ECON-1221 Chapter 7 - Notes from the Textbook

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

Study Session Meta (delete when complete)

LO Coverage & Mastery

LO	Title	Status	Mastery	New Section(s)
1	Government purchases and taxes	✅ Complete	🔶 Understood	§1 (taxes/leakages) + §2 (G, budget balance)
2	Exports and imports	✅ Complete	🔶 Understood	§1 (import leakage) + §2 (X, NX, shift/rotate)
3	Equilibrium with G and trade	✅ Complete	🔶 Understood	§2 (AE assembly) + §3 (solving equilibrium)
4	Why the multiplier shrinks	✅ Complete	🔶 Understood	§1 (leakage setup) + §3 (multiplier payoff)
5	Fiscal policy	✅ Complete	🔶 Understood	§4
6	Demand-determined output	✅ Complete	🔶 Understood	§5

Vocabulary Tracker

Term	Tier	Location	Note
Net tax rate ($t$)	T1	§1 [!idea] + [!error]	Woven in
MPC out of national income	T1	§1 [!idea] + [!error]	Woven in
Marginal propensity to import ($m$)	T1	§1 [!idea] + [!error]	Woven in
Fiscal policy	T1	§4 [!idea] + [!error]	Woven in
Simple multiplier (complete)	T1	§3 [!idea] + table	Woven in
AE function (complete)	T1	§2 [!error] (AE≠AD)	Woven in
Only the slope survives	T3	Only the Slope Survives a Change in a Linear Function	Spans Ch6–Ch8
Division is multiplication by reciprocal	T3	Division is Multiplication by the Reciprocal	Underlies multiplier notation

Current Position

Status: All LOs tested. Notes restructured for teaching flow. Mastery re-checks for LO1 and LO5 pending before exam.

Mastery Gaps (Review Before Exam)

• LO1: Initially confused $t$ with $(1-t)$ — thought smaller $t$ = smaller slope, forgot taxes enter as $(1-t)$ which inverts direction. Fixed but drill before exam.
• LO1: Forgot $-m$ when writing $z$ — wrote $MPC(1-t)$ but dropped import leakage. Needs practice with full $z=b(1-t)-m$.
• LO5: Initially reversed direction of tax cut on AE slope (said “flatter” when it should be “steeper”). Root cause: thinking in pure numbers rather than tracing the economic logic. Corrected via leakage heuristic: less leakage = steeper.
• LO1→LO5: Didn’t initially understand what “in terms of Y” means (substituting $Y_D$ out). Now solid.
• LO3: Couldn’t connect $Y=\frac{A}{1-z}$ to $\Delta Y=\frac{1}{1-z}\times \Delta A$ — two gaps: (1) didn’t see the change formula as subtraction of two equilibria, (2) unfamiliar with reading a fraction as multiplication by the reciprocal. Both now addressed with atomic notes. Drill before exam.
• LO3→LO4: Confused the multiplier ($\frac{1}{1-z}$) with equilibrium Y ($\frac{A}{1-z}$). Now clarified — three-expression table added. Drill the distinction.
• LO6: Correctly described fixed price assumption and diminishing returns but couldn’t identify WHEN it’s realistic (recession, not boom). Key insight: idle resources = cheap to expand = prices flat = demand-determined.

Notes Improvements Made

• Created atomic note: Only the Slope Survives a Change in a Linear Function
• Explained $m=0.1$ as assumed parameter (was unexplained textbook reference)
• Linked AE components back to Ch5 mnemonic “Can I Get Net eXports?” (replaced invented “sig-nix”)
• Formatted all callouts for skimmability (punchline on line 1, spacing below)
• Removed all [!Kai] callouts — folded content into main text or converted to [!tip]/[!attention]
• Added parameter vs variable callout near $m$ explanation, linking to Endogenous vs Exogenous Variables
• Created atomic note: Division is Multiplication by the Reciprocal
• Added NX slope interpretation callout (What / Why / So What)
• Updated Ch6 notes: added multiplier derivation steps, three-expression table, subtraction proof, “result over trigger” language
• Deleted duplicate Ch6 notes from 01 Spaces/Langara/ (keeping laptop-vault version only)
• Added demand-side vs supply-side section with mnemonics
• Full restructure: Reorganized from textbook LO order to teaching flow. Merged taxes + imports into “Three Leakages” (§1). Promoted dollar-tracing walkthrough to section backbone. Elevated three-expression distinction to first-class subsection. Eliminated all [!vocab] blocks. Added SCQA transitions.

