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Chapter 4
Elasticity
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Elasticity:
The responsiveness of dependent variable to change in independent variable
A measure of the extent to which quantity demanded and quantity supplied respond to variations in price, income, and other factors.
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Price Elasticity of Demand
Definition: % change in Qd due to 1% change in P.
Application: change in price on – total revenue for sellers– total expenditure for buyers– effectiveness of policy in influencing indi
vidual behaviors
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Exercise: 4.1, P.99
Known:– P=$400, Qd=10K;– P=$380, Qd=12K
Solve for: Ed Is D elastic? Should P go down from $400 to $380?
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Elastic Demand
|Ed| > 1: (|Ed| →∞) Elastic
– price changes by 1%, quantity demanded changes by more than 1%.
– price and total revenue are negatively related
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Inelastic Demand :
|Ed| < 1, (|Ed| = 0) Inelastic
– price changes by 1%, quantity demanded changes by less than 1%
– price and total revenue are positively related
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Unit Elastic Demand
|Ed| = 1, Unit Elastic
– price changes by 1%, quantity demanded also changes by 1%
– total revenue is maximized
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Perfectly Elastic and Perfectly Inelastic Demand Curves
Figure 4.8, P.106
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Mid-Point Method
Change in Q = Q2 - Q1 Change in P = P2 - P1 E = {(Q2-Q1)/[(Q2+Q1)/2]}
/ {(P2-P1)/[(P2+P1)/2]}
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Example:
1998 1999
P $3.70 $2.72
Qd 1.74B 1.9B
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Calculation
Change in Qd = 1.9 – 1.74 = 0.16 Change in P = 2.72 – 3.70 = - 0.98 Average Qd = (1.74 + 1.9) / 2 = 1.82 Average P = (3.70 + 2.72) / 2 = 3.21 E = (0.16/1.82) / (-0.98/3.21) = - 0.29 TR1998 = 6.438, TR1999 = 5.168
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What does it mean?
Elastic? (Ed = -0.29 absolute value < 1)
Impact on TR when P decreases Possible type of good
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Factors Affecting Elasticity of Demand
Substitutability Share in budget Necessity vs. Luxury Time span: short term vs. long term
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Price Elasticity of Demand
Definition: % change in Qd due to 1% change in P.
Formula: Ed = %ΔQd / %ΔP
= (ΔQd / Qd ) / (ΔP/P)
= (Δ Qd /ΔP) x P/QdSlope of D Initial position
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Determinants of Elasticity
Slope of the demand curve at the price Position of the point (price level) on the
demand curve
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Price Elasticity and the Steepness of the Demand Curve
Figure 4.5, P.104
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Fig. 4.5, P.104
Elasticity affected by both slope and position– At (4,4)
• Ed on D1=1/2• Ed on D2=2
– On D2• Ed at (4,4) = 2• Ed at (1, 10) = 1/5
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Price Elasticity Regions along a Straight-Line Demand Curve
Figure 4.7
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Conclusions:
For Straight-line Demand Curves: Ed at mid-point = 1
– P > Pm Elastic– P < Pm Inelastic
To increase TR– P > Pm: Lower P Higher TR– P < Pm: Higher P Higher TR
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Total Expenditure as a Function of PriceFigure 4.12
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Cross-Price Elasticity
Responsiveness of demand for one good to changes in the price of a related goods.
Ec = (Δ Qx/ ΔPy) x (Py/Qx)
Ec > 0, substitutes
Ec < 0, complements
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Income Elasticity of Demand
The responsiveness of demand to changes in consumer income
% change in Q divided by % change in Y Em = (Δ Q/ ΔY) x (Y/Q)
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Income Elasticity of Demand
0 < Em < 1: (Em = 0) Income Inelastic
Income changes by 1%, quantity demanded changes by less than 1%.
Em > 1: Income Elastic
Income changes by 1%, quantity demanded changes by more than 1%.
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Income Elasticity of Demand
Em = 1: Income Unit Elastic
Income changes by 1%, quantity demanded changes by 1%.
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Categories based on elasticity
Em > 0: Normal goods
– Em > 1: Luxury goods
– Em < 1: Necessity
Em < 0: Inferior goods
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Engel’s Law
with a given set of tastes and preferences, as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises
the income elasticity of demand of food is less than 1 (necessity)
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Engel’s Coefficient
% change in food expenditure / % change in total expenditure
% change in food expenditure / % change in income
– EC > 59%: absolutely poverty (绝对贫困 ); – 50% < EC <59%: barely enough food and clothing (温饱) ;
– 40% < EC < 50%: moderately well-off (小康)– 30% <EC < 40%: well-to-do (富足)– EC < 30%: wealthy (富裕)
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Summary: Elasticity of Demand
Price Elasticity Cross-Price
ElasticityIncome Elasticity
%ΔQd / %ΔP %ΔQd(x)/ %ΔP(y) %ΔQd / %ΔY
Elastic (horizontal)
Inelastic (vertical)
Unitary elastic
Complements
Substitutes
Normal vs. inferior
Luxury vs.necessity
Luxury/necessity
Substitutability
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Price Elasticity of Supply
Definition: % change in Qs due to 1% change in P.
Formula: Es = %ΔQs / %ΔP
= (ΔQs / Qs ) / (ΔP/P)
= (Δ Qs /ΔP) x P/Qs
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Again: slope and position
S’
Es at Point A:On S: (8/2)(1/2)=2On S’: (14/2)(1/6)=7/6
Es on S:At A: (8/2)(1/2)=2At B: (10/3)(1/2)=5/3
Conclusions:Es declines as Q increasesEs declines faster if slope is steeper
14
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Special Case: fig.4.14, P.113
Es = 1 everywhere If S is straight and
passes through origin
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Special cases:Perfectly inelastic and Perfectly elastic supply curves
Fig.4.15, P. 113 Fig. 4.16, P.114
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Price Elasticity of Supply
Es > 1: (Es →∞) Elastic
price changes by 1%, quantity supplied changes by more than 1%.
Es < 1, (Es = 0) Inelastic
price changes by 1%, quantity supplied changes by less than 1%
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Unit Elastic Supply
Es = 1, Unit Elastic
price changes by 1%, quantity supplied also changes by 1%
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Factors Affecting Elasticity of Supply
Availability of inputs:
– Flexibility; mobility; substitute Length of production period Difficulty of production Technology
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Incidence of Excise Tax
Who bears the real burden of tax, the buyer or the seller?
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Effect of an Excise Tax Levied on the Sales of Taxi Rides
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Effect of an Excise Tax Levied on Purchases of Taxi Rides
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The Revenue from an Excise Tax