1. Taxation, Prices, Efficiency, and the Distribution of Income
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. Price Distorting Taxes
A price distorting tax alters the relative price of goods.

5. Figure 11.1 A Price Distorting Tax Versus A Lump-Sum Tax
Expenditure on Other Goods
per Year (Dollars)
Gasoline per Year (Gallons) A B B' E' L L' T Y* QT YT U1 Q1 Y1 U3 E U2 QL
E''

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.

9. 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

10. Figure 11.2 Impact of A Unit Tax on Market Equilibrium
ST = MSC +
$0.25
Price (Dollars)
Gasoline per Year (Gallons) Q*
S = MSC
D = MSB
1.00 B
Tax Revenue
T = $0.25 Q1
1.15 = PG
0.90 = PN A C
Excess Burden DQ

11. Excess Burden of a Unit Tax
DWL = 1/2TQ
=1/2 ×T2 × (Q*/P*) × (ESED)/(ES – ED)
(A Step-by-step algebraic derivation is in the appendix to Chapter 11)

12. Implication of the DWL Calculation
A doubling of the per-unit tax quadruples the Deadweight Loss.

13. Figure 11.3 Excess Burden When Demand or Supply is Perfectly Inelastic
after Tax
Demand
Price
Quantity per Month q A
Price q B
Supply
Demand
Net Price
after Tax
Quantity per Month

14. 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.

16. 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.

17. Ad-Valorem Taxes
Ad-Valorem Taxes add a fixed percentage to the price of a good.
The primary example is sales taxes.

18. Incidence of an Ad-valorem tax
DWL = 1/2 TQ
T = tPG
= 1/2 t2PG2(Q*/P*) × (ESED)/(ES – ED)
if t is very small, then this is approximately
= 1/2 t2P*Q*(ESED)/(ES – ED)

19. 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).

20. Figure 11.4 Impact of an Ad Valorem Tax on Labor
5.00 Q*
D = Gross Wage S E
Excess
Burden
Wages (Dollars)
Labor Hours per Year
WG = 5.20
Tax Revenue
WN = 4.16 Q1
Net Wage = WG (I – t) 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 Buyers
Price (Dollars)
Price per Year (Gallons) 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
S = MC + $0.25
Price (Dollars)
Gasoline per Year (Gallons) D’ Q*
1.00
S = MC D B
.95
1.20 Q2
DQ’ E Q1
.90
1.15
DQ’ C A

24. Figure 11.7 Impact of a Tax on a Good with a Perfectly Elastic Supply
Price (Cents)
Housing per Month Square Feet Q* 50 D
MC = S' E
MC + T = S' E' 60 Q 1

25. Figure 11.8 Tax Incidence When Market Supply is Perfectly Inelastic
D = W S
WG* Q* E
Wages (Dollars)
Labor Hours per Year
tw*
WN= WG*(1-t) F G

26. Shifting Under Imperfect Competition
Monopolists can shift less of a given tax forward to consumers than can a competitive industry.

27. Figure 11.9 Shifting Under Monopoly
Price
Output per Year
MC + T QM MC PM D MR
DQM
DPM
QMT
PMT Q* T P*
DQ*
DP* Q* P*

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.
General Equilibrium Analysis and Shifting

29. Figure 11.10 Multimarket Analysis of Excess Burden
Clothing per Year B A
Price
Food per Year
QC1 PC DC S E1 PF DF
QF1
QC2 S'
DQC
PC(1 + t) E2 B E2 A S'
PF(1 + t)
DQF
QF2

30. Figure 11.11 Multi-market Analysis IncidenceA B
Price
Food per Year
Clothing per Year PG Q'
S' = MC + T E2 Q* E1 S P* D P QF S'
PF'
QF' E2 PN

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.

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

33. Figure 11.12 A Lorenz Curve 100 E Line of Equal Distribution 75 60 y
Percentage of Real Income 50
Area A 25 20
Area B 10 5 x 3 D 10 25 50 75
100
Percentage of Households

34. 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).

35. 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