ON THE EXISTENCE OF EQUILIBRIUM PRICE

The Debreu-Gale-Nikaido theorem [2] is a potential tool to prove the existence of a market equilibrium price. Walras' law is of a quantitative nature (i.e. it measures the value of the total excess demand), and it is interesting to note that the existence result holds true under some qualitative assumptions. In fact, the Debreu-Gale-Nikaido theorem states that the continuity of the excess demand function and Walras' law has the following implication : For some price and corresponding value of the excess demand function, it is not possible to respond with a new price system such that the value at the new price of every element in the value of the demand function associated with the old price system is strictly positive.