Suggestions by @longye-tian .
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Change bold non-definition words to italics (note: real balances are a definition).
I missed one comment on the structure of the overview (@longye-tian please feel free to fill in your comment)
Empirically testing the inflation rate Laffer curve.
$m_{t+1}^d/p_t =\gamma_1 - \gamma_2 \frac{p_{t+1}}{p_t}, \quad t \geq 0$ -> $\frac{m_{t+1}^d}{p_t} =\gamma_1 - \gamma_2 \frac{p_{t+1}}{p_t}, \quad t \geq 0$ where $\gamma_1$ and $\gamma_2$ are positive parameters.
Remove the repetition of definition of $b_t$ 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
Remove - if steady-state is a noun.
$\bar R < 1$ -> $\bar R \le 1$
$\bar R \in [\frac{\gamma2}{\gamma1}, 1]
\equiv [\underline R, \overline R]$ -> $\bar R \in [\frac{\gamma_2}{\gamma_1}, 1] \equiv [\underline R, \overline R]$
$R_t \in \bar R = [\underline R, \overline R], \quad t \geq 0$ -> $R_t \in [\underline R, \overline R], \quad t \geq 0$
two values of $R$ -> Two steady-state values of $R$
$R_l$ ->$R_\ell$
An equilibrium sequences are not unique -> equilibrium sequences are not unique
Remove the repetitive
$$\begin{aligned}
b_t & = b_{t-1} R_{t-1} + g \cr
R_t^{-1} & = \frac{\gamma_1}{\gamma_2} - \gamma_2^{-1} b_t
\end{aligned}$$
Suggestions by @longye-tian.
Code
solveto calculate the inverseContent
\equiv [\underline R, \overline R]$ ->
0 & {R_u}^{-1} \end{bmatrix}$