/dP) (P/Q)
Therefore, the second term in the MR expression above is the
inverse of Ep
⎛
1 ⎞
M R = P ⎜1 +
⎟
Î
E
⎝
P ⎠
If, for example, P=24 and Ep = -2
Î MR = 4 (1 + 1/-2) = 2
In perfect comp., we know that Ep = ∞ and MR = P
Î MR = P ( 1 + 1/ ∞ ) = P
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Application of Elasticity — Elasticity and
Pricing Policy for Profit Maximization
We know that for profit max. MR must be equal to MC
⎛
1
MC = M R = P ⎜ 1 +
E
⎝
Solving for P, we get
P
⎞
⎟
⎠
Î P = MC = [1 /(1+1/Ep)]
If, for example, MC = £10 and Ep = -2
ÎSolving for P we get:
P = 10 (1 /(1+1/-2)] = £20
If, on the other hand, Ep = -5,
Then,
Î P = 10 (1 /(1+1/-5)] = £12.5
Therefore, we see that for profit maximization, given MC,
Î price is inversely related to its price elasticity
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Real World Price & Income Elasticities
Price Elasticity
Income Elasticity
Fresh meat
1.4
0.0
Alcoholic beverages
1.3
1.7
Services
1.0
1.8
Durable goods
0.9
1.5
Fresh vegetables
0.6
0.1
Housing*
0.5
2.0
Tobacco*
0.5
0.4
Gasoline*
0.25
0.75
Residential Electricity*
0.2
0.1
Beer*
0.5
0.6
Good
* Estimates for Cyprus
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Elasticity and Air Fares
How should air fares be changed to increase revenues?
Holiday travellers can use boats, and cars or trains (for
domestic travel). They can also plan their vacation and
shop around for discounts and special prices.
so demand may be elastic (greater than one, e.g. - 1.3)
and an increase in fares will reduce the number of journeys demanded
and total spending
Business travellers do not have good travel options
demand may be inelastic (less than one, e.g. - 0.5)
so raising fares will have less effect on journeys demanded
and revenue will improve
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Price & Income Elasticities for Airline Travel
Price Elasticity
Income Elasticity
First Class
0.45
1.50
Regular Economy
1.30
1.38
Excursion fare
1.83
2.37
Type of Ticket
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Determinants of Price Elasticity of
Demand
Price elasticity is affected by:
The number of close substitutes
Î the more the substitutes, the higher EP
How narrowly the product is defined
Î EP (car industry) > EP (small car) > EP (1200 cc)
The time available for adjustments in prices to
take place; the more time available to adjust to
price changes the more elastic the demand
Î E long term > E short term
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SR & LR Price Elasticities in US
Commodity
SR Elasticity
LR Elasticity
Radio & TV Repair
0.47
3.84
Motion Picture
0.87
3.67
Tobacco Products
0.46
1.89
Electricity (Household)
0.13
1.89
Bus Transport (local)
0.20
1.20
Medical Insurance
0.31
0.92
Gasoline
0.30
0.66
Stationery
0.47
0.56
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Income Elasticity of Demand
Point Definition
∆Q / Q ∆Q I
EI =
=
⋅
∆I / I
∆I Q
Linear Function
I
= a3 ⋅
Q
Normal Good
EI > 0
EI
Inferior Good
EI < 0
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Income Elasticity of Demand
Demand Response to 1% Rise in Income
Good
Income
Elasticity
Quantity
Demanded
Normal
Positive
Rises
-Luxury
Above 1
-Necessity
Inferior
Budget
Share
Example
Rises more
than 1%
Rises
BMW
0< Ep <1
Rises less
than 1%
Falls
Food
Negative
Falls
Falls
Bread
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Application of Income Elasticity
1. Long-range planning of firm’s growth
Over LR, we expect people’s incomes to rise. High income
elasticities are good news for luxury good producers in
the LR. Over the SR, however, there will more volatility.
Î Income elasticity for cars was estimated to be 2.5 –3.9.
This may explain why car sales fall dramatically during
recessions and rebound strongly during recoveries
2. Developing Marketing Strategies
Income elasticity of market segments influences
•the location and nature of distribution outlets
•The extent and focus of advertising
•The choice of promotional activities
Î Sellers of luxury items direct advertising and promotions
to YUBBIE groups whose incomes are expected to rise
21
Cross-Price Elasticity of Demand
Point Definition
Linear Function
Substitutes
E XY > 0
E XY
E
∆QX / QX ∆QX PY
=
=
⋅
∆PY / PY
∆PY QX
XY
PY
= a4 ⋅
QX
Complements
E XY < 0
22
Using Elasticity in Managerial
Decision Making
Knowing the elasticity of demand with respect to the
major controlled and uncontrolled variables and forces, the
firm can determine the optimal policies to maximize its
objective function(s)
If the demand for the product is inelastic (Ep < 1),
the firm would be hesitant to lower prices, since this will lead to
lower TR
If the firm has estimated that the cross-price elasticity of its
product w.r.t. a competitors product’s price is very high, it will be
quick to respond to a competitor’s price reduction so that it does
not lose sales and market share.
Î Therefore, the first should first identify the important variables
and then try to obtain estimates of the marginal effects of a
change in each vbl. on demand.
Î This will be accomplished using regression analysis.
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Other Factors Related to Demand
Theory
International Convergence of Tastes
Globalization of Markets
Influence of International Preferences on
Market Demand
Growth of Electronic Commerce
Cost of Sales
Supply Chains and Logistics
Customer Relationship Management
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