In a picture attached is the question, attached also Powerpoint slide of lecture if needed.• Measurement
of Poverty and
Inequality
Thimpu, Bhutan
Measurement of Poverty and Inequality
• Measurement of Poverty
• Lorenz curves
• Gini coefficients and
aggregate measures of
inequality
Measuring Poverty:
• How do we measure poverty? Some of the
measures are discussed below.
• Measuring Absolute Poverty
– Headcount Ratio
– Total poverty Gap
– Foster-Greer-Thorbecke Measure
The Headcount Index
• Measuring Absolute Poverty
– Headcount Index: H/n (H = number below Poverty
line, n = population).
– Counts the total number of poor under a
benchmark dollar number as percentage of
population
– For example, what is the percentage of people
in Bhutan who live under $1/day?
– Easy to understand measure, but treats all poor as
a homogeneous group. If there are a large
.
number of people just above the benchmark, the
index may underestimate the problem.
Total Poverty Gap Ratio
TPGR = (1/ n) i=1 (Yp −Yi ) / Yp
H
Yp is the absolute poverty line, Yi is an individual’s income and H is
the total number of people below Yp and n is the population. Yi
must be less than Yp.
Question: What is the TPGR for four people who earn 10, 20, 30
and 40 where the poverty line is 35?
Answer: [(35 – 10)/35 + (35 – 20)/35 + (35 – 30)/35]/4 ≈ 32%
Question: What is the TPGR for four people who earn 5, 15, 25
and 40 where the poverty line is 35?
Answer: [(35 – 5)/35 + (35 – 15)/35 + (35 – 25)/35]/4 ≈ 43% TPGR
increased.
Poverty Measurement: Measuring
TPGR
Foster-Greer-Thorbecke Measure
– Foster-Greer-Thorbecke measure
H
1

P =  [(Yp − Yi ) / Yp]
n i=1
Foster-Greer-Thorbecke Measure
• When α = 0, we get the headcount ratio.
• When α = 1, we get poverty gap ratio.
• When α = 2, we poverty gap squared ratio.
Poverty Gap Squared Ratio
• Question: What is the PGSR for four people who earn
10, 20, 30 and 40 where the poverty line is 35?
• Answer: [{(35 – 10)/35}2 + {(35 – 20)/35} 2 + {(35 –
30)/35} 2]/4 ≈ 18%
• Question: What is the TPGR for four people who earn
5, 15, 25 and 40 where the poverty line is 35?
• Answer: [{(35 – 5)/35} 2 + {(35 – 15)/35} 2 + {(35 –
25)/35} 2]/4 ≈ 29%. PGSR increased.
The Role of α in Foster-Greer-Thorbecke
Measure
H
1

P =  [(Yp − Yi ) / Yp]
n i=1
Higher α gives greater weight to those observations that fall far below the poverty line
than those that are closer to it. The variable α is a sensitivity measure in FGT (Foster,
Greer, Thorbecke) family of poverty measures.
Absolute Poverty:
Extent and Magnitude
• Extreme Poverty
– $2-a-day headcount shows minimal progress (sometimes
$1.80 is used)
– Incidence of extreme poverty is uneven.
– The number of people under extreme poverty has not
changed very much, but the percentage has gone down.
– Population-adjusted poverty has gone down
– To get an idea of world poverty, watch:

