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slides_04_utilitarianism.pdf

slides_04_utilitarianism.pdf - Econ 473 Class 4 Theory and...

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Econ 473 Class 4 Theory and Measurement: Utilitarianism and critiques A snapshot of current inequality
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Next Today: I Illustrate Atkinson’s inequality measure I A discussion of utilitarianism and some alternatives I Measurement epilogue I Recent and not so recent evolution of inequality
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Atkinson’s inequality measure A ε Y - Ny e Y = 1 - y e ¯ y = 1 - U - 1 ( ¯ U ) ¯ y I U - 1 ( ¯ U ): income required to reach utility ¯ U . I Perfect equality: ¯ y = y e A ε = 0. I A measure of inequality based on ethical, not statistical, foundations.
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Atkinson’s inequality measure A ε Y - Ny e Y = 1 - y e ¯ y = 1 - U - 1 ( ¯ U ) ¯ y I U - 1 ( ¯ U ): income required to reach utility ¯ U . I Perfect equality: ¯ y = y e A ε = 0. I A measure of inequality based on ethical, not statistical, foundations. Interpretation: Fraction of income that could be sacrificed without loss of social welfare if income was equally redistributed.
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Atkinson’s inequality measure A ε Y - Ny e Y = 1 - y e ¯ y = 1 - U - 1 ( ¯ U ) ¯ y For a constant inequality aversion utility function: A ε = 1 - y e ¯ y = 1 - " 1 N N X i =1 y i ¯ y 1 - ε # 1 1 - ε
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Atkinson’s inequality measure A ε Y - Ny e Y = 1 - y e ¯ y = 1 - U - 1 ( ¯ U ) ¯ y For a constant inequality aversion utility function: A ε = 1 - y e ¯ y = 1 - " 1 N N X i =1 y i ¯ y 1 - ε # 1 1 - ε I ε is key here, and parameterizes society’s inequality aversion I Using this measure requires taking a stand on ε – but other measures also imply making similar implicit judgements. I Here, the judgement is explicit.
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Exploring Atkinson’s inequality measure See Atkinson.xls . Scenarios: 1. benchmark
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Exploring Atkinson’s inequality measure See Atkinson.xls . Scenarios: 1. benchmark 2. The Gini declines (because there is less inequality in the middle), but all other measures increase (because there is more inequality between the extremes).
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Exploring Atkinson’s inequality measure See Atkinson.xls . Scenarios: 1. benchmark 2. The Gini declines (because there is less inequality in the middle), but all other measures increase (because there is more inequality between the extremes). 3. Atkinson declines if ε large enough (the poorest better off), rises for low ε (weight of the poor not as high).
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Exploring Atkinson’s inequality measure See Atkinson.xls . Scenarios: 1. benchmark 2. The Gini declines (because there is less inequality in the middle), but all other measures increase (because there is more inequality between the extremes). 3. Atkinson declines if ε large enough (the poorest better off), rises for low ε (weight of the poor not as high). 4. The SWF for ε = 1 is unchanged, as growth compensates for the increase in inequality. A ε rises by more than ¯ y for ε > 1 SWF declines for ε > 1. See this next.
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Exploring Atkinson’s inequality measure See Atkinson.xls . Scenarios: 1. benchmark 2. The Gini declines (because there is less inequality in the middle), but all other measures increase (because there is more inequality between the extremes).
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