How Fixed-Amount Transactions and Liquidity Constraints Amplify Wealth Inequality: A Kinetic Model Deviating from the Maximum Entropy Benchmark
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917073180950528 |
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| author | Liuh, Jihyuan |
| author_facet | Liuh, Jihyuan |
| contents | This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum entropy principle, which predicts an exponential Boltzmann-Gibbs distribution with moderate inequality for unconstrained wealth exchange, we demonstrate that these realistic trading rules drive the system toward a highly unequal steady state. We develop a self-consistent mean-field theory, deriving a master equation where agent income follows a Poisson process coupled to the poverty rate. Numerical solution reveals a stationary distribution characterized by a substantial pauper class, high Gini coefficient, and exponential tail--significantly deviating from the maximum entropy benchmark. Agent-based simulations confirm these findings. We identify the poverty trap as the key mechanism: the liquidity constraint creates asymmetric economic agency, where zero-wealth agents become passive recipients, unable to participate in wealth circulation. This work establishes that substantial inequality can emerge spontaneously from equal-opportunity exchanges under basic economic constraints, without requiring agent heterogeneity or multiplicative advantage, providing a mechanistic foundation for understanding poverty as an emergent property of exchange rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How Fixed-Amount Transactions and Liquidity Constraints Amplify Wealth Inequality: A Kinetic Model Deviating from the Maximum Entropy Benchmark Liuh, Jihyuan Physics and Society General Economics Economics This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum entropy principle, which predicts an exponential Boltzmann-Gibbs distribution with moderate inequality for unconstrained wealth exchange, we demonstrate that these realistic trading rules drive the system toward a highly unequal steady state. We develop a self-consistent mean-field theory, deriving a master equation where agent income follows a Poisson process coupled to the poverty rate. Numerical solution reveals a stationary distribution characterized by a substantial pauper class, high Gini coefficient, and exponential tail--significantly deviating from the maximum entropy benchmark. Agent-based simulations confirm these findings. We identify the poverty trap as the key mechanism: the liquidity constraint creates asymmetric economic agency, where zero-wealth agents become passive recipients, unable to participate in wealth circulation. This work establishes that substantial inequality can emerge spontaneously from equal-opportunity exchanges under basic economic constraints, without requiring agent heterogeneity or multiplicative advantage, providing a mechanistic foundation for understanding poverty as an emergent property of exchange rules. |
| title | How Fixed-Amount Transactions and Liquidity Constraints Amplify Wealth Inequality: A Kinetic Model Deviating from the Maximum Entropy Benchmark |
| topic | Physics and Society General Economics Economics |
| url | https://arxiv.org/abs/2511.08202 |