Session Log

Date	LOs Covered	Mastery Results	Key Clarifications
2026-03-01	LO1, LO5 (partial LO2)	LO1: 🔶 Understood (apply gap on $(1-t)$ direction), LO5: 🔶 Understood (shift vs rotate solid, direction tripped once)	Change formula proof, tax wedge direction, shift vs rotate for $\Delta G$ vs $\Delta t$, full $z$ formula must include $-m$
2026-03-01	LO2, LO3, LO4, LO6	All 🔶 Understood	NX slope meaning (What/Why/So What), multiplier vs equilibrium Y distinction, change formula derivation (subtraction of two equilibria), fractions as multiplication, recession = when demand-determined assumption holds

Note on Organization

This note reorganizes the textbook’s LOs to follow how understanding actually built during study sessions. The core question this chapter answers is: What happens to the spending chain — and the multiplier — when we add realistic leakages?

Textbook LO	Section Here
LO1 (Government purchases and taxes)	§1 (tax leakage) + §2 (G, budget balance)
LO2 (Exports and imports)	§1 (import leakage) + §2 (X, NX, shift/rotate)
LO3 (Equilibrium with G and trade)	§2 (AE assembly) + §3 (solving)
LO4 (Why the multiplier shrinks)	§1 (leakage setup) + §3 (payoff)
LO5 (Fiscal policy)	§4
LO6 (Demand-determined output)	§5

What changed from Chapter 6?

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

Assumption	Ch6	Ch7	Ch8 (coming)
Closed economy (no trade)	✓ Assumed	✗ Removed — X and IM added	✗
No government (no taxes)	✓ Assumed	✗ Removed — G and T added	✗
Constant price level	✓ Assumed	✓ Still assumed	✗ Removed

The critical consequence: $Y_D\ne Y$ anymore.

In Ch6, no taxes meant disposable income equaled national income. Now $Y_D=Y-T$, and since $T$ depends on $Y$, every formula downstream changes. This single change — taxes creating a wedge between Y and Y_D — drives most of what’s new in this chapter.

Prerequisites — already in your vault

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

• Government purchases vs transfer payments → [[ECON-1221 Chapter 5 - Notes from the Textbook#what-are-government-purchases-g_a|What are government purchases ($G_a$)?]]
• Net exports, why add X, why subtract IM → [[ECON-1221 Chapter 5 - Notes from the Textbook#what-are-net-exports-nx_a|What are net exports ($N{X}_a$)?]]
• Marginal propensity to spend (z) and Zpender mnemonic → What is the marginal propensity to spend?
• Simple multiplier derivation → The algebra of the simple multiplier (formal derivation)
• AE = C + I (simplified) → How do the formulas in this chapter connect?

Notation clarifications

Notation traps across sources

Symbol	Textbook writes	Professor writes	Meaning
Autonomous consumption	lowercase $c$	$\overline{C}$	Same thing — the y-intercept of the consumption function
Disposable income	$Y_D$	$Y_{Disp}$	Same thing — income after net taxes
Aggregate demand (Ch8)	$Y^D$ (superscript)	$Y^D$ (superscript)	DIFFERENT from $Y_D$ — this is the demand curve, not disposable income

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

The formula chain (road map)

Compressed overview — each step is taught in the sections below.

$$\begin{array}{rlrl}\text{[ Given ]}& & & \text{Where}\{\begin{array}{l}a=30,b=0.8,t=0.1,m=0.1\\ \\ I_0=75,G_0=51,X_0=72\end{array}\\ & & & \\ \text{[ Tax wedge ]}& & Y_D& =(1-t)Y=0.9Y\\ & & & \\ \text{[ Consumption ]}& & C& =a+b{Y}_D=a+b(1-t)Y\\ & & & \\ \text{[ Consumption ]}& & C& =30+0.8(0.9)Y=30+0.72Y\\ & & & \\ \text{[ AE components ]}& & AE& =C+I+G+(X-IM)\\ & & & \\ \text{[ Substitute ]}& & AE& =\underset{A}{\underbrace{[a+I_0+G_0+X_0]}}+\underset{z}{\underbrace{[b(1-t)-m]}}\cdot Y\\ & & & \\ \text{[ AE function ]}& & AE& =228+0.62Y\\ & & & \\ \text{[ Slope ]}& & z& =b(1-t)-m=0.8(0.9)-0.1=0.62\\ & & & \\ \text{[ Equilibrium ]}& & AE& =Y⟹228+0.62Y=Y\\ & & & \\ \text{[ Solve ]}& & 228& =0.38Y\\ & & & \\ \text{[ Answer ]}& & Y& =\boxed{600}\\ & & & \\ \text{[ Multiplier ]}& & \frac{1}{1-z}& =\frac{1}{0.38}=\boxed{2.63}\end{array}$$

