What will you learn in this chapter?
• Concept of elasticity.
• Calculate price elasticity of demand and supply using the mid‐point method.
• Explain how the determinants of price elasticity of demand and supply affect the degree of elasticity.
• Calculate cross‐price and income elasticities of demand, and interpret the sign of the elasticities.
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1© 2014 by McGraw‐Hill Education 1
Chapter 4
Elasticity
© 2014 by McGraw‐Hill Education 2
What will you learn in this chapter?
• Concept of elasticity.
• Calculate price elasticity of demand and supply
using the mid‐point method.
• Explain how the determinants of price
elasticity of demand and supply affect the
degree of elasticity.
• Calculate cross‐price and income elasticities of
demand, and interpret the sign of the
elasticities.
© 2014 by McGraw‐Hill Education 3
• Elasticity is a measure of the responsiveness to
a change in a market condition.
• The concept applies to supply and demand.
• It measures the response to a change in:
– the price of the good.
– the price of a related good.
– income.
What is elasticity?
2© 2014 by McGraw‐Hill Education 4
Price elasticity of demand
Quantity of coffee (millions of cups)
1. When price
Decreases by 25%...
2. quantity
demanded
increases
by 50%.
0
0.50
1.00
1.50
2.00
2.50
3.00
5 10 15 20
Price ($)
D
A
B
• The price elasticity of demand measures the magnitude
of change in the quantity demanded from a change in
its price. In other words, it estimates price sensitivity.
© 2014 by McGraw‐Hill Education 5
Calculating price elasticity
• The midpoint method calculates the elasticity at
the midpoint of any two points. The formula is:
ߝ ൌ %∆ೂ%∆ು ൌ ሺೂమషೂభሻ/ሾሺೂమశೂభሻ/మሿሺುమషುభሻ/ሾሺುమశುభሻ/మሿ
where point 1 is ሺ ଵܲ, ܳଵሻ and point 2 isሺ ଶܲ, ܳଶሻ.
• The midpoint elasticity is the difference of any
two numbers divided by their average.
© 2014 by McGraw‐Hill Education 6
Active Learning: Calculating the price
elasticity of demand
Find the price elasticity of demand using the
midpoint formula for the points along a demand
curve: ($10,350) and ($20, 150).
3© 2014 by McGraw‐Hill Education 7
• Consumers are more sensitive to price changes
for some goods and services than for others.
• Many factors determine consumers’
responsiveness to price changes.
– Availability of substitutes.
– Degree of necessity.
– Cost relative to income.
– Adjustment time.
– Scope of the market.
Determinants of price elasticity of demand
© 2014 by McGraw‐Hill Education 8
• All goods and services can be broadly
categorized based on elasticity.
• The main categories are:
– Elastic: A change in price causes a relatively large
percentage change in quantity demanded.
– Inelastic: A change in price causes a relatively small
percentage change in quantity demanded.
Categorizing elasticities
© 2014 by McGraw‐Hill Education 9Quantity
0
5
10
5 10
Price ($)
At prices
higher than $5,
the quantity
demanded is 0.
D
Price ($)
Quantity
0
5
10
5 10
At any
price, the
quantity
demanded
is the
same.
D
Consumers
will buy any
quantity at a
price of $5
Categorizing elasticities
At the extremes, demand can be either perfectly elastic or
perfectly inelastic.
Perfectly elastic (|εd| = ∞) Perfectly inelastic (|ε d | = 0)
4© 2014 by McGraw‐Hill Education 10
Categorizing elasticities
10
0
1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8 9 10
Price ($)
Quantity
Elastic (|εd | >1)
quantity
demanded
increases by 60% .
quantity
demanded
increases by 20%.
D
Inelastic (|εd | < 1)
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10
Price ($)
Quantity
D
Between these two extremes, the elasticities are divided into
three categories.
Quantity
quantity
demanded
increases by 40%.
Unit‐elastic (|εd | = 1)
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10
Price ($)
D
When price declines by the same amount (say 40%)
© 2014 by McGraw‐Hill Education 11
• Knowing whether the demand for a good is
elastic or inelastic is extremely useful in
business.
– Allows managers to determine whether a price
increase will cause total revenue to rise or fall.
• Total revenue is the amount that a firm
receives from the sale of goods and services.
– Total revenue (TR) equals price paid (P) multiplied
by quantity sold (Q), or TR = P x Q.
Using price elasticity of demand
© 2014 by McGraw‐Hill Education 12
Using price elasticity of demand
Quantity
Price ($)
1. As price
Increases
0
50
100
150
200
250
300
350
400
450
500
2 4 6 8 10 12 14 16 18 20
2. quantity
decreases.
2+3= total revenue
after the price change.
1+2= total revenue
before the price
change.
Price effect
Quantity effect
D
12
3
An increase in price affects total revenue in two ways.
