Chapter 6: Income Redistribution

1
Chapter 6 Income Redistribution

• If the government actively pursues a policy of
  equitable distribution, what is considered
  equitable?
• As always, EQUITY and EFFICIENCY are the two
  conflicting issues the government deals with.

2
Chapter 6 Income Redistribution

• History of Income Distribution
• Rationales for Income Redistribution
• Cash vs. In-Kind Transfers
• Overview

3
History - Income Distribution

• In 2008
• The poorest 20 of the population received 4 of
  before-tax income
• The poorest 60 received 29 of before-tax income
• This is represented in the LORENZ CURVE, where a
  45 line represents equal income distribution
• Note that income inequality has increases
  slightly since 1980.

4
86e01310
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Lorenz Evaluation

• -Between 1980 and 2008, income share of the top
  20 increased, and income share of all other
  quintiles decreased
• -often blamed on globalization and welfare
  cutbacks
• -But similar changes occurred between 1961 and
  1991, when welfare programs expanded and there
  was economic growth
• -this increase in income inequality may just be
  temporary

6
Theory - The Poverty Line

• POVERTY LINE -real income needed to provide a
  minimally adequate standard of living
• -Statistics Canada instead uses Low Income
  Cut-Off-Lines (LICO) where a family would use
  54.7 of its income on food, clothing, and
  shelter as defined by 1992 expenditure patterns

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History - The Poverty Line

• The 2008 Low Income Cut-Off line for an
  unattached individual was
• 22,171 for an in a 500,000 or greater urban area
  
• 15,562 in a rural area
• The 2008 LICO line for a family of 4 was
• 41,198 for an in a 500,000 or greater urban area
  
• 28,361 in a rural area

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The Poverty Line

• -The next graph shows Canadians below the cut-off
  line over time from 1980 to 2004
• -note that poverty figures followed income
  figures and the recession
• -note that the statistics for children living in
  low income is above average
• -note that although overall the elderly living in
  poverty has decreased, 33.7 of elderly peoples
  living alone in 2008 lived in poverty

9
The Poverty Line
10
History - Poverty By Province

• 2008 poverty varies across Canada, from 9.1 of
  families in Alberta to 16 of families in Quebec

11
Poverty By Province

• -35.1 half single-mother families are below the
  poverty line (improved from 2005), and single
  father families fare worse than two-parent
  families
• -a second paycheque is often required for a
  reasonable standard of living
• -stay-at-home parents have a disadvantage
• -unfortunately, studies show that stay-at-home
  parents have a huge positive effect on their
  children, especially in early years

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Theory - Calculation Difficulties

• All these numbers dont take into account
  IN-KIND income
• -When a household member does work (childcare,
  housecleaning, roof shoveling, tax filing,
  plumbing, etc), it is not counted as income
• -If these activities were paid for, they would
  appear as income
• -Single parent households therefore have a lower
  income (in-kind or reported)
• -Stay at home parents have a higher true income
  than reported

13
Further Issues

• -all the above data is before-tax, and therefore
  doesnt consider higher taxes for higher incomes
• -keep in mind that a person 1 below the poverty
  line is treated the same as someone 10,000 below
  the poverty line in this chart
• GAP RATIO (Income-LICO)/LICO
• -the aggregate low income gap ratio has decreased
  to 33 in 2008 from 35 in 1980

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Theory Family Categories

• -Statistics Canada lists a household as a group
  of individuals sharing a common dwelling and
  related by blood, marriage (including common-law)
  or adoption
• -Anyone else is considered (such as someone with
  unrelated roomates) an unattached individual
• -2008 unattached individual income was 36,800,
  and family income was 89,700
• -The average family had 3 people

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Family Categories

• -Families have savings in consumption (especially
  the consumption of housing)
• -Statistics Canada considers a second adult of a
  family unit to increase household needs by 40,
  and each child to increase household needs by 30
• -Therefore the average family has needs of 1.7
  unattached individuals. A family receiving
  89,700 thus has the equivalent unattached
  individual income of 52,764
• -This is arbitrary, but argues the average
  3-person family is better off

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Theory Data and Distribution

• -Typical income data is yearly, which is not
  perfect, as income tends between years (person A
  may have a higher income due to being older than
  person B)
• -Income distribution in Canada has varied little
  since 1951
• -This is odd, since social programs increased
  greatly after WWII
• -perhaps preventing a huge income shift?
• -could have further programs done more?

