Kai Mallari's Notes'

ECON-1221 Chapter 7 - Notes from the Textbook_backup

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Ragan, C. T. S. (2024). Macroeconomics (18th Canadian ed.). Pearson Canada.

Note on Organization

This chapter adds government and foreign trade to the Ch6 model. The core question: What happens to the macro model β€” and especially the multiplier β€” when we stop pretending there’s no government and no trade?

Textbook LOSection Here
LO1 (Government purchases and taxes)Β§1
LO2 (Exports and imports)Β§2
LO3 (Equilibrium with G and trade)Β§3
LO4 (Why the multiplier shrinks)Β§4
LO5 (Fiscal policy)Β§5
LO6 (Demand-determined output)Β§6

What changed from Chapter 6?

Ch6 operated under three simplifying assumptions. Ch7 removes the first two while keeping the third.

AssumptionCh6Ch7Ch8 (coming)
Closed economy (no trade)βœ“ Assumedβœ— Removed β€” X and IM addedβœ—
No government (no taxes)βœ“ Assumedβœ— Removed β€” G and T addedβœ—
Constant price levelβœ“ Assumedβœ“ Still assumedβœ— Removed

The critical consequence: anymore.

In Ch6, no taxes meant disposable income equaled national income. Now , and since depends on , every formula downstream changes. This single change β€” taxes creating a wedge between Y and Y_D β€” drives most of what’s new in this chapter.

Prerequisites β€” already in your vault

Don't re-learn these. Reference back if rusty.

Notation clarifications

Notation traps across sources

SymbolTextbook writesProfessor writesMeaning
Autonomous consumptionlowercase Same thing β€” the y-intercept of the consumption function
Disposable incomeSame thing β€” income after net taxes
Aggregate demand (Ch8) (superscript) (superscript)DIFFERENT from β€” this is the demand curve, not disposable income

The key distinction: (subscript) = disposable income. (superscript) = aggregate demand. Don’t mix them up.

Parameters vs variables β€” what gets given vs what you solve for

Values like , , and are parameters (exogenous) β€” they’re structural assumptions baked into the model. On an exam, they’ll be given to you. You never solve for them.

Values like , , , and are variables (endogenous) β€” they’re determined inside the model by the equations. These are what you solve for.

The rule: parameters are inputs you plug in; variables are outputs the model produces. Full explanation: Endogenous vs Exogenous Variables

How do the formulas in this chapter connect? (Road map)

This is a compressed overview showing the chain of formulas from start to finish. Each step is explained in detail in the sections below β€” use this as a road map, not a substitute.

Every formula flows from one change: taxes now exist, so .

Starting point β†’ taxes create a wedge between Y and :

