Download Our Friend Elasticity

Our Friend Elasticity
Or, how I learned to love percentages
Direction of Change versus
Sensitivity
• A summary of the all of the determinants of demand and
supply are given in their respective functions. These
functions assist in distinguishing between a movement
from a shift of a curve AND the direction of change for
each of the determinants.
• To increase the explanatory power of the demand and
supply model, and to make it more interesting, we need to
not only know the direction of change but how much each
of the determinants affects demand and supply.
• This concept of responsiveness is called elasticity.
Measuring Responsiveness or
Sensitivity
•
•
The initial candidate for measuring sensitivity is the concept of slope. Slope
tells us the change in the quantity demanded or demand from a change in one
of its determinants (i.e. ΔQd /ΔP in the case of prices)
The problems with slope are:
– Slope is unit dependent. If the units in which the currency (dollars to pesos) or
quantity changes (boxes of apples to individual apples) it will change the slope.
For example, the change from dollars to pesos will decrease the slope.
– Slope gives no indication of the beginning point. It also doesn’t tell us where we
started (e.g. a stock goes up by a $1. A large increase if the purchases price was $1
a small increase if the purchase price was $1,000)
•
Therefore, we use percentage changes.
– Percentages are not unit dependent. If the measure of quantity is changed from
boxes to individual apples the percentage change will remain the same.
– Percentages always refer to a starting point. Since percentage are always taken
from a starting point, the base, they better measure the extent of change.
•
We will return to this point shortly when we calculate elasticities along a
straight-line (constant slope) demand curve.
Various Elasticities
• Ep = Price elasticity of demand = %change
in quantity demanded/% change in price
• Ey = Income elasticity of demand =
%change in demand/% change in income
• Ex =Cross-price elasticity of demand =
%change in demand/% change in the price
of a related good
An Intuitive Approach to Elasticity
•
•
•
Since price elasticity of demand (Ep) is always negative (law of demand) we ignore the
negative sign and take the absolute value of price elasticity.
%ΔQd = Output Effect and %ΔP = Price Effect
Ep > 1 or Elastic
–
–
•
Ep < 1 or Inelastic
–
–
•
%ΔQd < %ΔP a given %ΔP creates a smaller %ΔQd or Output Effect < Price Effect
Quantity demanded is not sensitive to price. If price falls significantly, quantity demanded will
increase slightly, or vice versa.
Ep = 1 or Unit Elastic
–
–
•
%ΔQd > %ΔP a given %ΔP creates a larger %ΔQd or Output Effect > Price Effect
Quantity demanded is sensitive to price. If price falls slightly, quantity demanded will increase
by a large amount, or vice versa.
%ΔQd = %ΔP a given %ΔP creates an equal %ΔQd or Output Effect = Price Effect
If price falls, quantity demanded will increase by the same relative amount, or vice versa.
Note, in the above descriptions percentages are a easier and clearer way of explaining
sensitivity.
Using Elasticity: The Relationship
between P, Q and TR
•
•
•
•
•
•
As P↑ the law of demand tells us that Q↓. What happens to TR is not clear
(P↑ x Q↓ = TR ?)
The increase in price, the price effect, increases TR, ceteris paribus, but the
decrease in quantity demanded, the output effect, ceteris paribus, would
increase would TR. So, change in TR hinge about the relative strength of the
price and output effects. Elasticity provides the key because it tells us the size
of the price and output effect.
The strength of the price effect is measured by the %ΔP and that of the output
effect by the %ΔQd.
For example, if the %ΔP = 5% and the %ΔQd =10%, the output effect is
larger that the price effect. So if P↓ the Q↑ will strong enough to cause TR↑.
Second example, For example, if the %ΔP = 10% and the %ΔQd =5%, the
price effect is larger that the output effect. So, the P↓ will be stronger than
the Q↑ and TR↓.