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Family Data
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Theory - Poverty Conclusion

• -EXACT income inequality sources are highly
  studied and still debated
• -Studies show family income inequality comes from
  differences in wages and salaries for family
  heads
• BUT
• -Property income (interest and dividends)
  accounts for little of the inequality

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Theory - Poverty Conclusion

• WHY different wages?
• Wage f(strength, intelligence, effort,
  education, marriage decisions, discrimination,
  welfare, luck)
• -computer technology is making education a huge
  factor of wage,
• -BUT DOESNT EXPLAIN EVERYTHING

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Theory - Rationales for Income Redistribution

• There are a variety of rationales for income
  redistribution, all requiring unique underlying
  assumptions
• Utilitarianism
• The Maxmin Criterion
• Pareto Efficient Income Redistribution (Insurance
  and Alturism)
• Nonindividualistic Views
• Other (ie Fairness/Good Rules, etc)

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1) Theory - Utilitarianism

• -Social welfare is a function of undividual
  utility
• WF(U1, U2,,Un)
• -Certain utilitarianism philosophers (Bentham and
  Mill) argued that public policies should be
  guided by the principle, greatest good for the
  greatest number"

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Utilitarianism

• -Economists typically interpret this idea through
  an additive social welfare function
• WU1U2Un
• -The utilitarian therefore supports income
  distribution as long as it increases social
  welfare

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Utilitarianism Assumptions

• -In order to take this analysis further, one
  needs to add 3 assumptions
• Individuals have identical utility functions only
  depending on income Uf(I)
• Diminishing marginal utility of income exists
• Total societal income is fixed
• -Therefore welfare is maximized when incomes are
  completely equal

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Utilitarian Example

• Consider a society with two people, Richard (who
  starts rich) and Po (who starts poor).
• Graphically, our x axis can represent the entire
  income available in society (assumption 3)
• Richard and Pos marginal utilities are measured
  along opposite sides, as they are both functions
  of income, and both diminishing due to assumption
  2
• -They are symmetrical due to assumption 1

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Utilitarian Welfare

MUR
MUP
Richards income is Ox, and Pos income is Ox.
O
O
x
The distribution expressed by point x (Richard is
richer than Po) implies a high MU for Po and a
low MU for Richard.
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Utilitarian Example

• Redistribution of income makes one person worse
  off and another better off
• -The change in utility is expressed by the area
  under the utility curve
• -we see that if Richard gives money to Po, Pos
  gained utility is greater than Richards lost
  utility, resulting in higher social welfare
• -social welfare is thus maximized at I, where
  both people have half the available income

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Utilitarian Welfare

MUR
MUP
If income moved from x to w, Richard would lose
utility tvxw while Po would gain utility rsxw.
s
r
t
v
x
w
I
O
O
Societys gain would therefore be rsvt. Social
welfare would be maximized at point I.
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Utilitarian Criticism

• -This result seems too easy society is best off
  if everyone has EXACTLY the same income
• In order to evaluate this result, we have to look
  back to Utilitarianisms underlying assumptions

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Utilitarian Assumption 1

• We cant ACTUALLY measure utility, nor can we
  determine if people have identical utility
  functions. However
• It seems reasonable
• -If people are similar in other characteristics
  (height, weight, etc.), why not utility?
• 2) It should be so (ethics)
• -Perhaps government should act according to
  identical utility functions, to avoid bias
• ASSUMPTION 1 IS WEAK, BUT MAY SURVIVE

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Utilitarian Assumption 2

• We can prove diminishing marginal utility of a
  GOOD, but not of INCOME
• -Perhaps someone can keep spending income on
  different things to keep his marginal utility
  high
• If Marginal Utility is constant, then a dollar
  taken away from Richard causes a decrease in
  utility equal to the utility gained by Po
• ASSUMPTION 2 FAILS?

