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