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
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.
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.
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).
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.
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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• Fall '17
• MarkusPoschke

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