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so E^ is the endowment of X and E^ of Y.
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So that's the economy.
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You start from the economy and you go to equilibrium.
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And equilibrium is a price vector P_X
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P_Y and allocations X^,
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Y^, I in I, such that summation over all
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the I's of X^ equals the summation for all the I's of e^_x.
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So I's final consumption of X, plus j's final consumption of
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X, plus everybody else's final
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consumption of X, those are the sum of the
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X^'s, is equal to the sum of everybody's endowment.
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And similarly for the Y's,