1. Efficient taxation

2. The excess burden of taxation
Taxes affect individual welfare in 2 ways
They reduce individuals’ net income (by the amount of the tax paid) → an inward shift of our budget constraint → an income effect
They distort individuals’ choices by affecting the relative prices → a change of the slope of the budget constraint → a substitution effect
The distortion of the individual decisions due to the tax is called excess burden of taxation (aka deadweight loss or welfare cost of taxation)
Efficiency in taxation is the minimization of the second effect for every unitary amount of tax revenue

3. Efficient taxation – Excess burden
Efficient taxation minimizes distortions of individual choices
The (hypothetical) tax that minimizes EB is the ‘lump sum’ tax
With a lump sum tax individuals suffer a U loss because of foregone income, but their behaviour is not affected
Lump sum taxes do not exist → “head tax” is the closest example, but see reactions to poll tax in UK → there is always an EB
Goal of efficient taxation becomes minimization of MEB
EB is loss of utility over and above that due to income loss due to taxation

4. Government levies tax on barley
Excess Burden Defined
Government levies tax on barley A
Pounds of corn per year Ca Cb E1 C1 i F D B0 B1
Pounds of barley per year

5. Effect of Tax on Consumption Bundle
Pounds of corn per year G Ca E2 Cb E1 C1 i ii F D B0 B1
Pounds of barley per year

6. Excess Burden of the Barley Tax
Pounds of corn per year G Ca
Tax Revenues H M
Equivalent variation E2 Cb E1 C1 i ii F I D B0 B3 B1
Pounds of barley per year

7. Description of diagram - 1
2 goods consumed, o=barley (horizontal axis) and f=corn (vertical axis)
Before tax budget constraint has a slope AD=-(Po/Pf)
Before tax horizontal intercept 0D=I/Po where I=income
Introduction of an ad valorem tax on barley to
After tax slope becomes AF=-[(1+ to) Po/Pf]
After tax horizontal intercept is 0F=I/Pf

8. Questions and Answers Pounds of corn per year A E1 Ca i J R E2 Cb S C1ii F K D
B1 = B2 B3
Pounds of barley per year

9. Description of diagram - 2
Before taxing barley equilibrium choices are at E1, after tax equilibrium choices are at E2
For each Q of corn, the distance between AF and AD measures the amount of the tax paid (→ tax revenues)
at E2 tax paid equals E2G
The point of calculating an EB is whether to entails a utility loss greater than that needed to generate E2G of tax revenues
If so → excess burden (EB)

10. Description of diagram - 2
Measurement of EB requires assessing the equivalent variation (=the change of income that bears the same effect on utility as the tax induced change of a price of a commodity, here barley)
‘Artificial’ budget HI is tangent to ii and parallel to before-tax budget AD → no change of relative prices
Parallel distance indicates the income loss that moves individual from i to ii and reduces his/her utility without distorting his/her choices
Equilibrium is at E3 → distance E3M is the equivalent variation
E3M > E2G
Tax to produces EB equal to E2N → the tax induced utility loss is larger than revenues

11. Lump sum taxes
The only tax that does not generates EB is a lump sum tax
It does not entail changes of relative P → does not distort individual choices
Not much used in real world because politically very costly (Thatcher’s downfall due to ‘community charge’)
Under lump sum taxation everybody is taxed in the same way (head/capitation tax: poll tax)
An ‘equitable’ lump sum tax would make everybody pay according to his/her potential income (=actual ability to pay)
Problem: potential income is not observable
Actual income is a poor proxy (more on this later)

12. Welfare economics and EB
FTWE requires that MRSof=MRTof
With tax to → MRSof=(1+to)Po/Pf
This formula is the algebraic representation of equilibrium point E2
Producer receives only Po → the difference goes to the tax authority
Condition of profit maximization for producer entails MRTof=Po/Pf
With tax to → MRSof>MRTof→ FTWE condition violated
A Pareto superior move would be consuming less barley and more corn to re-establish MRSof=MRTof → but tax tof does not generate financial incentives to do so
Utility loss measured by EB
EB exists because the tax to opens a tax wedge between the P perceived by the consumer (1+to)Po and the P perceived by the producer Pof
Lump sum tax does not open this tax wedge → FTWE respected

13. Personal income tax and EB
Actual personal Y might seem a good proxy for potential personal Y
Y tax produces the same change of the budget constraint as a lump sum tax
If Y was constant and fixed the two taxes would be equivalent
In fact, they are not
Y is result of a labour/leisure choice
As if there were 3 goods: barley, corn and leisure l
PE requires
MRSof=MRTof
MRSol=MRTol
MRSfl=MRTfl
Y tax tw violates equalities 2 and 3
MRSfl=[(1-tw)w]/Pf, while MRTfl=w/Pl
To have an inefficiency, one violation is enough
To evaluate the overall efficiency loss due to income taxation, one must assess the EB that each tax generates

14. EB and inelastic demand
If the Q demanded of a good does not change after the imposition of a tax (inelastic demand) → there is still EB because the tax affects the demand of other goods
2 kinds of reactions to tax to
Uncompensated response: from E1 to E2 composed by
Income effect: from E1 to E3: due only to the loss of Y (relative P unchanged, the budget constraint is parallel to the before-tax budget constraint) → equivalent to introduction of a lump sum tax
Substitution effect (compensated response): Po increases wrt Pf because of to, individual moves from E3 to E2 along the same indifference curve ii (with E3<E2)
Compensated response:↑P↓AD
Reduction of relative P of corn “compensates” individual of the loss of Y due to tax on barley
Alternatively, individual receives enough Y to remain on the same after tax indifference curve ii
Important because it reveals the EB: shift from E3 to E2 points out E2N → EB
PE violated because in the movement from E3 to E2 the relative P (MRS) change
Important analysis for policy purposes → many believe that if a tax on labour does not affect LS, the tax has no adverse consequences → not true!

