ECO102 Lecture 04

1
- $t_{0} = 0.2$
- $t_{1} = 0.6$
- $C = 16 + 0.75 Y_{0}$
- $T = 8$
- $t = 0.2$
- $I = 20$
- $G = 40$
- $N X = 10 - 0.1 Y$
- When tax rate is $0.2$ equilibrium GDP is high
- When tax rate is higher, GDP goes lower, slope is lower.
  - #tk illustrate this
- Budget balance curve has a slow of $0.2$ , when you increase tax, budget balance gets steeper.
  - #tk illustrate this
- Tax $0.2$
  - $Y_{D} = Y - 08 - 0.2 Y$
    - $Y_{D} = 0.8 Y - 8$
  - $C = 16 + 0.75 (0.8 Y - 8)$
    - $C = 0.6 Y + 10.0$
  - $A E_{0} = C + I + G + N X$
    - $A E_{0} = (10 + 0.6 Y) + (20) + (40) + (10 - 0.1 Y)$
    - $A E_{0} = 0.5 Y + 80$
- Tax $0.6$
  - $Y_{D} = Y - 8 - 0.6 Y$
    - $Y_{D} = 0.4 Y - 8$
  - $C = 16 + 0.75 (0.4 Y - 8)$
    - $C = 0.3 Y + 10.0$
  - $A E_{1} = C + I + G + N X$
    - $A E_{1} = (0.3 Y + 10) + (20) + (40) + (10 - 0.1 Y)$
    - $A E_{1} = 0.2 Y + 80$
- Govt Budget
  - $B_{0} = 8 + 0.2 Y - 40$
    - $B_{0} = 0.2 Y - 32$
  - $B_{1} = 8 + 0.6 Y - 40$
    - $B_{1} = 0.6 Y - 32$
  - $Y_{0} = 160$
  - $B_{0} = 0$
  - $Y_{1} = 100$
  - $B_{1} = 28$
- Tax changes the slope but not the intercept.
  - When govt changes tax, gdp contracts
- ECO102 Lecture 03#7. Expansionary Fiscal Policy. This is the Contractionary Fiscal Policy
- Budget balance has the same intercept of $- 32$
  - Have the $\frac{A E}{45}$ graph
  - And the Budget graph
  - Show the $b_{0}$ and $b_{1}$ and the two lines $B_{0}$ and $B_{1}$
- Tax revenue:
  - #tk illustrate this section
  - Increasing the tax rate has two direct impacts on tax revenues.
    - Revenues go up
    - But GDP goes down.
    - Direct tax revenues, increase by less than the amount of real gdp decline.
  - When $t_{0} = 0.2$
  - We have $t Y = 32$
  - $t_{1} = 0.6$
Monetary Policy
- An $A E$ economy is described by $C = 14 + 0.9 Y_{D}$ $T = 10$ $t = 0.1$ $i = 10$ $G = 4$ $N X = 1 - 0.01 Y$
- $I = 25 - r$
  - Investment spending depends on the real interest rate: $r$ .
  - Interest rate is the opportunity cost of investing in physical capital
    - #tk so not other investments?
- When $r_{0} = 15$
  - $I_{0} = 10$
  - When rates are cut, investment spending increases.
- $r_{1} = 3$
  - $I_{1} = 22$
- Central banks cut rates, how?
  - Chartered banks like RBC, etc have an account at bank of canada.
  - Bank of Canada has an 'overnight' rate.
    - This is the rate of interest charged to chartered banks.
  - If interest rate is $15 %$ and TD has excess funds at BoC, they'd be paid $15 %$ on those excess funds. Vice versa for borrowing too.
  - When the central bank changes the overnight rate, it affects the profitability of the chartered banks who pass these savings on.
- $A E_{0} = (5 + 0.81 Y) + (10) + (4) + (1 - 0.01 Y)$
  - $A E_{0} = 0.8 Y + 20$
- $A E_{1} = (5 + 0.81 Y) + (22) + (4) + (1 - 0.01 Y)$
  - $A E_{1} = 0.8 Y + 32$
- Cross
  - $Y_{0} = 100$
  - $Y_{1} =$
    - $Y = 0.8 Y + 32$
    - $Y = 160.0$
- $60 ↑$ in Real GDP by a $12$ dollar increase in investments.
```
		left=-5; right=200;
		top=200; bottom=-5;
		---
		y=0.8x+32
		y=0.8x+20
		y=x
		(160,160)
		(100,100)
```
  - Budget balance increases because tax revenues rise.
  - $t = 0.1$
  - When $Y_{0}$ , $Y t = 10$
  - When $Y_{1}$ , $Y t = 16$
  - $6 $$ increase in govt revenue.
  - #tk create graph for $B_{0} = B_{1}$ with equilibrium $A$ and $B$
- Net exports
  - $N X_{1} = N X_{0} = 1 - 0.01 Y$
  - Trade balance is originally $0$
  - $N X_{0} = 1 - 0.01 (100) = 0$
  - $N X_{1} = 1 - 0.01 (160) = - 0.6$
  - We have negative net exports.
  - #tk graph
- Savings
  - Upward slope
  - $S = Y_{D} - C$
  - $Y_{0} ⟹ S_{0} = - 6$
