Taxation and Equity ADE Fall 2015-2016 Department of Public Economics 1.

Taxation and Equity

ADEFall 2015-2016

Department of Public Economics

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Outline

1. Introduction: What do we mean by equity and why does it matter?

2. The benefit principle

2.1. Definition

2.2. Provision of private goods

2.3. Provision of public goods

2.4. Advantages and drawbacks

3. The ability-to-pay principle

3.1. Definition

3.2. Indicators of the ability-to-pay

3.3. Definition of vertical equity

3.4. Measures of progressivity

3.5. Advantages and drawbacks

4. Summary - key points

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Introduction: What do we mean by equity?

• There are different types of public services:

a) A concert in a town’s celebration

b) Healthcare

c) Trash collection

d) Universities

e) Roads

•Should these all be funded in the same way?

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• Both the French and American revolutions were (at least in part) the result of unfair taxation!

• A British poll tax lead to Thatcher being forced out

The question of how these are funded is very important since it will determine the degree of social acceptance of the tax system


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Pareto efficient taxation:

A given level of revenue should be raised by a tax structure such that no one can be made better of without making someone else worse off

The choice among those Pareto efficient structures depends on the social welfare function

[A short recap: Pareto efficiency]

6Source: Rosen and Gayer

• An allocation is Pareto efficient if no one can be made better off without making at least one individual worse off.

• A case, you probably know: the Contract Curve

A2

A1

Ax2

Ax1

More preferred

OA

Bx2

Bx1

More preferred

For consumer B.

OB

B2

B1

B2

B1

Bx1

Bx2

More preferred

For consumer B.OB

Edgeworth’s Box

A2

A1

Ax2

Ax1

OA

B2

B1

Bx1

Bx2

OB

Pareto-Improvement

• An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Pareto-improving allocation

• Where are the Pareto-improving allocations?

Pareto-Improvements

A2

A1

Ax2

Ax1

OA

B2

B1

Bx1

Bx2

OB

The set of Pareto-improving allocations

Person i

Person j

0

0’

y

x

ig

jgg

p1

p

jp2

ip2

p2

p3

p4

The contract curve

[A short recap: Pareto efficiency]

Source: Rosen and Gayer


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Fairness (equity) depends on the social welfare function the policy maker applies. Limiting cases are associated with Jeremy Bentham and John Rawls:

1. Objective of Utilitarianism (Bentham): seeking “the greatest good for the greatest number”

• social welfare is defined by the sum of the utilities of the people in the population

• distribution of utilities doesn’t matter here


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Fairness (equity) depends on the social welfare function the policy maker applies. Limiting cases are associated with Jeremy Bentham and John Rawls:

1. Objective of Utilitarianism (Bentham): seeking “the greatest good for the greatest number”

• social welfare is defined by the sum of the utilities of the people in the population

• distribution of utilities doesn’t matter here

Assumption: utility is measurable!


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2. Objective of Rawlsianism (Rawls): maximizing the welfare of the worst-off individual

• society is as strong as its weakest link• veil of ignorance

• welfare is maximized when the welfare of the individual with the lowest utility is maximized – distribution matters.

)

Objective of Utilitarianism (Bentham) Example: Utility Possibilities Curve

j’s utility

i’s u

tility

U

U

p3

q

p1

Objective of Utilitarianism (Bentham)Example: Social Indifference Curve

j’s utility

i’s u

tility W = F(Ui, Uj)

Increasingsocialwelfare

Objective of Utilitarianism (Bentham) Example: Maximizing Social Welfare

j’s utility

i’s u

tility

i

ii

iii

Objective of Rawlsianism (Rawls)Example: Maximizing Social Welfare

j’s utility

i’s u

tility

ii)

Rawls Vs BenthamExample: Maximizing Social Welfare

j’s utility

i’s u

tility

i

ii

Rawls Vs BenthamExample: Maximizing Social Welfare

j’s utility

i’s u

tility

i

ii

Preferred by Bentham

Preferred by Rawls


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„The subjects of every state ought to contribute towards the support of thegovernment as nearly as possible in proportion to their respective abilities; that is in proportion to the revenue which they respectively enjoy under the protection of the state.”

Source: Smith (1776), Book V, Ch. II, Part II, p. 310

Long historical debate:

There are two main principles of tax equity (or fairness):

a) The benefit principle

b) The ability-to-pay principle

Introduction: Requirements of equity


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Two principles:

• Horizontal Equity: treat equal people in an equal way

• Vertical Equity: treat different people in different ways

How do we decide who is equal (unequal) to whom?

On what basis do we decide?

• Income?• Wage rate?• Wealth?• Consumption?• Total utility?• Benefit gained from public expenditure?


Not as obvious as it seems: Income means also effort!

• Feldstein (1976 JPubE) - On the Theory of Tax Reform translated the principles of equitable taxation into:

• Feldstein’s Horizontal Equity Principle: Two people with the same utility before taxation must have the same utility after taxation.

