Merge pull request #241 from QuantEcon/in_line_with_manual

In line with manual

README.md

@@ -2,7 +2,7 @@
 
 An undergraduate lecture series for the foundations of computational economics
 
-## Content Ideas 
+## Content ideas 
 
 Content ideas in no particular order.
 

lectures/_static/lecture_specific/graphviz/graphviz_generation.ipynb

@@ -54,7 +54,7 @@
    "id": "75d07327-0fcc-41f1-8d36-b8b8d4eb1060",
    "metadata": {},
    "source": [
-    "## Lake Model"
+    "## Lake model"
    ]
   },
   {
@@ -101,7 +101,7 @@
    "id": "194ca10b-dd02-4210-adbc-c2bb8b699d45",
    "metadata": {},
    "source": [
-    "## Markov Chains I\n",
+    "## Markov chains I\n",
     "\n",
     "### Example 1\n",
     "\n",
@@ -202,7 +202,7 @@
    "id": "360e6241-2bdc-425e-903a-dab3c5ef0485",
    "metadata": {},
    "source": [
-    "## Markov Chains II\n",
+    "## Markov chains II\n",
     "\n",
     "### Irreducibility"
    ]
@@ -330,7 +330,7 @@
    "id": "5df3cbb7-f540-4375-8448-c2aaa5526d56",
    "metadata": {},
    "source": [
-    "### Markov Chains"
+    "### Markov chains"
    ]
   },
   {
@@ -375,7 +375,7 @@
    "id": "395fa1f8-6e8d-4ac5-bc71-f34b0b9c1e9c",
    "metadata": {},
    "source": [
-    "### Poverty Trap"
+    "### Poverty trap"
    ]
   },
   {
@@ -456,7 +456,7 @@
    "id": "b43e5057-94eb-45e4-80e5-9f85a3c8be52",
    "metadata": {},
    "source": [
-    "### Weighted Directed Graph"
+    "### Weighted directed graph"
    ]
   },
   {

lectures/cagan_ree.md

@@ -595,7 +595,7 @@ 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 implementing a regime change that sustains a permanently lower inflation rate.
 
-#### Technical Details about whether $p$ or $m$ jumps at $T_1$
+#### Technical details about whether $p$ or $m$ jumps at $T_1$
 
 We have noted that  with a constant expected forward sequence $\mu_s = \bar \mu$ for $s\geq t$, $\pi_{t} =\bar{\mu}$.
 

lectures/cobweb.md

@@ -92,7 +92,7 @@ plt.show()
 
 
 
-## The Model
+## The model
 
 Let's return to our discussion of a hypothetical soy bean market, where price is determined by supply and demand.
 
@@ -196,7 +196,7 @@ Combining the last two equations gives the dynamics for prices:
 The price dynamics depend on the parameter values and also on the function $f$ that determines how producers form expectations.
 
 
-## Naive Expectations
+## Naive expectations
 
 To go further in our analysis we need to specify the function $f$; that is, how expectations are formed.
 
@@ -392,7 +392,7 @@ For example,
 ts_plot_price(m, 10, ts_length=15)
 ```
 
-## Adaptive Expectations
+## Adaptive expectations
 
 Naive expectations are quite simple and also important in driving the cycle that we found.
 

lectures/commod_price.md

@@ -103,7 +103,7 @@ from scipy.stats import beta
 ```
 
 
-## The Model
+## The model
 
 Consider a market for a single commodity, whose price is given at $t$ by
 $p_t$.

lectures/cons_smooth.md

@@ -13,7 +13,7 @@ kernelspec:
 
 +++ {"user_expressions": []}
 
-# Consumption smoothing
+# Consumption Smoothing
 
 ## Overview
 

lectures/eigen_II.md

@@ -146,7 +146,7 @@ We can then take transpose to obtain $A^\top w = \lambda w$ and obtain $w^\top A
 This is a more common expression and where the name left eigenvectors originates.
 
 (perron-frobe)=
-### The Perron-Frobenius Theorem
+### The Perron-Frobenius theorem
 
 For a square nonnegative matrix $A$, the behavior of $A^k$ as $k \to \infty$ is controlled by the eigenvalue with the largest
 absolute value, often called the **dominant eigenvalue**.
@@ -478,7 +478,7 @@ $$
 $$
 ```
 
-We can see the Neumann series lemma in action in the following example.
+We can see the Neumann Series Lemma in action in the following example.
 
 ```{code-cell} ipython3
 A = np.array([[0.4, 0.1],
@@ -492,7 +492,7 @@ print(r)
 
 The spectral radius $r(A)$ obtained is less than 1.
 
