The Distribution Function of Government:
(“Economics” – Chapter 12)
Recall… Government Intervention in markets and the
economy is most often justified by arguing for government
to serve one of the three following functions:
1. Allocation Function – (discussed in previous topic)
2. Distribution Function – government policies aimed at
changing the final distribution of goods/services across
consumers, usually with the intention of realizing a
“fairer” apportionment of consumption/income/wealth.
3. Stabilization Function – (discussed in next topic)
“Redistribution” – government policies designed to alter
the distribution of income/wealth/consumption across
members of society.
There are broadly two different ways to directly
“redistribute”
1. Income Support – monetary payments (such as
unemployment benefits and social security
payments) made to certain individuals, which
directly alter the distribution of income within a
society.
2. Redistribution In-Kind – public provision of
goods/services (such as healthcare, education,
housing, food) for certain individuals, which alter
the consumption of goods/services within society.
1
Any such policies are based upon the premise that the
distribution of income/consumption that results from the
free market system is not best.
 But, “what distribution of income is best or most
desirable?” Is a “more even distribution of income”
necessarily an “ideal” for which we should strive?
 What determines income and wealth (and therefore
consumption) in a free market system?
7 Determinants of Productivity, Income, and Wealth:
1. Natural Talent and Ability – ability is not distributed
equally at birth; some people possess attributes (e.g.,
intelligence, strength) that make them more productive
2. Acquired Skills – individual productivity depends in
large part upon skills and experiences acquired during
education, training, and work experience
3. Effort – productivity is often largely dependent upon
effort (“workers” are more productive than “shirkers”)
4. Compensating Differentials – differences in wages
that results from differences in working conditions
(e.g., risky jobs pay more; “glamour jobs” pay less)
5. Inherited Wealth – wealth is distributed less evenly
than income (due partly to differences in inheritances)
6. Accumulated Savings – the stock of wealth that a
person has at any point in time is partly determined by
previous consumption/savings decisions
7. Seemingly Unrelated Market Conditions – income
depends in part upon economic conditions beyond our
control; a worker’s value depends greatly upon the
price of the product he helps produce (e.g., wage of a
coal miner would increase if we ran out of oil)
2
How is income distributed in the U.S.?
United States
1980
Real Per Capita GDP $25,640
% of Income earned
17.68%
by Bottom 50%
% of Income earned
43.30%
by Bottom 75%
% of Income earned
67.87%
by Bottom 90%
% of Income earned
91.54%
by Bottom 99%
1989
$31,877
1998
$37,238
2007
$43,926
14.96%
13.67%
12.26%
37.72%
34.37%
31.29%
61.00%
56.23%
51.95%
85.81%
81.53%
77.17%
Can we graphically illustrate the distribution of income
across members of society? Can we develop a single
numerical measure of income inequality?
 Lorenz Curve – a graph illustrating the cumulative
amount of income earned by each cumulative portion
of the population
 “More even” distribution of income  Lorenz Curve
“closer to 45-degree line”
 Gini-Coefficient – a quantitative measure of income
inequality based upon the Lorenz Curve, defined as
the ratio of “the area between 45-degree line and the
Lorenz Curve” to “the entire area below 45-degree
line.”
3
Lorenz Curve and Gini-Coefficient:
“ 45 0 – Line” or
“Line of Perfect
Income Equality”
Fraction of
Total Income
1
.7717
.5195
.3129
Lorenz Curve
for U.S. (2007)
.1226
Fraction of Total
Population
0
0
.50
.75
.90
.99
1
Green



(Gini-Coefficient) = Green  Blue 


Fraction of Total Income
1
“ 45 0 – Line” or
“Line of Perfect
Income Equality”
Lorenz Curve
for U.S. (2007)
0
0
1
Fraction of Total
Population
4
 Extreme Equality => Lorenz Curve on 45-degree line
=> Gini-Coefficient equal to zero: G  0  0
0
Fraction of Total Income
1
1
2
Fraction of Total
Population
0
1
0
 Extreme Inequality (one person having all income) =>
Lorenz Curve lies along horizontal axis => GiniCoefficient equal to one: G 
1
1
2
1
2
Fraction of Total Income
0
1
Fraction of Total
Population
0
1
0
United States
Gini Coefficient
1980
.403
1989
.431
1998
.456
2007
.463
 The distribution of incomes in the U.S. has become
“less equal” over the past three decades
5
Question: Even if you “value income equality,” should you
“always prefer a smaller value of the Gini-Coefficient”?
