ECO102 Lecture 03

Pre-Lecture

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

Lecture

ECO102 Lecture 03 Raw

1. The Government Sector

Government Spending ( $G$ ):
- Defined as $G = 4$ (Autonomous).
- This is a component of Gross Domestic Expenditure: $G D E = C + I + G + (X - Im)$ .
Taxation:
- Indirect Taxes ( $T_{i n d i r e c t}$ ): $T_{i n d i r e c t} = 10$ .
- Direct Tax Rate ( $t$ ): $t = 0.1$ (10% of income).
Government Budget Balance ( $B$ ):
- Formula: $B = Revenue - Spending$ .
- Revenue $= T_{i n d i r e c t} + t Y$ .
- Spending $= G$ .
- $B = (10 + 0.1 Y) - 4$ .
- $B = 6 + 0.1 Y$ .
Visualizing the Budget Function:
- Scenario 1 ( $G = 4$ ): The line is $B = 6 + 0.1 Y$ .
  - y-intercept: 6.
  - Slope: 0.1.
  - Example at $Y = 100$ : $B = 6 + 0.1 (100) = 16$ .
- Scenario 2 ( $G_{1} = 16$ , Higher Spending):
  - New equation: $B_{1} = (10 + 0.1 Y) - 16$ .
  - $B_{1} = - 6 + 0.1 Y$ .
  - The line shifts downward. The vertical intercept is now $- 6$ .
  - At $Y = 100$ : $B = - 6 + 10 = 4$ .
Automatic Stabilizers:
- The Government budget acts as a stabilizer because tax revenues fluctuate with GDP ( $Y$ ).
- When GDP is high, tax revenues rise, cooling the economy (surplus increases).
- When GDP is low, tax revenues fall, mitigating the downturn (deficit increases).

2. The Household Sector

Consumption ( $C$ ):
- Households consume and save.
- Autonomous Consumption ( $a$ ): Consumption not dependent on income (e.g., basic necessities).
- Marginal Propensity to Consume ( $b$ or $M P C$ ): The portion of disposable income spent.
Consumption Function:
- $C = a + b Y^{D}$
- Disposable Income ( $Y^{D}$ ): Income remaining after all taxes.
  - $Y^{D} = Y - T_{i n d i r e c t} - t Y$ .
- Example Calculation:
  - Parameters: $a = 14, b = 0.9, T_{i n d i r e c t} = 10, t = 0.1$ .
  - $C = 14 + 0.9 (Y - 10 - 0.1 Y)$ .
  - $C = 14 + 0.9 (0.9 Y - 10)$ .
  - $C = 14 + 0.81 Y - 9$ .
  - $C = 5 + 0.81 Y$ .
- Key Distinction:
  - $0.9$ is the MPC out of disposable income.
  - $0.81$ is the slope of the consumption function relative to gross income ( $Y$ ). [COMPLETED: You spend 81 cents of every gross dollar earned because 10 cents goes to tax, leaving 90 cents, of which you spend 90%.]
Savings Function ( $S$ ):
- $S = Y^{D} - C$ or $S = Y - T_{t o t a l} - C$ .
- $S = Y - (10 + 0.1 Y) - (5 + 0.81 Y)$ .
- $S = Y - 10 - 0.1 Y - 5 - 0.81 Y$ .
- $S = 0.09 Y - 15$ .
- Check at $Y = 100$ :
  - $S = 0.09 (100) - 15 = 9 - 15 = - 6$ . (Households are dissaving/borrowing).

3. The Corporate Sector

Investment ( $I$ ):
- $I = 10$ (Autonomous).
- Includes Gross Fixed Capital Formation (machines, buildings) + Change in Inventories ( $Δ I N V$ ).
- Interest Rate Relationship:
  - Investment depends inversely on interest rates ( $r$ ).
  - $r$ represents the opportunity cost of capital.
  - If $r ↓$ , then $I ↑$ .
- Inventory Accounting:
  - Includes unused raw materials.
  - Includes finished goods not yet sold.

