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4. Utility representation of preferences Consider an individual with a rational preference relation >, namely a preference relation that satisfies completeness and transitivity. Show that

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4. Utility representation of preferences Consider an individual with a rational preference relation >, namely a preference relation that satisfies completeness and transitivity. Show that if u(x) =u(y) implies x zy, and u(x) >u(y) implies x> y, then u(.) is a utility function that represents this individual's preference relation 2

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