chapter 16 income taxation intermediate public economics

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Chapter 16 Income Taxation Intermediate Public Economics

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Page 1: Chapter 16 Income Taxation Intermediate Public Economics

Chapter 16

Income Taxation

Intermediate Public Economics

Page 2: Chapter 16 Income Taxation Intermediate Public Economics

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)

Page 3: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 4: Chapter 16 Income Taxation Intermediate Public Economics

Labor supply decision

p

Page 5: Chapter 16 Income Taxation Intermediate Public Economics

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

Page 6: Chapter 16 Income Taxation Intermediate Public Economics

Effect of a wage increase

Page 7: Chapter 16 Income Taxation Intermediate Public Economics

A tax threshold

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

Page 8: Chapter 16 Income Taxation Intermediate Public Economics

Several Thresholds

Page 9: Chapter 16 Income Taxation Intermediate Public Economics

Taxation and the participation decision

lm denotes the minimum working time

Page 10: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 11: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 12: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 13: Chapter 16 Income Taxation Intermediate Public Economics

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

Page 14: Chapter 16 Income Taxation Intermediate Public Economics

A model

The income tax function is chosen to maximize social welfare

Two constraints The government’s revenue requirements Self-selection

Page 15: Chapter 16 Income Taxation Intermediate Public Economics

A model

Assume There are two commodities: a consumption good an

d 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)

Page 16: Chapter 16 Income Taxation Intermediate Public Economics

Consumption function and taxation

Page 17: Chapter 16 Income Taxation Intermediate Public Economics

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 0 0 0.2

5,000 400 0.08 0.2

10,000 1,400 0.14 0.2

30,000 5,400 0.18 0.2

Page 18: Chapter 16 Income Taxation Intermediate Public Economics

Preferences

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

Page 19: Chapter 16 Income Taxation Intermediate Public Economics

Translation of indifference curves

Translate preferences into new space: U=U (x, l)=U (x, z / x)=u (x, z, s)

Page 20: Chapter 16 Income Taxation Intermediate Public Economics

Utility maximization

Max u (x, z, s) subject to x=c (z)=z –T (z)

Page 21: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 22: Chapter 16 Income Taxation Intermediate Public Economics

An example

1 2 1 2

1 2 1 2

There are two kinds of utility function: Cobb-Donglas UF

( ( , ) , 0, 0) and quasi=linear UF

( ( , ) ( ) ).

Example: log log

1 1

c du x x x x c d

u x x v x x

zU x l x

s

dU dx dzx s

.dx x

dz s

Page 23: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 24: Chapter 16 Income Taxation Intermediate Public Economics

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%.

( ) ( )

( ) 1 ( )

( ) 0

( ) 1

c z z T z

c z T z

c z

T z

Page 25: Chapter 16 Income Taxation Intermediate Public Economics

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

Page 26: Chapter 16 Income Taxation Intermediate Public Economics

Zero marginal rate of taxfor 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.

Page 27: Chapter 16 Income Taxation Intermediate Public Economics

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

Page 28: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 29: Chapter 16 Income Taxation Intermediate Public Economics

A model

-1

The Rawlsian optimal tax is the revenue maximizing tax schedule.

Agent monotonicity implies that ( ) is increasing and can be

inverted to the increasing inverse function ( ).

Consider ski

z s

z s

ll levels are continuously distributed in the population

according to a cumulative distribution function ( ) with associated

density function ( ) 0. The tax scheme ( ) induces the following

income dis

F s

f s T z-1 -1tribution ( ) ( ( )) with density ( ) ( ( )).G z F z s g z f z s

Page 30: Chapter 16 Income Taxation Intermediate Public Economics

The optimal Rawlsian tax From the first order condition of the revenue maximization

problem, small deviation from the optimal tax scheme must have

no effect on total tax revenue.

The revenue gain from the marginal tax change is [1 ( )]

The revenue loss associated with the incentive effect of tax

change is [ ( )] .1

The revenue maximizing tax scheme reguqires to equate the

revenue loss with the

s

G z z T

Tg z T z

T

revenue gain from marginal tax change for

any income level.

( ) 1 ( ) [1 ( )] [ ( )]

1 1 ( ) ( )ss

T T z G zG z z T g z T z

T T z g z

Page 31: Chapter 16 Income Taxation Intermediate Public Economics

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.

Page 32: Chapter 16 Income Taxation Intermediate Public Economics

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).