Also look at: How Rich Are You
http://www.globalrichlist.com/
Poverty Trends
• The next four slides give us an idea of world
poverty. Poverty is still very high in absolute
numbers – but it has gone down on a relative
scale.
• China is a big success story.
• The number of poor in sub-Saharan Africa has
increased substantially.
• South Asia has the largest number of poor
people.
96
98
Is there a trickle down effect?
• From your text:
• In about one in five cases of positive economic
growth, the income levels of the poor
decrease.
• For Latin America, this occurs about one-third
of the time.
• If overall growth rate is over 5% – poor people
definitely get less poor (only two exceptions:
Puerto Rico and Singapore)
99
100
Inequality Measures
• Inequality measures address the issue of
income dispersion.
• Although related, inequality measures are
different from poverty measures
• We will look at two inequality measures:
– Kuznets Ratio
– Gini Coefficient (from the Lorenz Curve)
101
Kuznets Ratio
• Arrange all individuals by ascending personal
incomes and then divide the total population
into quintiles (20% interval) or deciles (10%
interval
• Kuznets ratio = income received by top 20%
divided by income received by bottom 40%
• What is the Kuznets Ratio from the next
slide?
102
Kuznets Ratio
103
Calculation of Kuznets Ratio
• KR = (10.5 + 12 + 13.5 + 15)/(0.8 + 1 + 1.4 + 1.8
+1.9 + 2 + 2.4 + 2.7) = 51/14 = 3.64
Measure of Inequality: The Lorenz
Curve
• The horizontal axis shows the cumulative
numbers of income recipients (in percent, so
maximum is 100).
• The vertical axis shows the cumulative share
of total income received by each percentage
of population recipients (in percent, so
maximum is 100).
Figure 5.1
Figure 5.3
How to Calculate the Gini Coefficient




Use the triangle and the trapezoid method.
Recall:
Area of a triangle: (h)(0 + b)/2 = (h)(b)/2
Area of a trapezoid: (h)(a + b)/2
The Lorenz Curve
• The more the Lorenz line curves away from
the diagonal, the greater the degree of
inequality represented.
• The following slides show: How to plot Lorenz
Curve and how to calculate the Gini
Coefficient.

