1
Chapter 7 – Income
Redistribution,Conceptual
Issues
Public Economics
2
Introduction
? Will provide framework for thinking about
the normative and positive aspects of
government income redistribution policy.
3
Introduction
? Some questions whether economists
should be concerned with distributional
issues.
– Value judgments embodied in the,right”
income distribution.
– No scientific basis for the,right” distribution.
4
Introduction
? Focus on efficiency alone has problems.
– That focus,too,is a value judgment.
– Multiple equilbria.
– Decision makers do care about the income
distribution; economic analysis ineffective if it
doesn’t consider this policy-maker constraint.
5
Distribution of Income
? Can analyze household income,and see
how equally or unequally the,pie” is
distributed.
? Table 7.1 shows the percentage of
money income among households for
more than 30 years.
Table 7.1
7
Distribution of Income
? Richest 20% receives about 50% of total
income.
? Poorest 20% receives about 4% of total
income.
? Inequality has increased over time.
8
Distribution of Income:
Poverty
? The poverty line is a fixed level of real income
which is considered enough to provide a
minimally adequate standard of living.
? Inherently arbitrary,but still a useful benchmark.
– Trends over time
– Differences across groups
9
Distribution of Income:
Poverty
? Poverty line for a family of 4 was $18,244
in 2001.
? Median household income more than
double that,$42,228.
? Table 7.2 shows poverty rates for
selected groups in 2001.
Table 7.2
11
Distribution of Income:
Poverty
? Poverty rates in U.S,in 2001 might be
considered surprisingly high – 11.7% for
population as whole.
? Concentrated among certain groups,such as
female headed households,children,and
minorities.
? Elderly have lower poverty rates than the U.S,
average.
12
Distribution of Income:
Poverty
? Can also look at trends over time.
? See Table 7.3
? Poverty considerably lower than in 1960’s,
but not much progress since 1970.
Table 7.3
14
Interpretation Problems
? Poverty line (& poverty rate) is subject to
a number of criticisms.
? When interpreting the numbers,it is
useful to know the conventions and
limitations.
15
Interpretation Problem #1
?, Income” consists only of cash receipts.
– Excludes in-kind transfers like health
insurance,food stamps,and housing.
? Would reduce poverty rate by more than 20%.
– Excludes non-market work such as childcare
or housework.
– Ignores income flow from durable goods.
16
Interpretation Problem #2
? Income is before-tax.
– It ignores cash refunds from the Earned
Income Tax Credit,which has grown
dramatically in the last decade,and now
amounts to more than $31 billion annually.
– Ignoring this overstates poverty rates,and
also affects the trends over time.
17
Interpretation Problem #3
? Income is measured annually.
? Not obvious what the correct time frame should
be.
– Income does fluctuate from year-to-year.
– Lifetime income considerations seem relevant.
– Consider a,starving” college student,for example,
Not really,poor” in a lifetime sense.
18
Interpretation Problem #4
? Unit of observation
– Person,family,household?
– People often make decisions as an economic unit,and
there are economies of scale in household production.
? Classifications can matter for poverty numbers
– Bauman (1997) calculates that including the income of
non-family members (such as nonmarried cohabitors)
would reclassify 55% of people who are poor out of official
definition.
19
Rationales for Income
Redistribution
? Different kinds of social welfare functions
? Utilitarian
? Maximin criterion (Rawlsian)
? Pareto efficient
? Non-individualistic
20
Simple Utilitarianism
? The utilitarian social welfare function is:
? ?W F U U U n? 1 2,,.,,,
? Which depends on all n members of society,One
specific function form is:
W U U U n? ? ? ?1 2,,,
? This special case is referred to as an additive
social welfare function.
21
Simple Utilitarianism
? With the additive SWF that was given,also
assume:
– Identical utility functions that depend only on income
– Diminishing marginal utility of income
– Society’s total income is fixed
? Implication,government should redistribute to
obtain complete equality.
22
Simple Utilitarianism
? This can be illustrated with 2 people.
? See Figure 7.1
? Any income level other than I* does not
maximize the SWF.
