# Effect of Savings on a Gas-Like Model Economy with Credit and Debt

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## Abstract

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## 1. Introduction

## 2. Microscopic and Geometric Models for a System of Saving Agents

## 3. Statistical Ensembles for Agents with Credit and Debt

## 4. Statistical Ensambles for Money, Credit and Debt with Saving Propensity

#### 4.1. Case 1: Money and Savings

#### 4.2. Case 2: Savings, Money, Credit and Debt

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Gamma distribution function for distribution of money Equation (3) for different values of the saving propensity $\lambda $. The green curve corresponds to $\lambda =0$, the saving factor increases as it tends to the blue, so the darker blue curve corresponds to $\lambda =0.9$.

**Figure 2.**Constriction surfaces Equation (5) for three agents with $M=1$, for different values of $b=1,3/4,1/4,1/28$, which correspond to a saving propensity of $\lambda =0,0.1,0.5,0.9$, respectively.

**Figure 3.**Plot of the ratio of economic temperature and the average money per agent as function of the saving propensity.

**Figure 4.**Plot of the ratio between the entropy and the number of agents (18) as a function of the temperature T and the parameter b, with ${V}_{y}=1$. The curves are presented for the values of $b=1$ (red), $3/4$ (purple), $1/4$ (blue), $1/28$ (cyan), which correspond to a saving propensity of $\lambda =0,\phantom{\rule{0.166667em}{0ex}}0.1,\phantom{\rule{0.166667em}{0ex}}0.5,$ and $0.9$, respectively.

**Figure 5.**Plot of the ratio between the entropy and the number of agents (25) as a function of the temperature T and the parameter b for $d=0.1,\phantom{\rule{0.166667em}{0ex}}0.5,\phantom{\rule{0.166667em}{0ex}}1$. We note a change in the behavior of S as d grows. Again, the curves are for $b=1$ (red), $3/4$ (purple), $1/4$ (blue), $1/28$ (cyan), and correspondingly $\lambda =0,\phantom{\rule{0.166667em}{0ex}}0.1,\phantom{\rule{0.166667em}{0ex}}0.5,$ and $0.9$.

**Figure 6.**Graphic of the ratio $\frac{T}{d}$ from Equation (27) as function of savings propensity $\lambda $ for unitary average money per agent. The values of $d=$ 0.05, 0.1, 0.2, 0.5, 1. The approximation fails for $T=d$, so the dashed branches of the graph have no interpretation in the model.

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**MDPI and ACS Style**

Chacón-Acosta, G.; Ángeles-Sánchez, V.
Effect of Savings on a Gas-Like Model Economy with Credit and Debt. *Entropy* **2021**, *23*, 196.
https://doi.org/10.3390/e23020196

**AMA Style**

Chacón-Acosta G, Ángeles-Sánchez V.
Effect of Savings on a Gas-Like Model Economy with Credit and Debt. *Entropy*. 2021; 23(2):196.
https://doi.org/10.3390/e23020196

**Chicago/Turabian Style**

Chacón-Acosta, Guillermo, and Vanessa Ángeles-Sánchez.
2021. "Effect of Savings on a Gas-Like Model Economy with Credit and Debt" *Entropy* 23, no. 2: 196.
https://doi.org/10.3390/e23020196