ECO102 Lecture 03

Pre-Lecture

ECO102 - Week 03.pdf
ECO102 Pre-Lecture 03 Summary

Lecture

AE Model
- Aggregate Demand
- Aggregate Expenditure
Keynesian Macroeconomics
- Governments should stimulate the economy in bad times.
- Vice versa

Government Sector
$G = 4$
- Government Spending
- $G D E = C + I + G + (X - Im)$
- GDE
$T = 10$
- Indirect Taxes
- Not dependent on income
Tax rate is $t = 0.1$
- Direct Tax
$B = [10 - 0.1 Y] - 4$
- Govt Budget

B_{1}

the budget balance if

T = 20

and

G_{1} = 16

and

t = 0.1

Create a line where the slope is $t$
y-int is $10 - 4 = 6$ for this line
A vertical line as $y = 100$ as an example
Then government budget balance as $b = 16$

Create a tikz diagram to illustrate this.

\begin{document}
  \begin{tikzpicture}[xscale=0.08, yscale=0.4, every node/.style={font=\small}]
    % Axes
    \draw[->, thick] (0,0) -- (130,0) node[right] {$Y$ (Income)};
    \draw[->, thick] (0,0) -- (0,22) node[above] {$B$ (Budget Balance)};

    % Grid lines for clarity (optional)
    \draw[help lines, gray, step=10] (0,0) grid (120,20);

    % Scenario 1: B = 6 + 0.1Y
    % Points: (0, 6) and (120, 18)
    \draw[domain=0:120, smooth, variable=\x, blue, thick] plot ({\x}, {6 + 0.1*\x});
    \node[blue, right] at (120,18) {$B = 6 + 0.1Y$};

    % Scenario 2: B1 = 4 + 0.1Y
    % Points: (0, 4) and (120, 16)
    \draw[domain=0:120, smooth, variable=\x, red, thick] plot ({\x}, {4 + 0.1*\x});
    \node[red, right] at (120,16) {$B_1 = 4 + 0.1Y$};

    % Vertical line at Y = 100
    \draw[dashed, gray] (100,0) -- (100,20);
    \node[below] at (100,0) {$100$};

    % Point for B = 16 at Y = 100
    \draw[dashed, gray] (0,16) -- (100,16);
    \filldraw[black] (100,16) circle (20pt);
    \node[anchor=south east] at (100,16) {$(100, 16)$};

    % Intercepts
    \filldraw[blue] (0,6) circle (20pt);
    \node[blue, left] at (0,6) {$6$};

    \filldraw[red] (0,4) circle (20pt);
    \node[red, left] at (0,4) {$4$};

  \end{tikzpicture}
\end{document}

Government budget is an automatic stabiliser
- When GDP is high, then tax revenues will be big,
- Vice versa
If $G = 16$
- Then the budget balance shifts downwards.
- Vertical int at $y = - 6$
- With the same $x = 100$ example
- You will always have a worse balance