  - $Y_{1} ⟹ S_{1} = ?$
    - #tk
  - Private savings also increases
  - $S_{0} = S_{1}$ line
- #tk, draw all these diagrams as practice.
Paradox of Thrift
- Stabilization policy
- $I_{0} = 30$
- $I_{1} = 20$
- $C_{0} = 20 + 0.8 Y_{D}$
- $C_{1} = 10 + 0.8 Y_{D}$
- Stock market crash
- Households decrease autonomous consumption
- Businesses also reduce investments / spending.
- Economy reduces spending from $50 \to 30 = 20$
- If everyone cuts back on spending, then GDP $↓$ right?
- Meaning savings also goes down.
- So if everyone tries to save, we won't save globally as much as we wanted to.
- Graphs:
  - $\frac{A E_{0, 1}}{45}$
  - $S_{0}, S_{1}$
  - When autonomous spending is reduced, savings shifts upwards.
  - #tk illustrate
  - Show equilibrium $A$
  - If GDP eq didn't change, then the savings change is the $10$ dollars in autonomous change.
  - Since GDP eq does change, then we don't increase savings by $10$ dollars, we actually save by less.
Foreign Shock with Stabilization Policy
- This is that $\hat{y} = y_{0}$
  - Trying to make $\hat{y}$ , target gdp, the same as $y_{0}$
- USA Tariff on Canadian Goods
  - Meaning $N X ↓$ and $y_{1} < y_{0}$
  - So $G_{0} ↑ G_{1}$ govts increase spending. Which pushes GDP back to its original level.
  - Since $C = 20 + 0.8 (Y - 10 - 0.6 Y)$
    - $C = 0.32 Y + 12.0$
  - Graph: #tk
    - $A E_{0} = (0.32 Y + 12) + (20) + (8) + (40 - 0.12 Y)$
    - $A E_{0} = 0.2 Y + 80$
    - $y = x$
    - $Y = 0.2 Y + 80$
      - $Y = 100.0$
      - $(100, 100)$
    - when $N X ↓$
      - $A E_{1} = (0.32 Y + 12) + (20) + (8) + (20 - 0.12 Y)$
      - $A E_{1} = 0.2 Y + 60$
    - $y = x$
    - $Y = 0.2 Y + 60$
      - $Y = 75.0$
      - $(75, 75)$
    - Illustrate the $20$ dollar gap between $A E_{0}, A E_{1}$
    - $A E_{2} = (12 + 0.32 Y) + (20) + (28) + (20 - 0.12 Y)$
      - $A E_{2} = 0.2 Y + 80$
  - Graph: #tk
    - Net exports
    - $40 - 0.12 Y$
    - $20 - 0.12 Y$
    - Illustrate the $20$ dollar gap between $N X_{0}, N X_{1}$
    - Use the same $Y$
    - When $Y = 100 ⟹ N X = 28$ and $Y = 75 ⟹ N X = 31$
    - See that the gap is actually smaller than the intercept change because of changing GDP
    - Illustrate these points as $A, B, C$
    - Since eq GDP goes back to $100$ after increasing govt spend.
    - The balance of trade worsens by $C$ shifting back to $B$
    - Import spending returns to the original level.
  - Graph: #tk
    - $B_{0} = 10 + 0.1 Y - 8$
      - $B_{0} = 0.1 Y + 2$
    - When GDP is 100
      - $b_{0} = 12$
    - When govt increases spending by $20$
    - $B_{1} = 10 + 0.1 Y - 28$
      - $B_{1} = 0.1 Y - 18$
      - $b_{1} |_{Y = 75} = - 10.5$
      - A worse budget balance.
    - So it doesn't just go from $A \to B$ moving from $B_{0} \to B_{1}$ with $Y = 100$ . We also change the fact that $Y = 75$
    - #tk does the savings curve shift?
    - Since $S = Y_{D} - C$
      - I don't think so because govt spending doesn't affect private savings? Correct me.
Policy Targets, Balance the Budget
- Before we had an offset, as $\hat{y} = y_{0}$
- We can to get gdp, $\hat{y}$ equals to the original value it was before, to offset a shock.
- We want to change $T, T, t, r$ to achieve the goal. In this case we want $b = 0, n x = 0, s = 0$
- How to Effect $b = 0$ ?
  - $C = 40 + 0.6 Y$
  - $A E = (40 + 0.6 Y) + (10) + (160) + (30 - 0.1 Y)$
  - $A E_{0} = 0.5 Y + 240$
  - $Y = 0.5 Y + 240$
  - $Y = 480.0 ⟹ (480, 480)$
  - Budget balance:
    - $B_{0} = 10 + 0.25 Y - 160$
    - $B_{0} = 0.25 Y - 150$
    - $B_{0} = 0.25 (480) - 150 = - 30.0$ deficit
    - If our goal is to make $b_{0} = 0$
    - Then we need to reduce $G ↓$
