ECONOMIC INEQUALITY
Functional and Personal Distribution of Income
Functional Distribution
Personal Distribution
Ownership of Factors
Production
Wages
Rents
Profits
Household 1
Household 2
Household 3
Household 4
What’s wrong with an Unequal World?
Inequality can be viewed as an undesirable thing at 2 levels:
•
Intrinsic problems with inequity
•
Functional problems with inequity
Criteria for a ‘good’ index of Inequality
•
Anonymity Principle
–
who is earning the income should not matter.
Thus,
I = I(Y
1
, Y
2
, Y
3
, …
Y
n
) such that I is totally insensitive to all permutations
of income distribution (Y
1
, Y
2
, Y
3
, …
Y
n
) between individuals (1, 2, …, n)
•
Population Principle
–
cloning the entire population should not affect
inequality, since population share, and not population size matters
Thus,
I(Y
1
, Y
2
, Y
3
, …
Y
n
) = I(Y
1
, Y
2
, Y
3
,…
Y
n
; Y
1
, Y
2
, Y
3
,…
Y
n
)
•
Relative Income Principle
–
Relative incomes matter, while absolute
level does not. Thus, scaling up (or down) the entire income
distribution should not affect the Inequality Index.
I(Y
1
, Y
2
, Y
3
, …
Y
n
)
= I(λY
1
, λY
2
, λY
3
,… λY
n
)
•
Dalton Principle
–
If an income distribution is derived from another
one through a series of regressive transfers, then the derived
distribution is more unequal than the original one
I(Y
1
, …, Y
i
,…,
Y
j
, …,
Y
n
) < I(Y
1
, Y
i

δ, …,
Y
j
+ δ,…,
Y
n
) whenever Y
i
≤
Y
j;
and
δ>0
Inequality Measures
•
Definition of Economic Inequality
If a single person holds all of a given resource, inequality is at a
maximum.
If all persons hold the same percentage of a resource,
inequality is at a minimum.
Inequality studies explore the levels of
resource disparity and their practical and political implications.
•
The Lorenz Curve
The Lorenz Curve orders all observations and then plots the cumulative
percentage of the population against the cumulative percentage of the
resource.
Lorenz Curve
•
An equality diagonal represents perfect equality: at every point,
cumulative population equals cumulative income.
•
The Lorenz curve measures the actual distribution of income.
•
Area between red and blue lines: the difference between equality and
reality
The Lorenz Criterion
: If the Lorenz Curve of Distribution C lies
everywhere to the right of the Lorenz Curve of Distribution A, then
Distribution C is more unequal than Distribution A
Lorenz Curve and Inequality Axioms
An inequality measure is Lorenz consistent if and only if it is
simultaneously consistent with the anonymity, population,
relative income and Dalton principles.
Quantitative Measures of Income Inequality
Notations:
m

distinct income groups / classes
j

income class
n
j

number of individuals in the j
th
income class
n = ∑
j=1
m
total number of people
y
j
income of the j
th
income class
μ
 mean of income distribution (= total income / total population)
𝜇 ≡
1
𝑛
?=1
?
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 Fall '19