2
- Household sector
- GDE
  - $G D E = C + \dots$
  - This is $C$
- Consumes and saves
- Consumption has:
  - Autonomous as: $a$
    - Not dependent on income
  - Marginal propensity to consume: $b$
    - $M P C$
    - Marginal propensity to consume, before tax income.
- Consumption Function:
  - $C = a + b Y^{D}$
    - $Y^{D}$ : Disposable income
      - $Y^{D} = Y - T - t Y$
      - Minus direct and indirect taxes
  - In example: $C = 14 + (0.9) (Y - 0.1 Y - 10)$
    - $C = 0.81 Y + 5.0$
    - Upwards sloping line with slope of $0.81$
    - Intercept of $5$
    - So $0.81$ is our MPC before tax income.
  - Why do we have a difference between $0.81$ and $0.9$
    - You spend $0.81$ cents out of every gross dollar earned
    - $0.9$ means you spend $90$ cents out of every after tax dollar.
  - $S = Y - C - T - t Y$
    - Income minus consumption minus taxes
  - $S = Y - 5 - 0.81 Y - 10 - 0.1 Y$
  - $S \approx 0.09 Y - 15$
  - Slope is $0.09$
- If GDP is 100, then $s$ : savings is $- 16$ which is $0.09 \cdot 100 - 15$
- If GDP is 100, then $c$ : consumption is $86 $$
- $T + t (100) = 20$
  - We pay $20 $$ in tax
- $a$ depends on:
  - Level of confidence regarding future of economy.
  - What will happen if people become more confident of the economy?:
    - $a ↑$
    - Then $C ↑$
    - Because more spend $⟹ S ↓$
    - Vice versa as well.
3
- Corporate Sector
- Gross fixed capital investment plus inventories is $I = 10$
- This is the Investment part of GDE
- Autonomous
- Investment spending depends on interest rates.
  - This is the opportunity cost of business spending.
  - When they want to invest in physical capital, they need to borrow money. That's the interest rate, which is the price for borrowing.
  - When interest rates fall, $I ↑$
  - $I = G C F + Δ I N V$
  - $G C F$
    - Physical capital
  - $Δ I N V$
    - When you add items to your inventory
    - Raw materials unused
      - Not in value added
    - Finished goods inventory
    - #tk If you make $1000 $$ of product in 2026 and sell it all $800 $$ (no unfinished), is that still investment?
4
- Non-Resident Sector
- GDP = GDE = GDI
- This is the net exports
  - $X - Im$
- Exports used to balance $G D E = G D P$
- $Im = m Y$
- $m = 0.01$
  - This means $1$ cent per dollar is spent on imported goods
- $X = X (\underline{\underset{⏟}{P}}, \underset{+}{\underset{⏟}{P_{F}}}, \underset{+}{\underset{⏟}{Y_{F}}}, \underset{+}{\underset{⏟}{e}})$
  - $P$ is proxied by the CPI
  - When our goods go up in price, we buy less.
  - Vice versa
  - $P_{F}$ is the foreign price.
  - $Y_{F}$ foreign income
    - Means they'll buy more anyways.
    - US GDP goes up, so do Canadian Exports
  - $e$
    - Exchange rate
    - Price of a us dollar.
    - $CAD $ 1.8 ⟹ US $ 1$
    - If $e ↑$
      - $CAD $ 2 ⟹ US $ 1$
    - US can buy more of our stuff
    - This is a depreciation of our dollar.
  - Draw a line like $y = - 0.01 x + 1$
    - If GDP is 100, $x = 100$ then $y = 0$
    - When GDP increases, then our trade account has a trade deficit.
      - We import more than our exports.
    - If GDP decreases, we have a Trade Surplus
  - The trade account also works as an automatic stabiliser.
    - When the canadian economy is doing well, this has leakage (exports) out the economy and taps brakes.
    - Vice versa with exports too.
5
- Goods Market Equilibrium
- $G D P = G D E$
- Equilibrium
- $G D E$ is amount to buy, $G D P$ is amount to sell.
- $Y = G D P$
- $A E = G D E$
- $A E = C + I + G + (X - Im)$
  - $A E = (5 + 0.81 Y) + (10) + (4) + (1 - 0.01 Y)$
  - $A E = 0.8 Y + 20$
  - $Y = 1.25 A E - 25.0$
- Draw the $A E$ curve
  - #tk do all graphics too
  - $Y = A E$ is the goal.
  - $Y = 0.8 y + 20$
    - $y = 100$
    - Add a $45 °$ line.
    - $y = x$
    - $y = 100$ as an equilibrium GDP
- Government Budget Balance
  - $B = 10 + 0.1 Y - 4$
  - At $y = 100$ will give us a budget balance of $b = 16$
- Savings
  - $0.09 Y - 15$
  - When $y = 100$ as gdp we have $S = - 6$ , households are borrowing.
- Export graph
  - $N X = 1 - 0.01 Y$
  - When $y = 100$ as gdp
  - $N X = 1 - 0.01 (100)$
  - $N X = 0$
  - Balanced
6
- Capital Market Equilibrium
- $N A F = I + N X = 10 + 0 = 10$
- $N S = S + B = - 6 + 16 = 10$
- Net asset formation
- National savings
- Balanced when $y = 100$ as gdp
- If the goods market is in equilibrium, then the capital markets are in equilibrium.
- Why is National savings $N S = S + B$ ?
  - Includes private savings and government savings as $s$ and $b$ respectively.
- $N A F = I + N X$
  - Includes private investment and net exports
  - Net exports are included because:
    - Suppose if $N X = 18$ means more exports than imports.
    - Capital inflow