    - Or increase gdp
    - New level of $G$
    - $0 = 0.25 (480) - \hat{G}$
    - $\hat{G} = 120.0$ is our new govt spending?
    - #tk why is this not the answer and why do we use a Fake AE?
  - Fake AE?
    - $A E_{1} = (40 + 0.6 Y) + (10) + (10 + 0.25 Y) + (30 - 0.1 Y)$
    - $A E_{1} = 0.75 Y + 90$
    - Slopes originally were $0.5$ , not $0.75$ .
    - Since we are doing an intermediate calculation, we call this our Fake AE curve.
    - $Y = 0.75 Y + 90$
    - $Y = 360.0 ⟹ (360, 360)$
    - $Y = 360 ⟹ \hat{G} = 10 + (0.25) (360) = 100$
    - This is our new spending to eliminate $b_{0} = - 30$
  - New AE:
    - $A E = (40 + 0.6 Y) + 10 + 100 + (30 - 0.1 Y)$
    - $A E = 0.5 Y + 180$
    - This is our real AE curve with adjusted govt spending.
    - This is because we have the same slope.
```
    left=-5; right=600;
    top=600; bottom=-5;
    ---
    y=0.5x+180
    y=0.5x+240
    y=x
    (360,360)
    (480,480)
```
```
    left=-100; right=1200;
    top=600; bottom=-600;
    ---
    y=10+0.25x-160
    y=10+0.25x-60
    (0,-150)
    (0,-50)
    (480,0)
    (360,0)
```
    - Plot all numbers before drawing the graph to make it to scale.
    - Why do we need a $60 ↓$ in G to affect a $b_{0} = 0$
      - Is this because the AE multiplier? #tk
      - So above when I had the gripe, why I couldn't solve for $b_{0} = 0$ simply, can I take that and multiply it by the AE multiplier?
    - This is because the $60$ change in G results in a $2 (60) = 120$ change in GDP
    - The direct tax revenues fall too. Like the substitution and income effect at play here.
- Suppose it's impossible to reduce $G$
  - Then let's increase $T$ , indirect taxes to balance the budget.
  - Since $A E = 180 + 0.5 Y$
  - We have $Y_{D} = Y - 0.25 Y - T$
  - $B = \hat{T} + 0.25 Y - 160 = 0$
  - $\hat{T} + 0.25 Y - 160 = 0$
  - $\hat{T} = 160 - 0.25 Y$
  - $C = 48 + 0.8 (Y - T - 0.25 Y)$
  - $C = 48 + 0.8 (Y - (160 - 0.25 Y) - 0.25 Y)$
  - $C = 0.8 Y - 80.0$
  - $A E = (0.8 Y - 80) + 10 + 160 + (30 - 0.1 Y)$
    - $A E = 0.7 Y + 120$
    - $Y = 0.7 Y + 120$
    - $Y = 400.0$
  - $\hat{T} = 160 - 0.25 (400)$
    - $\hat{T} = 60.0$
    - To affect a $b_{0} = 0$
  - So we needed a $50 ↑ T$ to affect a $30 ↑ B$ .
    - This is because the increase in $T$ , then eq gdp goes $↓ 80 ⟹ 480 \to 400$ , meaning the budget also get affected.
    - The $80 $$ loss of GDP meaning direct tax revenues go down by $0.25 Y ⟹ 0.25 (80) ⟹ 20$ reduction in tax revenues.
    - That's why we need to increase tax revenues by extra.
    - Why do we have $Y = 400$ and not $Y = 360$
      - This is because $Δ T$ and $Δ G$
      - Before we have $480 \to 360$ now we have $480 \to 400$
      - This is because the change in $G$ spending hurts gdp more.
      - Since $M P C = 0.8$ , $C = 48 + 0.8 (Y - T - 0.25 Y)$
      - The change in $T$ affects GDP by the $M P C$
      - But $G$ affects the GDP directly.
      - Since the $A E mult. = 2.0$ . The change in eq gdp is $Δ y = mult. \times MPC \times Δ T$
      - When you increase taxes by $50$ the impact on GDP is $Δ T = 50 \cdot 2 \cdot 0.8 = 80.0$
      - Which is what we have.
Balanced increase in $G$ and $T$
- Imagine what will happen if you tell a politician, you can increase govt spending and GDP goes up by $mult. \times Δ G$
- Also increases in indirect tax results in gdp going down by a smaller amount as $M P C \times mult. \times Δ T$
- Since $B = T + t Y - G$ , the $Δ B = 0$ . It's neutral to the govt budget. But will make the economy grow due to the asymmetric affect on GDP
Everything except question above this one is on the test.

