ECON-1221 Chapter 6 - Notes from the Textbook

All credit for this text goes to...

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

Note on Organization

This note reorganizes the textbook’s LOs to follow a more natural learning progression. The core question this chapter answers is: What determines the short-run level of national income, and why do small changes in spending create big changes in income?

Textbook LO	Section Here
LO1 (Desired vs actual expenditure)	§1 (vocabulary only) + §5 (full mechanism)
LO2 (Determinants of C and I)	§2 + §3
LO3 (Equilibrium national income)	§5
LO4 (Simple multiplier)	§6

Simplifying Assumptions

The model in this chapter operates under three simplifying assumptions:

1. Closed economy — no trade with other countries (no exports or imports)
2. No government — and therefore no taxes
3. Constant price level

Because there is no government and no taxes, disposable income ( $Y_D$) equals national income ($Y$) in this model. This equivalence disappears once taxes are introduced in later chapters. The formulas use $Y_D$ specifically — don't substitute $Y$ just because they happen to be equal here.

How do the formulas in this chapter connect?

Every formula in this chapter flows from one starting identity. Here is how they connect:

Starting identity → disposable income is either consumed or saved:

$Y_D=C+S$

→ Consumption function gives us a rule for C:

$C=30+0.8Y_D$

→ Saving function is derived by substituting C into the starting identity:

$\begin{array}{rl}S& =Y_D-C\\ & =Y_D-(30+0.8Y_D)\\ & =-30+0.2Y_D\end{array}$

→ Propensities are ratios derived from C and S:

$\begin{array}{rlr}MPC& =\frac{\Delta C}{\Delta Y_D}=0.8& \text{(slope of C function)}\\ MPS& =\frac{\Delta S}{\Delta Y_D}=0.2& \text{(slope of S function)}\\ APC& =\frac{C}{Y_D}& \text{(ratio — falls as }{Y}_D\text{ rises)}\\ APS& =\frac{S}{Y_D}& \text{(ratio — rises as }{Y}_D\text{ rises)}\end{array}$

→ Investment function is autonomous (separate from the chain above):

$I=75\text{(horizontal line — doesn’t depend on }Y\text{)}$

→ AE function combines C and I:

$\begin{array}{rl}AE& =C+I\\ & =(30+0.8Y_D)+75\\ & =105+0.8Y\end{array}$

→ Marginal propensity to spend (z) — the slope of the AE function:

$z=\frac{\Delta AE}{\Delta Y}=0.8\text{(equals MPC in this simplified model)}$

→ Equilibrium condition sets AE equal to Y and solves:

$\begin{array}{rl}105+0.8Y& =Y\\ 105& =0.2Y\\ Y& =525\end{array}$

→ Simple multiplier tells you how much Y changes when autonomous expenditure changes:

$\text{Simple multiplier}=\frac{1}{1-z}=\frac{1}{1-0.8}=5$

Key identities that always hold:

$MPC+MPS=1$

$APC+APS=1$

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1. The Setup

This section establishes the vocabulary and ground rules the rest of the chapter depends on.

What is disposable income?

Disposable income ( $Y_D$) is the amount of income households receive after paying taxes.

$Y_D=Y-T$

Since there is no government in this model, $T=0$, so $Y_D=Y$.

Once you have disposable income, it splits into exactly two uses:

$Y_D=C+S$

Which rearranges to:

$S=Y_D-C$

There is no third option. Every dollar of disposable income is either consumed or saved.

The Trap

Don’t flip the subtraction. Saving is $S=Y_D-C$, not $C-S$. Disposable income minus consumption, not the other way around.

What is desired aggregate expenditure?

Desired aggregate expenditure (AE) is the total amount that households, firms, governments, and foreign buyers want to spend on domestically produced output — not what they actually end up spending. It is essentially desired GDP on the expenditure side — the same categories as GDP, but measuring what everyone planned to spend rather than what actually got spent.

Variant terms: desired expenditure is also called planned expenditure.

National income accounting measures actual expenditure:

$GDP=C_a+I_a+G_a+(X_a-I{M}_a)$

The macro model deals with desired expenditure:

$AE=C+I+G+(X-IM)$

The subscript ${}_a$ means actual. No subscript means desired. The four expenditure categories (C, I, G, X-IM) and their sub-formulas are testable.

The general definition of AE includes all four components — including government ( $G$) and foreign buyers ($X-IM$). The simplifying assumptions for this chapter strip it down to $AE=C+I$ because we assume a closed economy (no trade) and no government. Later chapters will add these components back in. The general definition is stated here because it's the full framework you'll eventually use.

The desired/actual distinction only applies to expenditure categories — not to income. There is no "desired national income" or "actual national income." Income is just $Y$. The subscript convention exists because expenditure plans can fail to match reality. Income doesn't have a plan to fail.

What is the difference between autonomous and induced expenditure?

Autonomous expenditure does not depend on national income. Induced expenditure changes systematically in response to changes in national income.