-Thus, we can apply the Neumann Series lemma to find $(I-A)^{-1}$.
+Thus, we can apply the Neumann Series Lemma to find $(I-A)^{-1}$.
 
 ```{code-cell} ipython3
 I = np.identity(2)      #2 x 2 identity matrix
@@ -518,7 +518,7 @@ np.allclose(A_sum, B_inverse)
 ```
 
 Although we truncate the infinite sum at $k = 50$, both methods give us the same
-result which illustrates the result of the Neumann Series lemma.
+result which illustrates the result of the Neumann Series Lemma.
 
 ## Exercises
 
@@ -583,7 +583,7 @@ The solution $x^{*}$ is given by the equation $x^{*} = (I-A)^{-1} d$
 
 1. Since $A$ is a nonnegative irreducible matrix, find the Perron-Frobenius eigenvalue of $A$.
 
-2. Use the Neumann Series lemma to find the solution $x^{*}$ if it exists.
+2. Use the Neumann Series Lemma to find the solution $x^{*}$ if it exists.
 
 ```{exercise-end}
 ```
@@ -603,7 +603,7 @@ r = max(abs(λ) for λ in evals)   #dominant eigenvalue/spectral radius
 print(r)
 ```
 
-Since we have $r(A) < 1$ we can thus find the solution using the Neumann Series lemma.
+Since we have $r(A) < 1$ we can thus find the solution using the Neumann Series Lemma.
 
 ```{code-cell} ipython3
 I = np.identity(3)

lectures/equalizing_difference.md

@@ -111,7 +111,7 @@ $$
 $$
 
 
-## Tweaked Model: Workers and Entrepreneurs
+## Tweaked model: workers and entrepreneurs
 
 
 We can add a parameter and reinterpret variables to get a model of entrepreneurs versus workers.

lectures/geom_series.md

@@ -61,7 +61,7 @@ from matplotlib import cm
 from mpl_toolkits.mplot3d import Axes3D
 ```
 
-## Key Formulas
+## Key formulas
 
 To start, let $c$ be a real number that lies strictly between
 $-1$ and $1$.
@@ -73,7 +73,7 @@ $-1$ and $1$.
 
 We want to evaluate geometric series of two types -- infinite and finite.
 
-### Infinite Geometric Series
+### Infinite geometric series
 
 The first type of geometric that interests us is the infinite series
 
@@ -95,7 +95,7 @@ To prove key formula {eq}`infinite`, multiply both sides  by $(1-c)$ and verify
 that if $c \in (-1,1)$, then the outcome is the
 equation $1 = 1$.
 
-### Finite Geometric Series
+### Finite geometric series
 
 The second series that interests us is the finite geometric series
 
@@ -148,7 +148,7 @@ money (i.e., deposits) in a fractional reserve system.
 The geometric series formula {eq}`infinite` is at the heart of the classic model of the money creation process -- one that leads us to the celebrated
 **money multiplier**.
 
-### A Simple Model
+### A simple model
 
 There is a set of banks named $i = 0, 1, 2, \ldots$.
 
@@ -254,7 +254,7 @@ $i=0, 1, 2, \ldots$ is
 \sum_{i=0}^\infty (1-r)^i D_0 =  \frac{D_0}{1 - (1-r)} = \frac{D_0}{r}
 ```
 
-### Money Multiplier
+### Money multiplier
 
 The **money multiplier** is a number that tells the multiplicative
 factor by which an exogenous injection of cash into bank $0$ leads
@@ -280,7 +280,7 @@ circumstances in which
   equal demand** (e.g., prices and interest rates are frozen)
 - national income is entirely determined by aggregate demand
 
-### Static Version
+### Static version
 
 An elementary Keynesian model of national income determination consists
 of three equations that describe aggregate demand for $y$ and its
@@ -342,7 +342,7 @@ The expression $\sum_{t=0}^\infty b^t$ motivates an interpretation
 of the multiplier as the outcome of a dynamic process that we describe
 next.
 
-### Dynamic Version
+### Dynamic version
 
 We arrive at a dynamic version by interpreting the nonnegative integer
 $t$ as indexing time and changing our specification of the
@@ -543,7 +543,7 @@ It follows that
 So if someone has a claim on $x$ dollars at time $t+j$, it
 is worth $x R^{-j}$ dollars at time $t$ (e.g., today).
 
