1 Chapter 11 Taxation, Prices, Efficiency, and the Distribution of Income.

1

Chapter 11

Taxation, Prices, Efficiency, and the Distribution of Income

2

Lump-Sum Taxes A Lump-sum tax is a fixed tax that is

owed by everyone and is not subject to anything taxpayers can change.

It is independent of income, consumption, or wealth.

An example is a Head Tax, which is constant for everyone.

3

Inefficiency in Taxation and the Lump-Sum Tax

Inefficiency in taxation results from the ability to avoid taxes by avoiding a taxed activity.

Because lump-sum taxes are unavoidable, they serve as the benchmark by which other taxes are measured in terms of efficiency.

4

A price distorting tax alters the relative price of goods.

Price Distorting Taxes

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Figure 11.1 A Price Distorting Tax Versus A Lump-Sum Tax

A

B B'

Ex

pe

nd

itu

re o

n O

the

r G

oo

ds

pe

r Y

ea

r (D

olla

rs)

Gasoline per Year (Gallons)

0

U2

QL

E''

Y*

QT

YT

U1

Q1

Y1

U3

E E'

L

L'

T

T

6

Individual Excess Burden of a Tax

The individual excess burden of a tax is the loss in well-being when a taxpayer pays taxes under a price-distorting tax instead of under a lump-sum tax.

7

Community Charges in the U.K. The Thatcher government replaced local

property taxes with a form of lump-sum tax called “the community charge.’’

The tax was set by each local council and charged a fixed amount per adult taxpayer.

Despite its efficiency, the lump-sum tax was viewed as so unfair by many taxpayers that they refused to pay it.

8

Unit Taxes

A unit tax adds to the price by a fixed amount. Examples include the 32 cents per pack of cigarettes and 24 cents per gallon of gasoline in federal taxes.

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Tax Terms

The Gross Price (PG) is the price paid by consumers.

The Net Price (PN) is the price received by producers after the tax is paid.

PN = PG – T

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Figure 11.2 Impact of A Unit Tax on Market Equilibrium

Pri

ce

(D

olla

rs)

Gasoline per Year (Gallons) 0

Excess Burden

Tax Revenue

T = $0.25

ST = MSC + $0.25

Q

Q*

S = MSC

D = MSB

1.00 B

Q1

1.15 = PG

0.90 = PN A

C

11

Excess Burden of a Unit Tax

DWL = 1/2TQ

=1/2 ×T2 × (Q*/P*) × (ESED)/(ES – ED)

(A Step-by-step algebraic derivation is in the appendix to Chapter 11)

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Implication of the DWL Calculation

A doubling of the per-unit tax quadruples the Deadweight Loss.

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Figure 11.3 Excess Burden When Demand or Supply is Perfectly Inelastic

Supply after Tax

Demand

Supply

Pri

ce

Quantity per Month 0 q

A

Pri

ce

0 q

B Supply

Demand

Net Price after Tax

Quantity per Month

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Efficiency Loss Ratio of a Tax

The Efficiency Loss Ratio is the deadweight loss per dollar of revenue raised DWL/R .

Estimates of U.S. tax system place ELR at between 25 and 40 cents per dollar of tax revenue raised.

15

Incidence of a Tax The Legal Incidence is the burden of a tax

as determined by those who are legally obligated to pay the tax. 

The Economic Incidence is the burden of a tax as determined by how much the parties are affected in terms of paying higher prices, or receiving lower prices.

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Shifting of Taxes Forward Shifting is the transfer of the

burden of a tax from the seller, who is legally obligated to pay it, to a buyer. 

Backward Shifting is the transfer of the burden of a tax from the buyer, who is legally obligated to pay it, to a seller.

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Ad-Valorem Taxes

Ad-Valorem Taxes add a fixed percentage to the price of a good.

The primary example is sales taxes.

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Incidence of an Ad-valorem tax

DWL = 1/2 TQ

= 1/2 t2PG2(Q*/P*) × (ESED)/(ES – ED)

if t is very small, then this is approximately

= 1/2 t2P*Q*(ESED)/(ES – ED)

T = tPG

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Using Excise Taxes on Alcohol to Internalize Externalities

Federal taxes on alcohol are per-unit rather than ad-valorem. 32 cents per six-pack of beer ($.10/oz) $13.50 per gallon of 100 proof liquor

($.25/oz) Externalities associated with alcohol

are estimated at $0.48 per ounce (of hard liquor).