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
                                                                                                                                                                          \begin{document}
                                                                                                                                                                          % --- DIAGRAM 1: GOVERNMENT BUDGET BALANCE ---
\begin{tikzpicture}[scale=0.8, every node/.style={font=\small}]
    % Axes
    \draw[->, thick] (0,0) -- (12,0) node[right] {$Y$ (Income)};                                                                                                              \draw[->, thick] (0,0) -- (0,8) node[above] {$B$ (Budget Balance)};

    % Budget Lines                                                                                                                                                            % B = 6 + 0.1Y -> (0,3) to (10,8) scaled
    \draw[domain=0:10, smooth, variable=\x, blue, thick] plot ({\x}, {3 + 0.2*\x});
    \node[blue, right] at (10,5.2) {$B = 6 + 0.1Y$};

    % B1 = 4 + 0.1Y -> (0,2) to (10,7) scaled
    \draw[domain=0:10, smooth, variable=\x, red, thick] plot ({\x}, {2 + 0.2*\x});                                                                                            \node[red, right] at (10,4.2) {$B_1 = 4 + 0.1Y$};

    % Equilibrium Marker
    \draw[dashed, gray] (8,0) -- (8,4.6);
    \node[below] at (8,0) {$100$};
    \filldraw[black] (8,4.6) circle (2pt) node[anchor=south east] {$(100, 16)$};

    % Intercepts
    \node[blue, left] at (0,3) {$6$};
    \node[red, left] at (0,2) {$4$};

    \node[above, font=\bfseries] at (6,8) {Government Budget Modelling};
\end{tikzpicture}

\vspace{1cm}

% --- DIAGRAM 2: THE KEYNESIAN CROSS (AE MODEL) ---
\begin{tikzpicture}[scale=0.8, every node/.style={font=\small}]
    % Axes
    \draw[->, thick] (0,0) -- (10,0) node[right] {$Y$};
    \draw[->, thick] (0,0) -- (0,10) node[above] {$AE$};

    % 45 Degree Line
    \draw[thick, gray] (0,0) -- (9,9) node[right] {$AE = Y$};

    % AE Line: AE = 20 + 0.8Y (Scaled: Intercept 2, Slope 0.5 for visual fit)
    \draw[domain=0:9, smooth, variable=\x, blue, ultra thick] plot ({\x}, {2 + 0.6*\x});
    \node[blue, right] at (9,7.4) {$AE = 20 + 0.8Y$};

    % Equilibrium Point
    \draw[dashed, darkgray] (5,0) -- (5,5);
    \draw[dashed, darkgray] (0,5) -- (5,5);
    \filldraw[red] (5,5) circle (2.5pt);
    \node[below] at (5,0) {$100$};
    \node[left] at (0,5) {$100$};

    \node[above, font=\bfseries] at (5,10) {Goods Market Equilibrium};
\end{tikzpicture}

\vspace{1cm}

% --- DIAGRAM 3: NET EXPORTS (TRADE BALANCE) ---
\begin{tikzpicture}[scale=0.8, every node/.style={font=\small}]
    % Axes
    \draw[->, thick] (0,0) -- (10,0) node[right] {$Y$};
    \draw[->, thick] (0,-2) -- (0,3) node[above] {$NX$};

