# Inflation and Speculation in a Dynamic Macroeconomic Model

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## Abstract

**:**

## 1. Introduction

## 2. The Keen Model

Households | Firms | Banks | Sum | ||
---|---|---|---|---|---|

Balance Sheet | |||||

Capital stock | $+pK$ | $+pK$ | |||

Deposits | ${D}_{h}$ | $+{D}_{f}$ | $-D$ | 0 | |

Loans | $-L$ | $+L$ | 0 | ||

Sum (net worth) | ${X}_{h}$ | ${X}_{f}$ | ${X}_{b}$ | X | |

Transactions | current | capital | |||

Consumption | $-p{C}_{h}$ | $+pC$ | $-p{C}_{b}$ | 0 | |

Investment | $+pI$ | $-pI$ | 0 | ||

Accounting memo [GDP] | [$pY$] | ||||

Wages | $+W$ | $-W$ | 0 | ||

Interest on deposits | $+{r}_{h}{D}_{h}$ | $+{r}_{f}{D}_{f}$ | $-{r}_{h}{D}_{h}-{r}_{f}{D}_{f}$ | 0 | |

Interest on loans | $-{r}_{L}L$ | $+{r}_{L}L$ | 0 | ||

Financial Balances | ${S}_{h}$ | Π | $-pI$ | ${S}_{b}$ | 0 |

Flow of Funds | |||||

Change in Capital Stock | $+pI$ | $+pI$ | |||

Change in Deposits | $+{\dot{D}}_{h}$ | $+{\dot{D}}_{f}$ | $-\dot{D}$ | 0 | |

Change in Loans | $-\dot{L}$ | $+\dot{L}$ | 0 | ||

Column sum | ${S}_{h}$ | Π | ${S}_{b}$ | $pI$ | |

Change in net worth | ${\dot{X}}_{h}={S}_{h}$ | ${\dot{X}}_{f}=\mathrm{\Pi}+(\dot{p}-\delta p)K$ | ${\dot{X}}_{b}={S}_{b}$ | $\dot{X}$ |

## 3. Keen Model with Inflation

#### 3.1. Specification and Equilibrium Points

#### 3.2. Local Stability Analysis

#### 3.2.1. Good Equilibrium

#### 3.2.2. Bad Equilibrium

#### 3.2.3. New Equilibria

## 4. Keen Model with Inflation and Speculation

#### 4.1. Assumptions and Equilibria

#### 4.2. Local Stability Analysis

#### 4.2.1. Equilibria with Finite Debt

#### 4.2.2. Equilibria with Infinite Debt and Finite Speculation

#### 4.2.3. Bad Equilibria with Infinite Debt and Infinite Speculation

## 5. Numerical Simulations and Qualitative Analysis

#### 5.1. Parameters, Equilibria and Stability

#### 5.1.1. Basic Keen Model

#### 5.1.2. Keen Model with Inflation

#### 5.1.3. Keen Model with Inflation and Speculation

#### 5.2. Dynamics and Behavior

#### 5.2.1. Keen Model with Inflation

#### 5.2.2. Keen Model with Inflation and Speculation

**Figure 5.**Sample trajectory of system (57) starting at $({\omega}_{0},{\lambda}_{0},{c}_{0},{f}_{0})=(0.75,0.90,0.05,-0.80)$ and modified parameters $({r}_{f},{\eta}_{p},\xi )=(0.02,0.4,1.21)$.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Grasselli, M.R.; Huu, A.N.
Inflation and Speculation in a Dynamic Macroeconomic Model. *J. Risk Financial Manag.* **2015**, *8*, 285-310.
https://doi.org/10.3390/jrfm8030285

**AMA Style**

Grasselli MR, Huu AN.
Inflation and Speculation in a Dynamic Macroeconomic Model. *Journal of Risk and Financial Management*. 2015; 8(3):285-310.
https://doi.org/10.3390/jrfm8030285

**Chicago/Turabian Style**

Grasselli, Matheus R., and Adrien Nguyen Huu.
2015. "Inflation and Speculation in a Dynamic Macroeconomic Model" *Journal of Risk and Financial Management* 8, no. 3: 285-310.
https://doi.org/10.3390/jrfm8030285