Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin



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Chap016 efficient and equitable taxation (1)

CHAPTER 16

  • Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
  • McGraw-Hill/Irwin

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

  • X per year
  • PX
  • DX
  • P0
  • X0
  • c
  • P0 + uX
  • b
  • X1
  • ∆X
  • a
  • Excess Burden
  • P0 + (uX + 1)
  • f
  • X2
  • i
  • ∆x
  • e
  • j
  • h
  • g
  • Marginal Excess Burden
  • marginal excess burden = area fbae = 1/2∆x[uX + (uX + 1)] = ∆X

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

A Reinterpretation of the Ramsey Rule

  • 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

  • Z per year
  • $
  • A Natural Monopoly
  • DZ
  • MRZ
  • ACZ
  • MCZ
  • ZM
  • PM
  • ACM
  • Z*
  • P*
  • ZA
  • Marginal Cost Pricing with Lump Sum Taxes
  • Benefits received principle
  • Average Cost Pricing
  • A Ramsey Solution

Optimal Income Taxation-Edgeworth’s Model

  • W = U1 + U2 + … + Un
  • Individuals have identical utility functions that depend only on their incomes
  • Total amount of income fixed
  • Implications of model for income tax

Optimal Income Taxation-Modern Studies

  • Supply-side responses to taxation
  • Linear income tax model (flat income tax)
    • Revenues = -α + t * Income
  • Stern [1987]
  • Gruber and Saez [2002]
  • Income
  • Tax Revenue
  • t = marginal tax rate

Politics and the Time Inconsistency Problem

  • Public choice analysis of tax policy
  • Time inconsistency of optimal policy

Other Criteria for Tax Design

  • 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

  • (Dollars of underreporting)
  • (Dollars of underreporting)
  • $
  • $
  • MC = p * marginal penalty
  • MC = p * marginal penalty
  • MB = t
  • MB = t
  • R*
  • R* = 0

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

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