Update money_inflation.md

longye-tian commented 1 month ago

Dear John @jstac ,

I have update lecture money_inflation.md according to #437. In particular, it involves,

Code

Change bold non-definition words to italics
$m_{t+1}^d/p_t =\gamma_1 - \gamma2 \frac{p{t+1}}{pt}, \quad t \geq 0$ -> $\frac{m{t+1}^d}{p_t} =\gamma_1 - \gamma2 \frac{p{t+1}}{p_t}, \quad t \geq 0$ where $\gamma_1$ and $\gamma_2$ are positive parameters.
Remove the repetition of definition of $bt$ and $R{t-1}$
Remove the $()$ in 26.6
Check capitalization for titles
gross rates of return on currency -> gross rates of return on currency and real balance
$\bar R < 1$ -> $\bar R \le 1$
$\bar R \in [\frac{\gamma2}{\gamma1}, 1] \equiv [\underline R, \overline R]$ -> $\bar R \in [\frac{\gamma_2}{\gamma_1}, 1] \equiv [\underline R, \overline R]$
$R_t \in \bar R = [\underline R, \overline R], \quad t \geq 0$ -> $R_t \in [\underline R, \overline R], \quad t \geq 0$
two values of $R$ -> Two steady-state values of $R$
$Rl$ ->$R\ell$
An equilibrium sequences are not unique -> equilibrium sequences are not unique

Remove the repetitive

$$\begin{aligned}
b_t & = b_{t-1} R_{t-1} + g \cr
R_t^{-1} & = \frac{\gamma_1}{\gamma_2} - \gamma_2^{-1} b_t
\end{aligned}$$

"code plot outcomes" -> "code plot to outcomes"
Set $ \Lambda= \begin{bmatrix} {R_l}^{-1} & 0 \cr 0 & {R_u}^{-1} \end{bmatrix}$
$Q y_0 = y^_0 = \begin{bmatrix} y^_{1,0} \cr 0 \end{bmatrix}$ -> $Q^{-1} y_0 = y^_0 = \begin{bmatrix} y^_{1,0} \cr 0 \end{bmatrix}$.

Best 👻 Longye

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