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So if you want to maximize the sum of utilities you have to
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such that X^a+X^b =84
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which is the sum of 4 and 80
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and Y^ Y^ = 6,000.
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So the claim is that if all these two million people meet in
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a room like this and start shouting at each other,
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and trading and offering deals and stuff,
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it's going to come down to a final allocation which we've
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written over there were A gets 77 of the first good and B gets
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7 of the first good, and that final allocation is
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going to maximize the sum of utilities.
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So why should that be the case?