5© 2014 by McGraw‐Hill Education 13
Using price elasticity of demand
0
1
2
3
4
5
1 2 3 4 5 6 7 8 109
Price ($)
Quantity (thousands)
When demand is
elastic, the quantity
effect outweighs the
price effect.
D
Price effect
Quantity effect
0
1
2
3
4
5
1 2 3 4 5 6 7 8 109
Price ($)
Quantity (thousands)
When demand is inelastic,
the price effect outweighs
the quantity effect.
D
Price effect
Quantity effect
The magnitude of the price and quantity effects
are determined by the elasticity of demand.
© 2014 by McGraw‐Hill Education 14
Active Learning: Calculating the change in
total revenue
Find the change in total revenue using the following two
points along a demand curve: ($20, 150) and ($10,350).
© 2014 by McGraw‐Hill Education 15
Using price elasticity of demand
P ($) Q TR ($)
50 0 0
45 1 45
40 2 80
35 3 105
30 4 120
25 5 125
20 6 120
15 7 105
10 8 80
5 9 45
0 10 0
Inelastic
demand:
decreasing
price
revenue
Elastic
demand:
decreasing
revenue
price
Total revenue ($)
0
25
50
75
100
125
21 3 4 5 6 7 8 9 10
QuantityQuantity
0
Price ($)
5
10
15
20
25
30
35
40
45
50
1 2 3 4 5 6 7 8 9 10
D
The relationship between P, Q, TR, and εd is
summarized as follows.
6© 2014 by McGraw‐Hill Education 16
• The concept of elasticity can also be applied to
supply.
• The price elasticity of supply measures producers’
response (in quantity) to a change in price.
– Uses same midpoint formula but replaces quantity
demanded with quantity supplied.
– Elasticity is always positive.
– Same interpretation:
• Elastic: εs >1.
• Unit Elastic: εs =1.
• Inelastic: εs <1.
Price elasticity of supply
© 2014 by McGraw‐Hill Education 17
• Producers are more sensitive to price changes
for some goods and services than for others.
• Many factors determine producers’
responsiveness to price changes.
– Availability of inputs.
– Flexibility of the production process.
– Adjustment time.
Determinants of price elasticity of supply
© 2014 by McGraw‐Hill Education 18
Cross‐price elasticity of demand
• The cross‐price elasticity of demand is a measure of
how the quantity demanded of one good changes when
the price of a different good changes.
• The midpoint formula calculates the elasticity between
the quantity demanded of good A and the price of good
B:
ߝ, ൌ %∆ೂಲ%∆ುಳ ൌ ሺೂమషೂభሻ/ሾሺೂమశೂభሻ/మሿሺುమషುభሻ/ሾሺುమశುభሻ/మሿ
• The cross‐price elasticity of demand can be positive or
negative.
– ߝ,>0: the two goods are substitutes.
– ߝ,<0: the two goods are complements.
7© 2014 by McGraw‐Hill Education 19
Income elasticity of demand
• The income elasticity of demand is a measure of how
much the quantity demanded changes in response to a
change in consumers’ incomes.
• The midpoint formula calculates the elasticity between
the quantity demanded of a good and consumer’s
income:
ߝூ ൌ %∆ೂ%∆ ൌ ሺೂమషೂభሻ/ሾሺೂమశೂభሻ/మሿሺమషభሻ/ሾሺమశభሻ/మሿ
• The income elasticity of demand can be positive or
negative.
– ߝூ>0: the good is normal. If ߝூ>1, then it is a luxury.
– ߝூ<0: the good is inferior.
© 2014 by McGraw‐Hill Education 20
Active Learning: Calculating the income
elasticity of demand
• When consumers’ income is $100, they buy 250
units of a good. When consumers’ income
increases to $200, they buy 500. Find the income
elasticity of demand using the midpoint formula.
• Is the good inferior or normal?
• Is it a luxury good?
© 2014 by McGraw‐Hill Education 21
Four measures of elasticity
Measure Equation Negative Positive More elastic Less elastic
% change in quantity demanded
% change in price Always Never
Over time, for
substitutable
goods and
luxury items
In the short
run, for unique
and necessary
items
% change in quantity supplied
% change in price
Always
Over time,
with flexible
production
In the short
run, with
production
constraints
% change in quantity demanded of A
% change in price of B
For
comple-
ments
For
substitutes
For near perfect
substitutes
and strong
complements
For loosely
related goods
% change in quantity demanded
% change in income
For
inferior
goods
For normal
goods
For luxury items
with close
substitutes
For unique
and necessary
items
Never
8© 2014 by McGraw‐Hill Education 22
Summary
• Elasticity is the first of several concepts used to
apply the concepts of supply and demand to
business and policy questions.
– Indicates the sensitivity of quantity to a change in:
• Price.
• Price of a related good.
• Income.
• The price elasticity of demand can be used to
set prices so firms can maximize revenue.