Compare to Ch6 where $z=MPC=0.8$ and multiplier $=5$.

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1. Tracing the Dollar — The Three Leakages

In Ch6, 80¢ of every dollar got re-spent ($z=MPC=0.8$). Now three things drain money before it returns to the domestic spending stream. Trace what happens to $1 of additional national income — the answer is $z$.

Leakage 1: Taxes ($t$)

Net tax revenue = total tax revenue minus total transfer payments, positively related to Y.

$T=tY$ where $t$ is the net tax rate (also called the marginal propensity to tax) — the fraction of each $1 of Y collected as net taxes.

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 — income tax, corporate tax, GST, provincial sales tax, property taxes, minus EI, CPP, welfare, and subsidies, all compressed into one number.

Mental model: the tax funnel

Every dollar of national income flows through this funnel before reaching households. The funnel catches $t$ cents. What comes out — $(1-t)$ cents — is disposable income.

Transfer programs have built-in eligibility rules tied to income. When GDP rises, more people are employed, fewer qualify for EI and welfare, and government pays out less. So when Y↑, tax revenue↑ AND transfers↓, both pushing net taxes higher.

These are automatic stabilizers — they cushion the economy without any new policy decision.

Result: Only $(1-t)$ cents of each dollar reach households.

$$\begin{array}{rl}{Y}_D& =(1-t)Y\\ & \\ Y_D& =0.9Y\end{array}$$

With $t=0.1$:

If $Y=600$, then $T=60$, so $Y_D=540$.

Leakage 2: Saving ($(1-b)$ of $Y_D$)

The consumption function is still $C=a+b{Y}_D$, but now $Y_D=(1-t)Y$. Four 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 $Y_D$:

$$\begin{array}{rl}C& =a+b(1-t)Y\\ & \\ C& =30+0.8(0.9)Y\\ & \\ C& =30+0.72Y\end{array}$$

The MPC out of national income = $b(1-t)$. In numbers: $0.72=0.8\times 0.9$.

Households still consume 80¢ of every dollar they receive. But they only RECEIVE 90¢ of every dollar of national income.

The Trap

MPC out of national income ≠ MPC out of disposable income.

The MPC out of $Y_D$ is still 0.8 — households haven’t changed. The wedge comes from taxes taking a cut BEFORE households see the income. That’s why $b(1-t)=0.72<0.8=b$.

Result: Of the 90¢ that reaches households, 72¢ is consumed, 18¢ is saved.

Leakage 3: Imports ($m$)

Imports are induced — they rise as national income rises, because almost all consumption goods have some import content.

Almost every good Canadians consume has import content — cars use imported components, clothes use imported cotton, restaurant meals use imported produce. As consumption rises with income, imports rise through two channels:

• Intermediate goods: Canadian firms buy foreign components
• Final goods: Canadian households buy foreign products directly

$IM=mY$

Parameter	Textbook example	What it represents	Realistic Canada
$m$	0.1 (10¢ per $1 of Y)	Import leakage rate	~0.35 (35¢ per $1)

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 $z=b(1-t)-m$ — it drains from the spending chain every round.

Result: Of the 72¢ consumed, 10¢ leaves the country.

What survives: $z$

$z=b(1-t)-m$ — the marginal propensity to spend on domestic output.

$1 of additional national income enters the system. What happens to it?

Step	What happens	Amount left
Start	$1 of national income	$1.00
Tax leakage	Government takes $t=10¢$	$0.90 disposable
Saving leakage	Household saves $(1-b)=20\%$ of $0.90	$0.72 consumed
Import leakage	Of spending, $m=10¢$ goes abroad	$0.62 domestic

$$\begin{array}{rl}z& =b(1-t)-m\\ & \\ z& =0.8(0.9)-0.1\\ & \\ z& =0.62\end{array}$$

That 62¢ becomes someone else’s income, and the cycle repeats — each round 62% survives. This is why the multiplier is $\frac{1}{1-0.62}=2.63$, not the 5 from Ch6.

Unlike in Ch6, $z\ne MPC$. 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

Parameters vs variables — what gets given vs what you solve for

$m=0.1$, $t=0.1$, $b=0.8$ are parameters (exogenous) — structural assumptions baked into the model. On an exam, they’ll be given to you.

$Y$, $C$, $AE$, $NX$ are variables (endogenous) — determined inside the model. These are what you solve for.

Full explanation: Endogenous vs Exogenous Variables

From "full formula" to "change formula" — why the constant disappears

In any linear function, the constant cancels when you calculate changes — only the slope survives. $\Delta C=b(1-t)\cdot \Delta Y$, not the full $C=a+b(1-t)Y$. The autonomous part ($a$) drops out when you subtract.

Why economists write $\frac{1}{1-z}\times \Delta A$: Dividing by $(1-z)$ is the same as multiplying by $\frac{1}{1-z}$. They 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 proof: Only the Slope Survives a Change in a Linear Function

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2. Building the Complete AE Function

Now that we know the leakage rate ($z=0.62$), we need the full AE function. That means assembling all four components: “Can I Get Net eXports?”

Government purchases (G)

Government purchases are autonomous with respect to national income. G does not depend on Y.

$G=G_0=51$

Government decides how much to spend through political/budgetary processes. On a graph, G is a horizontal line — same shape as autonomous investment from Ch6.

Quick refresher: G vs transfers

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	✅	Government buying labour → production occurs
Buying office supplies	✅	Government buying goods → production occurs
Commissioning a consultant study	✅	Government buying services → production occurs
Welfare payments	❌	Transfer — no production purchased
Employment Insurance	❌	Transfer — just moving money
Subsidies to firms	❌	Transfer — just moving money

Transfers affect AE indirectly — when recipients spend the transfer on consumption, THAT spending enters AE through C.

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) — it captures both sides in one variable.

"The government" = ALL levels combined

Federal, provincial, territorial, and municipal. Provincial and municipal governments actually account for MORE purchases of goods and services than the federal government does.

Exports (X)

Exports are autonomous with respect to Canadian national income. X does not depend on Y.

$X=X_0=72$

Foreign buyers’ decisions depend on THEIR income, THEIR preferences, exchange rates, and international relative prices — not on Canadian national income.

The net export function (NX)

Imports were introduced in §1 as a leakage. Here we combine them with exports to get the NX function:

$$\begin{array}{rl}NX& =X-IM\\ & \\ NX& =X_0-mY\\ & \\ NX& =72-0.1Y\end{array}$$

Since X is constant but IM rises with Y, net exports fall as Y rises. The slope $-m$ tells you how fast they fall.

What does the slope of NX actually mean?

What: $-m$ is the rate at which net exports erode 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 and 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 $m$) → smaller $z$ → smaller multiplier. An economy that imports more per dollar of income gets less domestic bang from every stimulus dollar. This is why Canada’s real multiplier is much smaller than the textbook’s model suggests — our actual $m\approx 0.35$, not 0.1.

Y	X	IM = 0.1Y	NX = X − IM
0	72	0	72
300	72	30	42
600	72	60	12
720	72	72	0
900	72	90	−18

At $Y=720$, exports exactly equal imports (NX = 0). Below that, Canada runs a trade surplus. Above that, a trade deficit.

The NX function is NOT analogous to (MPC vs MPS). $C+S=Y_D$ is an identity — all income is either consumed or saved. But $X+IM$ doesn't equal anything in particular. 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↑ → foreigners buy more Canadian goods → X↑ → NX shifts up (parallel)

Because the US is Canada's largest trading partner, US GDP changes directly affect Canadian exports.

US boom → Canadian exports rise. US recession → Canadian exports fall.

2. Changes in international relative prices

The most important cause of relative price changes is the exchange rate.

