General Economic Equilibrium with Financial Markets and Retainability

A theory of general economic equilibrium with incomplete financial markets is developed with many new features, including currency-denominated prices which enable treatment of currency-based derivative instruments and collateralized contracts. Prices in such models with standard market structure have previously been articulated only in “units of account” which have no link to an actual currency and are subject to indeterminancy in scaling. That shortcoming, which prevents ordinary price comparisons between different states, present and future, has stemmed from a focus on consumption as the sole source of economic value, but here retention of goods is allowed to influence their utility as well. The “goods” are not just commodities and thus can encompass other elements essential to finance. The framework is that of an economy operating in a currency agents find attractive to retain, in balance with other needs. The attractiveness comes from Keynesian considerations about uncertainty which until now have not been brought in. An altered view of time and states helps by loosening the grip of perfect foresight in future markets. Existence is established with a single currency denominating the units of account in all states, and price indeterminancy is thereby removed. All contracts issued in the financial markets can be interpreted then as “real contracts.” Endogenously generated transaction costs on sales of contracts keep the financial markets from getting out of hand and lead to bid-ask spreads, including a gap between interest rates for lending and borrowing money. To this end, equilibrium is given a variational formulation that brings fresh tools to the subject. A different way of proving existence in that setting, not merely in a generic sense and without normalizing to a price simplex or arbitrarily fixing “price levels” in the future states, makes use of duality bounds for the budget constraints. In the currency framework of the model, the proof of equilibrium is able moreover to proceed under far weaker assumptions than usual on the agents’ preferences and endowments.