4. The Non-Resident Sector

Net Exports ( $N X$ ):
- $N X = X - Im$ .
- Imports ( $Im$ ): Assume dependent on income. $Im = m Y$ .
  - $m = 0.01$ (Marginal Propensity to Import).
- Exports ( $X$ ): Dependent on external factors, not domestic $Y$ .
  - Determinants: Domestic Price ( $P$ ), Foreign Prices ( $P_{F}$ ), Foreign Income ( $Y_{F}$ ), Exchange Rate ( $e$ ).
  - If $Y_{F} ↑$ (US booms), they buy more Canadian exports ( $X ↑$ ).
  - If $e ↑$ (CAD depreciates), our goods are cheaper for them ( $X ↑$ ).
- Equation:
  - If $N X = 1 - 0.01 Y$ , then autonomous Exports $X = 1$ .
Trade Balance as Stabilizer:
- When domestic economy booms ( $Y ↑$ ), Imports rise ( $Im ↑$ ).
- This lowers Net Exports ( $N X ↓$ ), creating a leakage that slows the boom.

5. Goods Market Equilibrium

Equilibrium Condition:
- $Y = A E$ (Output = Planned Expenditure).
Aggregate Expenditure ( $A E$ ) Function:
- $A E = C + I + G + (X - Im)$ .
- $A E = (5 + 0.81 Y) + 10 + 4 + (1 - 0.01 Y)$ .
- Combine constants: $5 + 10 + 4 + 1 = 20$ .
- Combine $Y$ terms: $0.81 Y - 0.01 Y = 0.8 Y$ .
- $A E = 20 + 0.8 Y$ .
Solving for Equilibrium:
- $Y = 20 + 0.8 Y$ .
- $Y - 0.8 Y = 20$ .
- $0.2 Y = 20$ .
- $Y = 100$ .
State of Sectors at Equilibrium ( $Y = 100$ ):
- Budget: $B = 6 + 0.1 (100) = 16$ (Surplus).
- Savings: $S = 0.09 (100) - 15 = - 6$ (Dissaving).
- Net Exports: $N X = 1 - 0.01 (100) = 0$ (Balanced Trade).

6. Capital Market Equilibrium

Identity: $N A F = N S$ (Net Asset Formation = National Savings).
- $N A F = I + N X$ .
- $N S = S + B$ (Private Savings + Government Savings).
Verification at $Y = 100$ :
- $N A F = 10 + 0 = 10$ .
- $N S = - 6 + 16 = 10$ .
- $10 = 10$ . The markets clear.

7. Expansionary Fiscal Policy

Scenario: Government Spending increases by 12 ( $G$ goes from $4 \to 16$ ).
New AE Function:
- $A E_{n e w} = (5 + 0.81 Y) + 10 + 16 + (1 - 0.01 Y)$ .
- $A E_{n e w} = 32 + 0.8 Y$ .
New Equilibrium:
- $Y = 32 + 0.8 Y$ .
- $0.2 Y = 32$ .
- $Y = 160$ .
The Multiplier:
- $Δ Y = 160 - 100 = 60$ .
- $Δ G = 12$ .
- Multiplier $= \frac{60}{12} = 5$ .
- Theoretical Calculation: $\frac{1}{1 - slope of AE} = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$ .
Impact on Budget:
- Spending increased by 12, but the deficit did not worsen by 12.
- Initial $B = 16$ .
- New $B = 6 + 0.1 (160) - 12$ (Wait, formula changed because G changed).
- New $B = (10 + 0.1 Y) - 16 = - 6 + 0.1 (160) = - 6 + 16 = 10$ .
- The budget surplus fell from $16 \to 10$ (a drop of 6), even though spending rose by 12.
- Why? Increased $Y$ generated extra tax revenue, "paying for" half the spending increase.

2. Responses to #tk Flags

#tk Item 1: Inventory Investment Classification

Question: If you make $1000 of product in 2026 and sell $800 of it (with no unfinished goods), is that still investment?

Answer: Yes, the unsold portion is Investment.
In Macroeconomic accounting, GDP measures production within a specific time period.

The $1000 produced contributes $1000 to GDP.
The $800 sold counts towards Consumption ( $C$ ).
The remaining $200 worth of goods sits in the warehouse. This is classified as Inventory Investment ( $Δ I N V$ ).
Therefore, $C = 800$ and $I_{i n v e n t o r y} = 200$ . Total $G D P = 1000$ .
Even though the firm didn't intend to buy its own products, national accounting treats unsold inventory as if the firm "bought" it from itself to carry into the next period.

