Perspectives of an amateur economist
Bob Easton
Applied Mathematics
Politics and economics are knotted together in the daily news. I am trying to understand a little of both. Why do conservatives embrace "free markets". Is there a mathematical definition of a "market"? So far I have not found one. The Nobel prize winning economist Gerhard Debru gave a precise definition of an economy. His work forms a basis for many mathematical models which are used to "explain" prices and market behavior, and to inform policy decisions. I will try to explain the concept of general equilibrium in a market economy and its relationship to Pareto-optimal equilibria in pure exchange economies. Pareto-optimal means that no one can make a trade that increases their welfare without decreasing another person's. Thus no further "free" trades occur. Using the Brouwer fixed point theorem Debru showed there is a price system that supports each Pareto-optimal equilibria. I will discuss this result. It is my impression that economics is a very young science, and that opportunities for mathematicians to contribute to its development abound.