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02. Graphing min. utility functions

# 02. Graphing min. utility functions - Shomu Banerjee ECON...

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Shomu Banerjee ECON 201 Drawing Indifference Curves for “Min” Utility functions Suppose you’re given a utility function u ( x 1 , x 2 ) = min{ x 1 , 2 x 2 }, i.e., the minimum of the two values x 1 or 2 x 2 . Here is how one draws the indifference curves that correspond to this utility function. Pick a particular utility level for which you wish to draw the indifference curve, say, the utility level 4. Then all those ( x 1 , x 2 ) combinations that satisfy 4 = min{ x 1 , 2 x 2 } lie on the same indifference curve. To find these combinations, begin with a few combinations at random. If you pick the point (1, 1), the utility level is min{1, 2} = 1—in other words, this combination only yields a utility level of 1, not 4. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 x 1 x 2 8 (4, 4) (4, 3) (4, 2) u = 4 u = 1 (1, 1) Try (4, 4) instead. Then the utility level attained is u (4, 4) = min{4, 8} = 4, so this combination would certainly lie on the indifference curve for utility level 4. Try reducing the consumption of the second good: pick (4, 3). Then the utility level attained is u

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02. Graphing min. utility functions - Shomu Banerjee ECON...

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