Adopted from Mike Fladlien
Step 1—Raw Data
Adrian
$ 90.00
Bob
15.00
Cathy
70.00
Derek
200.00
Eddie
125.00
Step 2—Arrange in Ascending Order
Bob
$15.00
Cathy
70.00
Adrian
90.00
Eddie
125.00
Derek
200.00
Step 3—Find Total Income
Bob
$ 15.00
Cathy
70.00
Adrian
90.00
Eddie
125.00
Derek
200.00
Total
$500.00
Step 4-Find % of Income
Bob
15.00
15/500 = 3%
Cathy
70.00
70/500 = 14%
Adrian
90.00
90/500 = 18%
Eddie
125.00
125/500 = 25%
Derek
200.00
200/500 = 40%
Total
$500.00
Step 5 – Find Cumulative % of Income
Bob
3%
3%
Cathy
14%
17%
Adrian
18%
35%
Eddie
25%
60%
Derek
40%
100%
Step 6 – Plot the Data
Lorenz Curve
Cumm Percent of Income
120
100
80
60
40
20
0
0
20
40
60
80
Cumm Percent of Households
100
120
Step 7 – Find Area Under Lorenz Curve
Step 8a – Finding the Gini Coefficient
• Subtract Area
under Lorenz
Curve from 0.5.
• 0.5 – 0.33 = 0.17
• This is the area
between perfect
equality and
Lorenz Curve
Step 8b – Find the Gini Coefficient
• The Gini Coefficient is found by taking the
ratio of the Area capsulated by the area of the
right triangle. In this case, 0.17/0.50 or 0.34.
• One could simply multiply by 2
Step 9a–Finding the Gini Coefficient
• Gini shows income disparity
• A high Gini shows that wealth is concentrated
among a few
• A low Gini shows more equitable distribution
Selected Gini Coefficients
Measuring Inequality
The Lorenz Crossing Problem
Figure 5.9
In this case,
the Gini
Coefficient
may be the
same for L1
and L2. But
obviously
income
distributions
are different.
The Lorenz Crossing Problem
Hard to
compare
between B
and C.
The Lorenz Curve for the United
States, 2006
Tutorial
• In a certain country, the population consists of
five blue people and five green people. Each
green person has an income of $1 per year.
Each blue person has an income of $3 per
year. Calculate the Gini coefficient.
Household Income in the United States
by Quintiles, 2006
Income Distribution in the United
States, 2006
Income per Capita Versus Inequality
Poverty, Inequality, and Social Welfare
• Does the Lewis Model predict more
Inequality?
• Does the Solow Model predict more
inequality?
Growth and Inequality
• Kuznets’s inverted-U hypothesis.
• Kuznets found that economic growth first
raises, then lowers income inequality.
Kuznet’s Inverted U
The Kuznets Curve in England and
Wales, 1823–1915
Selected Income Distribution Estimate
Income and Inequality in Selected Countries
Change in Inequality in Selected Countries, with
or without Growth
Income Inequality in the United States:
1947–2005
What’s so bad about inequality?
• John Rawls: “The
principles of justice are
chosen behind a veil of
ignorance.”
• Society A: A society where
90% are miserably poor, but
10% are quite well off.
• Society B: somewhat
inefficient, but all earn
more or less the same
income.
• Under a “veil of ignorance”
(you do not know which
society you will be born to)
would you like your world
be more like A or like B?
What’s so bad about inequality?
• Most people will probably choose B.
What’s so bad about inequality?
• Saving Rates by Income Quintile, 2003.
• The rich save more.
• From Harrod-Domar Model, or from the Solow model, high savings is a
good thing.
• Why not give more income to the rich so that they can save?
What’s so bad about inequality?
• The problem with this suggestion is as follows:
• The highest return to investment is in
education or human capital (remember h is
Solow?)
• Stocks, bonds or physical capital generally
have a much lower return compared to return
on education.
What’s so bad about inequality?
• Initially, return to education is much higher than
return to physical capital investment.
• All people first invest in education.
• As more investment in education takes place, return
to education falls.
• Return to education eventually becomes equal to
return to physical capital.
• Return to education then falls below the return to
physical capital.
Why Income distribution May Matter in very poor countries:
Marginal Products of Physical vs. Human Capital
Why Income distribution May Matter in very poor countries:
Marginal Products of Physical vs. Human Capital
Invest in
education/human
capital up to this point.
Return to physical
capital is higher after
this point.
What’s so bad about inequality?
• In a poor country with a lot of inequality, the
rich will invest in human and physical capital.
• The poor will invest only in human capital. The
poor must sop investing because the poor will
run out of money.
What’s so bad about inequality?
A country of one poor and one
rich.
The poor
person stops
investing here.
The rich person
stops investing
here.
147
What’s so bad about inequality?
A country of one poor and one
rich where rich gives some money
to the poor.
The poor person
gets money from
the rich and
invests more in
human capital
The rich person
gives some of
his money to
the poor person.
What’s so bad about inequality?
• The second case is better for the country as a
whole because the summation of the two
areas under the marginal product curve is
higher in the second case.
• This result does not hold if both persons are to
the right of l* to begin with.
Relationship Between Income Inequality and
Sociopolitical Instability
• Sociopolitical instability however does not
seem to be strongly correlated with inequality
(Gini Coefficient).
• See the next slide.
Relationship Between Income Inequality and
Sociopolitical Instability
Capital in the Twenty-First Century

Economists lost interest in income distribution
issues

Kuznet’s inverted U, lulled them into the belief that
income distribution would not matter in the long
run – capitalism will be “fair” in the long run.

For a while, income distribution did become more
equal – but started becoming more unequal.
Solow Model
Y = Kα L1-α
Capitalists’ income:
K.MPK = K.αKα-1L1- α = αKαL1- α = αy
Worker’s Income:
L.MPL = L.(1-α)KαL1- α -1 = (1-α)KαL1- α = (1-α)y
Income distribution remains the same between the
capitalists and the workers during growth:
αy/(1-α)y = α/(1-α)
Lewis Model
Lewis Model
Lewis Model seems to support Kuznet’s inverted U,
although it is not clear why inverted U will occur in
developed countries.
Piketty: Capital in the 21st Century