Exchange rate change	Effect on X	Effect on IM	Effect on NX
CAD depreciates (weaker dollar)	X↑	IM↓ (m falls)	NX shifts up, becomes flatter
CAD appreciates (stronger dollar)	X↓	IM↑ (m rises)	NX shifts down, becomes steeper

CAD depreciates relative to euro:

• Canadians switch from French wine to B.C. wine → imports fall
• Europeans find Quebec furniture and Maritime vacations cheaper → exports rise
• Overall: NX shifts up and becomes flatter

Prices and exchange rates are exogenous in this model — we can discuss what happens IF they change, but we can't explain WHY they change yet. The price level becomes endogenous in Ch8. Exchange rate in Ch19.

Shift vs rotate — the general rule

Things that change autonomous exports (X) shift NX parallel. Things that change m rotate NX by changing its slope.

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)

Assembling the complete AE function

Same four components from Ch5: "Can I Get Net eXports?"

From What is GDP measured from the expenditure side? — same categories, now with behavioural formulas:

Component	Ch5 (measurement)	Ch7 (behavioural formula)	Autonomous or Induced?
Consumption	$C_a$	$C=a+b(1-t)Y$	Both
Investment	$I_a$	$I=I_0=75$	Autonomous
Government purchases	$G_a$	$G=G_0=51$	Autonomous
Net eXports	$X_a-I{M}_a$	$NX=X_0-mY=72-0.1Y$	Both

Substituting all behavioural functions:

$$\begin{array}{rl}AE& =C+I+G+(X-IM)\\ & \\ & =[a+b(1-t)Y]+I_0+G_0+[X_0-mY]\\ & \\ & =\underset{\text{Autonomous }(A)}{\underbrace{[a+I_0+G_0+X_0]}}+\underset{\text{Slope }(z)}{\underbrace{[b(1-t)-m]}}\cdot Y\end{array}$$

With the textbook’s numbers:

$$\begin{array}{rl}AE& =[30+75+51+72]+[0.8(0.9)-0.1]Y\\ & \\ AE& =228+0.62Y\end{array}$$

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 all three leakages.

The Trap

AE ≠ 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 - Notes from the Textbook].

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 — 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	$0.72-0.1$ — slope of AE

Budget balance

The budget balance = $T-G$. It tells you whether the government is taking in more than it spends.

Situation	Condition	Name
Revenue > Spending	$T>G$ → $T-G>0$	Budget surplus
Spending > Revenue	$T<G$ → $T-G<0$	Budget deficit
Revenue = Spending	$T=G$ → $T-G=0$	Balanced budget

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.

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. Deficits and government debt are covered in Chapter 16.

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 revenue goes to interest payments rather than programs. This creates a feedback loop: more interest → less room for spending → harder to grow → 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. This is Chapter 16 territory.

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3. Equilibrium and the Multiplier

We have $AE=228+0.62Y$. Set $AE=Y$ and solve — same method as Ch6, same formula, very different number.

Finding equilibrium

$$\begin{array}{rl}228+0.62Y& =Y\\ & \\ 228& =0.38Y\\ & \\ Y& =\boxed{600}\end{array}$$

At $Y=600$:

• $C=462$,
• $I=75$,
• $G=51$,
• $NX=72-60=12$.
• Total AE = $462+75+51+12=600$ ✓

The adjustment mechanism is identical to Ch6:

• If $Y<600$: AE > Y → inventories falling → firms increase production → Y rises
• If $Y>600$: AE < Y → inventories rising → firms decrease production → Y falls

Why the multiplier shrank

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

The multiplier shrank from 5 to 2.63 — because z got smaller, not because the formula changed.

Each round of the multiplier, three things drain money out:

Leakage	Rate	What happens to the money
Saving	$(1-b)$ of $Y_D$	Exits → financial markets
Net taxes	$t$ of each $1 of Y	Exits → government
Imports	$m$ of each $1 of expenditure	Exits → foreign economies

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 → smaller multiplier.

Three expressions — don’t confuse them

Expression	Formula	What it gives you
Equilibrium Y	$\frac{A}{1-z}$	The level of national income
Change in Y	$\frac{\Delta A}{1-z}$	How much Y changes when A changes
The multiplier itself	$\frac{1}{1-z}$	The scaling factor — how many dollars of Y per dollar of ΔA

The change formula comes from subtracting two equilibria:

$$\begin{array}{rl}{Y}_{new}-Y_{old}& =\frac{A_{new}}{1-z}-\frac{A_{old}}{1-z}\\ & \\ & =\frac{A_{new}-A_{old}}{1-z}\\ & \\ & =\frac{\Delta A}{1-z}\end{array}$$

The multiplier ($\frac{1}{1-z}$) is what remains when you factor out $\Delta A$. It’s the structural property of the economy — how much any $1 of autonomous spending gets amplified.