Summary of P, Q and TR
• Ep > 1 Responsive or elastic
– %ΔQd > %ΔP or Output Effect > Price Effect - if P
goes down (up) total revenue goes up (down)
• Ep < 1 Not responsive or inelastic
– %ΔQd < %ΔP Output Effect < Price Effect - if P goes
down (up) total revenue goes down (up)
• Ep = 1 unit elastic
– %ΔQd = %ΔP Output Effect = Price Effect - if P goes
down (up) total revenue stays the same
Figure 2 Total Revenue
Price
$4
P × Q = $400
(revenue)
P
0
Demand
100
Quantity
Q
Copyright©2003 Southwestern/Thomson Learning
Figure 2 Total Revenue
Price
Price Effect
Output
Effect
$4
P↓ -$1 Q =100→∆TR = -$100
$3
$300
0
Q↑ +20
P=$3
→ ∆TR=
$+60
100
Q
120
Demand
Quantity
The Mid-point Formula: Calculating
Price Elasticity
• Economists, when calculating elasticity, using the
midpoints between the new (P1 and Q1) and old
(P0 and Q0) prices and quantities, rather than the
old price and quantity that others typically use.
• Ep = %ΔQd/ %ΔP
= (Q1- Q0)/[(QQ+ Q1)/2]
(P1- P0)/[(P0+ P1)/2]
Calculating Price Elasticity the Price Elasticity of
Demand
(100 - 50)
ED 
Price
$5

4
0
Demand
50
(4.00 - 5.00)
(100  50)/2
(4.00  5.00)/2
67 percent
 -3
- 22 percent
100 Quantity
Demand is price elastic
Linear Demand Curve:Elasticity
Elasticity Along a Linear Demand
Curve
8
E>1
7
6
Price
As P↓
and Q↑
the P
base is
smaller
so the
price
effect
grows.
5
E=1
4
3
E<1
2
1
0
0
2
4
6
8
10
12
Quantity
As P↓ and Q↑ the Q base is larger so the
output effect shrinks.
14
Determinants of Price Elasticity
•
•
•
•
•
Availability of close substitutes
Necessity versus luxury
Definition of the market
Time horizon
Percentage of consumer budget
Elasticity of Other Demand Curves
• Perfectly Elastic
• Perfectly Inelastic
• Unit Elastic
Figure 1 The Price Elasticity of Demand
(e) Perfectly Elastic Demand: Elasticity Equals Infinity
Price
1. At any price
above $4, quantity
demanded is zero.
$4
Demand
2. At exactly $4,
consumers will
buy any quantity.
0
3. At a price below $4,
quantity demanded is infinite.
Quantity
Figure 1 The Price Elasticity of Demand
(a) Perfectly Inelastic Demand: Elasticity Equals 0
Price
Demand
$5
4
1. An
increase
in price . . .
0
100
Quantity
2. . . . leaves the quantity demanded unchanged.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(e) Perfectly Elastic Supply: Elasticity Equals Infinity
Price
1. At any price
above $4, quantity
supplied is infinite.
$4
Supply
2. At exactly $4,
producers will
supply any quantity.
0
3. At a price below $4,
quantity supplied is zero.
Quantity
Copyright©2003 Southwestern/Thomson Learning
Other Demand Elasticities
• Income Elasticity of Demand – Sign is important: Normal Good EY>0
–
Inferior Good EY<0
– EY>1 Income-elastic and a luxury good because as Y↑ the % of Y
spend on the good (TE/Y) ↑
– EY<1 Income-inelastic and a necessity because as Y↑ the % of Y
spend on the good (TE/Y) ↓ EY=1 Income-unit elastic because as
Y↑ the % of Y spend on the good (TE/Y) stays constant
• Cross-price Elasticity –
– Sign is important: Substitute Ex>0 (PR↑ QR↓ Q↑)
–
Complement Ex<0 (PR↑ QR↓ Q↓)
Elasticity of Supply
• Price elasticity of supply = %change in quantity
supplied/% change in price
Es = %ΔQs/ %ΔP
= (Q2- Q1)/[(Q2+ Q1)/2]
(P2- P1)/[(P2+ P1)/2]
• Perfectly elastic and inelastic supply
• Relatively elastic, relatively inelastic and unit
elastic (crossing the Q or P axis or the origin)
• Supply curves where elasticity varies
Figure 6 The Price Elasticity of Supply
(a) Perfectly Inelastic Supply: Elasticity Equals 0
Price
Supply
$5
4
1. An
increase
in price . . .
