标题： 经济物理学超越一般均衡：商业周期模型 显示英文标题

标题： Econophysics Beyond General Equilibrium: the Business Cycle Model

摘要： 当前商业周期理论是一般均衡理论的应用。 本文提出了一个不使用一般均衡框架的商业周期模型。 我们将代理的风险评估视为他们在经济空间中的坐标x，并通过他们的风险坐标建立所有经济代理的分布。 我们建议按大尺度对代理及其变量进行聚合，以与单个代理的风险尺度进行比较，以及按小尺度对经济空间上的经济领域进行比较。 这种模型类似于从多粒子系统的动力学描述过渡到流体动力学近似。 具有风险坐标x的代理的广延变量决定了作为x函数的宏观变量，类似于流体动力学变量。 代理之间的经济和金融交易定义了它们变量的演变。 具有风险坐标x和y的代理之间的交易聚合决定了作为x和y函数的宏观交易，并定义了在点x和y处宏观变量的演变。 我们用类似流体动力学的经济方程描述宏观交易的演变和相互作用。 我们表明，商业周期是经济方程在宏观交易上的系统的结果。 作为例子，我们描述了信用交易CL(t,x,y)，它表示从经济空间中点x的债权人提供的贷款到点y的借款人，以及贷款偿还交易LR(t,x,y)，它描述了从点y的借款人到点x的债权人的偿还。 我们使用类似流体动力学的经济方程，并从中推导出描述整个经济的宏观信用C(t)和宏观贷款偿还LR(t)的商业周期波动的常微分方程组。 商业周期波动的本质被解释为经济空间上有限经济域内经济变量的“平均风险”的振荡。 显示英文摘要

摘要： 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.