• Feldstein’s Vertical Equity Principle (No-Reversals Principle): If person i has greater utility than person j before taxation, then person i must have greater utility than person j after taxation.

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• Discussed by early thinkers(Locke, Rousseau, Bentham,Mill, and Smith)

• Definition: a tax system is equitable (or fair) if every citizen contributes to the cost of the public goods according to:

a) the benefit received from the Public Sectorb) independently of the ability-to-pay

Smart people benefit more from school. Should smart people pay more taxes?

The Benefit Principle

• Examples of public revenues according to the benefit principle: • Fees • Public prices • Copayments

• What about straightforward transfers of wealth?• Pensions • Unemployment Benefit approach is not appropriate for these

• Important distinction: Public vs. private goods Numerical example

The Benefit Principle

[A short recap: Public and private goods]

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rival

excludable

yes no

yesprivate good(e.g. medical

visits)

natural monopoly

nocommon resource

public good(e.g.

fireworks)

Source: Rosen and Gayer

NOTE: the State can provide both private goods and public goodsNOTE2: not all public goods are provided by the State

Private goods provided by the public sector:

• the individuals consume different quantities of goods (given that the private goods are excludable and rivalrous).

• Payment according to the quantity consumed:

The Benefit Principle: Private Goods

The case of medical visits

Question: What are the individual payments given two demand functions and a supply function?

Assumption: Two individuals i=1,2 with the demand functions for medical service:

D1: q1=5-p1

D2: q2=7-p2

The Benefit Principle: Private Goods - Example

Step 1: Demand function

The aggregated demand is the horizontal aggregation of individual demands (since the total quantity consumed equals the quantities consumed by each individual). Given that p=p1=p2:


Graphically:

D1+D2

D1 D2

5 7

5

7

12


P

Q


The aggregated demand is the horizontal aggregation of individual demands (since the total quantity consumed equals the quantities consumed by each individual). Given that p=p1=p2:

D1+D2: q=q1+q2=(5-p1)+(7-p2)=12-2*p for p<5

q=q2=7-p for p>5 (given that q1=0 for p>5)


Assumption: The supply of medical service is S: q=1+p

The good will be provided efficiently if: MU1=MU2=MC. This condition exists in equilibrium (D1+D2=S)

Step 2: Calculation the equilibrium price and quantities

S: q=1+p, D: q=12-2p, 12-2p=1+p, 3p=11, p=11/3

Solution: p=3.6

andq1=1.3q2=3.3


Graphically:

S

D1+D2

D1 D2

5 7

5

7

12





S: q=1+p, D: q=12-2p, 12-2p=1+p, 3p=11, p=11/3

Solution: p=3.6

andq1=1.3q2=3.3


Graphically:

q=4.6

S

D1+D2

p=3.6

D1 D2

5 7

5

7

12 q2=3.3 q1=1.3





Solution: p=3.6

andq1=1.3q2=3.3

Step 3: Calculate the individual contributions

Solution: Individual 1 pays: T1=p*q1=3.6*1.3=4.7Individual 2 pays: T2=p*q2=3.6*3.3=11.9


• The individuals consume the same quantity (remember: public goods are nonexludable and nonrivalrous).

• Payment according to the utility function that the good produces:

The Benefit Principle: Public Goods

The case of fireworks ina town’s celebration

Assumption: 2 individuals i=1, 2 with the next demand functionsof fireworks:

D1: p1=5-q1

D2: p2=7-q2



The aggregated demand is the vertical aggregation of individual demands (since the sum of the prices paid by each individual must defray the cost of the total quantity of the public good). Given that q=q1=q2:

D1+D2: p=p1+p2=(5-q1)+(7-q2)=12-2*q for q<=5

p=p2=7-q for q>5 (given that p1=0 for q>5)


D1+D2

D1 D2

5 7

5

7

12


Assumption: The supply of fireworks is S: p=q-1

The good will be provided efficiently if: MU1+MU2=MC (Samuelson condition). This condition exists in equilibrium (D1+D2=S), that comes given by:


SD1+D2

D1 D2

5 7

5

7

12


Assumption: The supply of fireworks is S: p=q-1

The good will be provided efficiently if: MU1+MU2=MC (Samuelson condition). This condition exists in equilibrium (D1+D2=S), that comes given by:


Solution: q=4.3

and p1=0.7 p2=2.7

Step 3: Calculate the individual contributions

Solution: Individual 1 pays : T1=q*p1=4.3*0.7=3Individual 2 pays: T2=q*p2=4.3*2.7=11.6


q=4.3

SD1+D2

p=p1+p2=3.4

p2=2.7

p1=0.7D1 D2

5 7

5

7

12


Advantage: the co-payment (financing a part of the price according to the benefit principle) might rationalize the demand of public goods

Limitation: the provision of a pure public good is suboptimum since the impossibility to observe the individuals’ marginal utilities (the free-rider problem).

