04 demand elasticity -revised
TRANSCRIPT
Chapter Four Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Chapter 4
DemandElasticity
Chapter Four Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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OverviewThe economic concept of elasticityThe price elasticity of demandThe cross-elasticity of demandThe income elasticity of demandElasticity of supply
Chapter Four Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Learning objectivesdefine and measure elasticity
apply concepts of price elasticity, cross-elasticity, and income elasticity of demand
understand determinants of elasticity
show how elasticity affects business revenue
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The economic concept of elasticity
Elasticity: the percentage change in one variable relative to a percentage change in another.
Example, if A = f(B, other factors), then
Bin changepercent Ain changepercent Elasticity oft Coefficien
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Price elasticity of demand Price elasticity of demand: the
percentage change in quantity demanded caused by a 1 percent change in price. The general formula for calculation is:
Price %Quantity %E
p
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Price elasticity of demand Arc elasticity: elasticity which is
measured over a discrete interval of a curve
Ep = coefficient of arc price elasticity Q1 = original quantity demanded Q2 = new quantity demanded P1 = original price P2 = new price
2/)(2/)( 21
12
21
12
PPPP
QQQQEp
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Price elasticity of demand Point elasticity: elasticity measured at a
given point of a demand (or a supply) curve. If Q = f(P), then
EX = (dQ/dP) × (P1 /Q1 )where: * dQ/dP is the derivative of Q with respect to P. * P1 and Q1 are the current values.
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Price elasticity of demandWhen do we use point and arc elasticity?
It depends on the available information: If we have the demand function, we
can use the point elasticity formula. If we don’t, and instead we have 2
pairs of prices and quantities, we use the arc elasticity formula.
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Price elasticity of demand Look into your textbook p. 105, problem 2, part a.
We are given the demand function, from which we get (dQ/dP) = -2, and we are asked to calculate the price elasticity of demand at the price P=5. At this price the quantity is Q=20-2×5=10. Therefore
EP = -2 × (5/10) = -1 Now make the calculations at P=9.
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Price elasticity of demand Look into your textbook p. 107,
problem 12, part a. Here we have 2 pairs of Q and P. We use the arc elasticity formula.
EP = (60/100)/(-1/3) =-1.8
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Price elasticity of demand
Elasticity varies along a linear demand curve Although the slope
is the same, elasticity varies along the D curve.
Economic Reason?
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Price elasticity of demand Some demand curves have constant
elasticity
such a curve has a nonlinear equation:
Q = aP-b
where –b is the elasticity coefficient
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Price elasticity of demand Categories of elasticity: (let Ep represent
the absolute value of price elasticity of demand ) Relatively elastic demand: Ep > 1 Relatively inelastic demand: 0 < Ep < 1 Unitary elastic demand: Ep = 1 Perfectly elastic demand: Ep = ∞ Perfectly inelastic demand: Ep = 0
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Price elasticity of demand Factors affecting demand elasticity
ease of substitution proportion of total expenditures durability of product
possibility of postponing purchasepossibility of repairused product market
length of time period
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Price elasticity of demand Derived demand: the demand for
products or factors that are not directly consumed, but go into the production of a another (final) product
The demand for such a product or factor exists because there is demand for the final product
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Price elasticity of demand The derived demand curve will be more
inelastic: the more essential is the component the more inelastic is the demand curve
for the final product the smaller is the fraction of total cost
going to this component the more inelastic is the supply curve of
cooperating factors
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Price elasticity of demand A long-run demand
curve will generally be more elastic than a short-run curve.
As the time period
increases, consumers find ways to adjust to the price change, via substitution or shifting consumption.
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Price elasticity of demand The relationship between price and total
revenue TR depends on elasticity. Why? By itself, a price fall will reduce TR. BUT
because the demand curve is downward sloping, the drop in price will also increase quantity demanded. In order to know the final effect on TR, we need to know:
Which effect will be stronger?
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Price elasticity of demand As price decreases
revenue rises when demand is elastic
revenue falls when it is inelastic
revenue reaches it peak if elasticity =1
the lower chart shows the effect of elasticity on total revenue
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Price elasticity of demand Marginal revenue: the change in total
revenue resulting from changing quantity by one unit
QuantityMR
Revenue Total
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Price elasticity of demand
For a linear demand curve, marginal revenue curve is twice as steep as the demand
curve
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Price elasticity of demand at the point where
marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum
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Price elasticity of demand Examples: some real world elasticities
coffee: short run -0.2, long run -0.33 kitchen and household appliances: -0.63 meals at restaurants: -2.27 airline travel in U.S.: -1.98 beer: -0.84, Wine: -0.55
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Price elasticity of demand Examples: some real world elasticities
white pan bread:-0.69 cigarettes: short run -0.4, long run -0.6 wine imports: -0.15 crude oil: -0.06 internet services: -0.6 to -0.7
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Cross-elasticity of demand Cross-elasticity of demand: the
percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product
B
Ax P
QE
%%
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Cross-elasticity of demand Arc cross-elasticity
Exercise: Calculate the cross elasticity of demand in part b, problem 12, p. 107 of the textbook. It must be
(50/65)×(-1/3) = -2.3 Are these two goods substitutes or complements?
How do you know?
2/)(2/)( 21
12
21
12
BB
BB
AA
AA
PPPP
QQQQEX
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Cross-elasticity of demand Point cross-elasticity EX = (dQA /dPB) × (PB /QA ) Exercise: In problem 10 p. 72 of the textbook,
calculate the cross elasticity of demand. Let the concerned company be A and the competitor
B. Then (dQA /dPB) = 3. And the current PB = $500, and the current QA = 251400. Therefore E = 3 × (500/251400) = 5.96.
Are these two goods A and B substitutes or complements? How do you know?
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Cross-elasticity of demand The sign of cross-elasticity for substitutes
is positive
The sign of cross-elasticity for complements is negative
Two products are considered good substitutes or complements when the coefficient is larger than 0.5 (in absolute value)
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Income elasticity Income elasticity of demand: the
percentage change in quantity demanded caused by a 1 percent change in income
Y is shorthand for income
YQEY
%%
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Income elasticity Arc income elasticity
2/)(2/)( 21
12
21
12
YYYY
QQQQEY
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Income elasticity Categories of income
elasticity Normal luxury
(superior) goods: EY > 1
Normal necessary goods: 0 ≤ EY ≤ 1
Inferior goods: EY < 0
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Other demand elasticities Examples: elasticity is encountered every
time a change in some variable affects demand
advertising expenditure interest rates population size
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Elasticity of supply Price elasticity of supply: the
percentage change in quantity supplied as a result of a 1 percent change in price
The coefficient of supply elasticity is a normally a positive number
Price %SuppliedQuantity %E
S
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Elasticity of supply Arc elasticity of supply
2/)(2/)( 21
12
21
12
PPPP
QQQQEs
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Elasticity of supply When the supply curve is more elastic, the
effect of a change in demand will be greater on quantity than on the price of the product.
When the supply curve is less elastic, a change in demand will have a greater effect on price than on quantity.
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Global application Example: price elasticities in Asia
Can the concepts of demand elasticity help explain the gain from trade to Asian countries?
End of chapter 4