Download - The Week Ahead
The Week Ahead
• Thursday (9/14) -- Attend University Forum on Health Care and then Come to class!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. 9 am
b. Noon
c. 5 pm
d. 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
Gain in Revenue
Loss in Revenue
Toll
Number of Cars
D
Po
Qo
P1
Q1
What is an Elasticity?
• The answer depends on the price elasticity of demandprice 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 demandprice elasticity of demand is the ratio of the percentage change in the quantity demanded to the percentage change in the price of the good.
Warning: Note that price elasticities of demand are expressed in absolute values!!!!
€
ηPD =abs Percentage Change in QD
Percentage Change in P
⎛
⎝ ⎜
⎞
⎠ ⎟=abs
ΔQD
QΔP
P
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Computing Price Elasticity (Midpoint Method)
• Compute Percentage Change in QD
• Compute Percentage Change in P
• Elasticity --- Compute the Ratio
Price
Donuts
Demand
$1
$.50
10 14
€
ΔQD
QMidpoint
= (14 −10)(10 +14) / 2
= 412
=13=.333
€
ΔPPMidpoint
= (.50 −1)(1+.50) / 2
=−.50.75
=−23=−.667
€
ηPD =abs .333
−.667
⎛
⎝ ⎜
⎞
⎠ ⎟=12=.50
What factors determine the value of ηDP?
ηDP 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
D
P
Q
DP
QPerfectly Elastic Demand Perfectly Inelastic Demand
€
ηPD =∞
€
ηPD =0
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 (ΔP/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 (ΔQD/Qo). Consequently the percentage change in spending will equal
(ΔSpending/Spendingo) = (ΔP/Po) - (ΔQD/Qo)
Now divide both sides of the above equation by (ΔP/P)
€
ΔSpendingSpendingoΔP Po
=1−ΔQD Qo
ΔP Po
Will Toll Road Rise or Fall?
If:
ηDP > 1 (elastic) revenues will fall
ηDP = 1 (unitary) revenues will stay the same
ηDP < 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?
– The percentage change in price is equal to (-5)/((10+5)/2)=-5/7.5=-.667
• If DP = 1.50
(ΔQD/Qo) = - (-.667)(1.50) = 1.00Or increase by 100%
• If DP = .50
(ΔQD/Qo) = - (-.667)(.50) = .333Or Increase by 33.3%
price
Quantity
10
5
5
Inelastic Demand
Elastic Demand
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:
– Hence the new level of output (Q1) when we know the percentage change in output (X) is the following (after some algebra)
€
ΔQ(Q1 +Qo) 2
=2(Q1−Qo)(Q1 +Qo)
=X
€
Q1 =Qo2 + X2 −X
What has happened to total revenue?
• Initially the total spending was $50
• If ηDP = 1.50 (elastic)
(ΔQD/Qo) = - (-.667)(1.50) = 1.00
Q1=5(2+1)/(2-1)=15Total Revenue = $5(15)=$75
• If ηDP = .50 (inelastic)
(ΔQD/Qo) = - (-.667)(.50) = .333
Q1=5(2+.333)/(2-.333)=7Total Revenue = $5(7)=$35
price
Quantity
10
5
5
Inelastic Demand
Elastic Demand
7 15
Other Elasticities -- Income
Shifts in Demand Curve due to Income changes
If
I < 0 good is inferior
0 < I < 1 good is normal and a necessity
I > 1 good is normal and a luxury
€
ηI =ΔQ Qo
ΔI Io
Other Elasticities -- Cross Price
Shift in Demand Curve due to changes in the price of other goods (OP)
If
CP < 0 goods are complements
CP > 0 goods are substitutes
€
ηCP = ΔQ Qo
ΔOP OPo
Other Elasticities -- Supply
Movement along a Supply Curve as Price changes
€
ηPS =Percentage Change in QS
Percentage Change in P=ΔQS Qo
ΔP 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• 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)
Stax
D
S
Price
QuantityQo
Po
DP
SP
QT
Tax Incidence:Different Demand Elasticities
D
S
StaxPrice
QuantityQo
Po
DP
SP
QT
D
S
StaxPrice
QuantityQo
Po
DP
SP
QT
Elastic Demand -- Tax Falls on Suppliers Inelastic Demand -- Tax Falls on Consumers
Different Supply Elasticities
D
S
StaxPrice
QuantityQo
Po
DP
SP
QT
D
S
Stax
Price
QuantityQo
Po
DP
SP
QT
Elastic Supply -- Tax Falls on Consumer 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
D
S
StaxPrice
QuantityQo
Po
DP
SP =
QT
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