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CHAPTER 11 Taxation & Efficiency: Efficient & Equitable Taxation Pounds of corn per year Excess Burden Defined Government levies tax on barley A Ca Cb E1 C1 i F B0 D B1 Pounds of barley per year Pounds of corn per year Effect of Tax on Consumption Bundle Tax revenue A Ca G E2 Cb E1 C1 F B0 i ii D B1 Pounds of barley per year Pounds of corn per year Excess Burden of the Barley Tax A Ca G H Tax Revenues M Equivalent variation E2 Cb E1 C1 F B0 B3 I i ii D B1 Pounds of barley per year 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? (1 tb ) Pb MRS bc Pc Pb MRTbc Pc Questions and Answers Does an income tax entail an excess burden? MRSlb MRTlb MRSlc MRTlc MRSbc MRTbc Pounds of corn per year Questions and Answers If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden? A • Uncompensated E1 i Ca • Income effect • Substitution effect -compensated effect J R • Compensated demand curve E2 Cb C1 response S F B1 = B2 B3 K ii D Pounds of barley per year Price per pound of barley Excess Burden Measurement with Demand Curves (1 + tb)Pb Pb a Excess burden = ½ ηPbq1tb2 Tax revenues Excess burden of tax g f h d S’b i Sb Db q2 q1 Pounds of barley per year Preexisting Distortions Theory of the Second Best Double-dividend hypothesis Price per unit of housing services Excess Burden of a Subsidy Ph m Excess burden n (1 – s)Ph q o v Sh r u Sh’ Dh h1 h2 Housing services per year Wage rate per hour Excess Burden of Income Taxation Excess burden = ½ εωL1t2 f w (1 – t)w g Excess burden SL d i h a L2 L1 Hours per year The Allocation of Time Between Housework and Market Work Excess burden = ½ (ΔH)tw2 $ b (1 – t)VMPmkt a w1 $ w2 w1 (1 – t)w2 e VMPmkt 0 Hours worked in home per year d H* c H1 VMPhome Hours worked in 0’ market per year 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? Appendix A – Formula for Excess Burden A = ½ * base * height = ½ * (di) * (fd) fd = ∆Pb = (1 + tb) * Pb – Pb = tb * Pb di = ∆q η = (∆q/∆Pb)(Pb/q) ∆q = η(q/Pb)∆Pb since ∆Pb = tb * Pb ∆q = η(q/Pb)*(tbPb) = η * q * tb since di = ∆q A = ½(di)(fd) = ½(ηqtb)*(tbPb) = ½ * η * Pb * q * (tb)2 Price per gallon of rum Price per gallon of gin Appendix B – Multiple Taxes and the Theory of the Second Best f (1 + tg)Pg (1 + tr)Pr Pr Pg c g b h a d Dr’ e Dg g2 g1 Gallons of gin per year Dr r3 r1 r2 Gallons of rum per year Optimal Commodity Taxation w(T – l) = PXX + PYY wT = PXX + PYY + wl wT = (1 + t)PXX + (1 + t)PYY + (1 + t)wl 1 wT = PXX + PYY + wl 1+t The Ramsey Rule marginal excess burden = area fbae = 1/2∆x[uX + (uX + 1)] = ∆X PX Marginal Excess Burden Excess f Burden b P0 + (uX + 1) g P0 + uX P0 i h c j e a ∆x X2 ∆X X1 DX X0 X per year The Ramsey Rule Continued change in tax revenues = area gfih – area ibae = X2 – (X1 – X2)uX marginal tax revenue = X1 ∆X marginal tax revenue per additional dollar of tax revenue = ∆X/(X1 - ∆X) marginal tax revenue per additional dollar of tax revenue for good Y = ∆Y/(Y1 - ∆Y) To minimize overall excess burden = ∆X/(X1 - ∆X) = ∆Y/(Y1 - ∆Y) Therefore: X Y X1 Y1 A Reinterpretation of the Ramsey Rule t X X tYY t X Y tY X inverse elasticity rule The Corlett-Hague Rule In the case of two commodities, efficient taxation requires taxing commodity complementary to leisure at a relatively high rate Equity Considerations Equity implications of inverse elasticity rule Vertical equity Optimal departure from Ramsey Rule Application: Taxation of the Family Under federal income tax law, fundamental unit of income taxation is family Is excess burden minimized by taxing each spouse’s income at same rate? Should husbands face higher marginal tax rates than wives? Optimal User Fees A Natural Monopoly $ PM Marginal Cost Pricing with Lump Sum Taxes Benefits received principle Average Cost Pricing A Ramsey Solution ACM ACZ P* MCZ MRZ ZM ZA DZ Z* Z per year Optimal Income Taxation-Edgeworth’s Model W = U1 + U 2 + … + Un Individuals have identical utility functions that depend only on their incomes Total amount of income fixed Implications of model for income tax Supply-side responses to taxation Linear income tax model (flat income tax) Revenues = -α + t * Income Stern [1987] Gruber and Saez [2002] α= lump sum grant Tax Revenue Optimal Income Taxation-Modern Studies t= marginal tax rate Income Politics and the Time Inconsistency Problem Public choice analysis of tax policy Time inconsistency of optimal policy Other Criteria for Tax Design Horizontal equity Utility definition of horizontal equity Transitional equity Rule definition of horizontal equity Costs of Running the Tax System Costs of administering the income tax in the U.S. Types of costs Compliance Administration Tax Evasion Evasion versus Avoidance Policy Perspective: Architectural Tax Avoidance Methods of tax evasion Keeping two sets of books Moonlight for cash Barter Deal in cash Positive Analysis of Tax Evasion $ MC = p * marginal penalty MC = p * marginal penalty $ MB = t R* (Dollars of underreporting) MB = t R* = 0 (Dollars of underreporting) Costs of Cheating Psychic costs of cheating Risk aversion Work choices Underground economy Changing Probabilities of Audit Normative Analysis of Tax Evasion Tax evaders given weight in the social welfare function Tax evaders given no weight in the social welfare function Expected marginal cost of cheating = penalty rate * probability of detection Probability of detection = f (resources devoted to tax administration) Draconian vs. just retribution penalties THANKS FOR YOUR ATTENTION