15. Measuring EB with demand curves
Consumer surplus before tax to was area aih, after tax becomes area agf with tax revenues equal to gfhd
difference fdi is EB
Measure of area fdi is 1/2εPoq1to2
→ compensated own elasticity of demand (proof later)
High ε entails large EB because the variation of Q for every tax induced change of P will be large
→ large distortions of individual choices=large inefficiency
to2 indicates that as to increases → EB grows by the square of it
MEB>AEB

16. Excess Burden Measurement with Demand Curves
Excess burden = ½ ηPbq1tb2
Price per pound of barley
Tax revenues
Excess burden of tax
(1 + tb)Pb
S’b g f h d i Pb Sb Db q2 q1
Pounds of barley per year

17. Implications of quadratic response
The formula 1/2εPoq1to2 has an important policy consequence
Doubling a tax quadruples the EB
EB increases with the square of the tax rate → it is more efficient to tax many commodities at a lower rate than to tax fewer at a higher rate
In the U.S. airplane tickets are taxed with a 10% flat rate
US$107billion=price per ticket * number of tickets sold
Annual EB of this tax equals ½*107*(0.1)2=535 million

18. Pre-existing distortions and the theory of the second best
Analysis so far measures EB under the hypothesis of no pre-existing distortions in the economy → never the case in reality
Theory of the second best → in the presence of existing distortions, policies that in isolation would increase efficiency can decrease it and vice versa
Common for environmental taxes. Pigouvian taxes correct an inefficiency represented by an externality (e.g. pollution)
Pigouvian taxes (e.g. taxes on gas) reduce the real wage of workers by raising transportation costs → effect on labour market → if income tax also distorts work incentives, Pigouvian taxes increases the inefficiencies of income taxes → tax interaction effect
One can use the revenues of Pigouvian tax to lower inefficient tax rates on labour → double dividend effect

19. EB of a subsidy Subsidy is equivalent to a negative tax
Just like a tax a subsidy has an EB
Example of a subsidy to the price of owner occupied housing (e.g. garbage collection)
Benefit associated to a subsidy
CS=nquo
Expenditure related to subsidy=nvuq
EB of the subsidy=ovu
Individuals consume a2 of services because they evaluate them at (1-s)Pa, while they actually cost Pa to society → inefficiency
Equivalent to saying that money transfers are Pareto superior to in kind subsidies→ individuals indifferent between in kind subsidy nquv and money transfer nouq → nouq less expensive

20. Excess Burden of a Subsidym
Price per unit of housing services
Excess burden n o v Ph Sh q r u
(1 – s)Ph
Sh’ Dh h1 h2
Housing services per year

21. Estimates of EB of income taxes
In the U.S. Tax system ihd is quite large
Feldstein (2006) estimates ε=0.2
If individual works 2000 hours per year at a wage of US$20 per hour, with a tax on earnings of 40%
tax revenues fgih=US$16,000
EB of Y tax idh=US$640
4% of tax revenues
Considering all tax interactions, Feldstein (2006) estimates that EB of US$1 of income tax revenues is 76 cents!
In other tax systems like where Y taxes are more progressive, overall EB are likely even larger

22. Excess Burden of Income Taxation
Excess burden = ½ εωL1t2
Excess burden SL
Wage rate per hour f i d w
(1 – t)w g h a L2 L1
Hours per year

23. Differential taxation of inputs
Some inputs are taxed differently according to the sector where the input is employed
E.g. Because of corporate income tax K used in corporations is taxed at a higher rate than K used by noncorporate business
Household labour is valuable but not taxed, while labour supplied on the market is subject to payroll and income taxes
Differential tax treatments of the same input distorts individual choices among sectors/tax treatment

24. The Allocation of Time Between Housework and Market Work
Excess burden = ½ (ΔH)tw2 $ $
(1 – t)VMPmkt b w2 a w1 w1
(1 – t)w2 e
VMPmkt
VMPhome d c
Hours worked in home per year H* H1
Hours worked in market per year 0’

25. Description of the diagram - 1
Total amount of labour in society is fixed at 00’
Moving away from 0 is increasing housework and viceversa
Movements along abscissa from 0 transfer labour from housework to market work and viceversa from 0’
VMP function measures value of MPL → monetary value of additional output produced with an additional hour of L in each sector
VMPL decreases as the number of hours worked increase
Optimal allocation of hours worked is found when the VMPL of the two types of work are equal
0H* hours of L for housework
0’H* supplied on the market

26. Description of the diagram - 2
If a tax t on market labour is introduced while housework remains untaxed → wage rate is lowered from VMPmkt to (1 – t)VMPmkt
The VMPmkt function pivots downwards
Amounts of hours worked in the market reduced from 0’H* to 0’Ht
abe is associated EB