From 9b2c9b02a702011a9b9285aa93ceaed96d291db4 Mon Sep 17 00:00:00 2001 From: Longye Tian Date: Fri, 13 Sep 2024 17:58:25 +1000 Subject: [PATCH] remark_money_inflation Add remark admonition for money_inflation.md --- lectures/money_inflation.md | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/lectures/money_inflation.md b/lectures/money_inflation.md index 216a9a63..d7e37ecd 100644 --- a/lectures/money_inflation.md +++ b/lectures/money_inflation.md @@ -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