Type	Core meaning	In the consumption function
Autonomous	Self-caused, independent — happens regardless of what else changes	The 30 in $C=30+0.8Y_D$ (the y-intercept)
Induced	Caused by another variable changing — reactive, a response	The $0.8Y_D$ (the slope × income)

The Trap

Autonomous ≠ needs. Induced ≠ wants. Someone might buy a car regardless of income changes (autonomous). Someone might upgrade their housing because they got a raise (induced). What matters is whether the spending responds to income changing, not whether it’s a necessity.

"Induced" appears across economics. It always means the same thing: caused by something else changing. In this chapter, consumption is induced by disposable income changes. If you see the word later, look for what variable is doing the inducing.

Autonomous and induced map directly to terminology from earlier courses:

This chapter	General economics term	Meaning
Autonomous	Exogenous	Determined outside the model’s main variable
Induced	Endogenous	Determined inside the model by its main variable

In this model, the main variable is national income (Y). Autonomous expenditure is exogenous to Y. Induced expenditure is endogenous — it’s generated by Y itself.

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2. The Consumption Engine

Consumption is the largest component of AE and the one that responds to income. Everything in this chapter eventually depends on how the consumption function works.

What is the consumption function?

The consumption function is the assumed relationship between desired consumption and disposable income. It is a tool that takes disposable income as input and returns desired consumption as output.

$\underset{\text{input}}{\underbrace{Y_D}}\stackrel{\text{consumption function}}{\to }\underset{\text{output}}{\underbrace{C}}$

“Assumed” means the textbook is acknowledging this is a simplification — real household behaviour is messier, but this linear relationship is close enough to be useful for the model.

The four determinants of desired consumption:

1. Disposable income — the key variable in this model
2. Wealth
3. Interest rates
4. Expectations about the future

The consumption function focuses on disposable income, holding the other three constant.

In the simplified model:

Formula	Meaning	Example
$C=30+0.8Y_D$	Desired consumption = autonomous consumption + (MPC × disposable income)	If $Y_D=300$: $C=30+0.8(300)=270$

What is autonomous consumption?

Autonomous consumption is the amount households desire to consume even when disposable income is zero. On the graph, it is the y-intercept of the consumption function.

It represents the baseline level of consumption that exists regardless of income. At zero income, this spending must be funded by dissaving (drawing down wealth or borrowing) — but at higher incomes, autonomous consumption is simply covered by income alongside induced consumption. The other three determinants — wealth, interest rates, expectations — are what determine its level.

Job loss scenario

• Someone loses their job. Disposable income drops to zero.
• They don’t stop spending entirely — they use savings, credit cards, borrow from family.
• That spending is autonomous consumption.
• Their savings shrink by the same amount — that’s why autonomous saving is negative (-30).

What is MPC?

MPC is the fraction of each additional dollar of disposable income that gets spent on consumption. It is the slope of the consumption function.

“Propensity” just means tendency or inclination — how much are you inclined to consume?

Formula	Meaning	Example
$MPC=\frac{\Delta C}{\Delta Y_D}$	Of the next dollar of disposable income, how much is consumed?	MPC = 0.8: earn $1more\to spend$0.80 more

MPC is constant at 0.8 in this model — it doesn’t change as disposable income changes.

What is APC?

APC is the fraction of total disposable income that goes to consumption. It is a ratio, not a slope.

Formula	Meaning	Example
$APC=\frac{C}{Y_D}$	Of all disposable income, what percentage is consumed?	At $Y_D=300$: $C=30+0.8(300)=270$, so $APC=270/300=0.90$ (90%)

APC falls as disposable income rises.

The Trap

APC is not a slope. MPC is the slope. APC is a ratio (total $C÷$ total $Y_D$) at a given point. MPC is the rate of change ($\Delta C÷\Delta Y_D$) along the line.

Why is APC always higher than MPC?

Starting from $APC=\frac{C}{Y_D}$, substitute $C=30+0.8Y_D$:

$\begin{array}{rl}APC& =\frac{C}{Y_D}\\ & =\frac{30+0.8Y_D}{Y_D}\\ & =\frac{30}{Y_D}+\frac{0.8Y_D}{Y_D}\\ & =\frac{30}{Y_D}+0.8\end{array}$

$\boxed{APC=MPC+\frac{30}{Y_D}}$

APC is always MPC plus autonomous consumption spread across total disposable income. As $Y_D$ rises, $\frac{30}{Y_D}$ shrinks, so APC falls toward MPC but never reaches it.

$Y_D$	$\frac{30}{Y_D}$	$APC$
100	0.300	1.100
150	0.200	1.000
300	0.100	0.900
600	0.050	0.850

The saving function as a mirror

The saving function is not a separate concept — it's the consumption function's mirror image. Once you know C, you automatically know S.

$\begin{array}{rl}S& =Y_D-C\\ & =Y_D-(30+0.8Y_D)\\ & =Y_D-30-0.8Y_D\\ & =-30+0.2Y_D\end{array}$

$Y_D$	$C$	$S=Y_D-C$	What’s happening
0	30	-30	Earning nothing, consuming 30. Dissaving.
100	110	-10	Still below break-even. Dissaving.
150	150	0	Break-even. Every dollar earned gets spent.
300	270	30	Earning more than spending. Saving.
600	510	90	Gap keeps growing.