Drawback: even when it’s efficient (case of private goods provided by the public sector) isn’t desirable because:

a) The majority of private goods provided by the public sector (transfer payments, education(?)) have a preferential and redistributive nature.

b) Cannot finance redistributive policy

These two drawbacks explain why the taxes based on the benefit principle (public prices, fees) are of a little importance (quantitatively). In practice, the majority of the collection is based on the ability-to-pay principle.

The Benefit Principle: Advantages and drawbacks

The Ability-to-pay Principle: Definition

Every taxpayer pays taxes according to:

a) The ability to pay

b) independently of the benefits obtained from the public sector

What do we mean by “ability to pay”?• Income?

• Capital gains, gifts, lottery winnings?• What about the individual’s circumstances?• Double taxation on saving (taxing income and returns on saving)

• Expenditure? • Hobbes:

• Saving and investment are beneficial (pro-social)• Consumption is anti-social (taking things out of the common pool)

• Progressive taxation easier with income

Many countries tax income and expenditure using the ability to pay approach most often

The Ability-to-pay Principle: Definition

Y

U(Y)• ASSUMPTION: Utility (U) is a

concave function of income

• Should taxes be set such that:

• Everyone’s utility falls by the same amount absolutely?

• Everyone’s utility falls by the same amount proportionally?

The Ability-to-pay Principle: Vertical equity

Tl

Y

U(Y)

Th

d

d

YhYl

• To make the reduction of welfare (U) equal (in absolute terms) for every taxpayer (d), the tax has to be larger for the taxpayer with greater income (Yh)

• BUT, HOW MUCH LARGER?

• Th must be even larger if we want the change in utility to be equi-proportional


There are 3 options:

• Progressive taxes: the tax increases proportionally in income

• Proportional taxes: the tax is independent of income

• Regressive taxes: the tax decreases proportionally in income


We want a tax system that produces an equitable split of the total sacrifice due to taxation.

1. All income earners sacrifice the same absolute amount of utility• Under diminishing marginal returns, higher earners will need to pay more Euros in tax• Tax could be progressive, neutral or progressive

2. An equi-proportional sacrifice of utility• Necessarily progressive

3. Least aggregate sacrifice of utility• Having paid tax, each earners’ marginal utility of money is equal• Under identical utility functions, everyone has the same post-tax income• Would involve 100% marginal rates

Historically, the dominant choice has been the utilization of progressive income taxes, but rather for redistributive criteria.

The Ability-to-pay Principle: Income and Utility

εt,B =

B

BT

T

- If εt,B > 1 progressive tax- If εt,B = 1 proportional tax- If εt,B < 1 regressive tax

1. According to the elasticity of the tax burden with regard to the tax base

Let T = tax paid and B = tax base

The Ability-to-pay Principle: 3 Measures of Progressivity

B

BT

T

B

T

T

B

BTBT

ATR

MTRεt,B = = = =

- If MTR > ATR progressive

tax

- If MTR = ATR

proportional tax

- If MTR < ATR regressive

tax

2. According to the average tax rate and marginal tax rate

ATR: Tax rate that affects the comprehensive tax base

MTR: Tax rate that affects the last unit of the tax base

Let T = tax paid and B = tax base


𝜏𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙=∆𝑇𝑎𝑥 𝑅𝑒𝑣𝑒𝑛𝑢𝑒∆𝑇𝑎𝑥 𝐵𝑎𝑠𝑒

𝜏𝑎𝑣𝑒𝑟𝑎𝑔𝑒=𝑇𝑎𝑥𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝑇𝑎𝑥 𝐵𝑎𝑠𝑒

• If > 0 progressive tax

• If = 0 proportional tax

• If < 0 regressive tax

3. According to the relation between the average tax rate and the variation of the tax base

ATRB

T(B)

BB T(B)

B2 MTRB T(B)

B2 B MTR

T(B)

B

B2 MTR ATR

B

ATRB

ATRB

ATRB


Advantages: Generates resources to finance• Pure public goods• Preferential goods• Redistribution between the wealthy and the poor

Drawbacks: Negative effects on the economic efficiency • Taxes are distortionary • High administrative costs

The Ability-to-pay Principle: Advantages and Drawbacks

1. The benefit principle is Pareto efficient, but it’s…

• difficult to apply in the case of public goods• difficult to finance preferential private goods• doesn’t allow to redistribute

2. Because of this the majority of taxes follows the ability-to-pay principle, that…

• allows to redistribute wealth from the rich to the poor • guarantees the provision of preferential goods to the whole population

…. but

• it’s Pareto inefficient • it has high administrative costs

Summary

Taxation and Equity ADE Fall 2015-2016 Department of Public Economics 1.

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Transcript of Taxation and Equity ADE Fall 2015-2016 Department of Public Economics 1.