    % NX Line: NX = 1 - 0.01Y (Scaled)
    \draw[domain=0:9, smooth, variable=\x, teal, thick] plot ({\x}, {1.5 - 0.15*\x});

    % Zero point (Y=100)
    \filldraw[black] (10/1,0) circle (0pt); % Reference
    \node[below] at (10,0) {$100$};

    % Labels
    \node[teal, above right] at (1,1.35) {Surplus ($NX > 0$)};
    \node[teal, below right] at (7,-0.5) {Deficit ($NX < 0$)};

    \node[above, font=\bfseries] at (5,3) {Net Exports and Automatic Stabilisation};
\end{tikzpicture}

\vspace{1cm}

% --- DIAGRAM 4: CAPITAL MARKET EQUILIBRIUM ---
\begin{tikzpicture}[scale=0.8, every node/.style={font=\small}]
    % Axes
    \draw[->, thick] (0,0) -- (10,0) node[right] {$Y$};
    \draw[->, thick] (0,0) -- (0,8) node[above] {$NS, NAF$};

    % NS = 0.19Y - 9 (Scaled for visibility)
    \draw[domain=2:9, smooth, variable=\x, orange, thick] plot ({\x}, {-1 + 0.6*\x});
    \node[orange, right] at (9,4.4) {$NS (S+B)$};

    % NAF = 11 - 0.01Y (Scaled for visibility)
    \draw[domain=0:9, smooth, variable=\x, purple, thick] plot ({\x}, {5 - 0.1*\x});
    \node[purple, right] at (9,4.1) {$NAF (I+NX)$};

    % Intersection at Y=100 (Scaled to x=6 approx)
    \draw[dashed, gray] (6,0) -- (6,2.6);
    \filldraw[black] (6,2.6) circle (2pt);
    \node[below] at (6,0) {$100$};

    \node[above, font=\bfseries] at (5,8) {Capital Market Equilibrium};
\end{tikzpicture}

\end{document}

7
- Expansionary Fiscal Policy
- $G ↑$ or $T ↓, t ↓, r ↓$ in order to grow
- $A E = 5 + 0.81 Y + 10 + 4 + 1 - 0.01 Y$
- $A E = 0.8 Y + 20$
  - $y = 100$
  - $b = 16$
  - $s = - 6$
  - $n x = 0$
- Initial equilibrium at $G = 4$
- Now what if $A E = 5 + 0.81 Y + 10 + 16 + 1 - 0.01 Y$
- $A E = 0.8 Y + 32$
  - Equilibrium is now $y = 160$
    - $Y = A E$
    - $Y = 32 + 0.8 Y$
    - $Y = 160.0$
  - Add lines:
    - $y = x$
    - $A E_{0}$
    - $A E_{1}$
    - $y = 160$
    - $y = 100$
  - Why?
    - $G ↑ 12$ and $y ↑ 60$
      - Imagine the impact when economists told govt that increase spending by $12 $$ to grow the economy by $60 $$ .
      - Impact on politics?
      - Keynesian Macroeconomics resulted in politicians spending a lot.
    - How
      - How does a $12 $$ increase result in $60 $$ increase?
      - It's a $\frac{60}{12} = 5.0 x$ increase.
      - Slope of the $A E$ curve was $0.8$ :
        
        If the govt gave someone an extra 100 bones: $G ↑ 100$
        
        $A E$ means you spend $80$ bones
        
        $G D I ↑ 80$
        
        Means those people who got that money, will spend $80 %$ of that again.
        
        Keeps recursing until it ends.
        
        $\frac{1}{1 - 0.8} = 5.0 x$ multiplier based on the Geometric Series.
        
