Econophysics Beyond General Equilibrium: the Business Cycle Model

Abstract

Current business cycle theory is an application of the general equilibrium theory. This paper presents the business cycle model without using general equilibrium framework. We treat agents risk assessments as their coordinates x on economic space and establish distribution of all economic agents by their risk coordinates. We suggest aggregation of agents and their variables by scales large to compare with risk scales of single agents and small to compare with economic domain on economic space. Such model is alike to transition from kinetic description of multi-particle system to hydrodynamic approximation. Aggregates of agents extensive variables with risk coordinate x determine macro variables as functions of x alike to hydrodynamic variables. Economic and financial transactions between agents define evolution of their variables. Aggregation of transactions between agents with risk coordinates x and y determine macro transactions as functions of x and y and define evolution of macro variables at points x and y. We describe evolution and interactions between macro transactions by hydrodynamic-like system of economic equations. We show that business cycles are described as consequence of the system of economic equations on macro transactions. As example we describe Credit transactions CL(tax,y) that provide Loans from Creditors at point x to Borrowers at point y and Loan-Repayment transactions LR(t,x,y) that describe repayments from Borrowers at point y to Creditors at point x. We use hydrodynamic-like economic equations and derive from them the system of ordinary differential equations that describe business cycle fluctuations of macro Credits C(t) and macro Loan-Repayments LR(t) of the entire economics. The nature of business cycle fluctuations is explained as oscillations of "mean risk" of economic variables on bounded economic domain of economic space.