% Authorised packages only (TikZJax-friendly)
\usepackage{amsmath}
\usepackage{pgfplots}

\begin{document}

% ------------------------------------------------------------
% Global pgfplots settings (safe for TikZJax usage)
% ------------------------------------------------------------
\pgfplotsset{compat=1.16}

% ============================================================
% FIGURE 1: Keynesian cross — Tax rate change (t=0.2 vs t=0.6)
% AE0 = 0.5Y + 80, AE1 = 0.2Y + 80, 45-degree line
% Equilibria: A(160,160), B(100,100)
% ============================================================
\begin{tikzpicture}
  % en-CA: Keynesian cross for proportional tax rate changes
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=0, ymax=200,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(AE\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Keynesian Cross: Higher \(t\) flattens \(AE\) and lowers equilibrium \(Y\)}
  ]
    \addplot[black, thick, domain=0:200] {x};
    \addlegendentry{\(AE=Y\) (45-degree)}

    \addplot[blue, thick, domain=0:200] {0.5*x + 80};
    \addlegendentry{\(AE_0=0.5Y+80\) ( \(t=0.2\) )}

    \addplot[red, thick, domain=0:200] {0.2*x + 80};
    \addlegendentry{\(AE_1=0.2Y+80\) ( \(t=0.6\) )}

    % Equilibrium points
    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(160,160)};
    \node[blue] at (axis cs:160,160) [anchor=south west] {\(A(160,160)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(100,100)};
    \node[red] at (axis cs:100,100) [anchor=south west] {\(B(100,100)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 2: Budget balance lines — Tax rate change
% B0 = 0.2Y - 32, B1 = 0.6Y - 32
% Points: at Y0=160 => B0=0, at Y1=100 => B1=28
% ============================================================
\begin{tikzpicture}
  % en-CA: Budget balance becomes steeper when t rises
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=-40, ymax=100,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(B\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Budget Balance: Higher \(t\) makes \(B(Y)\) steeper (same intercept)}
  ]
    \addplot[gray, thick, domain=0:200] {0};
    \addlegendentry{\(B=0\)}

    \addplot[blue, thick, domain=0:200] {0.2*x - 32};
    \addlegendentry{\(B_0=0.2Y-32\)}

    \addplot[red, thick, domain=0:200] {0.6*x - 32};
    \addlegendentry{\(B_1=0.6Y-32\)}

