Finding Equilibrium in a Financial Model by Solving a Variational Inequality Problem

In this paper, a general multi-sector, multi-instrument model of financial flows and prices is developed, in which the utility function for each sector is assumed to be quadratic and constraints satisfy a certain accounting identity that appears in flow-of-funds accounts. Each sector uses conjectures of its influence upon the prices of instruments. The equilibrium conditions are first derived, and then the governing variational inequality is presented. Subsequently, a qualitative analysis of the model is conducted, and a concept of consistent conjectures is introduced and examined.