Application of Fixed Point Theorems : The Existence of General Equilibrium in a Market Economy

Usually in an economy with a finite amount of commodity markets, it reaches a general equilibrium only if and when at a given price set value, aggregate supply equals the aggregate demand within these individual markets. In this expository paper, we will take an algebraic topological approach – first starting with general definitions of terms. Later, we will use this approach to understand and prove a crucial tool in the Brouwer’s Fixed Point Theorem. Further, we will generalize this result into the Kakutani’s Fixed Point Theorem. Ultimately, we will be able to use this result to prove the existence of a general equilibrium in an economy