1. EFFICIENT AND EQUITABLE TAXATION
Chapter 16

2. 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 t

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

4. 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

5. A Reinterpretation of the Ramsey Rule
inverse elasticity rule

6. The Corlett-Hague Rule
In the case of two commodities, efficient taxation requires taxing commodity complementary to leisure at a relatively high rate

7. Equity Considerations
Equity implications of inverse elasticity rule
Vertical equity
Optimal departure from Ramsey Rule

8. 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?

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

10. 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

11. Optimal Income Taxation— Modern Studies
Tax Revenue
α = lump sum grant
t = marginal tax rate
Supply-side responses to taxation
Linear income tax model (flat income tax)
Revenues = -α + t * Income
Mankiw, Weinzierl, Yagan [2009]

12. Politics and the Time Inconsistency Problem
Public choice analysis of tax policy
Time inconsistency of optimal policy

13. Other Criteria for Tax Design
Horizontal equity
Utility definition of horizontal equity
Transitional equity
Rule definition of horizontal equity

14. Costs of Running the Tax System
Costs of administering the income tax in the U.S.
Types of costs
Compliance
Administration

15. 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

16. Positive Analysis of Tax Evasion
MC = p * marginal penalty
MC = p * marginal penalty $ $
MB = t
MB = t R*
(Dollars of underreporting)
(Dollars of underreporting)
R* = 0

17. Costs of Cheating Psychic costs of cheating Risk aversion Work choices
Underground economy
Changing Probabilities of Audit

18. 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

19. Chapter 16 Summary
Optimal 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 equity
Should be neutral concerning economic incentives
Should be administratively easy
Should have low compliance costs