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

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.

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.

Price Distorting Taxes A price distorting tax alters the relative price of goods.

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''

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.

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.

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.

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

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

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)

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

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

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.

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.

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.

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

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)

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).

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'

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.

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

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

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

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

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

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*

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

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

Figure 11.11 Multi-market Analysis Incidence A 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

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.

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

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

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).

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