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Add remark admonition for money_inflation.md
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longye-tian committed Sep 13, 2024
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Expand Up @@ -385,13 +385,21 @@ m_t & = b_{t-1} p_t
\end{aligned}
$$ (eq:method1)
**Remark 1:** method 1 uses an indirect approach to computing an equilibrium by first computing an equilibrium $\{R_t, b_t\}_{t=0}^\infty$ sequence and then using it to back out an equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequence.
```{prf:remark}
:label: method_1
Method 1 uses an indirect approach to computing an equilibrium by first computing an equilibrium $\{R_t, b_t\}_{t=0}^\infty$ sequence and then using it to back out an equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequence.
```
**Remark 2:** notice that method 1 starts by picking an **initial condition** $R_0$ from a set $[\frac{\gamma_2}{\gamma_1}, R_u]$. Equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequences are not unique. There is actually a continuum of equilibria indexed by a choice of $R_0$ from the set $[\frac{\gamma_2}{\gamma_1}, R_u]$.
```{prf:remark}
:label: initial_condition
Notice that method 1 starts by picking an **initial condition** $R_0$ from a set $[\frac{\gamma_2}{\gamma_1}, R_u]$. Equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequences are not unique. There is actually a continuum of equilibria indexed by a choice of $R_0$ from the set $[\frac{\gamma_2}{\gamma_1}, R_u]$.
```
**Remark 3:** associated with each selection of $R_0$ there is a unique $p_0$ described by
```{prf:remark}
:label: unique_selection
Associated with each selection of $R_0$ there is a unique $p_0$ described by
equation {eq}`eq:p0fromR0`.
```
### Method 2
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