At any price vector, the total value of aggregate excess demand is zero when consumers exhaust their budgets. After normalization to a price simplex, choosing a price that maximizes the value of a candidate excess-demand vector is a useful Kakutani fixed-point theorem construction.

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Walras's law is an economic theory that states that in a general equilibrium model, the sum of the values of excess demands across all markets must equal zero. In simpler terms, it asserts that if there is excess supply in one market, there must be excess demand in another market, such that the overall market isn't deficient.