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6. (bonus question, 15 points) To test for convex preferences, the following theorem is useful. Theorem. A twice-differentiable utility function U(X.X) represents convex preferences if

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6. (bonus question, 15 points) To test for convex preferences, the following theorem is useful. Theorem. A twice-differentiable utility function U(X.X) represents convex preferences if and only if (1) U U-2UUU+UU

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