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(160,0)};
    \node[blue] at (axis cs:160,0) [anchor=south west] {\(Y_0=160,\;B_0=0\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(100,28)};
    \node[red] at (axis cs:100,28) [anchor=south west] {\(Y_1=100,\;B_1=28\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 3: Tax revenue — TR = tY, showing (t up, Y down)
% TR0=0.2Y with equilibrium point (160,32)
% TR1=0.6Y with equilibrium point (100,60)
% ============================================================
\begin{tikzpicture}
  % en-CA: Tax revenue lines and equilibrium outcomes
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=0, ymax=80,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(TR=tY\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Tax Revenue: \(t\uparrow\) raises \(TR\), but \(Y\downarrow\) offsets partly}
  ]
    \addplot[blue, thick, domain=0:200] {0.2*x};
    \addlegendentry{\(TR_0=0.2Y\)}

    \addplot[red, thick, domain=0:200] {0.6*x};
    \addlegendentry{\(TR_1=0.6Y\)}

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(160,32)};
    \node[blue] at (axis cs:160,32) [anchor=south west] {\((160,32)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(100,60)};
    \node[red] at (axis cs:100,60) [anchor=south west] {\((100,60)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 4: Keynesian cross — Monetary policy via I
% AE0 = 0.8Y + 20, AE1 = 0.8Y + 32, 45-degree line
% Equilibria: A(100,100), B(160,160)
% ============================================================
\begin{tikzpicture}
  % en-CA: Lower r -> higher I -> AE shifts up
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=0, ymax=200,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(AE\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Monetary Policy: \(I\uparrow\) shifts \(AE\) up (same slope), \(Y\uparrow\)}
  ]
    \addplot[black, thick, domain=0:200] {x};
    \addlegendentry{\(AE=Y\)}

    \addplot[blue, thick, domain=0:200] {0.8*x + 20};
    \addlegendentry{\(AE_0=0.8Y+20\)}

    \addplot[red, thick, domain=0:200] {0.8*x + 32};
    \addlegendentry{\(AE_1=0.8Y+32\)}

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(100,100)};
    \node[blue] at (axis cs:100,100) [anchor=south west] {\(A(100,100)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(160,160)};
    \node[red] at (axis cs:160,160) [anchor=south west] {\(B(160,160)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 5: Budget balance — same line, movement from A to B
% With T=10, t=0.1, G=4: B(Y)=10+0.1Y-4=0.1Y+6
% Points: Y=100 => 16, Y=160 => 22
% ============================================================
\begin{tikzpicture}
  % en-CA: Budget line does not shift; equilibrium moves along it
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=0, ymax=30,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(B\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Budget Balance with Monetary Policy: Same \(B(Y)\), new equilibrium \(Y\)}
  ]
    \addplot[gray, thick, domain=0:200] {0};
    \addlegendentry{\(B=0\)}

    \addplot[blue, thick, domain=0:200] {0.1*x + 6};
    \addlegendentry{\(B(Y)=0.1Y+6\)}

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,16)};
    \node[black] at (axis cs:100,16) [anchor=south west] {\(A:\;Y=100\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(160,22)};
    \node[black] at (axis cs:160,22) [anchor=south west] {\(B:\;Y=160\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 6: Net exports — NX(Y)=1-0.01Y with points at Y=100 and Y=160
% ============================================================
\begin{tikzpicture}
  % en-CA: NX falls as Y rises (imports rise with income)
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=-1.5, ymax=1.5,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(NX\)},
    legend pos=north east,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Net Exports: \(NX(Y)=1-0.01Y\)}
  ]
    \addplot[blue, thick, domain=0:200] {1 - 0.01*x};
    \addlegendentry{\(NX=1-0.01Y\)}

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,0)};
    \node[black] at (axis cs:100,0) [anchor=south west] {\(Y=100,\;NX=0\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(160,-0.6)};
    \node[black] at (axis cs:160,-0.6) [anchor=south west] {\(Y=160,\;NX=-0.6\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 7: Private saving — S(Y)=0.09Y-15 with points
% Y=100 => -6, Y=160 => -0.6
% ============================================================
\begin{tikzpicture}
  % en-CA: Saving schedule and equilibrium points
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=200, ymin=-20, ymax=10,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(S\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Private Saving: \(S(Y)=0.09Y-15\)}
  ]
    \addplot[gray, thick, domain=0:200] {0};
    \addlegendentry{\(S=0\)}

