Fix minor typos

Author: HengchengZhang

lectures/intro_supply_demand.md

@@ -177,7 +177,7 @@ plt.show()
 
 Consumer surplus gives a measure of total consumer welfare at quantity $q$.
 
-The idea is that the inverse demand curve $d_0 - d_1 q$ shows willingness to
+The idea is that the inverse demand curve $d_0 - d_1 q$ shows willingness to 
 pay at a given quantity $q$.
 
 The difference between willingness to pay and the actual price is the surplus.
@@ -314,14 +314,13 @@ $$ (eq:old1)
 
 Let's remember the quantity $q$ given by equation {eq}`eq:old1` that a social planner would choose to maximize consumer surplus plus producer surplus.
 
-We'll compare it to the quantity that emerges in a competitive  equilibrium
-equilibrium that equates supply to demand.
+We'll compare it to the quantity that emerges in a competitive equilibrium that equates supply to demand.
 
 
 
 ### Competitive Equilibrium
 
-Instead of equating quantities supplied and demanded, we'll can accomplish the
+Instead of equating quantities supplied and demanded, we can accomplish the
 same thing by equating demand price to supply price:
 
 $$
@@ -353,7 +352,7 @@ It also brings a useful **competitive equilibrium computation strategy:**
 
 ## Generalizations
 
-In a {doc}`later lecture <supply_demand_multiple_goods>`,  we'll derive
+In a {doc}`later lecture <supply_demand_multiple_goods>`, we'll derive
 generalizations of the above demand and supply curves from other objects.
 
 Our generalizations will extend the preceding analysis of a market for a single good to the analysis of $n$ simultaneous markets in $n$ goods.
@@ -364,8 +363,7 @@ In addition
    **utility function** subject to a **budget constraint**.
 
  * we'll derive  **supply curves** from the problem of a producer who is price
-   taker and maximizes his profits minus total costs that are described by a
-   **cost function**.
+   taker and maximizes his profits minus total costs that are described by a **cost function**.
 
 ## Exercises
 
@@ -383,21 +381,18 @@ $$
 All parameters are positive, as before.
 
 
-
-
 ```{exercise}
 :label: isd_ex1
 
 Define a new `Market` class that holds the same parameter values as before by
-changes the `inverse_demand` and `inverse_supply` methods to
+changing the `inverse_demand` and `inverse_supply` methods to
 match these new definitions.
 
 Using the class, plot the inverse demand and supply curves $i_d$ and $i_s$
 
 ```
 
 
-
 ```{solution-start} isd_ex1
 :class: dropdown
 ```
@@ -428,7 +423,6 @@ Let's create an instance.
 market = Market()
 ```
 
-
 Here is a plot of inverse supply and demand.
 
 ```{code-cell} ipython3
@@ -451,16 +445,13 @@ ax.set_ylabel('price')
 plt.show()
 ```
 
-
 ```{solution-end}
 ```
 
 
-
 ```{exercise}
 :label: isd_ex2
 
-
 As before, consumer surplus at $q$ is the area under the demand curve minus
 price times quantity:
 
@@ -496,7 +487,6 @@ Plot welfare as a function of $q$.
 ```
 
 
-
 ```{solution-start} isd_ex2
 :class: dropdown
 ```
@@ -511,7 +501,6 @@ $$
 
 Here's a Python function that computes this value:
 
-
 ```{code-cell} ipython3
 def W(q, market):
     # Unpack
@@ -524,7 +513,6 @@ def W(q, market):
 
 The next figure plots welfare as a function of $q$.
 
-
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 ax.plot(q_vals, W(q_vals, market), label='welfare')
@@ -537,11 +525,9 @@ plt.show()
 ```
 
 
-
 ```{exercise}
 :label: isd_ex3
 
-
 Due to nonlinearities, the new welfare function is not easy to maximize with
 pencil and paper.
 
@@ -550,7 +536,6 @@ Maximize it using `scipy.optimize.minimize_scalar` instead.
 ```
 
 
-
 ```{solution-start} isd_ex3
 :class: dropdown
 ```
@@ -565,8 +550,6 @@ result = minimize_scalar(objective, bounds=(0, 10))
 print(result.message)
 ```
 
-
-
 ```{code-cell} ipython3
 maximizing_q = result.x
 print(f"{maximizing_q: .5f}")
@@ -576,7 +559,6 @@ print(f"{maximizing_q: .5f}")
 ```
 
 
-
 ```{exercise}
 :label: isd_ex4
 
@@ -601,12 +583,10 @@ price, in line with the first fundamental welfare theorem.
 ```
 
 
-
 ```{solution-start} isd_ex3
 :class: dropdown
 ```
 
-
 ```{code-cell} ipython3
 from scipy.optimize import newton
 
@@ -617,7 +597,5 @@ equilibrium_q = newton(excess_demand, 0.1)
 print(f"{equilibrium_q: .5f}")
 ```
 
-
 ```{solution-end}
 ```
-

lectures/supply_demand_multiple_goods.md

@@ -9,7 +9,7 @@ In this lecture, we study a setting with $n$ goods and $n$ corresponding prices.
 
 We shall describe two classic welfare theorems:
 
-* **first welfare theorem:** for a  given a distribution of wealth among consumers,  a competitive  equilibrium  allocation of goods solves a  social planning problem.
+* **first welfare theorem:** for a given distribution of wealth among consumers, a competitive  equilibrium  allocation of goods solves a  social planning problem.
 
 * **second welfare theorem:** An allocation of goods to consumers that solves a social planning problem can be supported by a competitive equilibrium with an appropriate initial distribution of  wealth.
 
@@ -174,7 +174,7 @@ Verify that setting  $\mu=2$ in {eq}`eq:old3` also implies that formula
 
 ## Digression: Marshallian and Hicksian Demand Curves
 
-Sometimes we'll use budget constraint {eq}`eq:old2` in situations in which a consumers's endowment vector $e$ is his **only** source of income.
+Sometimes we'll use budget constraint {eq}`eq:old2` in situations in which a consumer's endowment vector $e$ is his **only** source of income.
 
 Other times we'll instead assume that the consumer has another source of income (positive or negative) and write his budget constraint as
 
@@ -274,7 +274,7 @@ As an example, our consumer confronts **risk** meaning in particular that
 
   * there are two states of nature, $1$ and $2$.
 
-  * the consumer knows that probability that state $1$ occurs is $\lambda$.
+  * the consumer knows that the probability that state $1$ occurs is $\lambda$.
 
   * the consumer knows that the probability that state $2$ occurs is $(1-\lambda)$.
 
@@ -337,7 +337,7 @@ We can study how these things affect equilibrium prices and allocations.
 
 ## Economies with Endogenous Supplies of Goods
 
-Up to now we have described a pure exchange economy in which endowments of good are exogenous, meaning that they are taken as given from outside the model.
+Up to now we have described a pure exchange economy in which endowments of goods are exogenous, meaning that they are taken as given from outside the model.
 
 ### Supply Curve of a Competitive Firm