CHAPTER 15 Taxation and Efficiency Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

15-2 Excess Burden Defined Pounds of corn per year Pounds of barley per year E1E1 B1B1 C1C1 D F A CbCb CaCa B0B0 Government levies tax on barley i

15-3 Effect of Tax on Consumption Bundle Pounds of corn per year Pounds of barley per year E1E1 B1B1 C1C1 D F A CbCb CaCa B0B0 E2E2 i ii G

15-4 Excess Burden of the Barley Tax Pounds of corn per year Pounds of barley per year E1E1 B1B1 C1C1 D F A CbCb CaCa B0B0 E2E2 i ii G H B3B3 M I Tax Revenues Equivalent variation

15-5 Questions and Answers If lump sum taxes are so efficient, why aren’t they widely used? Are there any results from welfare economics that would help us understand why excess burdens arise?

15-6 Questions and Answers Does an income tax entail an excess burden?

15-7 Questions and Answers Pounds of corn per year Pounds of barley per year C1C1 D F A CbCb CaCa B 1 = B 2 E2E2 i ii E1E1 J B3B3 R K If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden? S Uncompensated response Income effect Substitution effect -compensated effect Compensated demand curve

15-8 Excess Burden Measurement with Demand Curves Pounds of barley per year Price per pound of barley a DbDb SbSb q1q1 q2q2 i h S’ b PbPb (1 + t b )Pb gf d Tax revenues Excess burden of tax Excess burden = ½ ηP b q 1 t b 2

15-9 Preexisting Distortions Theory of the Second Best Double-dividend hypothesis

15-10 Excess Burden of a Subsidy Housing services per year Price per unit of housing services m DhDh Sh’Sh’ h2h2 h1h1 u q ShSh (1 – s)P h PhPh no r Excess burden v

15-11 Excess Burden of Income Taxation Hours per year Wage rate per hour SLSL L1L1 L2L2 a g (1 – t)w w f i h Excess burden d Excess burden = ½ εωL 1 t 2

15-12 The Allocation of Time Between Housework and Market Work $ $ 0 0’ Hours worked in home per year Hours worked in market per year H* w1w1 w1w1 VMP home VMP mkt (1 – t)VMP mkt H1H1 a b e c d w2w2 (1 – t)w 2 Excess burden = ½ (ΔH)tw 2

15-13 Does Efficient Taxation Matter? Why no excess burden budget? Is efficiency the primary objective of government policy? Does excess burden mean a tax is bad?

15-14 Appendix A – Formula for Excess Burden A = ½ * base * height = ½ * (di) * (fd) fd = ∆P b = (1 + t b ) * P b – P b = t b * P b di = ∆q η = (∆q/∆P b )(P b /q) ∆q = η(q/P b )∆P b since ∆Pb = t b * P b ∆q = η(q/Pb)*(t b P b ) = η * q * t b since di = ∆q A = ½(di)(fd) = ½(ηqt b )*(t b P b ) = ½ * η * P b * q * (t b ) 2

15-15 Appendix B – Multiple Taxes and the Theory of the Second Best Gallons of gin per yearGallons of rum per year Price per gallon of gin Price per gallon of rum DgDg DrDr g1g1 PgPg Dr’Dr’ PrPr (1 + t r )P r r1r1 r2r2 r3r3 a b c g h d g2g2 e f ( 1 + t g )P g