From d3f3452fb4c0889e2af17c080d2cdc3cfe64a315 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 22 Jul 2024 13:21:58 +1000
Subject: [PATCH 01/17] [geom_series] Add an exercise

---
 lectures/geom_series.md | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 7a7d4c9d..09412785 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -856,12 +856,21 @@ 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
+## Exercise
 
-We will now go back to the case of the Keynesian multiplier and plot the
+```{exercise}
+:label: solow_ex1
+
+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
 of national income, and investment is fixed.
 
+```
+
+```{solution-start} solow_ex1
+:class: dropdown
+```
+
 ```{code-cell} ipython3
 ---
 mystnb:
@@ -959,3 +968,6 @@ plt.show()
 Notice here, whether government spending increases from 0.3 to 0.4 or
 investment increases from 0.3 to 0.4, the shifts in the graphs are
 identical.
+
+```{solution-end}
+```
\ No newline at end of file

From 3dd66486e0cc38582a783728724a0c7e3a0087d6 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 22 Jul 2024 14:25:38 +1000
Subject: [PATCH 02/17] Update the code

---
 lectures/geom_series.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 09412785..1f202ee5 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -860,11 +860,12 @@ will always be positive.
 
 ```{exercise}
 :label: solow_ex1
-
+```
 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
 of national income, and investment is fixed.
 
+```{exercise-end}
 ```
 
 ```{solution-start} solow_ex1

From 7de56eb1eff02d85998bbe4679e8b30512837dd7 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 22 Jul 2024 14:37:04 +1000
Subject: [PATCH 03/17] Update geom_series.md

---
 lectures/geom_series.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 1f202ee5..c6a5e3a3 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -858,8 +858,8 @@ will always be positive.
 
 ## Exercise
 
-```{exercise}
-:label: solow_ex1
+```{exercise-start}
+:label: geom_ex1
 ```
 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
@@ -868,7 +868,7 @@ of national income, and investment is fixed.
 ```{exercise-end}
 ```
 
-```{solution-start} solow_ex1
+```{solution-start} geom_ex1
 :class: dropdown
 ```
 

From f4343251fe2f8da7ba907314384510ef381c9881 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 22 Jul 2024 16:33:40 +1000
Subject: [PATCH 04/17] Update geom_series.md

---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index c6a5e3a3..6165a87b 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -856,7 +856,7 @@ 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.
 
-## Exercise
+## Exercises
 
 ```{exercise-start}
 :label: geom_ex1

From e121412e88b6d7f7c09be687f6bcfe2db7fb9705 Mon Sep 17 00:00:00 2001
From: shlff <shu.hu@anu.edu.au>
Date: Tue, 23 Jul 2024 17:15:57 +1000
Subject: [PATCH 05/17] split_exercises

---
 lectures/geom_series.md | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 1bbd4c14..cfc2b91a 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -900,10 +900,23 @@ plt.show()
 In this model, income grows over time, until it gradually converges to
 the infinite geometric series sum of income.
 
+```{solution-end}
+```
+
+```{exercise-start}
+:label: geom_ex2
+```
 We now examine what will
 happen if we vary the so-called **marginal propensity to consume**,
 i.e., the fraction of income that is consumed
 
+```{exercise-end}
+```
+
+```{solution-start} geom_ex2
+:class: dropdown
+```
+
 ```{code-cell} ipython3
 ---
 mystnb:
@@ -927,7 +940,20 @@ plt.show()
 Increasing the marginal propensity to consume $b$ increases the
 path of output over time.
 
+```{solution-end}
+```
+
+
+```{exercise-start}
+:label: geom_ex3
+```
 Now we will compare the effects on output of increases in investment and government spending.
+```{exercise-end}
+```
+
+```{solution-start} geom_ex3
+:class: dropdown
+```
 
 ```{code-cell} ipython3
 ---

From 7e791a7da78092571a3af5dd6ced751c908d07fa Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Tue, 23 Jul 2024 21:49:22 +1000
Subject: [PATCH 06/17] Update geom_series.md

---
 lectures/geom_series.md | 40 ++++++++++++++++++++++++++++++++++------
 1 file changed, 34 insertions(+), 6 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index cfc2b91a..b71188c1 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -854,9 +854,19 @@ will always be positive.
 ```{exercise-start}
 :label: geom_ex1
 ```
-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
-of national income, and investment is fixed.
+In this exercise, we go back to the case of the Keynesian multiplier.
+
+Now try to plot the time path of $y_t$, given that consumption is a constant fraction of national income, and investment is fixed.
+
+Given intial values:
+
+```{code-cell} ipython3
+i_0 = 0.3
+g_0 = 0.3
+b = 2/3
+y_init = 0
+T = 100
+```
 