? I* entails equal incomes.
Figure 7.1
24
Simple Utilitarianism
? Striking result is that full income equality should
be pursued,but some scrutiny required.
? Assumes identical utilities
? Assumes decreasing marginal utility
? Assumes total income fixed
– E.g.,no disincentives from this kind of redistributive
policy.
25
The Maximin Criterion
? The Rawlsian social welfare function is:
? ?W M in imu m U U U n? 1 2,,.,,,
? Social welfare in this case depends only on the
utility of the person who has the lowest utility.
? Rawls (1971) asserts it has ethical validity
because of the notion of original position.
– Notion that ex-ante individuals do not know where in the
income distribution they will be.
26
The Maximin Criterion
? These ethical claims are controversial:
– Still selfish view in original position
– Individuals extremely risk averse here
– All that is relevant is the welfare of the worst-
off person,even if a policy is extremely
detrimental to everyone else.
27
Pareto Efficient Income
Redistribution
? Suppose that utility of richer person does depend
on poorer person’s utility,That is:
? ?? ?U U I U IP E T E R P E T E R P A U L?,
? Government redistribution in this case could
improve efficiency,It may be difficult for the
private market to do this,if,for example,the rich
lack information on just who really is poor.
? Simply an externality problem.
28
Pareto Efficient Income
Redistribution
? Altruism plays a role in this example,but private
market could conceivable give charity.
? But not just altruism,Self-interest could play a
role,Suppose there is a possibility that,for
circumstances beyond your control,you become
poor.
– When well-off,pay,premiums.” When bad times hit,
collect,payoff.”
– Motivation of some social insurance programs.
29
Nonindividualistic views
? In previous cases,social welfare derived from
individual’s utilities.
? Some specify what the income distribution
should look like independent of individual
preferences.
? One example,commodity egalitarianism,
– Right to vote,food,shelter,education,perhaps health
insurance.
30
Processes versus Outcomes
? Some argue that a just distribution of income is
defined by the process that generated it.
? For example,“equal opportunity” in U.S.
– Ensuing outcome would be considered fair,regardless
of the income distribution it happened to entail.
– Fair bit of income mobility (Gottschalk,1997).
? Does raise problem of how to evaluate social
processes.
31
Expenditure Incidence
? Relative Price Effects
? Public Goods
? Valuing In-Kind Transfers
32
Relative Price Effects
? Suppose government subsidized housing of the
poor.
– As a first pass,redistribution from rich to poor.
? May have overall effects on housing prices
– Landlords may reap part of gain.
– Affects wages of construction workers
? Generally,any government program sets off a
chain of price changes,and the incidence is
unclear.
33
Public Goods
? Do rich and poor benefits similarly from the
provision of public goods?
? Difficult to measure,sensitive to assumptions
that are made.
34
Valuing in-kind transfers
? Government provides many benefits to the poor
in-kind – that is,direct provision of goods rather
than cash.
– Food stamps
– Medicaid
– Public Housing
? Estimating value is difficult,Not always valued at
dollar-for-dollar (if resale is difficult).
35
Valuing in-kind transfers
? Consider how the provision of an in-kind benefit
changes the budget constraint in Figure 7.2.
? In this case,giving an in-kind benefit lowers utility
relative to an equally costly cash transfer.
? Although the person is better off by having the in-
kind transfer than not having it,she would be
even happier with the cash transfer.
Figure 7.2
37
Valuing in-kind transfers
? A person can never be made better off with an
in-kind transfer that is equal in cost to a cash
transfer.
? There are instances,however,when a person is
indifferent between the two transfer schemes.
? See Figure 7.3.
Figure 7.3
39
Valuing in-kind transfers
? In this example,giving the transfer in-kind is not
binding.
40
Numerical Example,Baseline
? Assume that Jones has the following utility
function:
? ?U u C O C O? ?,
1
4
3
4
? Where C indicates the quantity of cheese
consumed,and O indicates the quantity of other
goods.
? Jones faces prices PC=2 and PO=1 for cheese and
other goods,respectively.