The saving function starts at -30 (not zero) because at zero income, autonomous consumption of 30 must be funded by dissaving.

When desired consumption exceeds income, desired saving is negative. When desired consumption is less than income, desired saving is positive.

left=0; right=400; bottom=-50; top=100;
---
y=-30+0.2x|red
y=0|black|dashed
(150,0)|label:Break-even (S = 0)
(0,-30)|label:Dissaving

MPS is the fraction of each additional dollar saved — the slope of the saving function:

Formula	Meaning	Example
$MPS=\frac{\Delta S}{\Delta Y_D}$	Of the next dollar of disposable income, how much is saved?	MPS = 0.2: earn $1more\to save$0.20 more

APS is the fraction of total income saved:

Formula	Meaning	Example
$APS=\frac{S}{Y_D}$	Of all disposable income, what percentage is saved?	At $Y_D=300$: $S=-30+0.2(300)=30$, so $APS=30/300=0.10$ (10%)

Why do MPC + MPS = 1 and APC + APS = 1?

Both proofs start from the same fact: every dollar of disposable income is either consumed or saved.

Proof that MPC + MPS = 1 (with numbers first):

Say disposable income goes up by $100.That$100 has to go somewhere — you either spend it or save it:

$\Delta Y_D=\Delta C+\Delta S$

$100=80+20$

Divide every piece by 100:

$\frac{100}{100}=\frac{80}{100}+\frac{20}{100}$

$1=0.8+0.2$

$1=MPC+MPS$

Proof that APC + APS = 1:

Start: $Y_D=C+S$ (income is either consumed or saved)

Divide every piece by $Y_D$:

$\frac{Y_D}{Y_D}=\frac{C}{Y_D}+\frac{S}{Y_D}$

$1=APC+APS$

Practical use: knowing one gives you the other for free. If MPC = 0.75, then MPS = 0.25 instantly. If APS = 0.15, then APC = 0.85. This becomes especially useful with the multiplier (§6), which depends on MPS.

These are two separate identities. APC + APS = 1 is about the total — how all income is split. MPC + MPS = 1 is about the next dollar — how any change in income is split. Don't add them together.

Reading the consumption function graph

All references in this section use $C=30+0.8Y_D$.

The graph has two key lines:

The 45° line — a reference line where $C=Y_D$. Every point on it represents spending exactly what you earn. Not an economic relationship — just a ruler.

The C line — plots $C=30+0.8Y_D$. Starts at 30 on the vertical axis (the autonomous consumption intercept) and rises with a slope of 0.8 (the MPC). Less steep than the 45° line because you only spend 80 cents of each dollar.

What is the break-even level of income?

The break-even level of income is where the consumption function crosses the 45° line — the point where desired consumption exactly equals disposable income and desired saving is zero.

Break-even occurs where $C=Y_D$. Since $C=30+0.8Y_D$, set them equal:

$\begin{array}{rl}{Y}_D& =30+0.8Y_D\\ Y_D-0.8Y_D& =30\\ 0.2Y_D& =30\\ Y_D& =\frac{30}{0.2}\\ Y_D& =150\end{array}$

Position relative to break-even	C line vs 45° line	Saving
Left of break-even ($Y_D<150$)	C line is above 45° line	Negative (dissaving)
At break-even ($Y_D=150$)	They cross	Zero
Right of break-even ($Y_D>150$)	C line is below 45° line	Positive

left=0; right=400; bottom=0; top=400;
---
y=x|black|dashed
y=30+0.8x|blue
(150,150)|label:Break-even
(0,30)|label:Autonomous C

The saving function graph plots the vertical gap between the C line and the 45° line. That's all it is. Desired saving is always equal to the vertical distance between the consumption function and the 45° line.

Movement along vs shift of the consumption function

Changes in disposable income cause movement along the consumption function. Changes in wealth, interest rates, or expectations cause shifts of the consumption function.

What changes	What happens on the graph	Textbook terminology
Disposable income	Move to a different point on the same C line	Movement along
Wealth, interest rates, or expectations	Entire C line moves up or down, parallel	Shift
MPC itself	Line rotates around the y-intercept — slope changes	Rotation

EXAM TRAP — movement along vs shift

When disposable income rises, the instinct is to think the C line must change somehow — get steeper, shift, something. It doesn’t. Disposable income is the x-axis. A bigger number just moves you to the right along the existing line.

The stove analogy: The consumption function is like a stove dial that’s already been set. Turning up the heat (moving along = more income) makes the pot hotter, but the dial setting (the slope = MPC) didn’t change. The dial only changes if you physically reach over and twist it (a rotation). The whole stove only moves if you pick it up and put it on a higher shelf (a shift from wealth, rates, or expectations).

What happened	Graph action	Example
Household gets a raise ($Y_D$ rises)	Move right along the same C line	Income goes from $300to$400 → C goes from $270to$350. Same line, different point.
Stock market booms (wealth rises)	Whole C line shifts up, parallel	At every income level, households spend more. Intercept changes from 30 to 90.
MPC changes from 0.8 to 0.9	C line rotates steeper around the intercept	Each dollar of income now produces $0.90ofconsumptioninsteadof$0.80.