-### Application to Asset Pricing
+### Application to asset pricing
 
 A **lease** requires a payments stream of $x_t$ dollars at
 times $t = 0, 1, 2, \ldots$ where
@@ -855,7 +855,7 @@ so $\frac{\partial p_0}{\partial r}$ will always be negative.
 Similarly, $\frac{\partial p_0}{\partial g}>0$ as long as $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, so $\frac{\partial p_0}{\partial g}$
 will always be positive.
 
-## Back to the Keynesian Multiplier
+## Back to the Keynesian multiplier
 
 We will now go back to the case of the Keynesian multiplier and plot the
 time path of $y_t$, given that consumption is a constant fraction

lectures/inequality.md

@@ -21,7 +21,7 @@ In this section we
 * provide motivation for the techniques deployed in the lecture and
 * import code libraries needed for our work.
 
-### Some History
+### Some history
 
 Many historians argue that inequality played a key role in the fall of the
 Roman republic.
@@ -82,7 +82,7 @@ import random as rd
 from interpolation import interp
 ```
 
-## The Lorenz Curve
+## The Lorenz curve
 
 One popular measure of inequality is the Lorenz curve.
 
@@ -126,7 +126,7 @@ income, consumption, etc.
 
 +++
 
-### Lorenz Curves of Simulated Data
+### Lorenz curves of simulated data
 
 Let's look at some examples and try to build understanding.
 
@@ -168,7 +168,7 @@ ax.set_xlim((0, 1))
 plt.show()
 ```
 
-### Lorenz Curves for US Data
+### Lorenz curves for US data
 
 Next let's look at the real data, focusing on income and wealth in the US in
 2016.
@@ -265,7 +265,7 @@ more extreme than income inequality.
 
 +++
 
-## The Gini Coefficient
+## The Gini coefficient
 
 The Lorenz curve is a useful visual representation of inequality in a
 distribution.
@@ -332,7 +332,7 @@ ax.text(0.04, 0.5, r'$G = 2 \times$ shaded area', fontsize=12)
 plt.show()
 ```
 
-### Gini Coefficient Dynamics of Simulated Data
+### Gini coefficient dynamics of simulated data
 
 Let's examine the Gini coefficient in some simulations.
 
@@ -399,7 +399,7 @@ coefficient.
 
 +++
 
-### Gini Coefficient Dynamics for US Data
+### Gini coefficient dynamics for US data
 
 Now let's look at Gini coefficients for US data derived from the SCF.
 
@@ -503,7 +503,7 @@ substantially since 1980.
 The wealth time series exhibits a strong U-shape.
 
 
-## Top Shares
+## Top shares
 
 Another popular measure of inequality is the top shares.
 

lectures/input_output.md

@@ -489,7 +489,7 @@ plt.show()
 
 +++ {"user_expressions": []}
 
-## Leontief Inverse
+## Leontief inverse
 
 We have discussed that gross ouput $x$ is given by {eq}`eq:inout_2`, where $L$ is called the Leontief Inverse.
 
@@ -515,7 +515,7 @@ $$
 
 This illustrates that an element $l_{ij}$ of $L$ shows the total impact on sector $i$ of a unit change in demand of good $j$.
 
-## Applications of Graph Theory
+## Applications of graph theory
 
 We can further study input output networks through applications of {doc}`graph theory <networks>`.
 

lectures/intro_supply_demand.md

@@ -55,7 +55,7 @@ import matplotlib.pyplot as plt
 ```
 
 
-## Supply and Demand
+## Supply and demand
 
 We study a market for a single good in which buyers and sellers exchange a quantity $q$ for a price $p$.
 
@@ -130,7 +130,7 @@ plt.show()
 
 
 
-### Consumer Surplus
+### Consumer surplus
 
 Let a quantity $q$ be given and let $p := d_0 - d_1 q$ be the
 corresponding price on the inverse demand curve.
@@ -195,7 +195,7 @@ $$
 
 
 
-### Producer Surplus
+### Producer surplus
 
 Let a quantity $q$ be given and let $p := s_0 + s_1 q$ be the
 corresponding price on the inverse supply curve.
@@ -256,7 +256,7 @@ $$
 $$
 
 
-### Social Welfare
+### Social welfare
 
 Sometimes economists measure social welfare by a **welfare criterion** that
 equals consumer surplus plus producer surplus, assuming that consumers and
@@ -318,7 +318,7 @@ We'll compare it to the quantity that emerges in a competitive equilibrium that
 
 
 
-### Competitive Equilibrium
+### Competitive equilibrium
 
 Instead of equating quantities supplied and demanded, we can accomplish the
 same thing by equating demand price to supply price: