Download Lecture 7: Chapter 5, Elasticity

The Week Ahead
• Thursday (9/14) -- Attend University Forum
on Health Care and then Come to class!
• Do Homework 5 on ‘Homework Assignment’
by Friday at ???
– Warning!!!! Some numbers in problems change
each time you open the assignment!!
• 1st Midterm Exam in Class -- Next Tuesday,
September 19
– Study Guide will be Available on Web on
Thursday, September 14
Survey of Due Date Times
•
I prefer that homework be due at:
a.
b.
c.
d.
9 am
Noon
5 pm
midnight
Elasticity and Tax
Incidence
Lecture 7
September 12, 2006
In This Lecture
• Elasticity Concept
• Price Elasticity and Total Spending
• Other Elasticity Concepts
– Income
– Cross Price
– Supply elasticity
• Tax Incidence
Survey:
Privatization of Toll Roads
• Do you think that publicly owned toll
roads should be leased to private firms
for operation?
a. No
b. Yes
Indiana Toll Road
• The state of Indiana has leased the toll road
to a foreign company. The tolls have not
been increased for over a decade and the
first major initiative for the firm is to raise the
tolls for trucks and cars.
• Will increasing tolls lead to more or less
revenues for the firm? Will a 20% increase in
tolls, for example, produce more revenues, or
is it possible that the toll revenues could fall?
Increasing the Toll
Toll
Gain in Revenue
P1
Loss in Revenue
Po
D
Q1
Qo
Number of Cars
What is an Elasticity?
• The answer depends on the price elasticity of
demand for trips on the toll road.
• An elasticity is a measure the responsiveness of an individual’s
decision to purchase (or supply) to a change in a factor
determining that decision.
• The price elasticity of demand is the ratio of the percentage
change in the quantity demanded to the percentage change in
the price of the good.
QD 
Percentage Change in QD 


D
Q
P  abs

abs



Percentage
Change
in
P
P




P 


Warning: Note that price elasticities of demand are expressed in
absolute values!!!!
Computing Price Elasticity
(Midpoint Method)
•
Price
Compute Percentage Change in QD
QD
(14  10)
4 1


  .333
QMidpoint (10 14) / 2 12 3
Demand
$1
•

$.50
Compute Percentage Change in P
P
PMidpoint
•

10
14
Donuts

(.50  1)
.50
2

   .667
(1 .50) / 2
.75
3
Elasticity --- Compute the Ratio
PD
 .333  1
 abs
  .50
.667  2
What factors determine the value of
DP?
 DP grows larger
– When close substitutes are available for the good.
•
Consumers are more likely to shift their consumption to these
substitutes as the price of the good rises.
– If the good is a necessity or a luxury.
• If the good is something you ‘need’ then you are less sensitive
to price changes than if it is a luxury.
– As the time period for adjustment of behavior increases
• Given more time, substitute consumption goods can be found.
Extremes of Elasticity
P
P
D
PD  

PD  0
D

Q
Perfectly Elastic Demand
Q
Perfectly Inelastic Demand
Elasticity and Total Revenue
• Suppose we know the price elasticity of demand for
toll road trips. How is this elasticity related to Total
Revenue?
• When a seller raises the price of a good, there are
two countervailing effects in action (except in the
rare case of a good with perfectly elastic or perfectly
inelastic demand):
– A price effect: After a price increase, each unit sold
sells at a higher price, which tends to raise revenue.
– A sales effect: After a price increase, fewer units are
sold, which tends to lower revenue.
Elasticity and Total Revenue
• If demand for a good is elastic (the price elasticity of
demand is greater than 1), an increase in price reduces
total revenue. In this case, the sales effect is stronger than
the price effect.
• If demand for a good is inelastic (the price elasticity of
demand is less than 1), a higher price increases total
revenue. In this case, the price effect is stronger than the
sales effect.
• If demand for a good is unit-elastic (the price elasticity of
demand is 1), an increase in price does not change total
revenue. In this case, the sales effect and the price effect
exactly offset each other.
The Price
Elasticity of
Demand Changes
Along the Demand
Curve
Spending = Revenue
Total Dollar Spending on a good is equal to
Spending = Po QDo
Now consider a given percentage change in the price (P/Po). Total dollar spending
will increase by the same percentage if customers do not change their quantity
purchases. However as the price increases, the customers will reduce their
spending by (QD/Qo). Consequently the percentage change in spending will equal
(Spending/Spendingo) = (P/Po) - (QD/Qo)
Now divide both sides of the above equation by (P/P)
Spending Spendingo
QD Qo
 1
P Po
P Po
Will Toll Road Rise or Fall?
If:
DP > 1 (elastic)
revenues will fall
DP = 1 (unitary)
revenues will stay the same
DP < 1 (inelastic)
revenues will increase
Predicting Changes in the Quantity
Demanded and Total Revenue
•
Assume initially the price is $10 and
the demand for the good is 5 units.
•
If you cut the price to $5, how much
will be demanded?
price
Inelastic Demand
–
10
Elastic Demand
•
The percentage change in price is
equal to (-5)/((10+5)/2)=-5/7.5=-.667
If DP = 1.50
(QD/Qo) = - (-.667)(1.50) = 1.00
Or increase by 100%
5
•
5
If DP = .50
(QD/Qo) = - (-.667)(.50) = .333
Or Increase by 33.3%
Quantity
What has happened to
the quantity demanded?
If you know the price elasticity of demand, you can use it to
calculate the new Q and Total Revenue:
– When using the midpoint method, the percentage change in Q was
computed as:
Q
2(Q1  Qo )

