1. Chapter 16 Income Taxation
Intermediate Public Economics

2. Introduction There are two main perspectives upon income taxation
Efficiency
Equity
The two major issues
The effect of taxation upon the supply of labor
The determination of the optimal level of income taxation (trade-off between efficiency and equity)

3. Taxation and Labor Supply
The effect of income taxation upon labor supply can be investigated using the standard model of consumer choice.
The utility function: U=U (x, T-l)=U (x, l).
The budget constraint facing the consumer: p x=[1-t]wl.
Pre-tax income: z=w l, then the utility function: U=U (x, z / w), and the budget constraint: p x=[1-t]z.

4. Labor supply decision p

5. Effect of a wage increase
Effect of a wage increase on labor supply is ambiguity
Substitution effect is positive
Income effect is negative
leisure is normal goods

6. Effect of a wage increase

7. A tax threshold
It can be expected that a number of consumers will cluster or “bunch” at the kink point b.

8. Several Thresholds

9. Taxation and the participation decision
lm denotes the minimum working time

10. Empirical evidence There are three major conclusions in theory
There are potential conflict between income and substitution effects which make it impossible to provide any clear cut results for those consumers at an interior solution.
Kinks in the budget constraint make behavior insensitive to taxes.
The participation decision can be very sensitive to taxation.

11. Empirical evidence
Surveys on labor supply have normally arrived at the conclusion that changes in the tax have little effect on the labor supply decision.
The different groups in the population have different reactions to changes in the tax system.
women
These results relate to the effect of a wage increase.

12. Modeling Income Taxation
A model must have several important attributes
There must be an unequal distribution of income in order for their to be equity motivations for taxation;
The income tax must affect the labor supply decisions of the consumers so that it has efficiency effects;
The structure must be sufficiently flexible that no prior restrictions are placed on the optimal tax functions that may arise.

13. A model
Setting
All the consumers have identical preferences but differ in their level of skill in employment
The hourly wage received by each consumer is determined by their level of skill
The economy is competitive so the wage rate is also equal to the marginal product of labor and firms price their output at marginal cost
The level of skill is private information and cannot be observed by the government, so an income tax is a second-best policy

14. A model The income tax function is chosen to maximize social welfare
Two constraints
The government’s revenue requirements
Self-selection

15. A model Assume There are two commodities: a consumption good and labor
Denote the income of a consumer with skill s by z (s)≡s l (s)
For a consumer with income z, the income tax paid is T (z)
Denote the consumption function c (z), then x (s)=c (z (s))=z (s) －T (z (s)) , (p=1)

16. Consumption function and taxation

17. Table: Tax liabilities under a hypothetical tax system
Income
Tax Liability
Average Tax Rate
Marginal Tax Rate
$ 2,000
$－200
－0.10
0.2
3,000
5,000
400
0.08
10,000
1,400
0.14
30,000
5,400
0.18

18. Preferences
The common utility function is denoted U=U (x, l)

19. Translation of indifference curves
Translate preferences into new space: U=U (x, l)=U (x, z / x)=u (x, z, s)

20. Utility maximization
Max u (x, z, s) subject to x=c (z)=z –T (z)

21. Agent monotonicity
At any point in z - x space the indifference curve of a household of ability s1 passing through a given consumption-income point is steeper than the curve of a household of ability s2 if s2>s1.

22. An example

23. Income and Ability
The first consequence of agent monotonicity is that high ability consumers will never earn less income than low ability. The solution for the high ability cannot be to the left of a since this would also be a better choice for the low ability.

24. Upper limit on tax rate
Economically, along the downward sloping section increased work effort is met with lower consumption. Hence there is no incentive to work harder and such points will not be chosen. So the marginal tax rate is less than 100%.

25. Lower limit on the tax rate
c1(z)→c’(z)>1,T’(z)<0
c2(z) →c’(z)<1,T’(z)>0
The new tax function is chosen so that the extra pre-tax income earned by the high ability is exactly equal to the reduction in earning by the low. The consumption of the low rises but that of the high ability falls by the same amount. The net effect of these changes is to transfer consumption to the low ability and work effort to the high. This change raise welfare because the marginal utility of consumption for the low ability is higher tan that for the high and, because of their greater ability, the extra work is less arduous for the high ability consumer.
From this it follows that the marginal tax rate must be non-negative so T’(z)≥0
Lower limit on the tax rate

26. Zero marginal rate of tax for the highest ability consumer
The optimal tax function must have a zero marginal rate of tax for the highest ability person. So the optimal tax system cannot be a progressive one.
The result is valid only for the highest ability consumer and it makes no prediction about the tax rate that will be faced by even the second-highest ability.

27. Conclusions The marginal tax rate should be between 0 and 1
The highest ability consumer should face a 0 marginal rate
The tax system should not be progressive

28. Rawlsian Tax
The Rawlsian social objective function concerns the welfare of the worst-off individuals.
Assuming tax revenue are entirely redistributed in the form of lump sum grants, for a Rawlsian government, the optimal income tax is simply that which maximizes the lump-sum grant, that is, which maximizes the revenue that can be extracted from taxpayers.

29. A model

30. The optimal Rawlsian tax

31. Interpretation
High marginal tax rates over some middle-income interval [z; z+dz] mean that for these middle-income individuals but also for the upper-income individuals, the government is collecting more taxes.
The proportion 1-G(z) is decreasing with z and converging to zero for the highest income level, so even though the redistribution motive is maximal under Rawlsian criterion, the optimal tax structure does not require marginal progressivity.
The cost of the high marginal tax rates over this interval is greater distortions for those with income in the range [z; z+dz]. The total distortion (and revenue loss) will be low, however, if there are relatively few taxpayers in this interval (low g(z)), or if those in it have a relatively low labor supply elasticity.

32. Conclusions
From the optimal tax structure, it follows that marginal tax rate must decrease everywhere as the labor supply elasticity increases and that marginal tax rates are decreasing when the hazard rate (g(z)/[1-G(z)])) is increasing (from Pareto distribution of income).
Maximal redistribution is better achieved when the tax schedule is regressive (concave) instead of progressive (convex).