 Recognize that the Gini-Coefficient tells us nothing
about “income levels,” but rather only describes “how an
amount of income is divided”
 Real Per Capita GDP increased from 1980 to 2007
United States
Gini Coefficient
Real Per Capita GDP
1980
.403
$25,640
1989
.431
$31,877
1998
.456
$37,238
2007
.463
$43,926
 Further, over these years, Real Household Income (i.e.,
adjusted for inflation) increased for every segment of the
population => Table below reports the “income cutoff
level” (in real terms, that is adjusted for inflation) for
each stated percentile in each year.
Real Household Income
20th Percentile
40th Percentile
60th Percentile
80th Percentile
95th Percentile
1980
$24,916
$41,950
$59,415
$83,372
$131,766
1989
$25,837
$45,207
$65,873
$96,145
$159,779
1998
$27,439
$47,882
$71,164
$106,318
$184,452
2007
$27,864
$49,510
$75,000
$112,638
$197,216
 Over the past three decades in the U.S.
 “Rich” have become “richer” => 35.1% increase
($83,372 to $112,638) in “cutoff of 80th Percentile”
 “Middle class” has become “richer” => 18% increase
($41,950 to $49,510) in “cutoff of 40th Percentile”
 “Poor” have become “richer” => 11.8% increase
($24,916 to $27,864) in “cutoff of 20th Percentile”
 Of these four years, which realization of incomes is most
desirable? To me, the obvious answer is 2007 (even
though it has the highest valued Gini Coefficient)
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Comparison of Income Inequality across countries:
 in general there is a trend for “societies with higher
levels of per person income to have a more even
distribution of income” (or equivalently, for “societies
with lower levels of per person income to have a less
even distribution of income”).
 Notable exceptions: U.S., Hong Kong, Singapore
(economies closer to the “free market” side of the
spectrum)
Country:
Norway
Singapore
United States
Canada
Sweden
United Kingdom
France
New Zealand
Russia
Mexico
South Africa
Brazil
Turkey
Colombia
India
Zimbabwe
Per Capita
GDP (PPP):
$55,600
$48,900
$46,000
$38,200
$36,900
$35,300
$33,800
$26,000
$14,600
$12,500
$10,300
$10,100
$9,400
$7,200
$2,700
$500
Gini
Coefficient:
0.28
0.52
0.45
0.32
0.23
0.34
0.28
0.36
0.41
0.51
0.65
0.57
0.44
0.54
0.37
0.50
 Again, even if you desire “income equality” recall that
the Gini Coefficient tells us nothing about income
levels => would you pick “India’s incomes”
( G  0.37 ; Per Capita GDP of $2,700) over the “U.S.’s
incomes” ( G  0.45 ; Per Capita GDP of $46,000)?
7
4 Arguments in Favor of Coercive Redistribution:
1.
Utilitarian Justice – total social welfare can be
increased by transferring income/wealth from the rich
to the poor, so long as the marginal utility of
income/wealth is diminishing.
 idea that society should strive for the “greatest
happiness for the greatest number of people” (i.e.,
attempt to maximize the summation of “utility” or
“happiness” over all members of society)
 arguments first put forth by Jeremy Bentham (17481835) and John Stuart Mill (1806-1873)
 if the value of $1 is greater if you have less money
(i.e., diminishing marginal utility), then social
welfare can be increased by taking $1 away from
Ted Turner and giving it to a homeless person
Jeremy Bentham's Auto-Icon at University College London
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2.
Rawlsian Justice (Social Contract Theory) – the
socially best income distribution is the one which
maximizes the well-being of the worst-off member of
society
 developed by the philosopher John Rawls in A
Theory of Justice (1971)
 consider the “ideal society” that would be designed
by someone in the “beforelife” behind a “veil of
ignorance” (i.e., not knowing what their realized lot
in life would be, but just knowing that it would be a
random draw in this “ideal society”)
 Rawls argues that such a person would be
particularly concerned about the situation of the
poorest person (i.e., the worst possible outcome)
 Therefore, he argues that this objectively ideal
society should implement policies to apply the
“maximin criterion”
 Maximin Criterion – a claim that the government
should aim to maximize the well-being of the worst
off person in society
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3.