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Utilitarian Assumption 3

• People typically gain utility from leisure, and
  therefore transfers discourage work and cause a
  reduction in overall income
• -Therefore each dollar transfer causes a
  reduction in available income
• -If we aim for a 50/50 balance, this balance
  suddenly becomes unequal as perhaps only 90 of
  the income is now available (so the balance
  becomes 50/40)
• ASSUMPTION 3 IS PROBLEMATIC

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Utilitarian Social Welfare
45 Line
In Utilitarianism, Social Indifference Curves are
straight lines
i
With no tax distortion, point ii is optimal
iii
ii
Makas Utility
With tax distortions, point iii is optimal
W
W
O
Susans Utility
Maka
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2) Theory - The Maxmin Criterion

• -if the social objective is the maximin
  criterion, society attempts to maximize the
  utility of the least well-off person
• Wmin(U1, U2,,Un)
• -This claims that society is only as well off as
  its worst member
• -There is an implicit argument for equality, but
  income variance is still allowed for
• -ie dont overtax the rich to pay the poor if
  it makes the poor lose their jobs

34
Maxmin Social Welfare
45 Line
Social Indifference Curves are right angles
i
With no tax distortion, point ii is optimal
W
Makas Utility
ii
W
iv
With tax distortions, point iv is optimal
O
Susans Utility
Maka
35
Maxmin vs. Utilitarian Social Welfare
45 Line
With no distortion, the results are identical
i
With tax distortion, maxmin theory argues for
more redistribution thus higher inefficiency
iii
Makas Utility
ii
iv
W
W
O
Susans Utility
Maka
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The Maxmin Criterion Criticism

• -this is based on John Rawls(1971) idea of an
  ORIGINAL POSITION
• -theoretically, if people didnt know their
  place in society, they would want the lowest
  place to be as well-off as possible
• -this assumes everyone is VERY risk adverse
• -Feldstein (1976) also points out that this
  condition allows for policies creating a few
  extreme rich and penalizing most of society as
  long as the poorest gains slightly

37
3) Theory Pareto Efficient Income
Redistribution

• Utilitarian and maxmin models do NOT provide
  Pareto Efficient Income redistribution
• -one person is made WORSE OFF (lose income)
• Income Redistribution can be a Pareto Improvement
  under concepts of
• Altruism
• Insurance

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3a) Theory - Altruism

• -Due to altruism, Richard may GAIN utility from
  giving money to Po (a Pareto improvement)
• -ideal redistribution would continue until
  Richards Marginal Utility gain from altruism
  equals his Marginal Utility loss from lower
  income
• -one may argue that the government can find the
  poor easier than Richard can

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Altruism

• -taken to the extreme, income distribution
  becomes a PUBLIC GOOD, because everyone gains
  utility from knowing the poor are taken care of
• -the free-rider problem argues for the
  government forcing redistribution payments
  (people will naturally wait someone else to take
  care of the poor)
• -Many argue that people dont need the government
  to redistribute their money, they could do it if
  they wanted

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3b) Insurance

• -many have self-interest reasons for favoring
  insurance
• -Income redistribution payments are premiums
  against the risk of becoming poor
• -Additionally, income redistribution is insurance
  against civil unrest
• -give the poor food so they dont become Robin
  Hood

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4) Theory - Nonindividualistic Views

• -Thus far we have argued that redistribution
  policy should come from the social welfare
  function
• -Some argue that social redistribution should be
  independent from individual tastes
• -Fair (1971) pointed out that Plato argued that
  in a good society

-Others simply argue that equal distribution is
paramount
42
5) Theory Other/Fairness

• -the previous models assumed that society should
  distribute ITS income as it sees fit
• -(assumes people dont own income)
• -one could examine the FAIRNESS of initial income
  earning or income redistribution
• -should EQUAL OPPORTUNITY be the goal, regardless
  of the income distribution that results?
• -in this case there would be no room for
  government redistribution

43
Other/Good Rules

• -Nozick (1974) argues that income belongs to
  individuals, and government should ensure good
  sets of rules to govern societys operation, not
  good income distribution
• -But how can one evaluate good rules without
  examining income distribution?