41
Numerical Example,Baseline
? What allocation of would Jones choose with
I=300?
? In this Cobb-Douglas utility function,Jones’
demand curve for cheese is:
C I
P C
*,?
?
?
??
?
??
?
?
?
?
?
? ? ?
?
?
?
?
?
? ??? ??? ?
?
? ?
1
4
1
4
3
4
300
2
37 5
42
Numerical Example,Baseline
? In addition,Jones’ demand curve for other
goods is:
O I
P O
* ?
?
?
??
?
??
?
?
?
?
?
? ?
?
?
?
?
?
?
? ??? ??? ?
?
? ?
3
4
1
4
3
4
300
1
225
? Jones’ utility is therefore equal to:
? ? ? ?U ? ?37 5 225 143 7614 34.,
43
Numerical Example,Cash transfer
? In addition to Jones’ initial income,assume the
government gives a cash transfer of $120.
? What consumption bundle does Jones now
choose,and what is her utility?
C I
P C
*,?
?
?
??
?
??
?
?
?
?
?
? ? ?
?
?
?
?
?
? ??? ??? ??? ?
1
4
1
4
3
4
420
2
52 5
44
Numerical Example,Cash transfer
? In addition,Jones’ demand curve for other
goods is:
O I
P O
* ?
?
?
??
?
??
?
?
?
?
?
? ?
?
?
?
?
?
?
? ??? ??? ?
?
? ?
3
4
1
4
3
4
420
1
315
? Jones’ utility is therefore equal to:
? ? ? ?U ? ?52 5 315 201 2614 34.,
45
Numerical Example,Binding in-
kind transfer
? In addition to Jones’ initial income,assume the
government gives an in-kind transfer of 60 units
of cheese,which she cannot resell.
? What consumption bundle does Jones now
choose,and what is her utility?
46
Numerical Example,Binding in-
kind transfer
? Note that the in-kind transfer costs the
government $120 (60 units x $2 per unit).
? When Jones was unconstrained,she used the
extra $120 to arrive at an allocation of
{C,O}={52.5,315}.
? Jones cannot attain this,because the minimum
amount of C she can consume is C=60 (the
amount of the in-kind transfer).
47
Numerical Example,Binding in-
kind transfer
? Thus,she uses all of her fungible income
($300) to purchase the good O:
O I
P O
* ? ?
?
?
?
?
? ? ??? ??? ?
300
1
300
? Jones’ utility is therefore equal to:
? ? ? ?U ? ? ?60 300 200 62 201 2614 34,,
48
Numerical Example,Non-binding
in-kind transfer
? In addition to Jones’ initial income,assume the
government gives an in-kind transfer of 30 units
of cheese,which she cannot resell,In addition
the government also gives a cash transfer of $60.
? What consumption bundle does Jones now
choose,and what is her utility?
49
Numerical Example,Binding in-
kind transfer
? Note that the total transfer costs the government $120,
The in-kind transfer costs the government $60 (30 units x
$2 per unit),and the cash transfer costs another $60.
? When Jones was unconstrained,she used the extra $120
to arrive at an allocation of {C,O}={52.5,315}.
? Jones can attain this,because the minimum amount of C
she can consume is C=30,which is less than C=52.5 (the
amount of the in-kind transfer).
50
Numerical Example,Binding in-
kind transfer
? Thus,she uses part of her fungible income ($360) to
purchase the good C and good O.
? Ultimately,she wants C=52.5,so she purchases 22.5
units of C with her fungible income (with the rest coming
from the in-kind benefit.
? She purchases 315 units of O with the remainder of her
fungible income.
? Utility is the same as the unconstrained case.
51
Valuing in-kind transfers
? Why give in-kind transfers if they tend to be
inefficient?
– Commodity egalitarianism
– May reduce welfare fraud (especially if the in-kind
transfer is an inferior good)
– Politically viable because they help the producer of the
in-kind good.
