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Chapter 11 Taxation, Prices Efficiency, and the Distribution of Income Copyright © 2002 Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. ALL RIGHTS RESERVED. Instructors of classes adopting PUBLIC FINANCE: A CONTEMPORARY APPLICATION OF THEORY TO POLICY, Seventh Edition by David N. Hyman as an assigned textbook may reproduce material from this publication for classroom use or in a secure electronic network environment that prevents downloading or reproducing the copyrighted material. Otherwise, no part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including, but not limited to, photocopying, recording, taping, Web distribution, information networks, or information storage and retrieval systems—without the written permission of the publisher. Printed in the United States of America ISBN 0-03-033652-X Copyright © 2002 by Thomson Learning, Inc. Lump-Sum Taxes A Lump-sum tax is a fixed tax that is owed by everyone and is not subject to something taxpayers can change. It is independent of income, consumption, or wealth. An example is a Head Tax, which is constant for everyone. Copyright © 2002 by Thomson Learning, Inc. 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. Copyright © 2002 by Thomson Learning, Inc. Price Distorting Taxes A price distorting tax is a tax that alters the relative price of goods. Copyright © 2002 by Thomson Learning, Inc. Figure 11.1 A Price Distorting Tax Versus A LumpSum Tax Expenditure on Other Goods per Year (Dollars) A T L Y* T YT Y1 E' E E'' U1 0 Copyright © 2002 by Thomson Learning, Inc. U2 B' L' QT QL Q1 Gasoline per Year (Gallons) U3 B 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. Copyright © 2002 by Thomson Learning, Inc. 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 Copyright © 2002 by Thomson Learning, Inc. Figure 11.2 Impact of A Unit Tax on Market Equilibrium ST = MSC +$0.25 Price (Dollars) S = MSC Tax Revenue 1.15 = PG 1.00 0.90 = PN C Excess Burden B A T = $0.25 DQ 0 Copyright © 2002 by Thomson Learning, Inc. D = MSB Q1Q* Gasoline per Year (Gallons) Excess Burden of a Unit Tax DWL = 1/2TDQ =1/2 ×T2 × (Q*/P*) × (ESED)/(ES – ED) (A Step-by-step algebraic derivation is in the appendix to Chapter 11) Copyright © 2002 by Thomson Learning, Inc. Implication of the DWL Calculation A doubling of the per unit tax quadruples the Deadweight Loss. Copyright © 2002 by Thomson Learning, Inc. Figure 11.3 Excess Burden When Demand or Supply is Perfectly Inelastic A Demand Supply after Tax B Supply Price Price Supply Demand Net Price after Tax 0 q Quantity per Month Copyright © 2002 by Thomson Learning, Inc. 0 q 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 it between 25 and 40 cents per dollar of tax revenue raised. Copyright © 2002 by Thomson Learning, Inc. Incidence of a Tax The Legal Incidence is the burden of a tax as determined by who is 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. Copyright © 2002 by Thomson Learning, Inc. Shifting of Taxes Forward Shifting is the transfer of the burden of the tax from the seller, who is legally obligated to pay it, to the buyer. Backward Shifting is the transfer of the burden of the tax from the buyer, who is legally obligated to pay it, to the seller. Copyright © 2002 by Thomson Learning, Inc. Ad-Valorem Taxes Ad-Valorem Taxes add a fixed percentage to the price of a good. The primary example is sales taxes. Copyright © 2002 by Thomson Learning, Inc. Incidence of an Ad-valorem tax DWL = 1/2 TDQ 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) Copyright © 2002 by Thomson Learning, Inc. Using Excise Taxes on Alcohol to Internalize Externalities Federal taxes on alcohol are per-unit rather than ad-valorem. Externalities associated with alcohol are estimated at $0.48 per ounce (of hard liquor). Copyright © 2002 by Thomson Learning, Inc. Figure 11.4 Impact of an Ad Valorem Tax on Labor Wages (Dollars) Excess S Burden WG = 5.20 5.00 E E' WN = 4.16 Tax Revenue D = Gross Wage Net Wage = WG (I – t) 0 Copyright © 2002 by Thomson Learning, Inc. Q1 Q* Labor Hours per Year Independence of Legal and Economic Incidence 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. Copyright © 2002 by Thomson Learning, Inc. Figure 11.5 Incidence of a Tax Collected From Buyers S = MSC C Price (Dollars) PG + T =1.15 1.00 PG = 0.90 A B D = MSB D' = MSB – T 0 Copyright © 2002 by Thomson Learning, Inc. Q1Q* Price per Year (Gallons) Figure 11.6 The More Inelastic the Demand, the Greater the Portion of a Tax Borne by Buyers Price (Dollars) S = MC + $0.25 C 1.20 1.15 1.00 .95 .90 S = MC E B A DQ’ D’ DQ’ 0 Copyright © 2002 by Thomson Learning, Inc. D Q1 Q2 Q* Gasoline per Year (Gallons) Price (Cents) Figure 11.7 Impact of a Tax on a Good with a Perfectly Elastic Supply E' 60 MC + T = S' E 50 MC = S' D 0 Q1 Q* Housing per Month Square Feet Copyright © 2002 by Thomson Learning, Inc. Figure 11.8 Tax Incidence When Market Supply is Perfectly Inelastic Wages (Dollars) S E W*G tw*G WN= W*G (1– t ) F D=W WN= WG (1– t) 0 Copyright © 2002 by Thomson Learning, Inc. Q* Labor Hours per Year Shifting Under Imperfect Competition Monopolists can shift less of a given tax forward to consumers than can competitive industry. Copyright © 2002 by Thomson Learning, Inc. Figure 11.9 Shifting Under Monopoly Price MC + T PMT DPM PM P*T DP* P* MC D DQM DQ* MR QMT QM Q*T Q* Copyright © 2002 by Thomson Learning, Inc. Output per Year 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. Copyright © 2002 by Thomson Learning, Inc. Figure 11.10 Multimarket Analysis of Excess Burden Price A B E2 E1 PF(1 + t) PF A DQF S' S E2 PC(1 + t) S' E1 PC B DC DQC DF QF2 QF1 0 QC2 QC1 Clothing per Year Copyright © 2002 by Thomson Learning, Inc. S Figure 11.11 Multimarket Analysis Incidence A B S' = MC + T S S S' Price E2 PG P* PN E1 P P'F E1 E2 D 0 Q' Q* Clothing per Year Copyright © 2002 by Thomson Learning, Inc. D 0 QF Q'F Food per Year 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. Copyright © 2002 by Thomson Learning, Inc. The Lorenz Curve The Lorenz Curve maps the cumulative percentage of households against their cumulative percentage of income. Copyright © 2002 by Thomson Learning, Inc. Figure 11.12 A Lorenz Curve Percentage of Real Income 100 E Line of Equal Distribution 75 y 60 50 25 20 10 5 3 0 Area A Area B x 10 25 50 75 Percentage of Households Copyright © 2002 by Thomson Learning, Inc. D 100 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). Copyright © 2002 by Thomson Learning, Inc. 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 Copyright © 2002 by Thomson Learning, Inc.