44
Other/Fairness (another look)

• -others argue that social mobility is paramount
• -it doesnt matter if people are poor now, as
  long as there is a decent chance of their
  situation changing
• -Chen (2009) showed that
• 1) 70 of Canadians moved to another decile
  group in 5 years and
• 2) 30-40 moved UP at least one decile
• Note decile groups (11-20,41-50, 91-100 etc)

45
Cash vs. In-Kind Transfers

• Thus far we have assumed income is redistributed
  in the form of cash transfers
• -Often the poor receive in-kind transfers (food,
  education, healthcare, etc)
• -There are a variety of pros and cons when
  comparing cash to in-kind transfers

46
Composite good, units
Example Consider a situation where an
individual consumes Fa food, yet the government
considers the minimum food an individual needs as
Fmin. Maximum food consumption is I/Pf
I
A
Food (units)
I/Pf
FA FMin
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Composite good, units
One option is to offer a food voucher FV,
increasing utility and consumption to point
B. Note that non-food consumption also increases
slightly
I

A
B

Food
I/Ph
FA FV FMin
I/(1-s)Ph
48
Composite good, units
Without the subsidy, C2 is the level of
consumption that could be undertook at the
minimum food consumption. Therefore V is the cost
of the food subsidy
I

A
B

V
C2
Food
I/Ph
FA FV FMin
I/(1-s)Ph
49
Composite good, units
An alternative to the subsidy would therefore be
a lump-sum transfer. In THIS case, the outcome is
the same
I

A
B

V
C2
Food
I/Ph
FA FV FMin
I/(1-s)Ph
50
Composite good, units
Depending on the utility function, the individual
COULD use some or all of the cash transfer on
composite goods rather than food, achieving
higher utility

B

I
A

V
C2
Food
I/Ph
FA FV FMin
I/(1-s)Ph
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Cash vs. In-Kind Transfers

• Cash transfers
• 1) give a higher level of utility
• -(people are happier)
• 2) are more highly valued (Whitmore 2002
  estimated food voucher value as 80 cents per
  dollar)
• 3) have lower administration costs
• -Blanchard (1982) estimated that US food stamp
  administration costs would be reduced by 36
  through a move to a cash transfer

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Theory Why In-Kind Transfers?

• If lump-sum cash transfers seem so preferred and
  efficient, why are in-kind transfers so common?
• Asymmetric Information
• Commodity Equalitarianism
• Paternalism
• Politics

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1) Asymmetric Info

• Asymmetric information can argue for in-kind
  transfers
• -with asymmetric information, people who are not
  poor or in need may claim to be poor or in need
  to get a free handout
• -in this case, in-kind transfers may screen the
  truly needy from the truly greedy

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1) Asymmetric Info

• Assume we have two people, Muscles, who is in
  great shape, and Payne, who has an injured
  shoulder. We have the scenario
• UM CMH
• UPCPhT
• RCMCBT
• Where Cconsumption
• Hbase utility from being healthy
• hmarginal utility of therapy
• Texpenditure on therapy
• Rsociety resources