Labor Theory of Value – the theory that the value of
a commodity depends upon the amount of labor used
to produce it
 based upon the ideas of Karl Marx (1818-1883)
 mainstream economists do not agree with this
outdated notion => rather, the value of an item
clearly depends upon benefits to consumers
 e.g., if Ann spends 4 hours per day growing corn
and Bob spends 8 hours per day digging and then
filling ditches, is Bob’s output twice as valuable
 recognize that Marx’s notion attributes no value to
the capital (and other “non-labor inputs”) necessary
for the production process
 since a capitalist system provides returns for all
inputs (i.e., not only labor, but also capital and
land), labor is vastly underpaid relative to what
Marx believed was “fair”
 thus, in the interest of fairness, income/wealth must
be redistributed away from the owners of capital
and toward workers
4.
Overcoming the Free-Rider Problem
 suppose society prefers a more equal distribution of
income/wealth than what the market gives
 if we rely upon private charity to reduce inequality,
there is a free rider problem (recall the discussion
from market provision of public goods)
 thus, private charity does not provide enough
redistribution => have government redistribute, to
get an amount closer to the socially best level
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Redistribution Programs and Policies in the U.S.:
 Social Security System – a system of Federal
Government social insurance programs consisting of
1. Old Age and Survivors Insurance – pays cash
benefits to retired workers, their survivors, and their
dependents
2. Disability Insurance – pays cash benefits to disabled
workers and their dependents
3. Medicare – program which provides medical
insurance to people who are over age 65 or disabled
 Temporary Assistance for Needy Families – a welfare
program that provides cash benefits to low income
households
 Supplemental Security Income – a welfare program
which provides cash benefits to poor elderly people with
very low entitlements under traditional Social Security
 Unemployment Compensation – a state government
program that pays cash benefits to laid-off workers
 Medicaid – a welfare program which provides medical
care for people with low incomes
 Food Stamps – vouchers (with a face value greater than
their cost) available to low income families which can be
used to purchase food at grocery stores
 Public Housing – federal government program that
provides access to housing with rents capped at 30% of
income (e.g., no income => no rent)
 Earned Income Tax Credit – a refundable Federal
Income Tax Credit available to low income families with
children (i.e., some people who pay no income taxes end
up getting a check back from the IRS)
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Redistribution via Taxation:
Why impose taxes?
Three primary reasons for imposing taxes:
1. generate revenue for the government (in the U.S.,
over 90% of Federal Government revenue comes
from Income and Payroll Taxes; over 60% of State
Government revenue comes from income, advalorem, or social insurance taxes)
2. discourage certain behaviors, by altering the cost
or benefit of engaging in the activity (e.g., try to
discourage cigarette smoking by imposing per unit
taxes on each pack: $1.01 per pack Federal tax plus
state and perhaps local taxes => $6.86 per pack in
NYC => price of over $11 per pack in NYC)
3. redistribute income (in the U.S., we engage in a
great deal of redistribution indirectly, by imposing
higher income tax rates on the rich than on the poor
=> “progressive taxation”)
Would everyone agree: regardless of how much tax
revenue we want to raise, we should do so with a tax
system that is “fair”?
 What exactly do we mean by “fair”?
 Two notions of “fairness”
1. Horizontal Equity – two individuals of equal
economic capacity should have equal tax burdens
2. Vertical Equity – individuals of greater economic
capacity should not have a smaller tax burden
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 What exactly do we mean by “tax burden”?
 Common to describe a “tax structure” as Progressive,
Proportional, or Regressive, by examining how the
“Average Tax Rate” behaves as income is increased.
 Average Tax Rate (ATR) –the amount of total taxes
paid divided by income.
i. Progressive Tax – tax structure for which ATR
increases as the level of income is increased.
ii. Proportional Tax – tax structure for which ATR
remains constant as the level of income is
increased.
iii. Regressive Tax – tax structure for which ATR
decreases as the level of income is increased.
