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Left, a utility function ; right, . The heights differ, but the indifference curve through is the same, and every pair of bundles is ranked the same way, as long as is increasing. Utility only orders bundles.
- Try other transformations: the indifference curves and do not move. With V = −U the ranking flips.
- Along the tangent line at , a quasi-concave is highest at (Theorem 1). Choose Bowed out to see it fail.