fix some typos

Author: HumphreyYang

lectures/cagan_ree.md

@@ -50,7 +50,7 @@ In those experiments, we'll encounter an instance of a ''velocity dividend'' tha
 
 To facilitate using  linear matrix algebra as our main mathematical tool, we'll use a finite horizon version of the model.
 
-As in the {doc}`present values <pv>` and {doc}`consumption smoothing<cons_smooth>` lectures, the only linear algebra that we'll be  using are matrix multplication and matrix inversion.
+As in the {doc}`present values <pv>` and {doc}`consumption smoothing<cons_smooth>` lectures, the only linear algebra that we'll be  using are matrix multiplication and matrix inversion.
 
 
 ## Structure of the Model
@@ -593,7 +593,7 @@ By letting money jump according to equation {eq}`eq:eqnmoneyjump` the monetary a
 from **falling** at the moment that the unanticipated stabilization arrives.
 
 In various research papers about stabilizations of high inflations, the jump in the money supply described by equation {eq}`eq:eqnmoneyjump` has been called
-"the velocity dividend" that a government reaps from implementin a regime change that sustains a permanently lower inflation rate.
+"the velocity dividend" that a government reaps from implementing a regime change that sustains a permanently lower inflation rate.
 
 #### Technical Details about whether $p$ or $m$ jumps at $T_1$
 

lectures/cons_smooth.md

@@ -62,7 +62,7 @@ Our model has the following logical flow
 
  * verify that $a_{T+1}$ satisfies the terminal wealth constraint $a_{T+1} \geq 0$. 
 
-     * If it does, declare that the candiate path is budget feasible. 
+     * If it does, declare that the candidate path is budget feasible. 
 
      * if the candidate consumption path is not budget feasible, propose a path with less consumption sometimes and start over
 
@@ -400,7 +400,7 @@ $$
 v_t = \xi_1 \phi^t - \xi_0
 $$
 
-We say two and not three-parameter class because $\xi_0$ will be a function of $(\phi, \xi_1; R)$ that guarantees that the variation is feasibile. 
+We say two and not three-parameter class because $\xi_0$ will be a function of $(\phi, \xi_1; R)$ that guarantees that the variation is feasible. 
 
 Let's compute that function.
 

lectures/equalizing_difference.md

@@ -19,7 +19,7 @@ This notebook presents a model of the college-high-school wage gap in which the
 The model is "incomplete" in the sense that it is just one "condition" in the form of one 
 equation that would be part of set equations comprising all of the "equilibrium conditions" of   a more fully articulated model.
 
-The condition featured in our model determies  a college, high-school wage ratio that equalizes the
+The condition featured in our model determines  a college, high-school wage ratio that equalizes the
 present values of a high school worker and a college educated worker.
 
 It is just one instance of an  "equalizing difference" theory of relative wage rates, a class dating back at least to Adam Smith's **Wealth of Nations**.
@@ -33,7 +33,7 @@ Let
 
  * $R > 0$ be the gross rate of return on a one-period bond
 
- * $0$ denote the first  period after high school that a person can go to work
+ * $0$ denotes the first period after high school that a person can go to work
 
  * $T$ denote the last period a person can work
 
@@ -49,7 +49,7 @@ Let
 
 
 
-If someone goes to work immediately after high school  and  work for $T+1$ years, she earns present value
+If someone goes to work immediately after high school  and  works for $T+1$ years, she earns present value
 $$
 h_0 = \sum_{t=0}^T R^{-t} w_t^h = w_0^h \left[ \frac{1 - (R^{-1} \gamma_h)^{T+1} }{1 - R^{-1} \gamma_h } \right] \equiv w_0^h A_h 
 $$
@@ -113,7 +113,7 @@ $$
 ## Tweaked Model: Workers and Entrepreneurs
 
 
-We can add a parameter and reinterpret variables to get a model of entrepreuneurs versus workers.
+We can add a parameter and reinterpret variables to get a model of entrepreneurs versus workers.
 
 We now let $h$ be  the present value of a "worker".
 
@@ -128,7 +128,7 @@ where $\pi \in (0,1) $ is  the probability that an entrepreneur's "project" succ
 We set $D =0$.
 
 What we used to call the college, high school wage gap $\phi$ now becomes the ratio
-of a successful entreneur's earnings to a worker's earnings.  
+of a successful entrepreneur's earnings to a worker's earnings.  
 
 We'll find that as $\pi$ decreases, $\phi$ increases.