Y_D &= Y - T\\ &= Y - tY \\ &= (1 - t)Y \end{aligned}$$ **β†’ Consumption function** is still $C = a + bY_D$, but substituting: $$\begin{aligned} C &= a + b(1 - t)Y \\ &= 30 + 0.8(0.9)Y \\ &= 30 + 0.72Y \end{aligned}$$ **β†’ AE function** sums all four components: $$\begin{aligned} AE &= C + I + G + (X - IM) \\ &= [30 + 0.72Y] + 75 + 51 + [72 - 0.1Y] \\ &= \underbrace{228}_A + \underbrace{0.62}_{z} \cdot Y \end{aligned}$$ **β†’ Marginal propensity to spend** is now: $$\begin{aligned} z &= MPC(1 - t) - m \\ &= 0.8(0.9) - 0.1 \\ &= 0.62 \end{aligned}$$ **β†’ Equilibrium:** $$\begin{aligned} 228 + 0.62Y &= Y \\ 228 &= 0.38Y \\ Y &= 600 \end{aligned}$$ **β†’ Simple multiplier:** $$\begin{aligned} \text{Simple multiplier} &= \frac{1}{1 - z} \\[6pt] &= \frac{1}{1 - 0.62} \\[6pt] &= \frac{1}{0.38} \\[6pt] &= 2.63 \end{aligned}$$ Compare to Ch6 where $z = MPC = 0.8$ and multiplier = 5. --- # 1. How do government purchases and tax revenues relate to national income? (LO 1) ## How does government spending (G) behave? > [!idea] Government purchases are autonomous with respect to national income. G does not depend on Y. > Government decides how much to spend through political/budgetary processes β€” not as a mechanical function of how much income the economy produces. $$\begin{aligned} G &= G_0 \\ &= 51 \quad \text{(in the textbook's example)} \end{aligned}$$ On a graph with Y on the horizontal axis, G is a horizontal line β€” same shape as autonomous investment from Ch6. > [!tip] Quick refresher on the G vs transfers distinction > > From [[ECON-1221 Chapter 5 - Notes from the Textbook#what-are-government-purchases-g_a|What are government purchases ($G_a$)?]]: > > | Type | In G? | Why | > |---|---|---| > | Hiring a public servant | βœ… | Government buying labour β†’ production occurs | > | Buying office supplies | βœ… | Government buying goods β†’ production occurs | > | Commissioning a consultant study | βœ… | Government buying services β†’ production occurs | > | Welfare payments | ❌ | Transfer β€” no production purchased | > | Employment Insurance benefits | ❌ | Transfer β€” just moving money | > | Subsidies to firms | ❌ | Transfer β€” just moving money | > > Transfers place **no direct demand** on production. They affect AE **indirectly** β€” when recipients spend the transfer on consumption, THAT spending enters AE through C. > [!attention] G is autonomous, but transfer payments generally DO change as GDP rises or falls (e.g., more people claim EI during a recession). This is why we work with NET taxes (taxes minus transfers) β€” it captures both sides in one variable. > ## How do net taxes (T) behave? > [!idea] Net tax revenue is total tax revenue minus total transfer payments. > > > It is positively related to national income β€” as GDP rises, the government collects more tax and pays out fewer transfers. $$\begin{aligned} T &= tY \\ &= (0.1)Y \quad \text{(in the textbook's example)} \end{aligned}$$ where $t$ is the **net tax rate**. > [!error] The Trap > > **Don't think of $t$ as any single tax rate** (like the income tax rate). > > It's the NET effect of the entire tax-and-transfer structure on each additional dollar of national income β€” income tax, corporate tax, GST, provincial sales tax, property taxes, minus EI, CPP, welfare, and subsidies, all compressed into one number. Transfer programs have built-in eligibility rules tied to income. When GDP rises, more people are employed, fewer people qualify for Employment Insurance, fewer people qualify for welfare, and government pays out less in transfers. So when Y↑, tax revenue↑ AND transfers↓, both pushing net taxes (T = taxes βˆ’ transfers) higher. > [!tip] These are **automatic stabilizers** β€” they automatically cushion the economy without any new policy decision. > > > Both sides of net taxes move in the same direction: rising GDP increases tax revenue AND decreases transfer payments. This is why net tax revenue ($T = tY$) is positively related to national income. > [!tip] Mental model for $t$ > > Think of $t$ as a **tax funnel**. Every dollar of national income flows through this funnel before reaching households. The funnel catches $t$ cents of every dollar as net taxes. What comes out the other side β€” $(1 - t)$ cents β€” is disposable income. The funnel represents the ENTIRE tax-and-transfer system compressed into one number. ## What happens to disposable income? With taxes active, disposable income is no longer equal to national income: $$\begin{aligned} Y_D &= Y - T \\ &= Y - tY \\ &= (1 - t)Y \end{aligned}$$ > [!example] With $t = 0.1$: > > If $Y = 600$, then $T = 0.1 \times 600 = 60$, so $Y_D = 600 - 60 = 540$. > Equivalently: $Y_D = (1 - 0.1) \times 600 = 0.9 \times 600 = 540$. > [!error] The Trap > > **Every formula from Ch6 that used $Y_D$ is now affected.** > > In Ch6: $Y_D = Y$, so $C = 30 + 0.8Y$. > Now: $Y_D = 0.9Y$, so $C = 30 + 0.8(0.9Y) = 30 + 0.72Y$. > > The MPC out of disposable income ($b = 0.8$) hasn't changed β€” what changed is how much disposable income you GET from each dollar of national income. ## How does consumption relate to national income with taxes? The textbook walks through this in four explicit steps: **Step 1:** Set the net tax rate. $T = 0.1Y$ **Step 2:** Disposable income is what's left. $Y_D = Y - 0.1Y = 0.9Y$ **Step 3:** The consumption function from Ch6 still uses $Y_D$. $C = 30 + 0.8Y_D$ **Step 4:** Substitute $0.9Y$ for $Y_D$: $$\begin{aligned} C &= 30 + 0.8(0.9Y) \\ &= 30 + 0.72Y \end{aligned}$$ > [!idea] The MPC out of national income = MPC out of disposable income Γ— (1 βˆ’ t). In numbers: $0.72 = 0.8 \times 0.9$. > > > The household's spending behaviour hasn't changed β€” they still consume 80Β’ of every dollar they receive. But they only RECEIVE 90Β’ of every dollar of national income (the other 10Β’ goes to net taxes). > [!error] The Trap > > **MPC out of national income β‰  MPC out of disposable income.** > > The MPC out of $Y_D$ is still 0.8 β€” households haven't changed their behavior. The wedge comes from taxes taking a cut BEFORE households see the income. That's why $b(1-t) = 0.72 < 0.8 = b$. > [!tip] Tracing the dollar β€” a walkthrough > > > **\$1 of additional national income enters the system. What happens to it?** > > 1. Government takes $t = \$0.10$ in net taxes β†’ **\$0.90 left** (disposable income) > 2. Household consumes $b = 80\%$ of that \$0.90 β†’ **\$0.72 consumed** > 3. Of that \$0.72 consumed, $m = \$0.10$ goes to imports β†’ **\$0.62 spent on domestic goods** > > That \$0.62 is $z$ β€” the marginal propensity to spend on domestic output. The three leakages ($t$, saving, $m$) took the rest. > [!tip] From "full formula" to "change formula" β€” why the constant disappears > > > In any linear function, the constant cancels when you calculate changes β€” **only the slope survives**. This is why $\Delta C = b(1-t) \cdot \Delta Y$, not the full $C = a + b(1-t)Y$. The autonomous part ($a$) is the same before and after, so it drops out when you subtract. > > This is also why the multiplier formula works: $\Delta Y = \frac{\Delta A}{1-z}$ β€” the slope ($\frac{1}{1-z}$) survives, the original level of $A$ is irrelevant to the *change*. > > **Why it's written as $\frac{1}{1-z} \times \Delta A$:** This is just the fraction $\frac{\Delta A}{1-z}$ rewritten as multiplication β€” dividing by $(1-z)$ is the same as multiplying by $\frac{1}{1-z}$. Economists separate them to show the multiplier (structural) and the change (what you plug in) as distinct pieces. See [[Division is Multiplication by the Reciprocal]]. > > **Full explanation with proof, examples, and the trap (rotation vs shift):** [[Only the Slope Survives a Change in a Linear Function]] ## What is the budget balance? > [!idea] The budget balance = net tax revenue minus government purchases = $T - G$. It tells you whether the government is taking in more than it spends. > | Situation | Condition | Name | |---|---|---| | Revenue > Spending | $T > G$ β†’ $T - G > 0$ | **Budget surplus** | | Spending > Revenue | $T < G$ β†’ $T - G < 0$ | **Budget deficit** | | Revenue = Spending | $T = G$ β†’ $T - G = 0$ | **Balanced budget** | > [!attention] Since $T = tY$, the budget balance depends on the level of national income. At low Y, T is small and the government likely runs a deficit. At high Y, T is large and the government may run a surplus. The budget balance changes automatically as Y changes, even without any policy change. > > [!example] With $G = 51$ and $T = 0.1Y$: > > - At $Y = 400$: $T = 40$, budget balance = $40 - 51 = -11$ (deficit of \$11B) > - At $Y = 510$: $T = 51$, budget balance = $51 - 51 = 0$ (balanced) > - At $Y = 600$: $T = 60$, budget balance = $60 - 51 = +9$ (surplus of \$9B) When the government runs a deficit, it borrows by issuing bonds or Treasury bills (government debt). When it runs a surplus, it can buy back outstanding debt. Deficits and government debt are covered in detail in Chapter 16. > [!abstract] Beyond the Textbook > > > **What happens when a government can't or won't buy back its debt?** > > The debt accumulates. If debt grows faster than GDP, the debt-to-GDP ratio rises, and an increasing share of government revenue goes to interest payments rather than programs. This creates a feedback loop: more interest payments β†’ less room for spending or tax cuts β†’ harder to grow the economy β†’ debt-to-GDP ratio rises further. Countries that lose creditor confidence face rising interest rates on new borrowing, which accelerates the spiral (Greece 2010-2012). Canada experienced a fiscal crisis in the mid-1990s and responded with severe austerity, eventually returning to surpluses. This is Chapter 16 territory. > [!attention] "The government" = ALL levels combined > > When measuring the overall contribution of government purchases to AE, we include federal, provincial, territorial, and municipal governments combined. Provincial and municipal governments actually account for MORE purchases of goods and services than the federal government does. The federal government raises a little over half the tax revenue of other governments combined, then transfers a significant portion to provinces. --- # 2. How do exports and imports relate to national income? (LO 2) Government purchases and taxes handled one of the two simplifications we're removing. The other: Ch6 assumed a **closed economy** β€” no trade. Now we open it up. Exports bring foreign spending in; imports leak domestic spending out. ## How do exports (X) behave? > [!idea] Exports are autonomous with respect to Canadian national income. X does not depend on Y. > Foreign buyers' decisions depend on THEIR income, THEIR preferences, exchange rates, and international relative prices β€” not on Canadian national income. $$\begin{aligned} X &= X_0 \\ &= 72 \quad \text{(in the textbook's example)} \end{aligned}$$ ## How do imports (IM) behave? > [!idea] Imports are induced β€” they rise as national income rises, because almost all consumption goods have some import content. > **Why imports rise with income?