通过范德瓦耳斯建模实现非线性经济状态平衡

Max-Olivier Hongler, Olivier Gallay, Fariba Hashemi
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引用次数: 0

摘要

著名的范德瓦耳斯(VDW)状态方程量化了等体积气体的压力 $P$、体积 $V$ 和温度 $k_{B}T$ 之间的平衡关系。我们根据经济背景赋予新的变量解释:$P \rightarrow Y$,代表价格;$V \rightarrow X$,代表需求;$k_{B}T \rightarrow \kappa$,代表收入,以描述经济状态的平衡。在这种重新解释下,需求的价格弹性(PED)和需求的收入弹性(YED)都是非恒定因素,并可能表现出尖顶--灾难类型的奇异性。在这一经济框架内,与 VDW 液体-气体相变相对应的是一种替代机制,即一种产品或服务被另一种替代品所取代。通过从交通(拼车)、医疗(非专利药与原研药)以及德国电力市场的经验数据等几个方面进行举例说明,定性和定量地讨论了这一重新解释的概念相关性。
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Nonlinear Economic State Equilibria via van der Waals Modeling
The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between pressure $P$, volume $V$ and temperature $k_{B}T$ of a real gas. We assign new variable interpretations adapted to the economic context: $P \rightarrow Y$, representing price; $V \rightarrow X$, representing demand; and $k_{B}T \rightarrow \kappa$, representing income, to describe an economic state equilibrium. With this reinterpretation, the price elasticity of demand (PED) and the income elasticity of demand (YED) are non-constant factors and may exhibit a singularity of the cusp-catastrophe type. Within this economic framework, the counterpart of VDW liquid-gas phase transition illustrates a substitution mechanism where one product or service is replaced by an alternative substitute. The conceptual relevance of this reinterpretation is discussed qualitatively and quantitatively via several illustrations ranging from transport (carpooling), medical context (generic versus original medication) and empirical data drawn from the electricity market in Germany.
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