 Marginal Tax Rate (MTR) –the percentage of the
next dollar earned that must be paid in taxes.
 As a general rule (i.e., mathematical implication):
1. ATR will increase whenever MTR  ATR
2. ATR will decrease whenever MTR  ATR
Examples:
i. Progressive: U.S. Federal Income Tax
ii. Proportional: “flat tax” with no deductions whatsoever
(e.g., “flat tax” proposed by Steve Forbes in 1996 was
NOT a proportional tax, since the first $33,000 of
earnings were not taxed; income taxes in Albania
(10%), Bulgaria (10%), Czech Republic (15%), Iraq
(15%), Jamaica (25%), Hong Kong (16%), Mongolia
(10%), Russia (13%), Slovakia (19%), Ukraine (15%))
iii. Regressive: Social Security Payroll Tax – first
$102,000 taxed at a marginal rate of 6.2%, while
additional earnings are not taxed at all
13
So, back to the question of “What exactly do we mean by
‘fair’?”…
If “economic capacity” is equated to “income” and “tax
burden” is equated to “average tax rate,” then:
1. Horizontal Equity => two individuals with equal
incomes should have equal average tax rates
2. Vertical Equity => an argument against regressive
taxes, in favor of proportional or progressive taxes
However, if “tax burden” were instead equated to “total
dollars paid in taxes,” then even regressive taxes can be
“vertically equitable.”
i.e. – even for a regressive tax, “total dollars paid in
taxes” can increase as level of income increases.
Is “income” the only important determinant of “economic
capacity”?
 e.g. – consider the following two taxpayers:
1. 22 year old single college graduate earning
$50,000 per year
2. 45 year old high school educated married couple
with 4 kids earning a total of $50,000 per year
 Many of the “exemptions” and “deductions” built into
our tax code are based upon recognitions that things
other than income are important for determining
economic capacity
14
But, “Inequities” (both “vertical” and “horizontal”) can
easily result due to “deductions” and “exemptions”…
Consider the following five taxpayers in 2010:
AGI
Taxpayer (Line 37 of 1040)
Mitt R.
$21,646,507
Newt G.
$3,142,066
Barack O.
$1,728,096
Rick S.
$923,411
Joe B.
$379,178
Total Taxes Paid
(Line 60 from 1040)
$3,009,766
$994,708
$453,770
$263,442
$86,626
ATR
13.90
31.66
26.26
28.53
22.85
 If “ATR” is “tax burden” and “AGI” is “economic
capacity,” then these outcomes violates the notion of
“vertical equity”
 If instead “dollars paid in taxes is “tax burden” and
“AGI” is “economic capacity,” then these outcomes
do not violate the notion of “vertical equity”
Should the U.S. Federal Income Tax be modified or is the
current system “good”?
To begin to answer this question it is important to first have
an understanding of both:
I. the historical evolution of the U.S. Federal Income
Tax
II. the distribution of “tax burden” under the current
U.S. Federal Income Tax
15
U.S. Federal Income Tax
 16th Amendment to the U.S. Constitution ratified on
2/3/1913 – authorized congress to levy an income tax
 U.S. Federal Income Tax established in 1913
 Progressive Tax (increasing MTR)
 Primary source of U.S. Government tax receipts
I.
Historical Tax Rates (“married couple filing jointly”)
Year:
1913
1921
1928
1932
1941
1945
1954
1964
1980
1992
2000
2002
2012
# of Brackets:
7 brackets
56 brackets
23 brackets
55 brackets
32 brackets
24 brackets
24 brackets
26 brackets
16 brackets
3 brackets
5 brackets
6 brackets
6 brackets
Low MTR:
1.0%
4.0%
1.5%
4.0%
10.0%
23.0%
20.0%
16.0%
0%
15.0%
15.0%
10.0%
10.0%
High MTR:
7.0%
73.0%
25.0%
63.0%
81.0%
94.0%
91.0%
77.0%
70.0%
31.0%
39.6%
35.0%
35.0%
* In reality the “effective Low MTR” has always been 0%,
due to the presence of exemptions and deductions…
16
II.
Outcomes under current U.S. Federal Income Tax
(?) How many of you agree with the following statement:
“The rich don’t pay their fair share of taxes.”