The confusion comes from seeing $Y_D$ in the MPC formula and thinking “if $Y_D$ changes, MPC changes.” But MPC = $\frac{\Delta C}{\Delta Y_D}$ is a ratio of changes, not totals. Every extra dollar always splits 80/20 — the numerator and denominator move in lockstep. The formula where $Y_D$ in the denominator actually matters is APC = $\frac{C}{Y_D}$, which does fall as income rises. Don’t apply APC’s logic to MPC.

left=0; right=500; bottom=0; top=500;
---
y=30+0.8x|blue
y=90+0.8x|green|dashed
y=30+0.9x|orange|dotted
(300,270)|blue|label:A
(400,350)|blue|label:B (movement along)
(0,30)|black|label:Intercept
(450,450)|green|label:Shift (wealth ↑)
(400,390)|orange|label:Rotation (MPC ↑)
(450,390)|blue|label:Original C

What shifts the consumption function?

Those factors are baked into autonomous consumption. If one changes, the y-intercept changes and the whole line shifts parallel — same slope, different starting point.

A change in MPC, by contrast, rotates the line around the y-intercept — the intercept stays at 30 but the line gets steeper or flatter.

Quick mental model: when good things happen, we spend more and save less (C↑ S↓).

“Good things” = more resources (wealth↑), cheaper borrowing (interest rates↓), better outlook (optimism↑). All three push in the same direction: C shifts up, S shifts down, AE shifts up.

Reverse everything for bad things: wealth↓, rates↑, pessimism → C↓, S↑, AE shifts down.

The consumption and saving functions always shift in opposite directions by equal amounts — they’re mirror images.

What is household wealth?

Household wealth is the value of all accumulated assets minus accumulated debts.

Common assets: savings accounts, mutual funds, stocks/bonds, RRSPs, TFSAs, home ownership. Common debts: mortgages, car loans, credit-card debt, lines of credit.

What changes	Direction	What moves on the graph
Wealth increases	Consumption ↑ Saving ↓	C line shifts up (parallel), S line shifts down
Wealth decreases	Consumption ↓ Saving ↑	C line shifts down (parallel), S line shifts up
Interest rates decrease	Consumption ↑ Saving ↓	C line shifts up (parallel), S line shifts down
Interest rates increase	Consumption ↓ Saving ↑	C line shifts down (parallel), S line shifts up
Optimism increases	Consumption ↑ Saving ↓	C line shifts up (parallel), S line shifts down
Pessimism increases	Consumption ↓ Saving ↑	C line shifts down (parallel), S line shifts up

Why do interest rates affect consumption?

Household consumption is divided into durable goods (deliver benefits over several years) and non-durable goods (deliver benefits over short periods). Interest rates affect consumption because durable goods are often purchased on credit.

Type	Examples	Purchased on credit?
Durable goods	Cars, furniture, household appliances	Often yes
Non-durable goods	Groceries, restaurant meals, clothing	Rarely

The causal chain: interest rates fall → borrowing becomes cheaper → households buy more durable goods on credit → desired consumption rises at every income level → C line shifts up.

Interest rate changes hit durable goods consumption hardest because those are the purchases people finance with debt. Nobody borrows money for groceries.

Short-sighted vs forward-looking households

Short-sighted households spend based on current income. Forward-looking households spend based on expected lifetime (permanent) income. Most real households are somewhere in between.

Type	Behaviour	Consumption pattern
Short-sighted	Spends everything received, saves nothing (MPC = 1)	Consumption moves exactly with current income — big paycheque means big spending, small paycheque means small spending
Forward-looking	Plans over lifetime, smooths consumption	Consumption stays relatively flat — windfalls get saved, shortfalls get cushioned by drawing on savings

A consumption function based on the assumption that current income drives current consumption is called a Keynesian consumption function — this is what our model uses.

The life-cycle theory (Modigliani) and permanent-income theory (Friedman) model forward-looking behaviour.

Our model is a middle ground, not purely short-sighted. Current disposable income drives consumption (short-sighted logic), but MPC is 0.8, not 1 — meaning not every dollar gets spent (some forward-looking behaviour). A forward-looking household spreads a one-time $10,000bonusacrossmanyyears(smallspendingchange),butadjustssignificantlytoapermanent$10,000/year raise. Our MPC of 0.8 captures this middle ground — responsive to income changes, but not dollar-for-dollar.

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3. Investment

Investment is the most volatile component of GDP and the main source of short-run fluctuations. It combines with consumption in §4 to form the AE function.

What does “investment” mean in macroeconomics?

The Trap

Macro investment ≠ financial investment. This is one of the biggest vocabulary traps in introductory macro.

Term	Everyday meaning	Textbook (macro) meaning
Investment	Buying stocks, ETFs, bonds — financial assets	Spending on new capital goods that create productive capacity
Saving	Putting money aside	The part of disposable income not consumed — which funds financial investment

When you buy an ETF, nothing new gets produced. You’re buying an existing financial asset from someone else. In macro, that’s saving, not investment. When a firm builds a new factory, that is investment — new productive capacity gets created. That’s the $I$ in GDP.

