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Income inequality is necessary for Pareto optimality so that people will work as hard as they can. If income is distributed equally, then there must

"Income inequality is necessary for Pareto optimality so that people will work as hard as they can." "If income is distributed equally, then there must be Pareto optimality because you can't make one person better off without making someone else worse off." Are these statements true or false? Why or why not?

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