03 - 01 - Income Inequality.pdf - ECONOMIC INEQUALITY Functional and Personal Distribution of Income Functional Distribution Ownership of Factors

03 - 01 - Income Inequality.pdf - ECONOMIC INEQUALITY...

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ECONOMIC INEQUALITY
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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
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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
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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 )
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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 )
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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
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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.
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Lorenz Curve
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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
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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
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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.
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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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