Tom's afternoon March 21 edits of intro lectures

Author: thomassargent30

lectures/money_inflation.md

@@ -978,7 +978,7 @@ The same qualitive outcomes prevail in this lecture {doc}`money_inflation_nonlin
 ```
 
 
-## Equilibrium selection criterion 
+## Equilibrium selection 
 
 We have discovered that as a model of price level paths or model is **incomplete** because there is a continuum of "equilibrium" paths for $\{m_{t+1}, p_t\}_{t=0}^\infty$ that are consistent with the demand for real balances always equaling the supply.
   

lectures/money_inflation_nonlinear.md

@@ -424,16 +424,12 @@ p0_bars = (p0_l, p0_u)
 draw_iterations(p0s, model, line_params, p0_bars, num_steps=20)
 ```
 
-REQUEST FOR HUMPRHEY: PLEASE MAKE A CAPTION BELOW THE ABOVE GRAPH THAT WE CAN REFER TO AS WE DO 
-THE LECTURE MONEY_INFLATION.MD
 
-IF WE ZOOM, I CAN EXPLAIN QUICKLY.
+Staring at the paths of price levels in  {numref}`p0_path_nonlin` reveals that almost all paths converge to the **higher** inflation tax rate displayed in the stationary state Laffer curve. displayed in figure  {numref}`laffer_curve_nonlinear`.  
 
-Staring at the paths of price levels in  {numref}`p0_path_nonlin` show indicate that almost all paths converge to the **higher** inflation tax rate displayed in the stationary state Laffer curve. %displayed in figure  {numref}`infl_tax`.  
+Thus, we have reconfirmed  what we have  called the "perverse" dynamics under rational expectations in which the system converges to the higher of two possible stationary inflation tax rates.
 
-Thus, we have indeed discovered what we earlier called "perverse" dynamics under rational expectations in which the system converges to the higher of two possible stationary inflation tax rates.
-
-Those dynamics are "perverse" not only in the sense that they imply that the monetary and fiscal authorities that have chosen to finance government expenditures eventually impose a higher inflation tax than required to finance government expenditures, but because of the following "counterintuitive" situation that we can deduce by staring at the stationary state Laffer curve displayed in figure  {numref}`infl_tax`:
+Those dynamics are "perverse" not only in the sense that they imply that the monetary and fiscal authorities that have chosen to finance government expenditures eventually impose a higher inflation tax than required to finance government expenditures, but because of the following "counterintuitive" situation that we can deduce by staring at the stationary state Laffer curve displayed in figure  {numref}`laffer_curve_nonlinear`:
 
 * the figure indicates that inflation can be **reduced** by running **higher**  government deficits, i.e., by raising more resources through  printing money. 
 
@@ -442,3 +438,15 @@ Those dynamics are "perverse" not only in the sense that they imply that the mon
 The same qualitive outcomes prevail in this lecture {doc}`money_inflation` that studies a linear version of the model in this lecture`.
 ```
 
+We discovered that 
+
+ * all but one of the equilibrium paths converge to limits in which the higher of two possible stationary inflation tax prevails
+ * there is a unique equilibrium path associated with "plausible" statements about how reductions in government deficits affect a stationary  inflation rate
+
+As in  this lecture {doc}`money_inflation`,
+on grounds of plausibility, we  again recommend  selecting the unique equilibrium that converges to the lower stationary inflation tax rate. 
+
+As we shall see, we  accepting  this recommendation is a key ingredient of outcomes of the "unpleasant arithmetic" that we describe in   lecture {doc}`unpleasant`.
+
+In lecture, {doc}`laffer_adaptive`, we shall explore how  {cite}`bruno1990seigniorage` and others justified our equilibrium selection in other ways.
+

lectures/unpleasant.md

@@ -50,13 +50,6 @@ In addition to learning about ''unpleasant monetarist arithmetic", in this lectu
 
 <!-- #region user_expressions=[] -->
 
-Let's start with some imports:
-
-```{code-cell} ipython3
-import numpy as np
-import matplotlib.pyplot as plt
-from collections import namedtuple
-```
 
 ## Setup
 
@@ -327,7 +320,16 @@ Since the public has less currency (it's supply has diminished) it is plausible
 
 But that is not the end of the story, because this ''open market operation'' at time $0$ has consequences for future settings of $m_{t+1}$ and the gross-of-interest government deficit $\bar g_t$. 
 
-Let's dive in and implement our ''pseudo code'' in Python.
+
+Let's start with some imports:
+
+```{code-cell} ipython3
+import numpy as np
+import matplotlib.pyplot as plt
+from collections import namedtuple
+```
+
+Now let's dive in and implement our ''pseudo code'' in Python.
 
 ```{code-cell} ipython3
 # Create a namedtuple that contains parameters