 ```{exercise-end}
 ```
@@ -906,9 +916,17 @@ the infinite geometric series sum of income.
 ```{exercise-start}
 :label: geom_ex2
 ```
-We now examine what will
+Continuing to explore the model, we now examine what will
 happen if we vary the so-called **marginal propensity to consume**,
-i.e., the fraction of income that is consumed
+i.e., the fraction of income that is consumed.
+
+Here, b can take four different numbers.
+
+Given:
+
+```{code-cell} ipython3
+bs = (1/3, 2/3, 5/6, 0.9)
+```
 
 ```{exercise-end}
 ```
@@ -947,7 +965,17 @@ path of output over time.
 ```{exercise-start}
 :label: geom_ex3
 ```
-Now we will compare the effects on output of increases in investment and government spending.
+
+Use the same initial values:
+
+```{code-cell} ipython3
+b = 2/3
+y_init = 0
+T = 100
+```
+
+Compare the effects on $y$ of increasing investment $i$ from $0.3$ to $0.4$ and government spending $g$ from $0.3$ to $0.4$.
+
 ```{exercise-end}
 ```
 

From 07ef18f1402e418ee8eebc6ef761749e725c48e1 Mon Sep 17 00:00:00 2001
From: shlff <shu.hu@anu.edu.au>
Date: Wed, 24 Jul 2024 13:03:07 +1000
Subject: [PATCH 07/17] shu_edits

---
 lectures/geom_series.md | 44 ++++++++++++++++++-----------------------
 1 file changed, 19 insertions(+), 25 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index b71188c1..4e4fb44a 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -854,11 +854,15 @@ will always be positive.
 ```{exercise-start}
 :label: geom_ex1
 ```
-In this exercise, we go back to the case of the Keynesian multiplier.
+Consider a dynamic Keynesian multiplier model
 
-Now try to plot the time path of $y_t$, given that consumption is a constant fraction of national income, and investment is fixed.
+$$
+ y_t = c_t + i_t + g_t \ \ \textrm { and } \ \ c_t = b y_{t-1}.
+$$
+
+Assume that $i_t=i_0$ and $g_t=g_0$ for all $t \geq 0$.
 
-Given intial values:
+Plot the time path of $y_t$ with the following initial values:
 
 ```{code-cell} ipython3
 i_0 = 0.3
@@ -874,7 +878,6 @@ T = 100
 ```{solution-start} geom_ex1
 :class: dropdown
 ```
-
 ```{code-cell} ipython3
 ---
 mystnb:
@@ -890,14 +893,6 @@ def calculate_y(i, b, g, T, y_init):
         y[t] = b * y[t-1] + i + g
     return y
 
-# Initial values
-i_0 = 0.3
-g_0 = 0.3
-# 2/3 of income goes towards consumption
-b = 2/3
-y_init = 0
-T = 100
-
 fig, ax = plt.subplots()
 ax.set_xlabel('$t$')
 ax.set_ylabel('$y_t$')
@@ -916,18 +911,17 @@ the infinite geometric series sum of income.
 ```{exercise-start}
 :label: geom_ex2
 ```
-Continuing to explore the model, we now examine what will
-happen if we vary the so-called **marginal propensity to consume**,
-i.e., the fraction of income that is consumed.
 
-Here, b can take four different numbers.
+Continue from [exercise 1](#geom_ex1). 
 
-Given:
+Plot the time paths of $y_t$ with the same initial values but varying $b$ values:
 
 ```{code-cell} ipython3
 bs = (1/3, 2/3, 5/6, 0.9)
 ```
 
+Interpret the economic effect on $y_t$ of increasing $b$.
+
 ```{exercise-end}
 ```
 
@@ -942,7 +936,6 @@ mystnb:
     caption: "Changing consumption as a fraction of income"
     name: changing_consumption_as_fraction_of_income
 ---
-bs = (1/3, 2/3, 5/6, 0.9)
 
 fig,ax = plt.subplots()
 ax.set_ylabel('$y_t$')
@@ -965,17 +958,19 @@ path of output over time.
 ```{exercise-start}
 :label: geom_ex3
 ```
-
-Use the same initial values:
+Continue from [exercise 1](#geom_ex1) with the following values
 
 ```{code-cell} ipython3
-b = 2/3
-y_init = 0
-T = 100
+values = [0.3, 0.4]
 ```
 
-Compare the effects on $y$ of increasing investment $i$ from $0.3$ to $0.4$ and government spending $g$ from $0.3$ to $0.4$.
+First, plot the time paths of $y_t$ using the same initial valuesm but with $i$ 
+taking the values mentioned above.
 
+Next, plot the time paths of $y_t$ with the same initial values but let $g$ take
+the values abovementioned.
+
+Are the effects on $y_t$ of increasing $i$ and $g$ in these plots the same?
 ```{exercise-end}
 ```
 
@@ -994,7 +989,6 @@ fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10))
 fig.subplots_adjust(hspace=0.3)
 
 x = np.arange(0, T+1)
-values = [0.3, 0.4]
 
 for i in values:
     y = calculate_y(i, b, g_0, T, y_init)

From 44da5e26541751b30b97877e4a62e2222def152b Mon Sep 17 00:00:00 2001
From: shlff <shu.hu@anu.edu.au>
Date: Wed, 24 Jul 2024 13:22:26 +1000
Subject: [PATCH 08/17] fix

---
 lectures/geom_series.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 4e4fb44a..a21614a4 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -912,7 +912,7 @@ the infinite geometric series sum of income.
 :label: geom_ex2
 ```
 
-Continue from [exercise 1](#geom_ex1). 
+Continue from {ref}`geom_ex1`. 
 
 Plot the time paths of $y_t$ with the same initial values but varying $b$ values:
 
@@ -958,7 +958,7 @@ path of output over time.
 ```{exercise-start}
 :label: geom_ex3
 ```
-Continue from [exercise 1](#geom_ex1) with the following values
+Continue from {ref}`geom_ex1` with the following values
 
 ```{code-cell} ipython3
 values = [0.3, 0.4]

From 9871f29492f958e77a5c8a635ad702e29648ba34 Mon Sep 17 00:00:00 2001
From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com>
Date: Wed, 24 Jul 2024 17:05:06 +1000
Subject: [PATCH 09/17] Revise context.md

Co-authored-by: Matt McKay <mmcky@users.noreply.github.com>
---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index a21614a4..0da37b79 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -912,7 +912,7 @@ the infinite geometric series sum of income.
 :label: geom_ex2
 ```
 
-Continue from {ref}`geom_ex1`. 
+As an extension to {ref}`geom_ex1`. 
 
 Plot the time paths of $y_t$ with the same initial values but varying $b$ values:
 

From 68b6cd56128ca8b2ff602a77e4a828d255571f5e Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Wed, 24 Jul 2024 17:40:45 +1000
Subject: [PATCH 10/17] Modify context

---
 lectures/geom_series.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index a21614a4..2d70d02c 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -740,7 +740,7 @@ the value of a lease of duration $T$ approaches the value of a
 perpetual lease.
 
 Now we consider two different views of what happens as $r$ and
-$g$ covary
+$g$ covary.
 
 ```{code-cell} ipython3
 ---
@@ -964,7 +964,7 @@ Continue from {ref}`geom_ex1` with the following values
 values = [0.3, 0.4]
 ```
 
-First, plot the time paths of $y_t$ using the same initial valuesm but with $i$ 
+First, plot the time paths of $y_t$ using the same initial values but with $i$ 
 taking the values mentioned above.
 
 Next, plot the time paths of $y_t$ with the same initial values but let $g$ take

From 6a051d673eebd4061e512ce55787cc645f026212 Mon Sep 17 00:00:00 2001
From: shlff <shu.hu@anu.edu.au>
Date: Wed, 24 Jul 2024 17:48:34 +1000
Subject: [PATCH 11/17] edits

---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 0da37b79..ea7feef9 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -882,7 +882,7 @@ T = 100
 ---
 mystnb:
   figure:
-    caption: "Path of aggregate output tver time"
+    caption: "Path of aggregate output over time"
     name: path_of_aggregate_output_over_time
 ---
 # Function that calculates a path of y

From fc61b03fb0a71b351fe6623d5abc9a7fb1b608f1 Mon Sep 17 00:00:00 2001
From: Shu Hu <shu.hu@anu.edu.au>
Date: Fri, 11 Oct 2024 13:22:30 +1100
Subject: [PATCH 12/17] Update lectures/geom_series.md

Co-authored-by: Matt McKay <mmcky@users.noreply.github.com>
---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 62fb624e..f646d2c3 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -968,7 +968,7 @@ values = [0.3, 0.4]
 ```
 
 First, plot the time paths of $y_t$ using the same initial values but with $i$ 
-taking the values mentioned above.
+taking the values above.
 
 Next, plot the time paths of $y_t$ with the same initial values but let $g$ take
 the values abovementioned.

From 84303917b482fcb30c8b8f40d9118d793e25debe Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Fri, 11 Oct 2024 15:37:51 +1100
Subject: [PATCH 13/17] Clarify mentioned values

---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index e1ce89aa..46d61718 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -968,7 +968,7 @@ First, plot the time paths of $y_t$ using the same initial values but with $i$
 taking the values mentioned above.
 
 Next, plot the time paths of $y_t$ with the same initial values but let $g$ take
-the values abovementioned.
+the values mentioned above.
 
 Are the effects on $y_t$ of increasing $i$ and $g$ in these plots the same?
 ```{exercise-end}

From 2bc17a4c2bd43c92532ec585af62989a115e9752 Mon Sep 17 00:00:00 2001
From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 20:55:58 +1100
Subject: [PATCH 14/17] Update lectures/geom_series.md

Co-authored-by: Shu Hu <shu.hu@anu.edu.au>
---
 lectures/geom_series.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 8538f562..112e48d2 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -961,7 +961,7 @@ path of output over time.
 ```{exercise-start}
 :label: geom_ex3
 ```
-Continue from {ref}`geom_ex1` with the following values
+Continue from {ref}`geom_ex1`.
 
 ```{code-cell} ipython3
 values = [0.3, 0.4]

From 95b50241f2a2e6152e81af4ba1392b0df960cc30 Mon Sep 17 00:00:00 2001
From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 20:57:03 +1100
Subject: [PATCH 15/17] Update lectures/geom_series.md

Co-authored-by: Shu Hu <shu.hu@anu.edu.au>
---
 lectures/geom_series.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 112e48d2..41ce4707 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -962,7 +962,8 @@ path of output over time.
 :label: geom_ex3
 ```
 Continue from {ref}`geom_ex1`.
-
+First, plot the time paths of $y_t$ using the same initial values but with $i$ 
+taking the values below.
 ```{code-cell} ipython3
 values = [0.3, 0.4]
 ```

From 0244418756f9db6048fd5246d5d5672c9498039e Mon Sep 17 00:00:00 2001
From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 20:57:15 +1100
Subject: [PATCH 16/17] Update lectures/geom_series.md

Co-authored-by: Shu Hu <shu.hu@anu.edu.au>
---
 lectures/geom_series.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 41ce4707..43088eaf 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -968,7 +968,6 @@ taking the values below.
 values = [0.3, 0.4]
 ```
 
-First, plot the time paths of $y_t$ using the same initial values but with $i$ 
 taking the values above.
 
 Next, plot the time paths of $y_t$ with the same initial values but let $g$ take

From 06fd37326bbd97a5fbeb9645fb83c0e18b4df714 Mon Sep 17 00:00:00 2001
From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 20:57:38 +1100
Subject: [PATCH 17/17] Update lectures/geom_series.md

Co-authored-by: Shu Hu <shu.hu@anu.edu.au>
---
 lectures/geom_series.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lectures/geom_series.md b/lectures/geom_series.md
index 43088eaf..fe07db53 100644
--- a/lectures/geom_series.md
+++ b/lectures/geom_series.md
@@ -968,7 +968,6 @@ taking the values below.
 values = [0.3, 0.4]
 ```
 
-taking the values above.
 
 Next, plot the time paths of $y_t$ with the same initial values but let $g$ take
 the values mentioned above.