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never mind hers, it goes off the page,
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his budget set he starts with this endowment.
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If the prices are given px and py,
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px and py define a linear tradeoff between X_i and Y_i,
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in this case j,
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because the more X you consume the less Y you have to consume
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and there's going to be a linear tradeoff between the two
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given by rearranging these terms.
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px and py are fixed,
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so this is just a linear equation in xi and yi,
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and so that tradeoff is given by that budget set.
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So mister pink is going to try, given his opportunities on this budget set,