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    If you're given the utility functions of two different agents and are told to find the egalitarian allocation of 4 slices of cake, would you ensure they have the same amount of cake or ensure they have the same utility? I would make the two utility functions equal and say the total amount consumed should equal 4, but I'm not sure. Another part of the question asks if the egalitarian allocation is pareto efficient and I think by assuming earlier that total consumption is 4 i am assuming pareto efficiency which would make my answer circular.
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    Approached from pareto to egalitarian the situation is clearer. Pareto has no implications of fairness. It merely requires that one utility cannot be improved without impairment of another. Egalitarian requires that all utilities are equal, which is defined as fair.
    It may be possible to improve one utility without impairment of another but that would not then be egalitarian.
 
 
 
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