#tk Item 2: Graphics

Question: "Do all graphics too"

Explanation: You need to be able to construct three specific graphs to illustrate the expansionary policy described in Section 7:

The Keynesian Cross (Goods Market):
- Plot $Y$ on the x-axis and $A E$ on the y-axis.
- Draw a 45-degree line ( $Y = A E$ ).
- Draw the initial $A E_{0} = 20 + 0.8 Y$ . Mark the intersection at $Y = 100$ .
- Draw the shifted $A E_{1} = 32 + 0.8 Y$ (parallel shift upward by 12). Mark the new intersection at $Y = 160$ .
Government Budget Function:
- Plot $Y$ on x-axis, $B$ on y-axis.
- Line 1: $B = 6 + 0.1 Y$ (Initial). Point A at $Y = 100, B = 16$ .
- Line 2: $B = - 6 + 0.1 Y$ (After G increases). Shift down by 12.
- Point A' at $Y = 100$ shows the instantaneous deficit ( $B = 4$ ).
- Point B at $Y = 160$ shows the final outcome ( $B = 10$ ). The movement along the line from A' to B is due to the multiplier effect increasing tax revenue.
Leakages and Injections (Capital Market):
- Plot $Y$ on x-axis.
- Plot National Savings ( $N S = S + B$ ) which is an upward sloping line.
- Plot Net Asset Formation ( $N A F = I + N X$ ) which is likely downward sloping or flat (here, $I = 10$ is constant, $N X$ slopes down).
- Equilibrium is where the two lines cross.

TikZ Implementation:

\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}

#tk Item 3: Missing Formula Derivations

Question: Define $S, B, N X$ at the end of the notes.

Answer: This flag asks to formalize the equations used to solve the expansionary policy scenario. Based on the notes:

$S$ (Savings): $S = Y - C - T_{t o t a l} = Y - (a + b (1 - t) Y) - (T_{i n d i r e c t} + t Y)$ .
- In this lecture: $S = 0.09 Y - 15$ .
$B$ (Budget Balance): $B = T_{t o t a l} - G = (T_{i n d i r e c t} + t Y) - G$ .
- In this lecture: $B = 6 + 0.1 Y$ (initially).
$N X$ (Net Exports): $N X = X - m Y$ .
- In this lecture: $N X = 1 - 0.01 Y$ .
Policy Note: When the government uses fiscal policy ( $G ↑$ ), it shifts the $A E$ curve. It shifts the $B$ curve (down). It does not shift the $S$ or $N X$ curves directly; however, because equilibrium $Y$ changes, we move along the $S$ and $N X$ curves to new levels.

3. Lecture Summary

Thesis: The lecture demonstrates how short-run economic equilibrium is determined by Aggregate Expenditure (AE) and how government intervention (Fiscal Policy) can amplify economic output through the Multiplier Effect, while partially paying for itself through Automatic Stabilizers.

Key Concepts:

The AE Model Structure: Equilibrium GDP ( $Y$ ) occurs where planned spending equals production ( $A E = Y$ ). The slope of the AE curve is determined by the marginal propensities to consume ( $b$ ), tax ( $t$ ), and import ( $m$ ).
The Multiplier Effect: A small injection of autonomous spending (like Government Spending, $G$ ) leads to a larger increase in Equilibrium GDP because the initial spending becomes income for others, who then spend a portion of it, creating a cycle of consumption ( $k = \frac{1}{1 - slope of AE}$ ).
Automatic Stabilizers: Tax revenues and Imports depend on Income ( $Y$ ). As $Y$ rises, taxes collect more revenue (dampening deficits) and imports rise (lowering Net Exports), which naturally slows down an overheating economy and mitigates recessions without active policy changes.
Capital Market Consistency: The goods market equilibrium ( $Y = A E$ ) must effectively mirror the capital market equilibrium, where National Savings ( $S + B$ ) equals Net Asset Formation ( $I + N X$ ).