Buying capital goods is not consumption. The distinction is about purpose. A household buying a car to drive is consumption (C). A firm buying a delivery truck for the business is investment (I). The truck isn't "consumed" — it's used to produce things over many years. The categories in $GDP=C+I+G+(X-IM)$ don't overlap.

See also: ECON-1221 Chapter 5 - Notes from the Textbook for the full breakdown of GDP expenditure categories.

EXAM TRAP — "investment" vocab override

The everyday meaning of “investment” keeps overriding the textbook meaning under pressure. The test is this: did something new get built?

Action	Everyday label	Macro label	Why
Buy an ETF	”I’m investing”	Saving (S)	Nothing new was produced. You bought an existing financial asset.
Firm builds a new factory	—	Investment (I)	New productive capacity was created. Real bricks, real machines.
You put money in a savings account	Saving	Saving (S)	Correct in both worlds.

The interest rate trap specifically: When interest rates rise, the instinct is “great, my investments earn more” — but that’s financial investment (saving in macro terms). In macro, higher interest rates make the “do nothing” option more attractive for firms, so they build fewer factories and hold less inventory. Both consumption AND investment move in the same direction when interest rates change — both fall when rates rise, both rise when rates fall. If the answer feels like they move in opposite directions, the vocab trap is probably firing.

The three categories of investment

Investment has three components: inventory accumulation, residential construction, and new plant and equipment.

Category	What it is	Share of GDP	Volatility
Inventory accumulation	Changes in firms’ stocks of unsold goods	Small (fluctuates between -2% and +2%)	Very high relative to its own size
Residential construction	Newly built housing	~6-9%	High — sensitive to interest rates via mortgages
New plant and equipment	Factories, machinery, capital goods, IP	~10-16%	High in absolute terms

Investment is the most volatile component of GDP. In each of the last four Canadian recessions (1982, 1991, 2009, 2020), investment as a share of GDP fell significantly, while consumption, government purchases, and net exports were much smoother.

Volatility is relative to magnitude. On the graph, inventories look like a flat line hugging zero while plant and equipment towers above. The eye says "plant and equipment moves more." But look at the proportions:

Component	Average level (% of GDP)	Typical swing	Swing as % of its own average
Inventories	~0%	4 pp (from -2% to +2%)	N/A — base is ~0%, so percentage comparison breaks. The sign itself flips from negative to positive.
Plant & equipment	~13%	6 pp (from ~10% to ~16%)	~46%
Residential construction	~6.5%	4 pp (from ~5% to ~9%)	~62%

“The base” = the average level of that component. Inventories’ base is near zero, so any movement at all is proportionally enormous — like your bank account going from -$200to+$200. Plant and equipment’s base is ~13%, so a similar-sized swing is a smaller percentage of itself. Both matter, but they’re volatile in different ways — inventories are proportionally wild, plant and equipment is large in absolute GDP terms.

What is actually the most volatile?

The textbook uses “volatile” multiple times across different sections, which can create confusion. Here’s the hierarchy:

Level	What’s most volatile	Compared to what
GDP components	Investment as a whole	More volatile than consumption, government purchases, or net exports
Within investment	Inventory	Most volatile relative to its own magnitude (swings from -2% to +2% of GDP around a near-zero average)

Residential construction and plant/equipment also fluctuate, but investment as a category is the key volatility story for this course.

The three determinants of desired investment

Desired investment depends on the real interest rate, changes in the level of sales, and business confidence.

Determinant	Direction	Mechanism
Real interest rate rises	Investment ↓	Opportunity cost of using money for investment increases
Real interest rate falls	Investment ↑	Opportunity cost decreases, borrowing is cheaper
Sales level increases	Investment ↑ (temporary)	Firms build up inventory and capacity to match new demand
Sales level decreases	Investment ↓ (temporary)	Firms run down excess inventory, don’t need new capacity
Business confidence rises (optimism)	Investment ↑	Firms expect profitable future demand, invest now to capture it
Business confidence falls (pessimism)	Investment ↓	Firms don’t expect payoff, hold back on investment

In this simplified model, desired investment is treated as autonomous — it doesn't change when national income changes. This means investment adds to the AE intercept but doesn't change its slope.

How does the real interest rate affect investment?

The real interest rate is the opportunity cost of investment. Higher interest rates make investment more expensive; lower interest rates make investment cheaper.

The logic works the same way whether the firm borrows or uses its own money:

If the firm…	High interest rates mean…
Borrows to invest	Borrowing costs more — loan payments are higher
Uses its own cash to invest	The money could be earning more in a savings account — opportunity cost is higher

Either way, high real interest rates make the “don’t invest, just park the money” option more attractive. Low real interest rates make investing in the business more attractive.

The double incentive of high interest rates: High rates make borrowing expensive AND saving lucrative. Both channels push in the same direction — less consumption, less investment, more saving. Low rates reverse both: borrowing is cheap and saving earns little, so spending and investing become more attractive.

This applies to all three investment categories:

Inventories: Holding inventory ties up money that could be earning interest elsewhere. Higher rates → higher opportunity cost → firms hold less inventory.

Residential construction: Most houses are bought with mortgages. Interest is more than half of annual mortgage payments. Higher rates → more expensive mortgages → less housing demand.