    \addplot[blue, thick, domain=0:200] {0.09*x - 15};
    \addlegendentry{\(S=0.09Y-15\)}

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,-6)};
    \node[black] at (axis cs:100,-6) [anchor=south west] {\(Y=100,\;S=-6\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(160,-0.6)};
    \node[black] at (axis cs:160,-0.6) [anchor=south west] {\(Y=160,\;S=-0.6\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 8: Paradox of thrift — schematic Keynesian cross (generic)
% Two parallel AE lines; equilibrium falls when autonomous spending falls.
% Note: schematic because your notes do not pin down one numeric AE equation.
% ============================================================
\begin{tikzpicture}
  % en-CA: Schematic paradox of thrift diagram
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=260, ymin=0, ymax=260,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(AE\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Paradox of Thrift (Schematic): Lower autonomous spending \(\Rightarrow\) lower equilibrium \(Y\)}
  ]
    \addplot[black, thick, domain=0:260] {x};
    \addlegendentry{\(AE=Y\)}

    % Schematic lines (parallel shift down)
    \addplot[blue, thick, domain=0:260] {0.6*x + 80};
    \addlegendentry{\(AE_0\) (before thrift shock)}

    \addplot[red, thick, domain=0:260] {0.6*x + 60};
    \addlegendentry{\(AE_1\) (after thrift shock)}

    % Equilibria for the schematic choice:
    % Y=0.6Y+80 => Y=200; Y=0.6Y+60 => Y=150
    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(200,200)};
    \node[blue] at (axis cs:200,200) [anchor=south west] {\(A\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(150,150)};
    \node[red] at (axis cs:150,150) [anchor=south west] {\(B\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 9: Foreign shock with stabilization — AE0, AE1, AE2
% AE0=0.2Y+80 (Y=100), AE1=0.2Y+60 (Y=75), AE2 back to AE0
% ============================================================
\begin{tikzpicture}
  % en-CA: NX shock shifts AE down; fiscal stabilization shifts it back
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=140, ymin=0, ymax=140,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(AE\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Foreign Shock + Stabilization: \(NX\downarrow\) then \(G\uparrow\) to restore \(Y\)}
  ]
    \addplot[black, thick, domain=0:140] {x};
    \addlegendentry{\(AE=Y\)}

    \addplot[blue, thick, domain=0:140] {0.2*x + 80};
    \addlegendentry{\(AE_0=0.2Y+80\) (original)}

    \addplot[red, thick, domain=0:140] {0.2*x + 60};
    \addlegendentry{\(AE_1=0.2Y+60\) (after \(NX\downarrow\))}

    % AE2 coincides with AE0 numerically; label it distinctly near the line
    \node[blue] at (axis cs:20,84) [anchor=west] {\(AE_2\) (after \(G\uparrow\), back to \(AE_0\))};

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(100,100)};
    \node[blue] at (axis cs:100,100) [anchor=south west] {\(A(100,100)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(75,75)};
    \node[red] at (axis cs:75,75) [anchor=south west] {\(B(75,75)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 10: Foreign shock — NX lines with A, B, C
% NX0=40-0.12Y, NX1=20-0.12Y
% A: (100,28) on NX0
% B: (75,11)  on NX1
% C: (100,8)  on NX1 (after stabilization returns Y to 100)
% ============================================================
\begin{tikzpicture}
  % en-CA: NX schedule shifts down; equilibrium Y movements change observed NX too
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=140, ymin=-5, ymax=45,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(NX\)},
    legend pos=north east,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Foreign Shock: Net Exports lines and points \(A,B,C\)}
  ]
    \addplot[blue, thick, domain=0:140] {40 - 0.12*x};
    \addlegendentry{\(NX_0=40-0.12Y\)}

    \addplot[red, thick, domain=0:140] {20 - 0.12*x};
    \addlegendentry{\(NX_1=20-0.12Y\)}

