It is known that the price mechanism whereby the rate of change of a price is proportional to the excess demand of the corresponding commodity need not converge to a competitive equilibrium for a pure exchange economy with more than two commodities. On the other hand, there exist convergent price mechanisms, similar to the Newton iterative process, where the rate of change of the prices is determined by the excess demand and the marginal excess demands of all the commodities. This is a considerable informational requirement. It is shown that this requirement cannot be substantially reduced for any convergent price mechanisms, that is for price mechanisms expressed in terms of a difference or differential equation where the solutions converge to a competitive equilibrium.