New plant and equipment: Higher rates → more expensive to borrow for or justify building factories, buying machines, conducting R&D.

Beyond the Textbook

Connection to microeconomics: The textbook includes intellectual property (patents, processes from R&D) in the plant and equipment category. This connects to the very long run from micro, where investment in technology expands productive capacity. The logic is the same — IP creates something durable that the firm uses over time to produce future output, just like a factory does.

Beyond the Textbook

Connection to real estate: Interest rates and buyer’s vs seller’s markets are connected. High rates → fewer buyers can afford mortgages → sellers compete for a smaller buyer pool → buyer’s market (buyers have leverage, prices soften). Low rates → cheap mortgages bring more buyers in → buyers compete against each other → seller’s market (sellers have leverage, prices rise). This is the same interest rate → residential construction mechanism, just described from the real estate agent’s perspective.

How do changes in sales affect investment?

Changes in the level of sales cause temporary bouts of investment. Once firms have adjusted their inventory or capacity to match the new sales level, investment stops.

Key vocabulary:

Term	Meaning	Example
Level of sales	How much you’re selling right now — a snapshot	”Our sales are $120K this month”
Change in sales ($\Delta$Sales)	The difference between what you were selling and what you’re selling now	”Sales went from $100Kto$120K — $\Delta$Sales = +$20K”

Investment responds to $\Delta$Sales, not to Sales. A store selling $1M/monthwithstablesales($\Delta$Sales=0)haszeroinventoryinvestment.Astoreselling$50K/month whose sales just jumped from $30K($\Delta$Sales=+$20K) has active inventory investment — even though its sales level is far smaller.

The textbook example: a firm with $1Mmonthlysalesholds$100,000 in inventory (10% buffer). Sales permanently rise to $1.2M.Thefirmneeds$120,000 in inventory. During the build-up period, there is $20,000 of new inventory investment. Once the target is reached, inventory investment drops to zero — even though sales are still high.

Month	Monthly Sales	Target Inventory (10%)	Inventory Investment	Why
Before	$100K	$10K	$0	Already at target
Transition	$120K	$12K	$2K	Building up to new target
After	$120K	$12K	$0	Already at new target

The same logic applies to plant and equipment — if demand permanently rises beyond existing capacity, firms invest in new factories. Once built, investment drops back down.

Key exam concept: Investment is driven by $\Delta$Sales (changes), not the level of Sales. And it's temporary — a burst of investment followed by a return to normal once adjustment is complete. The level of sales determines how much inventory you want to hold. The change in sales determines whether you're currently investing in more inventory.

Why don’t firms hold more inventory buffer?

The optimal inventory level is where the cost of holding one more unit equals the expected cost of one more lost sale. This is MB = MC applied to inventory.

Firms balance two risks:

Risk	Cost
Too little inventory	Lost sales when demand spikes
Too much inventory	Money tied up that could be earning interest (opportunity cost)

The interest rate sets the opportunity cost of holding inventory, the volatility of sales determines how much buffer is needed, and the production trade-off constrains how much can be built up. The textbook only shows the middle factor, but the full picture connects all three.

Beyond the Textbook

Connection to microeconomics: This is the same MB = MC decision rule from micro applied to inventory. Optimal inventory, optimal production, optimal anything — the labels and context change, but the decision rule is always marginal benefit = marginal cost. Similarly, being inside the production possibilities boundary can be the rational choice when the marginal cost of reaching it exceeds the marginal benefit.

How does business confidence affect investment?

Investment is a bet on the future. Firms invest when they expect profitable future demand (optimism) and hold back when they don't (pessimism). Keynes called this intangible outlook "animal spirits."

When a firm invests, it increases future productive capacity. But it doesn’t know with certainty whether that capacity will be needed. The decision depends on expectations:

Outlook	Action	Logic
Optimism	Invest now	Expect higher future demand, want capacity ready to capture it
Pessimism	Hold back	Don’t expect payoff, so investment would be wasted

Keynes coined the term “animal spirits” during the Great Depression to describe why firms wouldn’t invest despite low interest rates — they were too pessimistic about the future to see any payoff. The term is still widely used to describe business sentiment driving investment fluctuations.

Beyond the Textbook

Connection to organizational behaviour: This parallels Vroom’s expectancy theory — when you expect the payoff is worth the effort, believe you can achieve it, and value the reward, you’re more likely to act. Firms invest when all three conditions are met: they expect demand (expectancy), believe they can produce profitably (instrumentality), and value the returns (valence).

Bull vs bear markets: Animal spirits and bull/bear markets are related but distinct. Bull/bear describes the actual direction of market prices. Animal spirits describes the confidence driving decisions. They feed each other — optimistic animal spirits fuel investment which can drive a bull market, and a bull market reinforces optimism — but one is about prices, the other is about psychology.

Why is the investment function a horizontal line?

Investment decisions are forward-looking — a factory takes years to build and lasts decades, so current GDP is nearly irrelevant. Because desired investment doesn't respond to current national income, the investment function is a flat horizontal line at $I=75$ billion.

National income (Y) is on the horizontal axis. If changing Y doesn’t change I, then I stays at 75 no matter where you are on the x-axis. The line can shift up or down when interest rates, sales, or business confidence change — but it stays flat because none of those determinants are national income.

