Lecture 4-3 (sept 22)

Lecture 4-3 (sept 22) - Lecture 4: Inequality Readings:...

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Lecture 4: Inequality Readings: Todaro, Chapter 5
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Introduction For now, we only studied average Y. But what if Y goes towards a small part of the population? 2 reasons to study inequality: Intrinsic, ethic, philosophical (is inequality natural, or unfair? Rawles’ veil of ignorance) Maybe inequality => Y?
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Today 1. Measure of inequality 2. Impact of inequality on growth
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1. Measure of inequality Inequality: personal capabilities, political freedom, non constant over a lifetime…complex! In economics: income inequality
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Remarks Income or wealth? Flow or stock? Short- term or long-term? Society 1: 2 incomes: 2000$, 3000$ Society 2: 2 incomes: 1000$, 4000$ But society 1: no mobility; society 2: total mobility, then? How to measure? With 2 persons: 20-80 and 30-70? With 3 persons: 20-30-50 and 22-22-56?
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Four criteria n individuals, with y 1 , y 2 ,…, y n 1. Anonymity principle: Individual A has x, B has y Individual A has y, B has x Which distribution is more unequal? 1. Population principle: population size does not matter (cloning?)
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Four criteria 3. Scale independence principle: A has 1000$, B 2000$ A has 2000$, B 4000$ Inequality? (allows comparison between countries with differing average incomes) 3. Dalton principle: Regressive transfer: transfer from a poor to rich To go from a distribution A to a distribution B by a sequence of regressive transfers: A more equal than B? useful to rank distributions
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Mathematically: Define I=I(y 1 , y 2 ,…, y n ) n I(y 1 , y 2 ,…, y n ) = I(y 2 , y 1 ,…, y n ) : ? n I(y 1 , y 2 ,…, y n ) = I(y 2 , y 1 ,…, y n , y 1 , y 2 ,…, y n ): ? n I(y 1 , y 2 ,…, y n ) = I(λ y 1 , λ y 2 ,…, λ y n ): ? n I(y 1 , …,y i ,…, y j ,…y n ) < I(y 1 , …,y i -δ,…, y j +δ,…y n ) : ?
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Mathematically: Define I=I(y 1 , y 2 ,…, y n ) n I(y 1 , y 2 ,…, y n ) = I(y 2 , y 1 ,…, y n ) : anonymity n I(y 1 , y 2 ,…, y n ) = I(y 2 , y 1 ,…, y n , y 1 , y 2 ,…, y n ): population n I(y 1 , y 2 ,…, y n ) = I(λ y 1 , λ y 2 ,…, λ y n ): scale independence n I(y 1 , …,y i ,…, y j ,…y n ) < I(y 1 , …,y i -δ,…, y j +δ,…y n ) : Dalton
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Measures of inequality 1 st idea: ratio of top 20% to bottom 40% 4 principles? ? Problem? 2 nd idea: Lorenz curve % 40 % 20 % 40 % 20 bottom top bottom top - + δ
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From Table 5.1 (p. 211) Percentile of income Recipients (deciles) % share of total income Cumulative share of total income 0% 0 10% 1.8 20% 3.2 30% 3.9 40% 5.1 50% 5.8 60% 7.2 70% 9.0 80% 13.0 90% 22.5 100% 28.5
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From Table 5.1 (p. 211) Percentile of income Recipients (deciles) % share of total income Cumulative share of total income 0% 0 0 10% 1.8 20% 3.2 30% 3.9 40% 5.1 50% 5.8 60% 7.2 70% 9.0 80% 13.0 90% 22.5 100% 28.5
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From Table 5.1 (p. 211) Percentile of income
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Lecture 4-3 (sept 22) - Lecture 4: Inequality Readings:...

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