** Almost every good Canadians consume has import content baked into it β€” Canadian-made cars use imported components, Canadian clothes use imported cotton, restaurant meals use imported produce. As consumption rises with income, imports rise automatically. This happens through two channels: - **Intermediate goods:** Canadian firms buy foreign components to manufacture domestic products - **Final goods:** Canadian households buy foreign products directly Because imports rise with $Y$, we model them as a fixed fraction of national income: $$IM = mY$$ where $m$ is the marginal propensity to import β€” an **assumed parameter** representing what fraction of each dollar of national income leaks to imports. Like $b = 0.8$ and $t = 0.1$, the value of $m$ is chosen to make the model workable. It is not derived from other variables. | Parameter | Textbook example value | What it represents | Realistic Canada | |---|---|---|---| | $m$ | 0.1 (10Β’ per \$1 of Y) | Import leakage rate | ~0.35 (35Β’ per \$1) | > [!error] The Trap > > **Imports are a leakage, not just a subtraction.** > > Money spent on foreign goods doesn't become Canadian income and doesn't generate the next round of domestic spending. That's why $m$ appears as a *subtraction* in $z = b(1-t) - m$ β€” it drains from the spending chain every round. ## What is the net export function? $$\begin{aligned} NX &= X - IM \\ &= X_0 - mY \\ &= 72 - 0.1Y \end{aligned}$$ Since X is constant but IM rises with Y, net exports **fall** as Y rises. The slope $-m$ tells you **how fast** they fall. > [!tip] What does the slope of NX actually mean? > > > **What:** $-m$ is the rate at which net exports reduce as national income rises. Every extra \$1 of Y sends $m$ cents abroad. > > **Why it matters:** Those cents that leak to imports are gone from the domestic spending chain. They don't become Canadian income, so they don't generate the next round of domestic C, I, or G. > > **So what:** $m$ appears in $z = b(1-t) - m$. A steeper NX slope (bigger $m$) β†’ smaller $z$ β†’ smaller multiplier. An economy that imports more per dollar of income gets **less domestic bang from every stimulus dollar** because more of each spending round exits the country. This is why Canada's real multiplier is much smaller than the textbook's simplified model suggests β€” our actual $m \approx 0.35$, not 0.1. | Y | X | IM = 0.1Y | NX = X βˆ’ IM | |---|---|---|---| | 0 | 72 | 0 | 72 | | 300 | 72 | 30 | 42 | | 600 | 72 | 60 | 12 | | 720 | 72 | 72 | 0 | | 900 | 72 | 90 | βˆ’18 | At $Y = 720$, exports exactly equal imports (NX = 0). Below that, Canada runs a trade surplus. Above that, a trade deficit. > [!attention] The NX function is NOT analogous to (MPC vs MPS). $C + S = Y_D$ is an identity β€” all income is either consumed or saved. But $X + IM$ doesn't equal anything in particular. A country can export far more than it imports (or vice versa). They're determined by different actors with different drivers. > ## What shifts the net export function? The NX function is drawn holding everything except domestic Y constant. Two major things can shift it: ### 1. Changes in foreign income Foreign income↑ β†’ foreigners buy more Canadian goods β†’ X↑ β†’ NX shifts **up** (parallel) Foreign income↓ β†’ X↓ β†’ NX shifts **down** (parallel) > [!idea] Because the US is Canada's largest trading partner, US GDP changes directly affect Canadian exports. > > > US boom β†’ Canadian exports rise. US recession β†’ Canadian exports fall. This is the trade linkage between the two economies. ### 2. Changes in international relative prices If Canadian prices rise relative to foreign prices: - Foreigners see Canadian goods as more expensive β†’ buy fewer β†’ **X falls** (NX shifts down) - Canadians see foreign goods as cheaper β†’ buy more β†’ **m rises** (NX rotates steeper) - Combined effect: NX shifts down AND becomes steeper If Canadian prices fall relative to foreign prices: opposite β€” NX shifts up and becomes flatter. > [!idea] The most important cause of relative price changes is the **exchange rate**. > > > | Exchange rate change | Effect on relative prices | Effect on X | Effect on IM | Effect on NX | > |---|---|---|---|---| > | CAD **depreciates** (weaker dollar) | Canadian goods cheaper for foreigners | X↑ | IM↓ (m falls) | NX shifts **up**, becomes **flatter** | > | CAD **appreciates** (stronger dollar) | Canadian goods more expensive | X↓ | IM↑ (m rises) | NX shifts **down**, becomes **steeper** | > [!example] CAD depreciates relative to euro: > > - Canadians switch from French wine to B.C. wine β†’ imports fall (m decreases β†’ IM curve rotates down) > - Europeans find Quebec furniture and Maritime vacations cheaper β†’ exports rise (X shifts up) > - Overall: NX shifts up and becomes flatter > [!attention] Prices and exchange rates are **exogenous** in this model β€” we can discuss what happens IF they change, but we can't yet explain WHY they change. The price level becomes endogenous in Ch8. The exchange rate is explained in Ch19. > ### Shift vs rotate β€” the general rule > [!idea] Things that change **autonomous** exports (X) shift NX **parallel**. Things that change **m** **rotate** NX by changing its slope. > > > Some changes (like exchange rates) do both. > > | What changes | What moves | Type of movement | > |---|---|---| > | Foreign income | X (autonomous) | Parallel shift of NX | > | Foreign preferences for Canadian goods | X (autonomous) | Parallel shift of NX | > | International relative prices | Both X AND m | Shift AND rotation of NX | > | Exchange rate | Both X AND m | Shift AND rotation of NX | > | Canadian firms switch to imported inputs | m only | Rotation of NX (steeper) | --- # 3. How do we find equilibrium with government and trade? (LO 3) We now have behavioural formulas for every component β€” $C$, $I$, $G$, and $NX$. Time to assemble the complete AE function, find equilibrium, and see what the multiplier looks like with all the leakages built in. ## What are the four components of AE? > [!tip] Same four components from Ch5: **"Can I Get Net eXports?"** > > From [[ECON-1221 Chapter 5 - Notes from the Textbook#what-is-gdp-measured-from-the-expenditure-side|What is GDP measured from the expenditure side?]] β€” same categories, now with behavioural formulas: > > | Component | Ch5 (measurement) | Ch7 (behavioural formula) | Autonomous or Induced? | > |---|---|---|---| > | **C**onsumption | $C_a$ | $C = a + b(1-t)Y$ | Both β€” $a$ is autonomous, $b(1-t)Y$ is induced | > | **I**nvestment | $I_a$ | $I = I_0 = 75$ | Autonomous | > | **G**overnment purchases | $G_a$ | $G = G_0 = 51$ | Autonomous | > | **N**et e**X**ports | $X_a - IM_a$ | $NX = X_0 - mY = 72 - 0.1Y$ | Both β€” $X_0$ is autonomous, $-mY$ is induced | ## What is the complete AE function? > [!error] The Trap > > **AE β‰  AD.** The desired AE function holds the price level constant and relates desired spending to Y. The aggregate demand function (Ch8) relates the *price level* to *equilibrium* Y. Same inputs, different graph axes, different curve. > > See [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]]. Substituting all behavioural functions: $$\begin{aligned} AE &= C + I + G + (X - IM) \\ &= [a + b(1-t)Y] + I_0 + G_0 + [X_0 - mY] \\ &= \underbrace{[a + I_0 + G_0 + X_0]}_{\text{Autonomous } (A)} + \underbrace{[b(1-t) - m]}_{\text{Slope } (z)} \cdot Y \end{aligned}$$ With the textbook's numbers: $$\begin{aligned} AE &= [30 + 75 + 51 + 72] + [0.8(0.9) - 0.1]Y \\ &= 228 + 0.62Y \end{aligned}$$ > [!idea] The AE function still has the same form as Ch6: $AE = A + zY$. > > > What changed is that $A$ now includes G and X, and $z$ now reflects the leakages from taxes and imports. > [!tip] Breaking down each piece of the AE function > > > | Piece | Value | What it is | Where it came from | > |---|---|---|---| > | $a = 30$ | Autonomous consumption | Ch6 consumption function | > | $I_0 = 75$ | Autonomous investment | Ch6 | > | $G_0 = 51$ | Autonomous government purchases | New in Ch7 | > | $X_0 = 72$ | Autonomous exports | New in Ch7 | > | **$A = 228$** | **Total autonomous expenditure** | Sum of above β€” **y-intercept** | > | $b(1-t) = 0.72$ | MPC out of national income | Consumption after tax wedge | > | $m = 0.1$ | Import leakage | Marginal propensity to import | > | **$z = 0.62$** | **Marginal propensity to spend** | $0.72 - 0.1$ β€” **slope of AE** | ## What is the new z? $$\begin{aligned} z &= b(1 - t) - m \\ &= 0.8(1 - 0.1) - 0.1 \\ &= 0.72 - 0.1 \\ &= 0.62 \end{aligned}$$ The textbook traces it dollar by dollar: National income rises by \$1 β†’ 10Β’ goes to net taxes β†’ 90Β’ becomes disposable income β†’ 80% of 90Β’ = 72Β’ consumed β†’ but 10Β’ of all expenditure goes to imports β†’ net spending on domestic goods = 62Β’. > [!attention] Unlike in Ch6, z β‰  MPC. The Zpender payoff from Ch6 has arrived β€” three things now determine z. > > > | Component | Effect on z | Direction | > |---|---|---| > | $b$ (MPC out of $Y_D$) | ↑ z | More consumption per dollar of disposable income | > | $(1 - t)$ | ↓ z below $b$ | Taxes take a cut before households see income | > | $-m$ | ↓ z further | Some spending leaks to foreign goods | ## Equilibrium national income Same condition as Ch6: $AE = Y$ (the 45Β° line). $$\begin{aligned} 228 + 0.62Y &= Y \\ 228 &= 0.38Y \\ Y &= 600 \end{aligned}$$ At $Y = 600$: $C = 462$, $I = 75$, $G = 51$, $NX = 72 - 60 = 12$. Total AE = $462 + 75 + 51 + 12 = 600$ βœ“ The adjustment mechanism is identical to Ch6: - If $Y < 600$: AE > Y β†’ inventories falling β†’ firms increase production β†’ Y rises - If $Y > 600$: AE < Y β†’ inventories rising β†’ firms decrease production β†’ Y falls --- # 4. Why does the multiplier shrink? (LO 4) In Ch6 the multiplier was 5. With the full model, it's 2.63. Same formula β€” smaller $z$. This section explains why, and what a realistic Canadian multiplier actually looks like. ## The simple multiplier in both models | Model | z | Multiplier | Why | |---|---|---|---| | Ch6 (no govt, no trade) | $z = MPC = 0.8$ | $\frac{1}{0.2} = 5$ | Only leakage is saving | | Ch7 (with govt and trade) | $z = 0.62$ | $\frac{1}{0.38} = 2.63$ | Saving + taxes + imports | > [!idea] The multiplier shrank from 5 to 2.63 β€” because z got smaller, not because the formula changed. > > > Taxes and imports create additional leakages that drain money from the spending stream each round. ## The leakage intuition Each round of the multiplier, three things drain money out: | Leakage | Rate | What happens to the money | |---|---|---| | Saving | $(1 - b)$ of $Y_D$ | Exits spending stream β†’ financial markets | | Net taxes | $t$ of each \$1 of Y | Exits spending stream β†’ government | | Imports | $m$ of each \$1 of expenditure | Exits spending stream β†’ foreign economies | > [!idea] The multiplier is the inverse of the TOTAL leakage rate. > > > In Ch6, total leakage = $1 - z = 0.2$ (just saving). In Ch7, total leakage = $1 - z = 0.38$ (saving + taxes + imports). More leakage β†’ smaller multiplier. ## How large is the multiplier in the real Canadian economy? The textbook's example uses easy numbers ($t = 0.1$, $m = 0.1$) that aren't realistic. With real Canadian values: | Parameter | Textbook example | Realistic Canada | |---|---|---| | MPC ($b$) | 0.8 | 0.8 | | Net tax rate ($t$) | 0.1 | **0.25** | | Marginal propensity to import ($m$) | 0.1 | **0.35** | | $z$ | 0.62 | **0.25** | | Simple multiplier | 2.63 | **1.33** | $$\begin{aligned} z &= 0.8(1 - 0.25) - 0.35 \\ &= 0.8(0.75) - 0.35 \\ &= 0.60 - 0.35 \\ &= 0.25 \end{aligned}$$ $$\begin{aligned} \text{Multiplier} &= \frac{1}{1 - 0.25} \\[6pt] &= \frac{1}{0.75} \\[6pt] &= 1.33 \end{aligned}$$ > [!idea] The realistic Canadian multiplier is only about 1.33 β€” far below the 5 from Ch6's toy model. > > > When a politician claims \$5B in government spending will "create" 15,000 jobs (implying a multiplier of 3), that claim is likely exaggerated. > [!abstract] Beyond the Textbook > > > **The bullshit-detector application:** Next time you hear a politician claim their spending program will create X thousand jobs "directly and indirectly," back out the implied multiplier. If total claimed impact / direct spending > 2, they're probably overstating. The analysis here suggests Canada's multiplier is closer to 1.3. This connects to the consulting diagnostic principle β€” always check whether the numbers imply plausible mechanisms. --- # 5. How does fiscal policy work? (LO 5) Now that we have the complete model and multiplier, the natural question is: **what can the government actually do with it?** Fiscal policy is how government deliberately changes $G$ or $t$ to move equilibrium Y. ## What is fiscal policy? > [!idea] Fiscal policy = the government's use of $G$ and $t$ to influence national income. Two tools only: government purchases and the net tax rate. > > [!error] The Trap > > **Fiscal policy β‰  monetary policy.** > > Fiscal = G and T (spending and taxes). Monetary = interest rates and money supply (later chapters). Don't mix them. See [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot#stabilization-policy|Stabilization policy]]. > [!attention] G does NOT include subsidies. > > > Subsidies are transfer payments to firms β€” they're on the T side (they reduce net taxes), not the G side. G is only purchases of currently produced goods and services. > > The net tax rate ($t$) IS the rate that captures taxes minus transfers. $T = tY$ already accounts for both. ## What is stabilization policy? > [!idea] Stabilization policy is any attempt to use government policy to keep real GDP close to potential GDP ($Y^*$). > > > When $Y < Y^*$, unemployment is high. When $Y > Y^*$, inflation pressures build. Fiscal policy is one tool for stabilization; monetary policy is the other (covered later). ## Changes in government purchases G is autonomous expenditure. Changing G shifts AE **up or down in parallel** (intercept changes, slope doesn't). $$\begin{aligned} \Delta Y &= \frac{\Delta G}{1 - z} \\[6pt] &= \Delta G \times \text{simple multiplier} \end{aligned}$$ > [!example] Government cuts consulting spending by \$200M. With realistic multiplier of 1.3: > > $\Delta Y = -200 \times 1.3 = -\$260M$ > [!example] Government increases highway repair spending by \$1B. With realistic multiplier of 1.3: > > $\Delta Y = +1000 \times 1.3 = +\$1.3B$ ## Changes in the net tax rate Changing the net tax rate changes the **slope** of AE (because $t$ is inside $z$). This means AE **rotates** rather than shifting in parallel. A tax cut ($t$ decreases): 1. $(1 - t)$ increases β†’ more of each dollar of Y reaches households as $Y_D$ 2. $z$ rises β†’ AE steepens β†’ equilibrium Y rises 3. The multiplier itself also gets larger (because z is bigger) A tax increase ($t$ increases): opposite β€” AE flattens, Y falls, multiplier shrinks. > [!error] The Trap > > **The simple multiplier does NOT apply to tax rate changes.