52
Recap of Income Redistribution,
Conceptual Issues
? Distribution of income
? Poverty line
? Social welfare functions
? Valuing In-Kind transfers
Chapter 7 – Income
Redistribution,Conceptual
Issues
Public Economics
2
Introduction
? Will provide framework for thinking about
the normative and positive aspects of
government income redistribution policy.
3
Introduction
? Some questions whether economists
should be concerned with distributional
issues.
– Value judgments embodied in the,right”
income distribution.
– No scientific basis for the,right” distribution.
4
Introduction
? Focus on efficiency alone has problems.
– That focus,too,is a value judgment.
– Multiple equilbria.
– Decision makers do care about the income
distribution; economic analysis ineffective if it
doesn’t consider this policy-maker constraint.
5
Distribution of Income
? Can analyze household income,and see
how equally or unequally the,pie” is
distributed.
? Table 7.1 shows the percentage of
money income among households for
more than 30 years.
Table 7.1
7
Distribution of Income
? Richest 20% receives about 50% of total
income.
? Poorest 20% receives about 4% of total
income.
? Inequality has increased over time.
8
Distribution of Income:
Poverty
? The poverty line is a fixed level of real income
which is considered enough to provide a
minimally adequate standard of living.
? Inherently arbitrary,but still a useful benchmark.
– Trends over time
– Differences across groups
9
Distribution of Income:
Poverty
? Poverty line for a family of 4 was $18,244
in 2001.
? Median household income more than
double that,$42,228.
? Table 7.2 shows poverty rates for
selected groups in 2001.
Table 7.2
11
Distribution of Income:
Poverty
? Poverty rates in U.S,in 2001 might be
considered surprisingly high – 11.7% for
population as whole.
? Concentrated among certain groups,such as
female headed households,children,and
minorities.
? Elderly have lower poverty rates than the U.S,
average.
12
Distribution of Income:
Poverty
? Can also look at trends over time.
? See Table 7.3
? Poverty considerably lower than in 1960’s,
but not much progress since 1970.
Table 7.3
14
Interpretation Problems
? Poverty line (& poverty rate) is subject to
a number of criticisms.
? When interpreting the numbers,it is
useful to know the conventions and
limitations.
15
Interpretation Problem #1
?, Income” consists only of cash receipts.
– Excludes in-kind transfers like health
insurance,food stamps,and housing.
? Would reduce poverty rate by more than 20%.
– Excludes non-market work such as childcare
or housework.
– Ignores income flow from durable goods.
16
Interpretation Problem #2
? Income is before-tax.
– It ignores cash refunds from the Earned
Income Tax Credit,which has grown
dramatically in the last decade,and now
amounts to more than $31 billion annually.
– Ignoring this overstates poverty rates,and
also affects the trends over time.
17
Interpretation Problem #3
? Income is measured annually.
? Not obvious what the correct time frame should
be.
– Income does fluctuate from year-to-year.
– Lifetime income considerations seem relevant.
– Consider a,starving” college student,for example,
Not really,poor” in a lifetime sense.
18
Interpretation Problem #4
? Unit of observation
– Person,family,household?
– People often make decisions as an economic unit,and
there are economies of scale in household production.
? Classifications can matter for poverty numbers
– Bauman (1997) calculates that including the income of
non-family members (such as nonmarried cohabitors)
would reclassify 55% of people who are poor out of official
definition.
19
Rationales for Income
Redistribution
? Different kinds of social welfare functions
? Utilitarian
? Maximin criterion (Rawlsian)
? Pareto efficient
? Non-individualistic
20
Simple Utilitarianism
? The utilitarian social welfare function is:
? ?W F U U U n? 1 2,,.,,,
? Which depends on all n members of society,One
specific function form is:
W U U U n? ? ? ?1 2,,,
? This special case is referred to as an additive
social welfare function.
21
Simple Utilitarianism
? With the additive SWF that was given,also
assume:
– Identical utility functions that depend only on income
– Diminishing marginal utility of income
– Society’s total income is fixed
? Implication,government should redistribute to
obtain complete equality.
22
Simple Utilitarianism
? This can be illustrated with 2 people.
? See Figure 7.1
? Any income level other than I* does not
maximize the SWF.