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Figure 11.4 Impact of an Ad Valorem Tax on Labor

WG = 5.20

Tax Revenue WN = 4.16

Q1

Wa

ge

s (

Do

llars

)

0Labor Hours per Year

ExcessBurden

Net Wage = WG (I – t)

E'

5.00

Q*

D = Gross Wage

S

E

21

Independence of Legal and Economic

Incidence

Economically, it does not matter whether the buyer or seller is legally liable for a tax.

The economic incidence of the tax is determined by supply and demand elasticities, the amount of the tax, and the original equilibrium price and quantity.

22

Figure 11.5 Incidence of a Tax Collected From BuyersP

ric

e (

Do

llars

)

Price per Year (Gallons) 0 Q*

1.00

D = MSB

S = MSC

B

Q1

D' = MSB – T

A

C PG + T =1.15

PG = 0.90

23

Figure 11.6 The More Inelastic the Demand, the Greater the Portion of a Tax Borne by Buyers

Pri

ce

(D

olla

rs)

Gasoline per Year (Gallons) 0

S = MC + $0.25

D’

.95

1.20

Q2

Q’

E

Q*

1.00

S = MC

D

B

Q1

.90

1.15

Q’

C

A

24

Figure 11.7 Impact of a Tax on a Good with a Perfectly Elastic Supply

Q 1

Pri

ce

(C

en

ts)

Housing per Month Square Feet

MC + T = S' E' 60

0 Q*

50

D

MC = S' E

25

Figure 11.8 Tax Incidence When Market Supply is Perfectly Inelastic

D = W

S

WG*

Q*

E

G

Wa

ge

s (

Do

llars

)

0 Labor Hours per Year

tw*

WN= WG*(1-t) F

WN= WG*(1-t)

26

Shifting Under Imperfect Competition

Monopolists can shift less of a given tax forward to consumers than can a competitive industry.

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Figure 11.9 Shifting Under MonopolyP

ric

e

Output per Year

QM

PM

MC + T

Q*

P*

QMT

PMT

Q*T

P*T

Q*

P*

QM

MC

PM

D

MR

28

General Equilibrium Analysis and Shifting When one good is taxed and another good is

not taxed, the impact of the tax is not confined to the taxed good.

Because a tax on one good lowers the profit that can be made to firms producing it, they may shift their productive resources to the other good so as to maximize their after-tax rate-of-return in both markets.

This has the effect of equalizing the after-tax rate-of-return.

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Figure 11.10 Multimarket Analysis of Excess Burden

QC2

S'

QC

PC(1 + t)E2

B

QC1

PC

DC

S E1

PF

DF

S E1

QF1

E2

A

S' PF(1 + t)

QF

QF2 0

Clothing per Year

BA

Pri

ce

Food per Year

30

Figure 11.11 Multi-market Analysis Incidence

PN

0

A B

Pri

ce

Food per Year

0 Clothing per Year

Q*

E1

S

P*

D

S

P

D

QF

E1 PG

Q'

S' = MC + T

E2 S'

PF'

QF'

E2

31

Government Taxes and Expenditures and

the Distribution of Income The Tax Incidence is who bears the burden of a tax. 

The Expenditure Incidence is who receives the benefits of a government program.

The Budget Incidence is the net analysis of a program’s tax and expenditure incidence.

The Differential Tax Incidence is the change in the tax incidence that results from substituting one equal yield tax for another.

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The Lorenz Curve

The Lorenz Curve maps the cumulative percentage of households against their cumulative percentage of income.

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Figure 11.12 A Lorenz Curve

Pe

rce

nta

ge

of

Re

al I

nc

om

e

Line of Equal Distribution

0 D

100 E

y

x

75

60 50

25 20 10

5 3

10 25 50 75 100 Percentage of Households

Area A

Area B

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The Gini Coefficient

The Gini Coefficient is the ratio of the area between the Lorenz curve and the perfect equality line (Area A in the previous slide) to the area under the perfect equality line (Areas A and B).

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Effective Tax Rates for All Federal

Taxes, 1998 Income Category (in quintiles)

Effective Tax Rate (percent)

Lowest 4.5

Second 13.3

Third 18.9

Fourth 22.1

Highest 28.7