1. Jonathan Gruber Public Finance and Public Policy
Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
Jonathan Gruber
Public Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

2. Introduction Markets do not take taxes lying down.
If there is some action that market participants can undertake to minimize the burden of a tax, they will do so.
This is true both for consumers and producers.

3. Introduction
This lesson will illustrate how attempts to minimize tax burdens have efficiency costs for society.
Since social efficiency is maximized at the competitive equilibrium (in the absence of market failures), taxing market participants entails deadweight loss.

4. TAXATION AND ECONOMIC EFFICIENCY Graphical approach
We now move from discussing the effects of taxation on equity to a discussion of its effect on efficiency.
The focus therefore turns from prices to quantities.
Consider the impact of a 50¢ per gallon tax on the suppliers of gasoline, illustrated in Figure 1.

5. The tax creates deadweight loss.
Figure 1
Price per
gallon (P) S2 S1
The tax creates deadweight loss.
The tax on gasoline shifts the supply curve. B
P2 = $1.80
DWL
P1 = $1.50 A
$0.50 C D1
Q2 = 90
Q1 = 100
Quantity in billions
of gallons (Q)

6. Taxation and economic efficiency Graphical approach
Before the tax was imposed, 100 billion gallons were sold. Afterwards, only 90 billion gallons are sold.
Recall that the demand curve represents the social marginal benefit of gasoline consumption, while the supply curve represents the social marginal cost.
SMB=SMC at 100 billion gallons
Production less than that amount results in deadweight loss. Beneficial trades are not made because of the 50¢ per gallon tax.

7. Taxation and economic efficiency Elasticities determine tax inefficiency
The efficiency consequences would be identical regardless of which side of the market the tax is imposed on.
Just as price elasticities of supply and demand determine the distribution of the tax burden, they also determine the inefficiency of taxation.
Higher elasticities imply bigger changes in quantities, and larger deadweight loss.
Figure 2 illustrates that deadweight loss rises with elasticities.

8. Demand is fairly inelastic, and DWL is small.
Figure 2
Demand is fairly inelastic, and DWL is small.
(a) Inelastic Demand
(b) Elastic demand P P
Demand is more elastic, and DWL is larger. S2 S2 S1 S1 B P2 B
DWL
DWL P2 P1 A P1 A C
50¢
Tax
50¢
Tax C D1 D1 Q Q Q2 Q1 Q2 Q1

9. Taxation and economic efficiency Elasticities determine tax inefficiency
With inelastic demand, there is a large change in market prices with consumers bearing most of the tax, but little change in quantity.
With more elastic demand, market prices change more modestly and the supplier bears more of the tax. The reduction in quantity is greater, as is the deadweight loss triangle.

10. Taxation and economic efficiency Elasticities determine tax inefficiency
The inefficiency of any tax is determined by the extent to which consumers and producers change their behavior to avoid the tax.
Deadweight loss is caused by individuals and firms making inefficient consumption and production choices in order to avoid taxation.

11. Tax avoidance in practice
Application
In reality, there are many inefficient, tax-avoiding activities.
For example, the Thai government levies a tax on signs in front of businesses, where the tax rate depends on whether the sign is completely in Thai (low tax), in Thai and English (medium tax), or completely in English (high tax).
Many signs are in English, with a small amount of Thai writing!

12. Deadweight loss in Thailand

13. 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

14. Taxation and economic efficiency Determinants of deadweight loss
This formula for deadweight loss has many important implications:
Deadweight loss rises with the elasticity of demand.
The appropriate elasticity is the Hicksian compensated elasticity, not the Marshallian uncompensated elasticity.
Deadweight loss also rises with the square of the tax rate.
That is, larger taxes have much more DWL than smaller ones.

15. Taxation and economic efficiency Determinants of deadweight loss
This point about DWL rising with the square of the tax rate can be illustrated graphically.
Marginal deadweight loss is the increase in deadweight loss per unit increase in the tax.
See Figure 3.

16. The next $0.10 tax creates a larger marginal DWL, BCDE. D P3
Figure 3 P S3 S2 S1
The next $0.10 tax creates a larger marginal DWL, BCDE. D P3
The first $0.10 tax creates little DWL, ABC. B P2 P1 A C
$0.10 E
$0.10 D1 Q Q3 Q2 Q1

17. Taxation and economic efficiency Determinants of deadweight loss
As the tax rate doubles, from 10¢ to 20¢, the deadweight loss triangle quadruples.
The area DBCE is three times larger than BAC. The total deadweight loss from the 20¢ tax is DAE.
As the market moves farther and farther from the competitive equilibrium, there is a widening gap between demand and supply. The loss of these higher surplus trades means marginal DWL gets larger.

18. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
The insight that deadweight loss rises with the square of the tax rate has implications for tax policy with respect to:
Preexisting distortions
Progressivity
Tax smoothing

19. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
Preexisting distortions are market failures that are in place before any government intervention.
Externalities or imperfect competition are examples.
Figure 4 contrasts the use of a tax in a market without any distortions and in one with positive externalities.

20. No positive externality
Figure 4 P S2 P S2 S1 S1
In a market with a preexisting distortion, taxes can create larger (or smaller) DWL.
SMC B G A E D C F H D1 D1 Q Q Q2 Q1 Q2 Q1 Q0
No positive externality
Positive externality

21. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
Imposing the tax in the first market, without externalities, results in a modest deadweight loss triangle equal to BAC.
When an existing distortion already exists where the firm is producing below the socially efficient level, the deadweight loss is much higher. The marginal deadweight loss from the same tax is now GEFH.
Of course, if there were negative externalities, such a tax would actually improve efficiency.

22. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
This insight about deadweight loss also demonstrates that a progressive tax system can be less efficient.
Consider two tax systems – one a proportional 20% payroll tax, and the other a progressive tax that imposes a 60% rate on the rich, and a 0% rate on the poor.
Figure 5 shows these cases.

23. Figure 5 S2 S3
Wage (W)
Wage (W) S2 S1 S1
DWL increases with the square of the tax rate. Smaller taxes in many markets are better. G
W3=23.90 B E
W2=11.18
W2=22.36 A D
W1=10.00
W1=20.00 C F D1 D1 I
Hours (H)
Hours (H)
H2=894
H1=1,000
H3=837
H2=894
H1=1,000
Low Wage Workers
High Wage Workers

24. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
Under the proportional system the efficiency loss for society is the sum of two deadweight loss triangles, BAC and EDF.
Under the progressive system, the efficiency loss is the triangle GDI – that is, it adds the area GEFI but does not include BAC.
Table 1 puts actual numbers to the picture.

25. Deadweight Loss from Taxation
Table 1
Low wage worker
Panel A
High wage worker
Panel B
Tax Rate Below $10,000
Tax Rate Above $10,000
Hours of labor supply
Deadweight Loss from Taxation
Total Deadweight Loss
No Tax
1000 (H1)
Proportional Tax
20%
894 (H2)
$115.71
(area BAC)
$231.42
(area EDF)
$347.13
(BAC + EDF)
Progressive Tax 0%
60%
837 (H3)
$566.75
(area GDI)
(EDF + GEFI)
A lower proportional tax creates less DWL than the higher progressive tax.

26. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
In this case, a proportional tax is more efficient.
The large increase in deadweight loss arises because the progressive tax is levied on a smaller tax base. In order to raise the same amount of revenues on a smaller base, the tax rate must be higher meaning a higher marginal DWL.
This illustrates the larger point that the more one loads taxes onto one source, the faster DWL rises. The most efficient tax systems spread the burden most broadly. Thus, a guiding principle for efficient taxation is to create a broad and level playing field.

27. Taxation and economic efficiency Deadweight loss and the design of efficient tax systems
The fact that DWL rises with the square of the tax rate also implies that government should not raise and lower taxes, but rather set a long-run tax rate that will meet its budget needs on average.
For example, to finance a war, it is more efficient to raise the rate by a small amount for many years, rather than a large amount for one year (and run deficits in the short-run).
This notion can be thought of as “tax smoothing,” similar to the notion of individual consumption smoothing.

28. The deadweight loss of taxing wireless communications
Application
An interesting applied example computing DWL is Hausman’s (2000) study of wireless communications. He found that:
The federal/state tax on wireless phones was as high as 25%.
There was 53¢ of DWL per $1 raised in revenue.
Fairly priced elastic commodity.
Imperfectly competitive market with high mark-ups.
Preexisting tax distortions.
Marginal DWL much higher – as high as 90¢ of DWL per $1 raised.

29. 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

30. 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

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

32. 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?

33. Optimal commodity taxation
Optimal commodity taxation is choosing tax rates across goods to minimize the deadweight loss for a given government revenue requirement.

34. 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 ∆x ∆X DX X2 X1 X0
X per year

35. 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

36. A Reinterpretation of the Ramsey Rule
inverse elasticity rule

37. Optimal commodity taxation Ramsey rule
The Ramsey Rule is:
It sets taxes across commodities so that the ratio of the marginal deadweight loss to marginal revenue raised is equal across commodities.

