Aggregate excess demand ($z(p)={\sum }_i{x}_i(p,p\cdot {\omega }_i)-{\sum }_i{\omega }_i$)

Aggregate excess demand subtracts total endowment from the sum of consumers' demand correspondences. A market-clearing price satisfies $z(p)=0$. Under Walras law, one equation is redundant after price normalization.