X
(Q1  Qo ) 2 (Q1  Qo )
– Hence the new level of output (Q1) when we know the percentage
changein output (X) is the following (after some algebra)
Q1  Qo

2 X
2 X
What has happened to total revenue?
•
Initially the total spending was $50
•
If DP = 1.50 (elastic)
(QD/Qo) = - (-.667)(1.50) = 1.00
Q1=5(2+1)/(2-1)=15
Total Revenue = $5(15)=$75
•
If DP = .50 (inelastic)
(QD/Qo) = - (-.667)(.50) = .333
Q1=5(2+.333)/(2-.333)=7
Total Revenue = $5(7)=$35
price
Inelastic Demand
10
Elastic Demand
5
5
7
15
Quantity
Other Elasticities -- Income
Shifts in Demand Curve due to Income changes
I 
If
I < 0

Q Qo
I Io
good is inferior
0 < I < 1
good is normal and a necessity
I > 1
good is normal and a luxury
Other Elasticities -- Cross Price
Shift in Demand Curve due to changes in the price of other goods (OP)
CP 
If
CP < 0
CP > 0

Q Qo
OP OPo
goods are complements
goods are substitutes
Other Elasticities -- Supply
Movement along a Supply Curve as Price changes
PS

Percentage Change in QS QS Qo


Percentage Change in P
P Po
What makes Suppliers more
Price Elastic?
• The price elasticity of supply tends to be larger when
– Inputs are easily available
– Greater flexibility in production
– There is ample time to adjust production to new conditions
• Explanation:
If the price a good or service rises, a supplier will want to
produce more. Increasing production may increase the per unit
cost of production. Why?
– technology (the fixity of some factors of production)
– lack of availability of inputs--then.
In these situations, firms will not increase their production as
much as when technology is flexible and inputs are easily
available. The passage of time may ease both of the
constraints.
Tax Incidence
Stax
Price
S
•
Initially the market is in equilibrium
without the tax, price is Po which is equal
to the initial supply and demand price
•
A tax is imposed upon suppliers,
consequently the supply curve shifts up
by the amount of the tax
•
Excess Demand is created and the price
to consumers rises to DP
•
The supply price falls to SP
•
The tax (DP-SP) is borne by consumers
by the amount (DP-Po) and by the
suppliers by the amount (Po-SP)
DP
Po
SP
D
QT
Qo
Quantity
Tax Incidence:
Different Demand Elasticities
Stax
Price
Stax
Price
S
S
DP
DP
Po
Po
SP
SP
D
D
QT
Qo
Quantity
Elastic Demand -- Tax Falls on Suppliers
QT Qo
Quantity
Inelastic Demand -- Tax Falls on Consumers
Different Supply Elasticities
Stax
Stax
Price
Price
S
S
DP
DP
Po
Po
SP
SP
D
D
QT
Qo
Quantity
Elastic Supply -- Tax Falls on Consumer
QT
Qo
Quantity
Inelastic Supply -- Tax Falls on Firm
Lessons
• If demand is more elastic than supply then
the tax will fall more upon suppliers because
suppliers are less able to avoid tax
• If supply is more elastic than demand then
the tax will fall more upon consumers
because consumers less able to avoid tax
Sin Taxes
Stax
Price
S
DP
SP = Po
D
Qo
QT
Quantity
More on Sin Taxes
• See Robert a Sirico, “The Sin Tax,
Economic and Moral Considerations,” at
the Acton Institute for the Study of
Religion and Liberty, at
http://www.acton.org/print.php
Conclusions about Sin Taxes
• Raise effective prices to the consumer
• Their incidence falls primarily on the consumer.
• Are unlikely to seriously discourage consumption
habits when those habits are seriously desired
• Will increase government revenue if transactions
remain in legal markets
• May decrease government revenue if people move
their business to illegal markets
• Sets up a moral hazard for policy makers who
vacillate between wanting to discourage undesirable
behavior and wanting to encourage it for revenue
purposes