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And Walras said, "Well, it has to clear.
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The last market we don't need to worry about."
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Why is that?
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Because if X^(A) X^(B) = E^(A) E^(B) that means collectively
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all the agents are spending on good X exactly all the money
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that they're collectively getting by selling good X.
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That's what the top equation says because when you multiply
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through the whole thing by P_X the total amount
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people are spending on good X is equal to the total amount agents
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are getting by selling all the good X.
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So since everybody's spending all their money that must mean
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the rest of their money collectively is just all their