EFFICIENT AND EQUITABLE TAXATION Chapter 16Optimal Commodity Taxationw(T l) = PXX + PYYwT = PXX + PYY + wlwT = (1 + t)PXX + (1 + t)PYY + (1 + t)wl 1 wT = PXX + PYY + wl 1 + t16-2The Ramsey RuleX per yearPXDXP0X0cP0 + uXbX1XaExcessBurdenP0 + (uX + 1)fX2ixejhgMarginalExcessBurdenmarginal excess burden = area fbae = 1/2xuX + (uX + 1) = X16-3The Ramsey Rule Continuedchange in tax revenues = area gfih area ibae = X2 (X1 X2)uXmarginal tax revenue = X1 Xmarginal 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 16-4A Reinterpretation of the Ramsey Ruleinverse elasticity rule16-5The Corlett-Hague RuleIn the case of two commodities, efficient taxation requires taxing commodity complementary to leisure at a relatively high rate16-6Equity ConsiderationsEquity implications of inverse elasticity ruleVertical equityOptimal departure from Ramsey Rule16-7Application: Taxation of the FamilyUnder federal income tax law, fundamental unit of income taxation is familyIs excess burden minimized by taxing each spouses income at same rate?Should husbands face higher marginal tax rates than wives?16-8Optimal User FeesZ per year$A Natural MonopolyDZMRZACZMCZZMPMACMZ*P*ZAMarginal Cost Pricing with Lump Sum TaxesBenefits received principleAverage Cost PricingA Ramsey Solution16-9Optimal Income TaxationEdgeworths ModelW = U1 + U2 + + UnIndividuals have identical utility functions that depend only on their incomesTotal amount of income fixedImplications of model for income tax16-10Optimal Income TaxationModern StudiesSupply-side responses to taxationLinear income tax model (flat income tax)Revenues = - + t * IncomeMankiw, Weinzierl, Yagan 2009IncomeTax Revenue = lump sumgrantt = marginaltax rate16-11Politics and the Time Inconsistency ProblemPublic choice analysis of tax policyTime inconsistency of optimal policy16-12Other Criteria for Tax DesignHorizontal equityUtility definition of horizontal equityTransitional equityRule definition of horizontal equity16-13Costs of Running the Tax SystemCosts of administering the income tax in the U.S.Types of costsComplianceAdministration16-14Tax EvasionEvasion versus AvoidancePolicy Perspective: Architectural Tax AvoidanceMethods of tax evasionKeeping two sets of booksMoonlight for cashBarterDeal in cash16-15Positive Analysis of Tax Evasion(Dollars of underreporting)(Dollars of underreporting)$MC = p * marginalpenaltyMC = p * marginalpenaltyMB = tMB = tR*R* = 016-16Costs of CheatingPsychic costs of cheatingRisk aversionWork choicesUnderground economyChanging Probabilities of Audit16-17Normative Analysis of Tax EvasionTax evaders given weight in the social welfare functionTax evaders given no weight in the social welfare functionExpected marginal cost of cheating = penalty rate * probability of detectionProbability of detection = f (resources devoted to tax administration)Draconian vs. just retribution penalties16-18Chapter 16 SummaryOptimal tax theory uses the tools of welfare economics to provide another view of the efficiency and equity considerations of tax design. In general, taxes:Should have horizontal and vertical equityShould be neutral concerning economic incentivesShould be administratively easyShould have low compliance costs16-19