ECON 100B Lecture Notes - Lecture 16: Pareto Efficiency, Upper Set, Indifference Curve
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U a (x1, x2) = x1 + x2. U b (y1, y2) = y1 + 3y2. U a (x1, x2) = min {x1, x2} U b (y1, y2) = min {y1, 2y2} U a (x1, x2) = max {x1, x2} U b (y1, y2) = min {y1, 3y2} kink occurs when x2 = x1 kink occurs when 1/3y1 = y2. U a (a) u a (b) U b (a) u b (b) and one inequality is strict: an allocation is called efficient if there is no other allocation that is more efficient. a is efficient if for all b. U a (a) u a (b) and u b (a) u b (b) Or u a (a) > u a (b) and u b (b) > u b (a) Or u a (b) > u a (a) and u b (a) > u b (b) U a (b) > u a (a) & u b (b) > u b (a)
