A parent has two children living in cities with different costs of living.The cost of living in city B is 3 times the cost of living in city A.The child in city A has an income of $3,000 and the child in city B has an income of $9,000.The parent wants to give a total of $4,000 to her two children.Her utility function is U(C_A, C_B)  C_AC_B, where C_A and C_B are the consumptions of the children living in cities A and B respectively.She will choose to give

A) the child in city B 1.50 times as much money as the child in city A.
B) the child in city A 3 times as much money as the child in city B.
C) the child in city B 3 times as much money as the child in city A.
D) each child $2,000, even though this will buy less goods for the child in city B.
E) the child in city A 1.50 times as much money as the child in city B.

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Steve Farina · Accepted Answer

Final Answer : D, Explanation :  Given the utility function and the desire to distribute $4,000 between her two children, the parent aims to equalize the additional utility each child gets from the money. Since the cost of living in city B is 3 times that of city A, giving each child the same amount ($2,000) does not equalize their purchasing power but ensures each child receives the same nominal amount, which is a straightforward way to divide the total amount without adjusting for cost of living differences.

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