Autonomous does not mean constant. Investment can and does change — it's the most volatile component of GDP. It just doesn't change because of national income. It changes because of interest rates, sales changes, and animal spirits.

left=0; right=700; bottom=0; top=200;
---
y=75|blue
y=100|green|dashed
y=50|red|dashed
(600,75)|blue|label:I = 75
(600,100)|green|label:I shifts up (rates ↓)
(600,50)|red|label:I shifts down (rates ↑)

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4. The AE Function

This section combines the consumption engine (§2) and investment (§3) into one function. Everything that follows depends on this.

Building the AE function

The AE function shows total desired spending at each level of national income. In this simplified model (no government, no trade), AE = C + I.

$\begin{array}{rl}AE& =C+I\\ & \\ & =(30+0.8Y_D)+75\\ & \\ & =105+0.8Y_D\end{array}$

Since $Y_D=Y$ in this model (no taxes):

$\boxed{AE=105+0.8Y}$

Component	Amount	Type
Autonomous consumption	30	Autonomous
Autonomous investment	75	Autonomous
Total autonomous expenditure	105	Autonomous
Induced consumption	0.8Y	Induced

The AE function has the same slope as the consumption function (0.8 = MPC) because investment is autonomous — it adds to the intercept but doesn’t change the slope. This is the function that determines equilibrium national income in §5.

left=0; right=700; bottom=0; top=700;
---
y=30+0.8x|blue|dashed
y=75|red|dashed
y=105+0.8x|purple
y=x|black|dashed
(200,190)|blue|label:C = 30 + 0.8Y
(200,75)|red|label:I = 75
(200,265)|purple|label:AE = 105 + 0.8Y
(525,525)|label:Equilibrium

What is the marginal propensity to spend?

The marginal propensity to spend ( $z$) is the fraction of any additional dollar of national income that gets spent on domestic output. It is the slope of the AE function.

$z=\frac{\Delta AE}{\Delta Y}$

Right now, $z=MPC=0.8$ and they look identical. But they measure different things:

Term	What it measures	What income?
MPC	Extra consumption per extra $1 of disposable income	$Y_D$
$z$ (marginal propensity to spend)	Extra total expenditure per extra $1 of national income	$Y$

Memory hook: z is for Zpender.

The danger is confusing MPS (marginal propensity to save) with $z$ (marginal propensity to spend). Two “marginal propensity to s-” concepts — easy to mix up under pressure.

z is for Zpender. $z$ measures how much the whole economy zpends when it gets another dollar. Big picture, economy-wide, feeds the multiplier.

MP_ is for My Personal dollar. MPC and MPS are a household splitting their personal paycheck — some to consumption, some to saving. They’re siblings. They share initials (MP_). They sum to 1.

$z$ is the outsider — different letter, different job, not part of the MP_ family.

If you’re doing this…	You need…	Memory cue
Calculating the multiplier: $\frac{1}{1-z}$	$z$	“How much of a zpender is the economy?”
Splitting a household dollar: MPC + MPS = 1	MPC, MPS	”My Personal dollar is Consumed or Saved”
Looking at the slope of AE	$z$	$z$ = slope of AE = the zpending line
Looking at the slope of the saving function	MPS	MPS = slope of S function

Right now $z=MPC$ because our economy is so simple that the whole economy behaves like one household. But $z$ will shrink later when taxes and imports start leaking money out before it gets zpent.

---

5. Equilibrium

This is where the desired vs actual distinction from §1 finally pays off. The adjustment mechanism that drives the economy toward equilibrium runs on unintended inventory changes — the gap between what firms planned and what actually happened.

Why does production equal income?

Every dollar a firm spends producing output becomes someone's income. Production and income are two names for the same flow — they are equal by definition, not just by coincidence.

This is the circular flow from ECON-1221 Chapter 5 - Notes from the Textbook. When firms produce $300Bofoutput,theypayout$300B in wages, rent, profit, and other factor payments. Those payments are national income. The symbol ≡ (identically equal to) is sometimes used instead of = to show that this isn’t just equal in certain conditions — it’s the same thing measured from two sides.

$\text{Total output produced}\equiv \text{National income}\equiv Y$

See Appendix: Chapter 5 Prerequisites for specific gaps to review.

What is a “demand-determined” equilibrium?

In this model, firms are assumed to be able and willing to produce whatever quantity is demanded without changing prices. Output adjusts to match demand, not the other way around. This is called demand-determined output.

This is an extreme assumption — normally firms moving up their supply curves would require higher prices. But it simplifies the model by making all adjustment happen through quantities (output goes up or down) rather than prices. This assumption gets relaxed in Chapter 8.

Because of this assumption, the equilibrium we find is purely about whether spending plans match output levels. Price changes aren't part of the adjustment mechanism in this model.

The equilibrium condition

National income is in equilibrium when desired aggregate expenditure equals actual national income. At this point, spending plans match production and there is no pressure for output to change.

