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4. What is the optimal income distribution between two citizens under these three assumptions: -The Social...

4. What is the optimal income distribution between two citizens under these three assumptions:

-The Social Welfare Function is Utilitarian. -

The total income is fixed. -

The two citizens have the same individual utility function,

which exhibits decreasing but positive marginal utility of income.

What are the implications of this result and why we do not see policies to enforce this degree of income distribution in the real world? Justify your answer mentioning one or more of the three assumptions. (Hint: draw a graph with total income in the horizontal axis, and two vertical axes in the extremes representing the marginal utility of income of each citizen).

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Answer #1

Optimal tax theory, which attempts to balance distribu tional concerns and efficiency considerations, incorporates a welfarist approach to redistribution.5 Welfarism resolves dis- tributional questions by maximizing social welfare, where so- cial welfare is determined by aggregating individuals welfare in some way. Welfarist analysis often assumes that everyone experiences income as having declining marginal utility, that the next dollar is always worth more to a poorer person than to a wealthier person. If income does have declining marginal utility, a welfarist who does not explicitly incorporate equality into her analysis (for example, a utilitarian, who sums individ- uals welfare to arrive at total social welfare) will, given certain other simplifying assumptions,6 conclude that the government should take dollars away from rich people and give them to poor people.7 Declining marginal utility is thus a key assump- tion underlying the welfarist approach to tax law.

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