We consider an economy with a fixed supply vector of goods and services and a number of consumers with linear utility functions and fixed budgets. Two main issues will be discussed.

First, we prove the existence of the equilibrium between the given supply and total demand. It means that there is such a unique vector of prices for goods and services that when each consumer maximize its utility function under the budget available the total demand is equals to the given supply.

Second, we will discuss the method for finding equilibrium. The method consists in maximizing utility functions at each step under fixed prices for goods and services and updating the prices using the current information about the given supply and obtained demand. The method can be interpreted as a pricing mechanism that guarantee convergence to the equilibrium.