Use red ink to draw a rawlsian isowelfare line

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Use red ink to draw a Rawlsian isowelfare line through the Rawlsian maximum. Use blue ink to draw a Cobb-Douglas isowelfare line through the Cobb-Douglas maximum. 31.3 (2) A parent has two children named A and B and she loves both of them equally. She has a total of \$1,000 to give to them.

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386 WELFARE (Ch. 31) (a) The parent’s utility function is U ( a, b ) = a + b , where a is the amount of money she gives to A and b is the amount of money she gives to B. How will she choose to divide the money? a = b = \$500 . (b) Suppose that her utility function is U ( a, b ) = - 1 a - 1 b . How will she choose to divide the money? a = b = \$500 . (c) Suppose that her utility function is U ( a, b ) = log a + log b . How will she choose to divide the money? a = b = \$500 . (d) Suppose that her utility function is U ( a, b ) = min { a, b } . How will she choose to divide the money? a = b = \$500 . (e) Suppose that her utility function is U ( a, b ) = max { a, b } . How will she choose to divide the money? a = \$1 , 000 , b = 0 , or vice versa. (Hint: In each of the above cases, we notice that the parent’s problem is to maximize U ( a, b ) subject to the constraint that a + b = 1 , 000. This is just like the consumer problems we studied earlier. It must be that the parent sets her marginal rate of substitution between a and b equal to 1 since it costs the same to give money to each child.)
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• Social welfare function, Social Choice and Individual Values

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