How large is the multiplier in the real Canadian economy?

The textbook’s example uses easy numbers 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

$$\begin{array}{rl}z& =0.8(1-0.25)-0.35\\ & \\ z& =0.60-0.35\\ & \\ z& =0.25\end{array}$$ $$\begin{array}{rl}\text{Multiplier}& =\frac{1}{1-0.25}\\ & \\ & =\frac{1}{0.75}\\ & \\ & =\boxed{1.33}\end{array}$$

The realistic Canadian multiplier is only about 1.33 — far below the 5 from Ch6's toy model.

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. Canada’s multiplier is closer to 1.3.

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4. Fiscal Policy

Now that we have the complete model and multiplier, the natural question is: what can the government actually do with it?

What is fiscal policy?

Fiscal policy = the government's use of $G$ and $t$ to influence national income. Two tools only: government purchases and the net tax rate.

The Trap

Fiscal policy ≠ monetary policy.

Fiscal = G and T (spending and taxes). Monetary = interest rates and money supply (later chapters). Don’t mix them. See Stabilization policy.

G does NOT include subsidies.

Subsidies are transfer payments to firms — they’re on the T side (they reduce net taxes), not the G side. G is only purchases of currently produced goods and services.

What is stabilization policy?

Stabilization policy is any attempt to use government policy to keep real GDP close to potential GDP ( $Y^{\ast }$).

When $Y<Y^{\ast }$, unemployment is high. When $Y>Y^{\ast }$, inflation pressures build. Fiscal policy is one tool; 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).

$$\begin{array}{rl}\Delta Y& =\frac{\Delta G}{1-z}\\ & \\ \Delta Y& =\Delta G\times \text{simple multiplier}\end{array}$$

Government cuts consulting spending by $200M. With realistic multiplier of 1.3:

\Delta Y = -200 \times 1.3 = -\260M$

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 → more of each dollar of Y reaches households as $Y_D$
2. $z$ rises → AE steepens → equilibrium Y rises
3. The multiplier itself also gets larger (because z is bigger)

A tax increase ($t$ increases): opposite — AE flattens, Y falls, multiplier shrinks.

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 — 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	✅ Yes
$\Delta I$	Parallel shift	✅ Yes
$\Delta X$	Parallel shift	✅ Yes
$\Delta t$	Rotation (slope change)	❌ No — solve new equilibrium
$\Delta m$	Rotation (slope change)	❌ No — 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 — steeper vs flatter AE

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 — chain dies fast
$z$ closer to 1	Steeper (nearly 45°)	Very large (→∞)	Almost all income gets re-spent — chain dies slowly

When an input to z changes:

• $t$ rises → $(1-t)$ falls → $z$ falls → AE flattens → multiplier shrinks
• $t$ falls → $(1-t)$ rises → $z$ rises → AE steepens → multiplier grows
• $m$ rises → $z$ falls → AE flattens → multiplier shrinks
• $m$ falls → $z$ rises → AE steepens → multiplier grows
• $b$ (MPC) rises → $z$ rises → AE steepens → multiplier grows

In all cases: bigger leakages → flatter AE → smaller multiplier.

Timing and magnitude are hard in practice.

The DIRECTION of fiscal policy is easy to determine (need more Y → expansionary). But the TIMING is uncertain (fiscal policy takes time) and the MAGNITUDE is uncertain (we can only estimate $Y^{\ast }$). These complications are explored in Chapter 9.

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5. The Boundary — When Is This Model Realistic?

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 — and sets up why Ch8 needs to introduce the supply side.

What does “demand determined” mean?

In this model, output is demand determined — firms produce whatever is demanded at the current price level.

National income depends only on how much is demanded — not on supply-side constraints.

When would we expect this to hold?

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.

Most real-world firms don't operate in perfect competition — 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 $Y^{\ast }$, firms hit capacity constraints. They can’t just produce more — so they start raising prices. At that point, output is no longer purely demand determined, and we need the AS curve (Ch8).

