diff --git a/lectures/money_inflation.md b/lectures/money_inflation.md index 2b3d1721..17ec7e0f 100644 --- a/lectures/money_inflation.md +++ b/lectures/money_inflation.md @@ -170,7 +170,7 @@ We shall describe two distinct but closely related ways of computing a pair $\ But first it is instructive to describe a special type of equilibrium known as a **steady state**. -In a steady state equilibrium, a subset of key variables remain constant or **invariant** over time, while remaining variables can be expressed as functions of those constant variables. +In a steady-state equilibrium, a subset of key variables remain constant or **invariant** over time, while remaining variables can be expressed as functions of those constant variables. Finding such state variables is something of an art. @@ -180,7 +180,7 @@ This is true in the present model. ### Steady states -In a **steady state** equilibrium of the model we are studying, +In a steady-state equilibrium of the model we are studying, $$ \begin{aligned} @@ -229,7 +229,7 @@ $$ R_t \in [\underline R, \overline R], \quad t \geq 0. $$ -Maximizing steady state seigniorage {eq}`eq:SSsigng` with respect to $\bar R$, we find that the maximizing rate of return on currency is +Maximizing steady-state seigniorage {eq}`eq:SSsigng` with respect to $\bar R$, we find that the maximizing rate of return on currency is $$ \bar R_{\rm max} = \sqrt{\frac{\gamma_2}{\gamma_1}} @@ -263,7 +263,7 @@ plt.rcParams['figure.dpi'] = 300 from collections import namedtuple ``` -Let's set some parameter values and compute possible steady state rates of return on currency $\bar R$, the seigniorage maximizing rate of return on currency, and an object that we'll discuss later, namely, an initial price level $p_0$ associated with the maximum steady state rate of return on currency. +Let's set some parameter values and compute possible steady-state rates of return on currency $\bar R$, the seigniorage maximizing rate of return on currency, and an object that we'll discuss later, namely, an initial price level $p_0$ associated with the maximum steady-state rate of return on currency. First, we create a `namedtuple` to store parameters so that we can reuse this `namedtuple` in our functions throughout this lecture @@ -337,7 +337,7 @@ plt.show() Let's print the two steady-state rates of return $\bar R$ and the associated seigniorage revenues that the government collects. -(By construction, both steady state rates of return should raise the same amounts real revenue.) +(By construction, both steady-state rates of return should raise the same amounts real revenue.) We hope that the following code will confirm this. @@ -349,7 +349,7 @@ g2 = seign(msm.R_l, msm) print(f'R_l, g_l = {msm.R_l:.4f}, {g2:.4f}') ``` -Now let's compute the maximum steady state amount of seigniorage that could be gathered by printing money and the state state rate of return on money that attains it. +Now let's compute the maximum steady-state amount of seigniorage that could be gathered by printing money and the state state rate of return on money that attains it. ## Two computation strategies @@ -434,7 +434,7 @@ As we shall see soon, selecting an initial $p_0$ in method 2 is intimately tied %b_0 = \gamma_1 - \gamma_0 R_0^{-1} %$$ -Remember that there exist two steady state equilibrium values $ R_\ell < R_u$ of the rate of return on currency $R_t$. +Remember that there exist two steady-state equilibrium values $ R_\ell < R_u$ of the rate of return on currency $R_t$. We proceed as follows. @@ -460,7 +460,7 @@ condition $R_0$. The quantity $1 - R_t$ can be interpreted as an **inflation tax rate** that the government imposes on holders of its currency. -We shall soon see that the existence of two steady state rates of return on currency +We shall soon see that the existence of two steady-state rates of return on currency that serve to finance the government deficit of $g$ indicates the presence of a **Laffer curve** in the inflation tax rate. ```{note} @@ -746,7 +746,7 @@ y^*_{t+1} = \Lambda^t y^*_t . $$ (eq:stardynamics) This equation represents the dynamics of our system in a way that lets us isolate the -force that causes gross inflation to converge to the inverse of the lower steady state rate +force that causes gross inflation to converge to the inverse of the lower steady-state rate of inflation $R_\ell$ that we discovered earlier. Staring at equation {eq}`eq:stardynamics` indicates that unless