** > > The multiplier formula $\Delta Y = \frac{\Delta A}{1-z}$ only works for **parallel shifts** in AE β€” changes in autonomous expenditure. When $t$ changes, the AE curve **rotates** (slope changes), which is NOT a parallel shift. You can't just plug a tax rate change into the multiplier formula. > > | Change | Type of AE movement | Use multiplier? | > |---|---|---| > | $\Delta G$ | Parallel shift | βœ… Yes | > | $\Delta I$ | Parallel shift | βœ… Yes | > | $\Delta X$ | Parallel shift | βœ… Yes | > | $\Delta t$ | Rotation (slope change) | ❌ No β€” solve new equilibrium | > | $\Delta m$ | Rotation (slope change) | ❌ No β€” solve new equilibrium | ## Expansionary vs contractionary fiscal policy | Policy | Action | AE movement | Effect on Y | |---|---|---|---| | **Expansionary** | ↑ G or ↓ t | AE shifts up / steepens | Y rises | | **Contractionary** | ↓ G or ↑ t | AE shifts down / flattens | Y falls | ## Slope heuristic β€” steeper vs flatter AE > [!tip] Quick reference for slopes between 0 and 1 > > > | z value | AE shape | Multiplier | Interpretation | > |---|---|---|---| > | $z$ closer to **0** | Flatter (nearly horizontal) | Closer to **1** | Almost all income leaks out each round β€” chain dies fast | > | $z$ closer to **1** | Steeper (nearly 45Β°) | Very large (β†’βˆž) | Almost all income gets re-spent β€” chain dies slowly | > > **When an input to z changes:** > - $t$ rises β†’ $(1-t)$ falls β†’ $z$ falls β†’ AE **flattens** β†’ multiplier **shrinks** > - $t$ falls β†’ $(1-t)$ rises β†’ $z$ rises β†’ AE **steepens** β†’ multiplier **grows** > - $m$ rises β†’ $z$ falls β†’ AE **flattens** β†’ multiplier **shrinks** > - $m$ falls β†’ $z$ rises β†’ AE **steepens** β†’ multiplier **grows** > - $b$ (MPC) rises β†’ $z$ rises β†’ AE **steepens** β†’ multiplier **grows** > > In all cases: bigger leakages β†’ flatter AE β†’ smaller multiplier. > [!attention] Timing and magnitude are hard in practice. > > The DIRECTION of fiscal policy is easy to determine (need more Y β†’ expansionary). But the TIMING is uncertain (fiscal policy takes time to have effects on real GDP) and the MAGNITUDE is uncertain (we can only estimate $Y^*$, so the gap between actual and potential GDP is imprecise). These complications are explored in Chapter 9. --- # 6. Why is output demand determined? (LO 6) Everything above assumed firms would produce whatever was demanded at a constant price. This section asks: **when is that assumption actually reasonable?** The answer reveals the boundaries of the entire Ch6–7 model β€” and sets up why Ch8 needs to introduce the supply side. ## What does "demand determined" mean? > [!idea] In this model, output is demand determined β€” firms produce whatever is demanded at the current price level. > > > National income depends only on how much is demanded β€” not on supply-side constraints. ## When would we expect this to hold? Two situations justify the assumption: | Situation | Why firms accommodate demand | |---|---| | **Unemployed resources / excess capacity** | Firms CAN produce more without hitting constraints or raising costs | | **Firms are price setters** | Firms with differentiated products adjust QUANTITY first, prices later. Only after demand changes persist do they adjust prices. | > [!attention] The price-setter explanation is important for microeconomics students. Most real-world firms don't operate in perfect competition β€” they sell differentiated products and have some control over pricing. In the short run, they absorb demand changes through production adjustments. This matches our short-run AE model. > ## When does this assumption break down? When the economy approaches or exceeds $Y^*$, firms hit capacity constraints. They can't just produce more β€” so they start raising prices. At that point, output is no longer purely demand determined, and we need the AS curve (Ch8). > [!error] The Trap > > **Demand-determined does NOT mean demand is the only thing that matters in macroeconomics.** > > It means that IN THIS MODEL, with the constant price level assumption, supply passively accommodates demand. The supply side is real β€” it's just not in this chapter's model yet. > > Ch8 makes the price level endogenous and considers supply-side influences (technology, factor prices). When demand AND supply interact, changes in AE cause both prices and real GDP to change. ## What's demand-side vs supply-side? > [!idea] The demand-side inputs to this model ARE the AE components: **C, I, G, NX** β€” "Can I Get Net eXports?" > > > Everything in Chapters 6–7 has been building the demand side. The AE function IS aggregate demand (before we put it on a price-level graph in Ch8). | Side | What it covers | Components | Mnemonic | |---|---|---|---| | **Demand side** | What's being spent β€” the AE function | **C**onsumption, **I**nvestment, **G**overnment, **N**et e**X**ports | "**C**an **I** **G**et **N**et e**X**ports?" | | **Supply side** | What the economy CAN produce β€” capacity | **L**abor supply, **T**echnology, **C**apital stock, **N**atural resources | "**L**ong **T**erm **C**apacity **N**eeds" | > [!tip] Why the mnemonic works > > Supply-side factors literally ARE long-term capacity needs β€” they determine how much the economy *can* produce ($Y^*$), not how much is *demanded*. The Keynesian cross model in Ch6–7 holds all of these constant and asks: given this capacity, how much will actually be demanded? > [!attention] The Ch8 bridge > > In Ch8, the AE components become the **aggregate demand curve** (AD), and the supply-side factors become the **aggregate supply curve** (AS). The fixed price assumption drops away, and both sides interact. Everything you've learned about what shifts AE still applies β€” it now shifts AD instead. --- # Vocabulary Reference | Term | Definition | |---|---| | Government purchases ($G$) | Government spending on currently produced goods and services β€” autonomous, does not include transfers | | Transfer payments | Government spending that does NOT purchase goods/services β€” just moves money (EI, welfare, CPP, subsidies) | | Net tax revenue ($T$) | Total tax revenue minus total transfer payments: $T = tY$ | | Net tax rate ($t$) | Fraction of each \$1 of Y collected as net taxes β€” captures entire tax-and-transfer system | | Budget balance | $T - G$: positive = surplus, negative = deficit, zero = balanced | | Budget surplus | $T > G$ β€” government takes in more than it spends | | Budget deficit | $T < G$ β€” government spends more than it takes in | | Exports ($X$) | Foreign spending on domestically produced goods β€” autonomous with respect to Canadian Y | | Imports ($IM$) | Domestic spending on foreign goods: $IM = mY$ | | Marginal propensity to import ($m$) | Fraction of each \$1 of Y spent on imports | | Net export function | $NX = X_0 - mY$ β€” falls as Y rises | | MPC out of national income | $b(1-t)$ β€” consumption per \$1 of Y, after tax wedge | | MPC out of disposable income ($b$) | Consumption per \$1 of $Y_D$ β€” unchanged from Ch6 | | Marginal propensity to spend ($z$) | $b(1-t) - m$ β€” slope of AE, the Zpender from Ch6 now fully loaded | | Simple multiplier | $\frac{1}{1-z}$ β€” same formula, smaller value because z is now smaller | | Fiscal policy | Government use of G and $t$ to influence national income | | Stabilization policy | Using fiscal and/or monetary policy to keep Y close to $Y^*$ | | Expansionary fiscal policy | ↑ G or ↓ $t$ to raise Y | | Contractionary fiscal policy | ↓ G or ↑ $t$ to lower Y | | Demand-determined output | Firms produce whatever is demanded without changing prices | | Price setters | Firms with market power that adjust quantity before price in the short run | | Automatic stabilizers | Tax-and-transfer features that automatically cushion GDP fluctuations without new policy decisions | --- # Appendix: Professor's Required Definitions β€” Status Tracker > [!warning] The following definitions are specifically required by the professor for "the most complete macroeconomic model we have studied." Track coverage here. > | # | Concept | Covered? | Where | |---|---|---|---| | a | Desired aggregate expenditure function | βœ… Ch7 Β§3 | This note | | b | Aggregate demand function | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | c | Aggregate supply function | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | d | AD shock (positive/negative) | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | e | AS shock (positive/negative) | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | f | Fiscal policy | βœ… Ch7 Β§5 | This note | | g | Stabilization policy | βœ… Introduced Ch7 Β§5 | This note + [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | h | Potential aggregate output | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | i | Simple multiplier | βœ… Ch6 + Ch7 Β§4 | This note + [[ECON-1221 Chapter 6 - Notes from the Textbook]] | | j | MPC out of disposable income | βœ… Ch6 | [[ECON-1221 Chapter 6 - Prependix Professor Definition]] | | k | MPC out of actual national income | βœ… Ch7 Β§1 | This note | | l | Marginal propensity to import | βœ… Ch7 Β§2 | This note | | m | Marginal propensity to tax | βœ… Ch7 Β§1 | This note | | n | Equilibrium of the macro economy | ❌ Partial β€” AE=Y here, AD-AS in Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | | o | Why AD curve has negative slope | ❌ Ch8 | [[ECON-1221 Chapter 8 - Professor Definitions Parking Lot]] | --- # Appendix: Complete Algebraic Exposition From the textbook's chapter appendix β€” the full model in equation form. **Behavioural equations:** | Eq. | Formula | Name | |---|---|---| | [1] | $AE = C + I + G + (X - IM)$ | Definition of AE | | [2] | $C = a + bY_D$ | Consumption function | | [3] | $I = I_0$ | Autonomous investment | | [4] | $G = G_0$ | Autonomous government purchases | | [5] | $X = X_0$ | Autonomous exports | | [6] | $IM = mY$ | Imports | | [7] | $T = tY$ | Net taxes | | [8] | $Y_D = Y - tY = (1-t)Y$ | Disposable income | **Substituting [8] into [2], then summing all components (substituting [3]-[6] and [9] into [1]):** $$\begin{aligned} [9] \quad C &= a + b(1 - t)Y \\[6pt] [10] \quad AE &= a + b(1-t)Y + I_0 + G_0 + X_0 - mY \end{aligned}$$ **Collecting terms:** $$\begin{aligned} [11] \quad AE &= \underbrace{[a + I_0 + G_0 + X_0]}_{A} + \underbrace{[b(1-t) - m]}_{z} \cdot Y \\ &= A + zY \end{aligned}$$ **Equilibrium condition:** $Y = AE$ $$\begin{aligned} [12] \quad Y &= A + zY \\ [13] \quad Y - zY &= A \\ [14] \quad Y(1 - z) &= A \\[6pt] [15] \quad \boxed{Y} &= \boxed{\frac{A}{1-z}} \end{aligned}$$ **If A changes by $\Delta A$:** $$\begin{aligned} \Delta Y &= \frac{\Delta A}{1 - z} \\[6pt] \boxed{\text{Simple multiplier}} &= \boxed{\frac{1}{1-z}} \end{aligned}$$ **With the textbook's numbers:** | Variable | Value | |---|---| | $a$ | 30 | | $b$ | 0.8 | | $t$ | 0.1 | | $m$ | 0.1 | | $I_0$ | 75 | | $G_0$ | 51 | | $X_0$ | 72 | | $A$ | 228 | | $z$ | 0.62 | $$\begin{aligned} Y &= \frac{228}{1 - 0.62} \\[6pt] &= \frac{228}{0.38} \\[6pt] &= 600 \end{aligned}$$

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