Inequality: Fundamental Concept to Understand: The implication of
r>g
Start from Harrod-Domar Model without depreciation:
g = s/v,
Introducing capital and labor in the HD model:
On the distribution side:
π = rK
Or,
π/Y= rK/Y = rv
Or,
r = π/Yv
Piketty: Capital in the 21st Century
(r – g) = (π/Yv) – (s/v)
Or,
v(r-g) = π/Y – s = π/Y – S(c+w)/Y
Where : S(c+w)= total savings by capitalists and workers.
(r – g) > 0, then, π – S(c+w) > 0
Or, if workers are saving little, profits will have a
tendency to rise. This may skew the profit/wage
distribution.
Piketty: Page 351
The primary reason for the hyper-concentration of
wealth in traditional agrarian societies and to a large
extent in all societies prior to World War I (with
the exception of the pioneer societies of the New
World, which are for obvious reasons very special
and not representative of the rest of the world or
the long run) is that these were low- growth
societies in which the rate of return on capital was
markedly and durably higher than the rate of
growth. This fundamental force for divergence, which
I discussed briefly in the Introduction, functions as
follows.
Piketty: Page 351
Consider a world of low growth, on the order of, say,
0.5– 1 percent a year, which was the case
everywhere before the Eighteenth and nineteenth
centuries. The rate of return on capital, which is
generally on the order of 4 or 5 percent a year, is
therefore much higher than the growth rate.
Concretely, this means that wealth accumulated in the
past is recapitalized much more quickly than the
economy grows, even when there is no income from
labor. For example, if g = 1% and r = 5%, saving
one- fifth of the income from capital (while
consuming the other four- fifths) is enough to
ensure that capital inherited from the previous
generation grows at the same rate as the economy.
Piketty: Page 351
If one saves more, because one’s fortune is large
enough to live well while consuming somewhat less
of one’s annual rent, then one’s fortune will
increase more rapidly than the economy, and in
equality of wealth will tend to increase even if one
contributes no income from labor. For strictly
mathematical reasons, then, the conditions are ideal
for an “inheritance society” to prosper— where by
“inheritance society” I mean a society characterized
by both a very high concentration of wealth and a
significant persistence of large fortunes from
generation to generation.
Piketty on Marx
Like his predecessors, Marx totally neglected the possibility
of durable technological progress and steadily increasing
productivity, which is a force that can to some extent serve
as a counterweight to the process of accumulation and
concentration of private capital. He no doubt lacked the
statistical data needed to refine his predictions. He probably
suffered as well from having decided on his conclusions in
1848, before embarking on the research needed to justify
them. Marx evidently wrote in great political fervor, which at
times led him to issue hasty pronouncements from which it
was difficult to escape.
Piketty on Marx
This is the basis of Marx’s prediction of an apocalyptic end
to capitalism: either the rate of return on capital would
steadily diminish (thereby killing the engine of accumulation
and leading to violent conflict among capitalists), or capital’s
share of national income would increase indefinitely (which
sooner or later would unite the workers in revolt). In either
case, no stable socioeconomic or political equilibrium was
possible.
Piketty on Marx
Marx took the Ricardian model of the price of
capital and the principle of scarcity as the basis of a
more thorough analysis of the dynamics of
capitalism in a world where capital was primarily
industrial (machinery, plants, etc.) rather than landed
property, so that in principle there was no limit to the
amount of capital that could be accumulated. In fact,
his principal conclusion was what one might call the
“principle of infinite accumulation,” that is, the
inexorable tendency for capital to accumulate and
become concentrated in ever fewer hands, with no
natural limit to the process.
Piketty on Kuznets
Turning from the nineteenth- century analyses of
Ricardo and Marx to the twentieth- century analyses
of Simon Kuznets, we might say that economists’
no doubt overly developed taste for apocalyptic
predictions gave way to a similarly excessive fondness
for fairy tales, or at any rate happy endings. According
to Kuznets’s theory, income inequality would
automatically decrease in advanced phases of
capitalist development, regardless of economic policy