? I* entails equal incomes.
Figure 7.1
24
Simple Utilitarianism
? Striking result is that full income equality should
be pursued,but some scrutiny required.
? Assumes identical utilities
? Assumes decreasing marginal utility
? Assumes total income fixed
– E.g.,no disincentives from this kind of redistributive
policy.
25
The Maximin Criterion
? The Rawlsian social welfare function is:
? ?W M in imu m U U U n? 1 2,,.,,,
? Social welfare in this case depends only on the
utility of the person who has the lowest utility.
? Rawls (1971) asserts it has ethical validity
because of the notion of original position.
– Notion that ex-ante individuals do not know where in the
income distribution they will be.
26
The Maximin Criterion
? These ethical claims are controversial:
– Still selfish view in original position
– Individuals extremely risk averse here
– All that is relevant is the welfare of the worst-
off person,even if a policy is extremely
detrimental to everyone else.
27
Pareto Efficient Income
Redistribution
? Suppose that utility of richer person does depend
on poorer person’s utility,That is:
? ?? ?U U I U IP E T E R P E T E R P A U L?,
? Government redistribution in this case could
improve efficiency,It may be difficult for the
private market to do this,if,for example,the rich
lack information on just who really is poor.
? Simply an externality problem.
28
Pareto Efficient Income
Redistribution
? Altruism plays a role in this example,but private
market could conceivable give charity.
? But not just altruism,Self-interest could play a
role,Suppose there is a possibility that,for
circumstances beyond your control,you become
poor.
– When well-off,pay,premiums.” When bad times hit,
collect,payoff.”
– Motivation of some social insurance programs.
29
Nonindividualistic views
? In previous cases,social welfare derived from
individual’s utilities.
? Some specify what the income distribution
should look like independent of individual
preferences.
? One example,commodity egalitarianism,
– Right to vote,food,shelter,education,perhaps health
insurance.
30
Processes versus Outcomes
? Some argue that a just distribution of income is
defined by the process that generated it.
? For example,“equal opportunity” in U.S.
– Ensuing outcome would be considered fair,regardless
of the income distribution it happened to entail.
– Fair bit of income mobility (Gottschalk,1997).
? Does raise problem of how to evaluate social
processes.
31
Expenditure Incidence
? Relative Price Effects
? Public Goods
? Valuing In-Kind Transfers
32
Relative Price Effects
? Suppose government subsidized housing of the
poor.
– As a first pass,redistribution from rich to poor.
? May have overall effects on housing prices
– Landlords may reap part of gain.
– Affects wages of construction workers
? Generally,any government program sets off a
chain of price changes,and the incidence is
unclear.
33
Public Goods
? Do rich and poor benefits similarly from the
provision of public goods?
? Difficult to measure,sensitive to assumptions
that are made.
34
Valuing in-kind transfers
? Government provides many benefits to the poor
in-kind – that is,direct provision of goods rather
than cash.
– Food stamps
– Medicaid
– Public Housing
? Estimating value is difficult,Not always valued at
dollar-for-dollar (if resale is difficult).
35
Valuing in-kind transfers
? Consider how the provision of an in-kind benefit
changes the budget constraint in Figure 7.2.
? In this case,giving an in-kind benefit lowers utility
relative to an equally costly cash transfer.
? Although the person is better off by having the in-
kind transfer than not having it,she would be
even happier with the cash transfer.
Figure 7.2
37
Valuing in-kind transfers
? A person can never be made better off with an
in-kind transfer that is equal in cost to a cash
transfer.
? There are instances,however,when a person is
indifferent between the two transfer schemes.
? See Figure 7.3.
Figure 7.3
39
Valuing in-kind transfers
? In this example,giving the transfer in-kind is not
binding.
40
Numerical Example,Baseline
? Assume that Jones has the following utility
function:
? ?U u C O C O? ?,
1
4
3
4
? Where C indicates the quantity of cheese
consumed,and O indicates the quantity of other
goods.
? Jones faces prices PC=2 and PO=1 for cheese and
other goods,respectively.
