On general equilibrium and market failure

Published originally on Nov 20,2007


One of the most powerful assertions of neo-classical economics is that perfectly competitive markets always clear with no leftover surplus products, demands or cash balances.This is sometimes referred to as Walrasian general equilibrium or Walras's law which states that excess demands in the aggregate system of equations in the system are always equal to zero. ``Assume there are n goods in the economy:n-1 commodities and paper money....to these n goods correspond n excess demand equations...Only n-1 of these equations place independent restrictions on the unknown equilibrium prices. For any set of prices which satisfies n-1 market excess demand equations must also necessarily ,satisfy the nth. This is, ...an alternative statement of Walras' law.`` ( Don Patinkin, Money , interest and Prices:An Integration of Monetary and Value Theory, NY: Harper and Row, 1965, p.36-37) Given certain assumptions of perfect foresight and frictionless trading general equilibrium in the pure system is the outcome. In order to prove this mathematically in a multiproduct multimarket system economists have to resort to some esoteric mathematics using a theorem called Brouwer's fixed point theorem which is derived from a branch of mathematics known as topology. The theorem shows how points in n dimensional space can be associated with other points in this space. Most if not all of of this esoterica is unknown to the ideologues of laissez-faire who trumpet the virtues of markets and refuse to acknowledge the realities of less than perfect foresight , rigidities and uncertainties that prevail in the real world economy. Particularly never remarked upon is the fact that even if we have a a market of as small as `` 2 primary goods, 50 produced goods, 10,000 consumers and 2000 firms`` there are more than 600,000 individual excess demand functions that have to balanced off in practice to achieve equilibrium. (James Henderson& Richard Quandt,Microeconomic Theory: a Mathematical Approach, New York, McGraw-Hill,1971,p.190 ) Given the uncertainties, distortions and rigidities that empirically actually prevail in the far larger and more complex real marketplace of the national and global economies it is no wonder that general equilibrium ought to be viewed as a far off likely unattainable illusion in the short and even medium run. And as Keynes famously put it ``The long run is a misleading guide to current affairs.In the long run we are all dead`` (Tract on monetary reform, ch.3)