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Full information gives this utility possibilities
curve coming from all possible income transfers.
UP
R
Note that utility is equal along the 45 line
(RH)/2
45
UM
H
(R-H)/2
RH
56
At a, Payne receives all income, and Muscles just
gains utility from his health
UP
a
R
At b, utilities are equal, but Payne receives
more money to make up for his injury
b
(RH)/2
c
R/2
45
d
UM
H
(R-H)/2
RH
R/2H
57
At c, income is equal, thus Payne has a lower
utility due to his injury
UP
a
R
At d, Muscles gets all income and Paynes utility
is zero
b
(RH)/2
c
R/2
45
d
UM
H
(R-H)/2
RH
R/2H
58
A maxmin theorem would perfer b, and a
Utilitarian would be indifferent along ad.
UP
a
R
Under full information, no vouchers are required,
only a cash transfer
b
(RH)/2
c
R/2
45
d
UM
H
(R-H)/2
RH
R/2H
59
With Asymmetric information, the most that Payne
could receive would be R/2, else muscles would
pretend to be injured for the subsidy
UP
R
Note that the utility possibilities curve has
decreased to cd
(RH)/2
c
R/2
45
d
UM
H
(R-H)/2
RH
R/2H
60
In-Kind Transfers w/Asymmetric Info

• If the marginal utility of therapygt0.5, in-kind
  transfers could alleviate this problem.
• If society taxes each person 50 cents, and then
  gives 1 to Payne, if his MU of therapy is
  greater than 0.5 (greater than his tax), this
  increases his utility
• This creates a kink in the utility possibilities
  curve with the slope 1-2h

61
With in-kind transfers, the utility possibilities
curve is improved to gcd
UP
R
A maxmin theory would prefer point e, and a
utilitarian would prefer a point along cd
g
(RH)/2
c
e
R/2
45
d
UM
H
(RH)/2
RH
R/2H
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Cash In-Kind Transfers w/Asymmetric Info

• Note that the optimal point along any of the
  above utility possibilities curve depends on the
  indifference curve derived from the social
  welfare function Wf(UM,UP)
• -This proves, however, that because a non-injured
  person wouldnt want therapy, in-kind transfers
  reduce the incentive to fake an injury under
  asymmetric information

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2) Commodity Egalitarianism

• Commodity Egalitarianism claims that commodities
  should be distributed equally
• -This makes sense for some commodities
• ie right to vote, basic foodstuffs, clean water
• -This is problematic for other commodities
• Ie healthcare (should sick and well get same
  care?), primary school (should smart and average
  children get same resources), video games (should
  people who dont play video games still get
  them?)

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3) Paternalism

• If someone has a paternalistic attitude towards
  the sick or poor, their utility increases when
  the sick or poor consume certain commodities
  (such as healthcare, or food or shelter)
• -This is a type of positive externality
• -Note that this often doesnt apply to all
  commodities (ie cigarettes or beer)
• -an In-Kind transfer ensures the commodity in
  question is consumed, thus dealing with the
  positive externality

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4) Politics

• In-Kind transfers also have the advantage of
  increasing the demand for the commodity in
  question (food, housing, etc)
• Also the public employees overseeing the
  transfers are given jobs, reducing unemployment
• -This can have a good effect on the economy
• -And therefore a positive political effect for
  the politician proposing it

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Income Transfer Overview

• Most people agree that the government should be
  involved in income transfer
• -But often disagree as to the perfect
  distribution of income
• -Due to asymmetric information, any lump-sum
  change must focus on income and therefore becomes
  a distortionary income tax
• -In-kind transfers are less efficient than
  lump-sum transfers.
• -but are used due to asymmetric information,
  commodity egalitarianism, paternalism politics

67
Chapter 6 Summary

• Utilitarians argue that income should be split
  equally, which requires
• W?U, with all Us equal
• Decreasing MU of income
• Fixed total income
• -since these assumptions (especially 3) are
  problematic, income redistribution is more
  difficult
• The maxmin criterion seeks to raise the utility
  of the worst off person
• -this has issues (often allows for odd results)

68
Chapter 6 Summary

• Income redistribution may a Pareto Improvement or
  a public good, if people gain utility from equity
• Other theories abound on what goods should be
  distributed equally and what a fair
  distribution is
• Income is hard to measure correctly
• In-kind transfers have efficiency disadvantages
• But other significant advantages