41
Numerical Example,Baseline
? What allocation of would Jones choose with
I=300?
? In this Cobb-Douglas utility function,Jones’
demand curve for cheese is:
C I
P C
*,?
?
?
??
?
??
?
?
?
?
?
? ? ?
?
?
?
?
?
? ??? ??? ?
?
? ?
1
4
1
4
3
4
300
2
37 5
42
Numerical Example,Baseline
? In addition,Jones’ demand curve for other
goods is:
O I
P O
* ?
?
?
??
?
??
?
?
?
?
?
? ?
?
?
?
?
?
?
? ??? ??? ?
?
? ?
3
4
1
4
3
4
300
1
225
? Jones’ utility is therefore equal to:
? ? ? ?U ? ?37 5 225 143 7614 34.,
43
Numerical Example,Cash transfer
? In addition to Jones’ initial income,assume the
government gives a cash transfer of $120.
? What consumption bundle does Jones now
choose,and what is her utility?
C I
P C
*,?
?
?
??
?
??
?
?
?
?
?
? ? ?
?
?
?
?
?
? ??? ??? ??? ?
1
4
1
4
3
4
420
2
52 5
44
Numerical Example,Cash transfer
? In addition,Jones’ demand curve for other
goods is:
O I
P O
* ?
?
?
??
?
??
?
?
?
?
?
? ?
?
?
?
?
?
?
? ??? ??? ?
?
? ?
3
4
1
4
3
4
420
1
315
? Jones’ utility is therefore equal to:
? ? ? ?U ? ?52 5 315 201 2614 34.,
45
Numerical Example,Binding in-
kind transfer
? In addition to Jones’ initial income,assume the
government gives an in-kind transfer of 60 units
of cheese,which she cannot resell.
? What consumption bundle does Jones now
choose,and what is her utility?
46
Numerical Example,Binding in-
kind transfer
? Note that the in-kind transfer costs the
government $120 (60 units x $2 per unit).
? When Jones was unconstrained,she used the
extra $120 to arrive at an allocation of
{C,O}={52.5,315}.
? Jones cannot attain this,because the minimum
amount of C she can consume is C=60 (the
amount of the in-kind transfer).
47
Numerical Example,Binding in-
kind transfer
? Thus,she uses all of her fungible income
($300) to purchase the good O:
O I
P O
* ? ?
?
?
?
?
? ? ??? ??? ?
300
1
300
? Jones’ utility is therefore equal to:
? ? ? ?U ? ? ?60 300 200 62 201 2614 34,,
48
Numerical Example,Non-binding
in-kind transfer
? In addition to Jones’ initial income,assume the
government gives an in-kind transfer of 30 units
of cheese,which she cannot resell,In addition
the government also gives a cash transfer of $60.
? What consumption bundle does Jones now
choose,and what is her utility?
49
Numerical Example,Binding in-
kind transfer
? Note that the total transfer costs the government $120,
The in-kind transfer costs the government $60 (30 units x
$2 per unit),and the cash transfer costs another $60.
? When Jones was unconstrained,she used the extra $120
to arrive at an allocation of {C,O}={52.5,315}.
? Jones can attain this,because the minimum amount of C
she can consume is C=30,which is less than C=52.5 (the
amount of the in-kind transfer).
50
Numerical Example,Binding in-
kind transfer
? Thus,she uses part of her fungible income ($360) to
purchase the good C and good O.
? Ultimately,she wants C=52.5,so she purchases 22.5
units of C with her fungible income (with the rest coming
from the in-kind benefit.
? She purchases 315 units of O with the remainder of her
fungible income.
? Utility is the same as the unconstrained case.
51
Valuing in-kind transfers
? Why give in-kind transfers if they tend to be
inefficient?
– Commodity egalitarianism
– May reduce welfare fraud (especially if the in-kind
transfer is an inferior good)
– Politically viable because they help the producer of the
in-kind good.
52
Recap of Income Redistribution,
Conceptual Issues
? Distribution of income
? Poverty line
? Social welfare functions
? Valuing In-Kind transfers