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 — 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?

The demand-side inputs to this model ARE the AE components: C, I, G, NX — "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 — the AE function	Consumption, Investment, Government, Net eXports	”Can I Get Net eXports?”
Supply side	What the economy CAN produce — capacity	Labor supply, Technology, Capital stock, Natural resources	”Long Term Capacity Needs”

Why the mnemonic works

Supply-side factors literally ARE long-term capacity needs — they determine how much the economy can produce ($Y^{\ast }$), 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?

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 — it now shifts AD instead.

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Vocabulary Reference

Term	Definition
Government purchases ($G$)	Government spending on currently produced goods and services — autonomous, does not include transfers
Transfer payments	Government spending that does NOT purchase goods/services — 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 (also called the marginal propensity to tax) — captures entire tax-and-transfer system
Budget balance	$T-G$: positive = surplus, negative = deficit, zero = balanced
Budget surplus	$T>G$ — government takes in more than it spends
Budget deficit	$T<G$ — government spends more than it takes in
Exports ($X$)	Foreign spending on domestically produced goods — 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	$NX=X_0-mY$ — falls as Y rises
MPC out of national income	$b(1-t)$ — consumption per $1 of Y, after tax wedge
MPC out of disposable income ($b$)	Consumption per $1 of $Y_D$ — unchanged from Ch6
Marginal propensity to spend ($z$)	$b(1-t)-m$ — slope of AE, the Zpender from Ch6 now fully loaded
Simple multiplier	$\frac{1}{1-z}$ — 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 $Y^{\ast }$
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

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Appendix: Professor’s Required Definitions — Status Tracker

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	✅ Ch7 §2	This note
b	Aggregate demand function	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
c	Aggregate supply function	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
d	AD shock (positive/negative)	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
e	AS shock (positive/negative)	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
f	Fiscal policy	✅ Ch7 §4	This note
g	Stabilization policy	✅ Introduced Ch7 §4	This note + ECON-1221 Chapter 8 - Notes from the Textbook
h	Potential aggregate output	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
i	Simple multiplier	✅ Ch6 + Ch7 §3	This note + ECON-1221 Chapter 6 - Notes from the Textbook
j	MPC out of disposable income	✅ Ch6	ECON-1221 Chapter 6 - Notes from the Textbook
k	MPC out of actual national income	✅ Ch7 §1	This note
l	Marginal propensity to import	✅ Ch7 §1	This note
m	Marginal propensity to tax	✅ Ch7 §1	This note
n	Equilibrium of the macro economy	❌ Partial — AE=Y here, AD-AS in Ch8	ECON-1221 Chapter 8 - Notes from the Textbook
o	Why AD curve has negative slope	❌ Ch8	ECON-1221 Chapter 8 - Notes from the Textbook

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Appendix: Complete Algebraic Exposition

From the textbook’s chapter appendix — the full model in equation form.

Behavioural equations:

Eq.	Formula	Name
[1]	$AE=C+I+G+(X-IM)$	Definition of AE
[2]	$C=a+b{Y}_D$	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]):

$$\begin{array}{rlrl}& [9]C& & =a+b(1-t)Y\\ & & & \\ & [10]AE& & =a+b(1-t)Y+I_0+G_0+X_0-mY\end{array}$$

Collecting terms:

$$\begin{array}{rlrl}& [11]AE& & =\underset{A}{\underbrace{[a+I_0+G_0+X_0]}}+\underset{z}{\underbrace{[b(1-t)-m]}}\cdot Y\\ & & & \\ & & & =A+zY\end{array}$$

Equilibrium condition: $Y=AE$

$$\begin{array}{rlrl}& [12]& Y& =A+zY\\ & & & \\ & [13]& Y-zY& =A\\ & & & \\ & [14]& Y(1-z)& =A\\ & & & \\ & [15]& Y& =\boxed{\frac{A}{1-z}}\end{array}$$

If A changes by $\Delta A$:

$$\begin{array}{rl}\Delta Y& =\frac{\Delta A}{1-z}\\ & \\ \boxed{\text{Simple multiplier}}& =\boxed{\frac{1}{1-z}}\end{array}$$

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

$$\begin{array}{rl}Y& =\frac{228}{1-0.62}\\ & \\ & =\frac{228}{0.38}\\ & \\ & =600\end{array}$$