38. Optimal commodity taxation Ramsey rule
The goal of the Ramsey Rule is to minimize deadweight loss of a tax system while raising a fixed amount of revenue.
The value of additional government revenues is the value of having another dollar in the government’s hands relative to its next best use in the private sector.

39. Optimal commodity taxation Ramsey rule
8 measures the value of having another dollar in the government’s hands relative to the next best use in the private sector.
Smaller values of 8 mean additional government revenues have little value relative to the value in the private market.

40. Optimal commodity taxation Inverse elasticity rule
The inverse elasticity rule, which expresses the Ramsey result in a simplified form, allows us to relate tax policy to the elasticity of demand.
The government should set taxes on each commodity inversely to the demand elasticity.
Less elastic items are taxed at a higher rate.

41. Optimal commodity taxation Equity implications of the Ramsey rule
Two factors must be balanced when setting optimal commodity taxes:
The elasticity rule: Tax commodities with low elasticities.
The broad base rule: It is better to tax a wide variety of goods at a lower rate, because deadweight loss increases with the square of the tax rate.
Thus, the government should tax all of the commodities that it is able to, but at different rates.

42. Price reform in Pakistan
Application
An interesting application of these rules is price reform in Pakistan.
Deaton (1997) found that the Pakastani government was paying subsidies for wheat and rice, and was collecting taxes on oils and fats.
The market conditions are summarized in Table 2.

43. Demand for Various Commodities in Pakistan Include Distributional
Table 2
Demand for Various Commodities in Pakistan
Good
Subsidy
Price
Elasticity
Policy
Change
Welfare
Gain
Include Distributional
Concerns
Wheat
40%
-0.64
Reduce subsidy
Small
Don’t reduce subsidy
Rice
-2.08
Large
Oil/Fat
-5%
-2.33
Reduce tax
Reduce tax further
With these elasticities, the taxes and subsidies should be changed.

44. Price reform in Pakistan
Application
The subsidies generate overconsumption of wheat and rice, and lead to particularly large efficiency losses for rice.
The tax on oils/fats also generates deadweight loss.
Using a framework similar to Ramsey’s, Deaton suggested a tax reform that would increase efficiency and be revenue neutral: reduce the tax on oils and fats, and make up for the lost tax revenues by reducing the subsidies to rice (especially) and wheat.

45. Price reform in Pakistan
Application
Deaton also found that distributional considerations might offset some of these conclusions.
Wheat and fats/oils were consumed quite heavily by the poor, but rice was consumed fairly evenly throughout the income distribution. This suggests not to decrease the wheat subsidy on equity grounds.

46. OPTIMAL INCOME TAXES
Optimal income taxation is choosing the tax rates across income groups to maximize social welfare subject to a government revenue requirement.
A key concern in the analysis is vertical equity.

47. Optimal income taxes A simple example
Imagine we make the following assumptions:
Identical utility functions
Diminishing marginal utility of income
Total income is fixed
Utilitarian social welfare function
The optimal income tax system in such a case gives everyone the same level of post-tax income.
Implies marginal tax rate of 100% for those with above-average income.
The unrealistic assumption is that total income (labor supply) is fixed with respect to taxes.

48. Optimal income taxes General model with behavioral effects
More generally, there are equity-efficiency tradeoffs.
Raising tax rates will likely affect the size of the tax base. Thus, increasing the tax rate on labor income has two effects:
Tax revenues rise for a given level of labor income.
Workers reduce their earnings, shrinking the tax base.
At high tax rates, this second effect becomes important.

49. Optimal income taxes General model with behavioral effects
The Laffer curve, which motivated the supply-side economic policies of the Reagan presidency is shown in Figure 7.
If tax rates are too high and we are on the wrong side of the Laffer curve, lowering tax rates increases revenue.

50. The Laffer curve demonstrates that at some point, tax revenue falls.
Figure 7
The Laffer curve demonstrates that at some point, tax revenue falls.
Tax revenues
right
side
wrong
side
τ*%
Tax rate
100%

51. Optimal income taxes General model with behavioral effects
The goal of optimal income tax analysis is to identify a tax schedule that maximizes social welfare, while recognizing that raising taxes has conflicting effects on revenue.
The optimal tax system meet the condition that tax rates are set across groups such that:
Where MUi is the marginal utility of individual i, and MR is the marginal revenue from that individual.

52. Optimal income taxes An example
As with optimal commodity taxation, this outcome represents a compromise between two considerations:
Vertical equity
Behavior responses
Figure 8 shows that optimal income taxation equates this ratio across individuals, leading to a higher tax rate for the rich.