Let’s focus on the “Top 1% of income earners.” What
percentage of “Total Income Taxes” should they pay?
a. 1%
b. 10%
c. 20%
d. 25%
All of the following figures are from…
http://taxfoundation.org/sites/taxfoundation.org/files/docs/ff285.pdf
…and are reported for 2009 (unless otherwise indicated).
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II.A) Disproportionate amount of tax dollars come from
“The Rich”
Group’s
Group’s
% Range
Income
Share of
Share of
of Income
Split
Income Taxes
Income
Top 1%
$343,927+
36.7%
16.9%
Top 5%
$154,643+
58.7%
31.7%
Top 10%
$112,124+
70.5%
43.2%
Top 25%
$66,193+
87.3%
65.8%
Top 50%
$32,396+
97.7%
86.5%
 “Top 5%” pay 58.7% of all income tax dollars
 “Bottom 95%” pay (100–58.7) = 41.3%
 “Top 10%” pay 70.5% of all income tax dollars
 “Bottom 90%” pay (100–70.5) = 29.5%
 “Top 1%” pay more income taxes than the “Bottom
90%” (36.7% versus 29.5%)
 “Top 1%” pay almost as much in income taxes as the
“Bottom 95%” (36.7% versus 41.3%)
 “Top 50%” pay 97.7% of all income tax dollars
 “Bottom 50%” only pay (100–97.7) = 2.3% of all
income tax dollars
 137.98 million tax returns with “positive AGI”
 Of these, 59 million (or 42.76% of the filed returns)
had federal income tax liability of $0
 These people not only got back every single dollar the
Federal government withheld, but in some cases
received money back from the IRS (recall the EITC)
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II.B) U.S. Federal Income Tax is clearly progressive
% Range
of Income
Top 1%
Top 2%-5%
Top 6%-10%
Top 11%-25%
Top 26%-50%
Bottom 50%
Average
Tax Rate
24.01%
16.4%
11.4%
8.25%
5.56%
1.85%
 Progressive since ATR is higher at higher incomes
II.C) Across income levels, ATR has “evolved” over time
1980
1988
1992
2000
2008
2009
Top 1%
34.47%
24.04%
25.05%
27.45%
23.27%
24.01%
Top 11-25%
14.80%
11.82%
11.39%
12.04%
9.29%
8.25%
Top 26-50%
11.91%
9.60%
9.42%
9.28%
6.75%
5.56%
Btm 50%
6.10%
5.06%
4.39%
4.60%
2.59%
1.85%
 Between 2000 and 2009:
 ATR of every income group decreased
 % decrease in ATR:
o 12.53% ([27.45–24.01]/[27.45]) decrease in ATR
for “Top 1%”
o 31.48% decrease in ATR for “Top 11-25%”
o 40.09% decrease in ATR for “Top 26-50%”
o 59.78% decrease in ATR for “Bottom 50%”
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Antipoverty Programs and Work Incentives:
 many policies aimed at helping the poor have the
unintended effect of discouraging the poor from escaping
poverty on their own
 therefore, “equity” or “fairness” should not be the only
consideration when considering redistribution policies
 all redistribution policies reduce incentives for people to
work, produce output, and earn income => people will
work less with policies in place (“cost-benefit principle”)
Disincentive effects of progressive taxation…
 incentives to earn additional income are reduced when
the Marginal Tax Rate is higher, since the worker gets to
“keep less of the next dollar earned.”
 experience of Ronald Reagan as an actor in Hollywood
when the highest MTR was over 90%: “As an actor in
Hollywood during the years when the marginal tax rate
was 90 percent, Reagan had reacted with rationality:
once he hit the higher tax brackets, he’d simply stop
working for the rest of the year. There was no point in
continuing.” (Commanding Heights, page 348)
Disincentive effects of “means tested” transfers…
 many transfers programs are “means tested” (i.e., you
only qualify if your income is below a certain threshold)
 as income rises, you may lose your benefits => no longer
eligible for welfare, Medicaid, food stamps, EITC
 historically, some poor families have faced “effective
marginal tax rates” (accounting for decreased benefits)
of OVER 100% as they lose their benefits => actually
BETTER OFF without earning the extra income!
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