General Equilibrium in a Segmented Market Economy with Convex Transaction Cost: Existence, Efficiency, Commodity and Fiat Money

Abstract

This study derives the monetary structure of transactions, the use of commodity or fiat money, endogenously from transaction costs in a segmented market general equilibrium model. Market segmentation means there are separate budget constraints for each transaction: Budgets balance in each transaction separately. Transaction costs imply differing bid and ask (selling and buying) prices. The most liquid instruments are those with the lowest proportionate bid/ask spread in equilibrium. Existence of general equilibrium is demonstrated under conventional assumptions, including convexity of the transaction technology. The structure of payment for purchases in equilibrium results from market segmentation and transaction costs. If a lowest-transaction-cost commodity is available, it becomes the common medium of exchange, commodity money. General equilibrium may not be Pareto efficient, but if a zero-transaction-cost instrument is available as the common medium of exchange then the equilibrium allocation is Pareto efficient. Fiat money is characterized as an otherwise worthless government-issued instrument of low transaction cost acceptable in payment of required taxes. Fiat money equilibrium with positively valued fiat money can then be shown to exist.

Keywords: Commodity Money, Fiat Money, Quasi-Equilibrium, General Equilibrium, Transaction Cost

JEL Classification: C62, E40, E42