        You can also do $\frac{Δ y}{Δ A E} = \frac{60}{12} = 5.0 x$
    - Impact on the budget
      - How does the increase of spending by govt, affect budget balance?
      - Graph:
        
        $B_{0} = 10 + 0.1 Y - 4$
        
        let $y = 100$ meaning $b_{0} = 10 + 0.1 (100) - 4 = 16$
        
        Label intersection as $A$
        
        If you spend more
        
        $B_{1} = 10 + 0.1 Y - 16$
        
        let $y = 100$ meaning $b_{1} = 10 + 0.1 (100) - 16 = 4$
        
        Label intersection as $A^{'}$
        
        But if GDP increases, direct taxes increase
        
        $y = 160$ means $b_{1} = 10 + 0.1 (160) - 16 = 10$
        
        Show arrow pointing from $A^{'}$ to new $b_{1}$
    - $b = 16 \to 10$
      - Imagine you talk to a $6$ year old. Tell him you have 16 bones, if you spend 12 bones, you have 10 dollars left?
      - Why is it $10$ ?
        
        Because GDP grew, direct tax $↑$ .
        
        So it only cost $6 $$ to increase the GDP that much
        
        Because of the multiplier.
    - Capital Markets
      - What's the impact on the capital markets?
      - $y = 100 \to 160$
      - $b = 16 \to 10$
      - $s = - 6 \to - 0.6$
        
        $0.09 (160) - 15$
      - $n x = 0$
        
        $n x = 1 - 0.01 y$
        
        $n x = 1 - (0.01) (160)$
        
        $n x = - 0.6$
      - $I = 10 \to 10$
      - $N S = N A F$
        
        $b + s = I + 0.6$
        
        $10 + 0.6 = 10 + 0.6$
$C = a + b Y^{D}$
- Consumption function
$Y^{D} = Y - T - t Y$
- Disposable Income after taxes
$C = a + b (Y - T - t Y)$
$C = a - b T + b (1 - t) Y$
$A E = C + I + G + X - m Y$
$A E = [a - b T + I + G + X] + [b (1 - t) - m] Y$
- $a$ : autonomous consumption
  - If canadian consumers were confident or not
- $- b T$
  - Indirect taxes
- $I$
  - Interest rates changes, opportunitiy costs of investmetns
- $G$
- $X$
  - $e$
  - $P_{F}$
  - $P$
  - $Y_{F}$
- $b$
  - $M P C$
  - Marginal propensity to consume
  - Changes the slope and intercept at the same time.
- $1 - t$
  - Tax rate by govt
- $m$
  - Changes in marginal propensity to import.
$S = ?$
$B = ?$
$N X = ?$
#tk
Notes: to Expand GDP
- $G$
  - Govt spending
  - Causes $A E$ to shift
  - Causes $B ↓$
  - Doesn't shift $N X$ or $S$
- $T$
  - Decrease indirect taxes
  - Shifts $A E$
  - Shifts $B$
  - Shifts $S$
  - Doesn't shift $N X$
- $t$
  - Changes tax rate
  - Cutting makes economy grow
  - $A E$ curve rotates
  - $B$ rotates
  - $S$ rotates
  - Doesn't affect net exports
- $r$
  - Decrease interest rates
  - $I ↑$
  - $A E$ is affected
  - Doesn't affect $B$ or $S$ or $N X$
- $e$
  - To stimulate the economy
  - You could devalue the currency.
  - Affects $A E$ and $N X$
  - Doesn't affect $B$ or $S$
- How does the govt choose what to do?
  - $G$ hard to eliminate
    - Eventually needs to cut back on spending to slow the economy down.
      - Family allowances
        
        Intended to stimulate economy
        
        Moms have a big MPC
        
        Hard to eliminate the spending
    - Construction projects are good
      - Once it's done construction, spending stops, but it's still good to stimulate.
      - Ex:
        
        IB building
        
        Also the construction workers have a high $M P C$ .
    - Takes time to implement an increase in spending.
  - $t, T$ are fast to eliminate to stimulate the economy.
    - If the govt dropped the tax to stimulate quickly. They can affect everyone, any $M P C$ .
  - $e$ and $r$ are secret stimulators, but invisible to consumers.