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,28)};
    \node[black] at (axis cs:100,28) [anchor=south west] {\(A(100,28)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(75,11)};
    \node[black] at (axis cs:75,11) [anchor=south west] {\(B(75,11)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,8)};
    \node[black] at (axis cs:100,8) [anchor=south west] {\(C(100,8)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 11: Foreign shock — Budget balance lines with equilibria
% B0=0.1Y+2 (G=8), B1=0.1Y-18 (G=28)
% Points:
%   A: Y=100 on B0 => 12
%   B: Y=75 on B0  => 9.5
%   C: Y=100 on B1 => -8
% ============================================================
\begin{tikzpicture}
  % en-CA: Fiscal stabilization worsens budget balance (higher G), even if Y returns
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=140, ymin=-30, ymax=20,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(B\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Foreign Shock + Stabilization: Budget balance before/after \(G\uparrow\)}
  ]
    \addplot[gray, thick, domain=0:140] {0};
    \addlegendentry{\(B=0\)}

    \addplot[blue, thick, domain=0:140] {0.1*x + 2};
    \addlegendentry{\(B_0=0.1Y+2\) (before \(G\uparrow\))}

    \addplot[red, thick, domain=0:140] {0.1*x - 18};
    \addlegendentry{\(B_1=0.1Y-18\) (after \(G\uparrow\))}

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,12)};
    \node[black] at (axis cs:100,12) [anchor=south west] {\(A(100,12)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(75,9.5)};
    \node[black] at (axis cs:75,9.5) [anchor=south west] {\(B(75,9.5)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, black] coordinates {(100,-8)};
    \node[black] at (axis cs:100,-8) [anchor=south west] {\(C(100,-8)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 12: Policy target — Balance budget by reducing G
% AE0=0.5Y+240 => Y=480
% AEnew=0.5Y+180 => Y=360
% ============================================================
\begin{tikzpicture}
  % en-CA: Changing G shifts AE in parallel; equilibrium Y changes via multiplier
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=600, ymin=0, ymax=600,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(AE\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Policy Target: Reduce \(G\) to eliminate deficit (Keynesian cross)}
  ]
    \addplot[black, thick, domain=0:600] {x};
    \addlegendentry{\(AE=Y\)}

    \addplot[blue, thick, domain=0:600] {0.5*x + 240};
    \addlegendentry{\(AE_0=0.5Y+240\)}

    \addplot[red, thick, domain=0:600] {0.5*x + 180};
    \addlegendentry{\(AE_1=0.5Y+180\)}

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(480,480)};
    \node[blue] at (axis cs:480,480) [anchor=south west] {\(A(480,480)\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(360,360)};
    \node[red] at (axis cs:360,360) [anchor=south west] {\(B(360,360)\)};
  \end{axis}
\end{tikzpicture}

\bigskip

% ============================================================
% FIGURE 13: Policy target — Budget lines before/after G reduction
% B0=0.25Y-150 (G=160), point at Y=480 => -30
% B1=0.25Y-90  (G=100), point at Y=360 => 0
% ============================================================
\begin{tikzpicture}
  % en-CA: Budget constraint line shifts up when G is reduced
  \begin{axis}[
    width=12cm, height=8cm,
    xmin=0, xmax=600, ymin=-60, ymax=60,
    axis lines=middle,
    xlabel={\(Y\)}, ylabel={\(B\)},
    legend pos=north west,
    grid=both, grid style={line width=0.2pt, draw=lightgray},
    tick label style={font=\small},
    label style={font=\small},
    title={Policy Target: Budget balance before/after changing \(G\)}
  ]
    \addplot[gray, thick, domain=0:600] {0};
    \addlegendentry{\(B=0\)}

    \addplot[blue, thick, domain=0:600] {0.25*x - 150};
    \addlegendentry{\(B_0=0.25Y-150\) ( \(G=160\) )}

    \addplot[red, thick, domain=0:600] {0.25*x - 90};
    \addlegendentry{\(B_1=0.25Y-90\) ( \(G=100\) )}

    \addplot[only marks, mark=*, mark size=2.2pt, blue] coordinates {(480,-30)};
    \node[blue] at (axis cs:480,-30) [anchor=south west] {\(A:\;Y=480,\;B=-30\)};

    \addplot[only marks, mark=*, mark size=2.2pt, red] coordinates {(360,0)};
    \node[red] at (axis cs:360,0) [anchor=south west] {\(B:\;Y=360,\;B=0\)};
  \end{axis}
\end{tikzpicture}

\end{document}