0
100
Quantity
2. . . . leaves the quantity supplied unchanged.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(b) Inelastic Supply: Elasticity Is Less Than 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
110
Quantity
2. . . . leads to a 10% increase in quantity supplied.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(d) Elastic Supply: Elasticity Is Greater Than 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
200
Quantity
2. . . . leads to a 67% increase in quantity supplied.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(c) Unit Elastic Supply: Elasticity Equals 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
125
Quantity
2. . . . leads to a 22% increase in quantity supplied.
Copyright©2003 Southwestern/Thomson Learning
• Determinants of elasticity of supply
– Ability to increase or decrease production (e.g
Ellensburg agates, farm crops, automobiles)
– Time period
Applications of Elasticity
• Farmers : fallacy of composition and good
crop/bad revenue years
• The economics of addictive drugs
• Pricing decisions and your future business
Figure 8 An Increase in Supply in the Market for Wheat
Price of
Wheat
2. . . . leads
to a large fall
in price . . .
1. When demand is inelastic,
an increase in supply . . .
S1
S2
$3
2
Demand
0
100
110
Quantity of
Wheat
3. . . . and a proportionately smaller
increase in quantity sold. As a result,
revenue falls from $300 to $220.
Copyright©2003 Southwestern/Thomson Learning
Government and Markets
• Price Controls
– Price Ceilings (e.g. rent control)
– Price Floors (e.g. water and dairy)
• Taxes
– Who appears to pay the tax?
• Buyers “pay” tax
• Sellers “pay” tax
– Who really pays the tax? Tax incidence and burden
Elasticity and Tax Incidence
•
A tax drives a wedge between the price the buyer pays and the seller receives.
–
–
–
Before Tax: Pe=PB=PS
After Tax: PB >PS by the amount of the tax.
Example: Per unit tax of $1. If the buyer pays $6 for one unit of the good, the seller receives $5 and $1 goes to
the government in tax.
PB↑ → MC to buyers↑ → QD↓
Tax Wedge →
PS↓ → MB to sellers↓ → QS↓
•
Taxes can be imposed on the buyer or the seller, but the government usually imposes them on the
seller for ease of collection. Tax imposition determines who nominally pays the tax, but who really
pays the tax depends on elasticities of demand and supply (and doesn’t depend upon whether the
buyers or the seller pays the tax!).
•
Who really pays the tax, the tax incidence or burden, depends upon how buyers and sellers respond
to price changes.
–
–
•
If the buyers can respond relatively more to price changes more than suppliers, suppliers pay more of the tax.
If the suppliers can respond relatively more than the buyers, then the buyers pay more of the tax.
Remember the water fight example!
Graphing Tax Incidence
• If the buyer pays the tax, a new demand curve is created to reflect the
fact that sellers receive lower prices.
• If the seller pays the tax, a new supply curve is created to reflect the
fact that buyers pay higher prices.
• In either case, the higher price to buyers causes buyers to decrease
their quantity demanded and the sellers to decrease their quantity
supplied. Thus both the buyers and the sellers will likely both pay part
of the tax.
• The tax incidence or burden is related to how each responds to price
changes or their price elastiticies.
– If ED>ES then buyers pay less of the tax and sellers more of the tax.
– If ED<ES then buyers pay more of the tax and sellers less of the tax.
• Note that the tax incidence or burden does NOT depend upon who
pays the tax to the government!
• Extreme examples:
–
–
–
–
Perfectly elastic demand
Perfectly elastic supply
Perfectly inelastic demand
Perfectly inelastic supply
• Less extreme examples (e.g. the luxury tax)
Applications
• Getting to Mr./Ms. Rich: Luxury Tax on Yachts
• Case study – The payroll tax: Federal Insurance
Contribution Act (FICA) for Social Security and
Medicare