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Charles' utility function is U(x;y)=xy. Anne's utility function is U(x;y)=1000xy. Diana's utility function is -xy. Elizabeth's utility function is U(x; y)=-1/(xy+1).Fergie' s utility function is xy-10000. Margaret's utility function is x/y. Philip's utility function is x(y + 1). (the goods x and y are two very expensive goods. We leave you to speculate about what they are.) Which of these persons have the same preferences as Charles?

I tried this question and found that the MUx/MUy is the same for Charles,Anne, Diana,Elizabeth, Fergies and Margaret.Yet the answer says only Anne,Fergie and Elizabeth have same preferences. I don't understand how. Also,how can we show that which, of the functions are MONOTONIC TRANFORMATIONS of Charles. I am sooooo confused :( What is the meaning of Same Preferences? (concave, convex etc)

gul
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1 Answers1

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You are only checking whether the utility functions generate the same indifference curves. This is necessary, but not sufficient: you should also check whether preferences are increasing or decreasing in $x$ and in $y$.

For Charles, Anne, Fergie and Elizabeth, utility increases in the northwest direction (increasing in $x$ and in $y$). For Diana, utility increases in the southeast direction (decreasing in $x$ and in $y$). For Margaret, utility increases in the southwest direction (increasing in $x$ and decreasing in $y$).

Note: you can find a more detailed discussion on https://economics.stackexchange.com/questions/5237/indifference-curves-and-preferences

mlc
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