You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: lectures/business_cycle.md
+8-8Lines changed: 8 additions & 8 deletions
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -15,11 +15,11 @@ kernelspec:
15
15
16
16
## Overview
17
17
18
-
This lecture is about illustrateing business cycles in different countries and period.
18
+
This lecture is about illustrating business cycles in different countries and period.
19
19
20
20
The business cycle refers to the fluctuations in economic activity over time. These fluctuations can be observed in the form of expansions, contractions, recessions, and recoveries in the economy.
21
21
22
-
In this lecture, we will see expensions and contractions of economies from 1960s to the recent pandemic using [World Bank API](https://documents.worldbank.org/en/publication/documents-reports/api).
22
+
In this lecture, we will see expansions and contractions of economies from 1960s to the recent pandemic using [World Bank API](https://documents.worldbank.org/en/publication/documents-reports/api).
23
23
24
24
In addition to what's in Anaconda, this lecture will need the following libraries to get World bank data
25
25
@@ -49,7 +49,7 @@ So let's explore how to query data together.
49
49
50
50
We can use `wb.series.info` with parameter `q` to query available data from the World Bank (`imfpy. searches.database_codes()` in `imfpy`)
51
51
52
-
For example, GDP growth is a key indicator to show the expension and contraction of level of economic activities.
52
+
For example, GDP growth is a key indicator to show the expansion and contraction of level of economic activities.
53
53
54
54
Let's retrive GDP growth data together
55
55
@@ -97,7 +97,7 @@ wb.series.info(q='consumption')
97
97
wb.series.info(q='capital account') # TODO: Check if it is to be plotted
Copy file name to clipboardExpand all lines: lectures/long_run_growth.md
+2-2Lines changed: 2 additions & 2 deletions
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -148,8 +148,8 @@ ax.set_ylabel("GDP per capita (current US$) ")
148
148
149
149
### Plot for lower middle income and low income
150
150
151
-
Finally, we compare time-series graphs of GDP per capita between a lower middle income country and a low income country. Again, keeping Pakistan fixed in our set as a lower middle income country, we choose Democratic Republic of Congo as our second country from a low income group. Congo is chosen for no particular reason apart from its unstable political atmoshpere and a dwindling economy.
152
-
On comapring we see quite a bit of difference between these countries. With Pakistan's GDP per capita being almost four times as much. Further strengthning our assumption that countries from different income groups can be quite different.
151
+
Finally, we compare time-series graphs of GDP per capita between a lower middle income country and a low income country. Again, keeping Pakistan fixed in our set as a lower middle income country, we choose Democratic Republic of Congo as our second country from a low income group. Congo is chosen for no particular reason apart from its unstable political atmosphere and a dwindling economy.
152
+
On comparing we see quite a bit of difference between these countries. With Pakistan's GDP per capita being almost four times as much. Further strengthening our assumption that countries from different income groups can be quite different.
Copy file name to clipboardExpand all lines: lectures/lp_intro.md
+1-1Lines changed: 1 addition & 1 deletion
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -412,7 +412,7 @@ By deploying the following steps, any linear programming problem can be transfor
412
412
413
413
1. **Objective Function:** If a problem is originally a constrained **maximization** problem, we can construct a new objective function that is the additive inverse of the original objective function. The transformed problem is then a **minimization** problem.
414
414
415
-
2. **Decision Variables:** Given a variable $x_j$ satisfying $x_j \le 0$, we can introduce a new variable $x_j' = - x_j$ and subsitute it into original problem. Given a free variable $x_i$ with no restriction on its sign, we can introduce two new variables $x_j^+$ and $x_j^-$ satisfying $x_j^+, x_j^- \ge 0$ and replace $x_j$ by $x_j^+ - x_j^-$.
415
+
2. **Decision Variables:** Given a variable $x_j$ satisfying $x_j \le 0$, we can introduce a new variable $x_j' = - x_j$ and substitute it into original problem. Given a free variable $x_i$ with no restriction on its sign, we can introduce two new variables $x_j^+$ and $x_j^-$ satisfying $x_j^+, x_j^- \ge 0$ and replace $x_j$ by $x_j^+ - x_j^-$.
416
416
417
417
3. **Inequality constraints:** Given an inequality constraint $\sum_{j=1}^n a_{ij}x_j \le 0$, we can introduce a new variable $s_i$, called a **slack variable** that satisfies $s_i \ge 0$ and replace the original constraint by $\sum_{j=1}^n a_{ij}x_j + s_i = 0$.
0 commit comments