choices or other differences between countries, until
eventually it stabilized at an acceptable level.
Piketty on Kuznets
Proposed in 1955, this was really a theory of the
magical postwar years referred to in France as the
“Trente Glorieuses,” the thirty glorious years from
1945 to 1975.9 For Kuznets, it was enough to be
patient, and before long growth would benefit
everyone. The philosophy of the moment was
summed up in a single sentence: “Growth is a rising
tide that lift’s all boats.”
Growth is a rising tide that lifts all boats?
According to Kuznets’s theory, income in
equality would automatically decrease
in advanced phases of capitalist development,
regardless of economic policy choices or other
differences between countries, until eventually it
stabilized at an acceptable level. Proposed in
1955, this was really a theory of the magical
postwar years referred to in France as the
“Trente Glorieuses,” the thirty glorious years
from 1945 to 1975.
Growth is a rising tide that lifts all boats?
For Kuznets, it was enough to be patient, and before long
growth would benefit everyone. The philosophy of the
moment was summed up in a single sentence: “Growth is a
rising tide that lifts all boats.”
Kuznets’s position was thus diametrically opposed to the
Ricardian and Marxist idea of an inegalitarian spiral and
antithetical to the apocalyptic predictions of the nineteenth
century.
Solow and Inequality
A similar optimism can also be seen in Robert
Solow’s 1956 analysis of the conditions necessary
for an economy to achieve a “balanced growth
path,” that is, a growth trajectory along which all
variables— output, incomes, profits, wages,
capital, asset prices, and so on— would progress
at the same pace, so that every social group would
benefit from growth to the same degree, with no
major deviations from the norm.
Income Inequality In the United States 1910-2010
Criticism of Piketty:
The One Percent across Two Centuries: A Replication of Thomas
Piketty’s Data on the Concentration of Wealth in the United States
Richard Sutch
October 2017
Abstract
This exercise reproduces and assesses the historical time
series on the top shares of the wealth distribution for the
United States presented by Thomas Piketty in Capital in the
Twenty-First Century. Piketty’s best-selling book has gained
as much attention for its extensive presentation of detailed
historical statistics on inequality as for its bold and
provocative predictions about a continuing rise in inequality
in the twenty-first century.
Here I examine Piketty’s US data for the period 1810 to
2010 for the top 10 percent and the top 1 percent of the
wealth distribution. I conclude that Piketty’s data for the
wealth share of the top 10 percent for the period 1870 to
1970 are unreliable. The values he reported are
manufactured from the observations for the top 1 percent
inflated by a constant 36 percentage points. Piketty’s data
for the top 1 percent of the distribution for the
nineteenth century (1810–1910) are also unreliable. They
are based on a single mid-century observation that
provides no guidance about the antebellum trend and only
tenuous information about the trend in inequality during
the Gilded Age.
The values Piketty reported for the twentieth century
(1910–2010) are based on more solid ground, but have
the disadvantage of muting the marked rise of
inequality during the Roaring Twenties and the decline
associated with the Great Depression. This article
offers an alternative picture of the trend in inequality
based on newly available data and a reanalysis of the
1870 Census of Wealth. This article does not question
Piketty’s integrity.
Inequality and Health
https://inequality.org/facts/inequality-andhealth/
Inequality and Health
Inequality and Health
Poor and Happy?
Don’t Worry, Be Happy?
World Happiness Report
https://worldhappiness.report/ed/2020/
Suppose that global relative returns to
schooling are the same in all
countries. Wages relative to no
schooling are given below:
Schooling
Years of Wage
Schooling Relative to
No
Schooling
No Schooling
0
1
4
1.65
Partial
Primary
8
2.43
Complete
Primary
10
2.77
Incomplete
Secondary
12
3.16
Complete
Secondary
14
3.61
Incomplete
Higher
16
4.11
Complete
Higher
Suppose that we are comparing two
countries (i and j) that are similar in
every respect except the education of
their population. In country i, all adults
have ten years of schooling. In
country j, all adults have 4 years of
schooling. Calculate the ratio of
output per worker in steady state in
the two countries.

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