53. Figure 8
MU/MR
Mrs. Poor
Mr. Rich
Optimal income taxation equates the ratio of (MU/MR) across individuals.
Tax rate
10%
20%

54. Optimal income taxes The structure of optimal tax rates: Simulation exercise
Simulation exercises are the numerical simulation of economic agents’ behavior based on measured economic parameters.
These are used to determine the optimal tax rates or other parameters of interest.
Gruber and Saez (2000) considered a tax rate with:
Guaranteed income level (as with welfare)
Utilitarian SWF
Revenue neutral
Four income categories
They weighed the equity-efficiency implications here; their results are presented in Figure 9.

55. The optimal income tax schedule starts off with a subsidy.
Figure 9
Tax payments
$46,650
$34,400
$10,320
$10,000
Family income
-$4,200
$16,364
$32,000
$75,000
$100,000
The optimal income tax schedule starts off with a subsidy.
The average rate does not exceed 47%.
-$11,000

56. Marginal rate are higher on the poor.
Figure 9
Optimal Tax Results
Income groups $0 To
$10K
$32K
$75K
and
Above
Guaranteed income
level
Marginal Tax Rates 68 66 56 49
$11,000
Average Tax Rates
-161 12 40 47
Marginal rate are higher on the poor.

57. Optimal income taxes The structure of optimal tax rates: Simulation exercise
Gruber and Saez (2000) found that marginal tax rates were highest on the poor and lowest on the rich, while average tax rates rose with income (because of the loss of the grant).
Results of these sorts of exercises can be sensitive to the formulation of the SWF.

58. TAX-BENEFITS LINKAGES AND THE FINANCING OF SOCIAL INSURANCE PROGRAMS
Tax-benefit linkages are direct ties between taxes paid and benefits received.
Summers (1989) shows that such linkages can affect the equity and efficiency of a tax. The link between payroll taxes and social insurance benefits can lead the incidence to fall more fully on workers than might be presumed.

59. Tax-benefits linkages and the financing of social insurance programs: The model
The key point of Summers’ analysis is that with taxes alone, only the labor demand curve shifts, but with tax-benefit linkages, the labor supply curve shifts as well.
That is, workers are willing to work the same amount of hours at a lower wage, because they get some other benefit as well, such as workers’ compensation or health insurance.
This is illustrated in Figure 10.

60. Mandated benefits also shift the supply curve.
Figure 10
Wage (W)
Wage (W) C
Creating smaller DWL. S1 S1
Mandated benefits also shift the supply curve. E S2 W1 A W1 A F W2 B W2 B W3 D D1 D1 D2 D2
Labor (L)
Labor (L) L2 L1 L2 L3 L1

61. Tax-benefits linkages and the financing of social insurance programs: The model
Wages adjust by more with the tax-benefit linkage, and employment falls by less.
Because of the smaller reduction in employment, deadweight loss is smaller than with a pure tax. The true “tax” is the difference between the statutory tax and the employee’s valuation of the benefit.
Figure 11 shows the case of full valuation of the benefit.

62. Figure 11
Wage (W) S1 W1 A
Benefits =
Program cost S2 W2 B D1 W3
With full valuation of the benefit, employment is not reduced and there is no DWL. D2
Labor (L) L2 L1

63. Tax-benefits linkages and the financing of social insurance programs: The model
With full valuation, the cost of the program is fully shifted onto workers in the form of lower wages, and there is no deadweight loss or employment reduction.

64. Tax-benefits linkages and the financing of social insurance programs: Issues raised
This raises some issues with tax-benefit linkages, especially with respect to employer mandates.
If there is no inefficiency, why doesn’t the employer simply provide the benefit without government intervention?
Market failures, such as adverse selection, may be present. The employer that provides a benefit such as workers’ compensation or health insurance may end up with high risks.

65. Tax-benefits linkages and the financing of social insurance programs: Issues raised
When are there tax-benefit linkages?
They are strongest when taxes paid are linked directly to a benefit for workers.
This generates the rise in labor supply.

66. Tax-benefits linkages and the financing of social insurance programs: Issues raised
There are a number of empirical studies that have examined the incidence of social insurance contributions on wages and employment.
Gruber (1994) examines a quasi-experiment involving mandated maternity benefits, and finds full wage shifting and little effect on labor supply.

67. Recap of Tax Inefficiencies and Their Implications for Optimal Taxation
Taxation and Economic Efficiency
Optimal Commodity Taxation
Optimal Income Taxes
Tax-Benefit Linkages and the Financing of Social Insurance Programs