4. Practice Questions

Remember/Understand Level

Define the Marginal Propensity to Consume (MPC) versus the slope of the AE curve. How does the tax rate ( $t$ ) affect the difference between them?
What constitutes "Investment" in the AE model? Explain why unsold inventory is included in this category.
Explain the concept of "Automatic Stabilizers" using the government budget balance as an example.

Apply/Analyze Level

Calculate the Equilibrium: Suppose $C = 50 + 0.75 Y^{D}$ , $I = 20$ , $G = 30$ , $X = 10$ , $I m = 0.1 Y$ , and the tax rate $t = 0.2$ . (Assume no indirect taxes). Calculate the equilibrium GDP.
Analyze a Shock: Using the data from Question 1, if Exports ( $X$ ) fall by 10 due to a foreign recession, by how much will domestic GDP ( $Y$ ) fall? (Hint: Calculate the multiplier).
Compare Policy Impacts: Why might a government choose to stimulate the economy by increasing $G$ (spending) rather than decreasing $t$ (tax rate)? Refer to the speed of implementation and the impact on the AE slope.

Evaluate/Create Level

Evaluate the "Paradox of Thrift": If households decide to save more (increasing the autonomous savings parameter), what happens to Equilibrium GDP? Paradoxically, what might happen to the total level of savings in the economy?

5. Challenging Concepts to Review

Concept 1: The Effective Multiplier

Why it's challenging: Students often confuse the simple multiplier ( $1 / (1 - M P C)$ ) with the complex multiplier that includes taxes and imports.
Study Strategy: Memorize the "Slope of AE" formula rather than just the multiplier formula.

Slope of AE = $b (1 - t) - m$ .
Then, Multiplier = $1 / (1 - Slope)$ .
Practice calculating the slope first, then the multiplier.

Concept 2: Net Asset Formation Vs. National Savings

Why it's challenging: The identity $I + N X = S + B$ is abstract. It's often hard to see why Net Exports are on the "Investment" side.
Study Strategy: Think of it as Uses of Funds = Sources of Funds.

Sources: Private Savings ( $S$ ) and Government Surplus ( $B$ ).
Uses: Investing in physical capital ( $I$ ) or lending to foreigners (which is what a trade surplus $N X$ represents—we send goods, they owe us money).

Concept 3: Budget Balance Vs. Change in Spending

Why it's challenging: In the lecture example, $G$ went up by 12, but the deficit only grew by 6. This is counter-intuitive.
Study Strategy: Visualize the Budget Line graph.

The shift down is the cost of the policy ( $G$ ).
The movement along the line (up and right) is the revenue recovery due to economic growth ( $t Δ Y$ ).
The final change is the net result of these two forces.

6. Your Action Plan

Immediate Review Actions

Review the [COMPLETED] notes in Section 1 and 2 to ensure the derivation of $B$ and $C$ functions makes sense ( $0.81 Y$ vs $0.9 Y^{D}$ ).
Read the "Response to #tk Item 2" and mentally visualize the three graphs described.
Verify the math in Section 7 (Expansionary Policy) to confirm the multiplier of 5 derived from the slope of 0.8.

Practice and Application

Answer the 3 "Remember/Understand" questions to solidify definitions.
Work through "Apply/Analyze" Question 1 (Calculating Equilibrium) using the step-by-step algebra method.
Attempt the "Evaluate" question regarding the Paradox of Thrift—write down the chain of events (Savings up $\to$ Consumption down $\to$ AE down $\to$ Y down).

Deep Dive Study

Focus on Concept 1: Create a flashcard for the Slope of AE formula: $M P C (1 - t) - m$ .
Focus on Concept 3: Draw the Government Budget graph ( $B$ vs $Y$ ) on a blank sheet of paper, illustrating the shift from $G$ and the movement from $Y$ .
Cross-reference the "Investment" definition with the textbook to ensure clarity on why Inventory is included.

Verification and Integration

Compare the formula for the Multiplier in these notes with your textbook to check for notation differences (some books use $z$ for imports or $c$ for consumption).
Connect this lecture to the next topic: How will Money Supply and Interest Rates (Lecture 4/5) shift the $I$ variable that we currently treat as constant?
ECO102 Lecture 03 Flashcards