$\text{Equilibrium: }AE=Y$

Using our AE function:

$\begin{array}{rl}AE& =Y\\ 105+0.8Y& =Y\\ 105& =Y-0.8Y\\ 105& =0.2Y\\ Y& =\frac{105}{0.2}\\ Y& =525\end{array}$

Equilibrium national income is $525 billion.

What does the equilibrium condition actually say?

Start from what we know. Y is actual national income, which by definition equals actual expenditure:

$Y=C_a+I_a+G_a+(X_a-I{M}_a)$

And AE is desired expenditure:

$AE=C+I+G+(X-IM)$

So the equilibrium condition $AE=Y$ is really:

$C+I+G+(X-IM)=C_a+I_a+G_a+(X_a-I{M}_a)$

Now look at each pair. Households buy what they intend to buy — nobody accidentally consumes. So $C=C_a$. The government spends what it budgets, so $G=G_a$. Exports and imports are what they are, so $X-IM=X_a-I{M}_a$.

Cancel everything that matches:

$\boxed{I=I_a}$

The entire equilibrium condition collapses to one question: does planned investment equal actual investment? And since the only part of investment that can surprise firms is inventory, that’s why the whole adjustment mechanism runs on unintended inventory changes. Inventory isn’t just one topic among many in this chapter — it’s the only place where desired and actual can diverge.

How inventories drive the economy to equilibrium

When AE ≠ Y, inventories change unintentionally, which signals firms to adjust production. The economy is pushed toward equilibrium by firms responding to unplanned inventory changes.

Condition	What happens	Inventory effect	Firm response	Result
$AE>Y$	People want to buy more than firms produce	Inventories fall (unintended depletion)	Firms increase production	Y rises toward equilibrium
$AE<Y$	Firms produce more than people want to buy	Inventories rise (unintended accumulation)	Firms reduce production	Y falls toward equilibrium
$AE=Y$	Spending plans match output	No unintended inventory change	No reason to change production	Equilibrium — Y stays

The Trap

Unsold inventory is unintended investment, not unintended consumption. In national income accounting, inventory counts as investment. The $I$ in $I_a$ and $I$ stands for investment, and inventory investment means change in shelves — not sales.

EXAM TRAP — the notation tracks SHELVES, not SALES The symbols $I_a$ and $I$ track what happened to the shelves, not what happened to sales. Sales and inventory move in opposite directions — worse sales means fuller shelves, better sales means emptier shelves. If you accidentally apply "actual vs plan" to sales instead of shelves, you will get the notation backwards every time.

The symbols:

• $I_a$ — the ${}_a$ means “actually happened” (to the shelves)
• $I$ — naked, no subscript, “just the plan” (for the shelves)

The method: Ask what happened to the shelves, then compare actual to plan (a vs p):

• Shelves grew more than planned → a > p → $I_a>I$
• Shelves shrunk more than planned → a < p → $I_a<I$

Example: Bakery produces 300, expects to sell 300, actually sells 250. Shelves gained 50 unplanned loaves. Planned shelf change = 0. Actual shelf change = +50. What actually happened (+50) is bigger than the plan (0). a > p → $I_a>I$.

Gaps between actual and desired don't shift the AE curve. The AE curve is built from desired expenditure. If the firm's plan didn't change but reality surprised them, that's a gap — not a shift. The curve only shifts when desired expenditure changes (e.g., a firm decides to invest more going forward).

Concrete example: A furniture company plans to sell 500 couches this month and produces 500. That’s their desired expenditure plan — no change from last month. A recession hits and customers only buy 400. Now 100 couches sit unsold in the warehouse. Actual investment ($I_a$) went UP (unplanned inventory), but desired investment ($I$) didn’t change — the firm never wanted those couches sitting there.

On the graph, the AE curve hasn’t moved because nobody changed their plans. Instead, the economy is sitting at a point where actual Y > desired AE — that’s the vertical distance between the 45° line and the AE curve. The gap triggers the firm to cut production next month, which moves Y back toward equilibrium.

Walking through the textbook example

At $Y=300$:

$\begin{array}{rl}AE& =105+0.8(300)\\ & =105+240\\ & =345\end{array}$

Desired spending ($345B)exceedsoutput($300B) by $45B.That$45B of extra demand is met by drawing down inventories. Firms see shelves emptying → increase production → Y rises.

At $Y=900$:

$\begin{array}{rl}AE& =105+0.8(900)\\ & =105+720\\ & =825\end{array}$

Output ($900B)exceedsdesiredspending($825B) by $75B.That$75B of unsold output piles up as inventory. Firms see warehouses filling → cut production → Y falls.

At $Y=525$:

$\begin{array}{rl}AE& =105+0.8(525)\\ & =105+420\\ & =525=Y\end{array}$

No unintended inventory change. No pressure to adjust. Equilibrium.

left=0; right=1000; bottom=0; top=1000;
---
y=x|black|dashed
y=105+0.8x|purple
(525,525)|label:Equilibrium (AE = Y)
(300,300)|black|open|label:Y = 300
(300,345)|purple|label:AE = 345 (excess demand)
(900,900)|black|open|label:Y = 900
(900,825)|purple|label:AE = 825 (excess supply)

In notation: when $AE>Y$, actual investment falls below desired ($I_a<I$) because inventory is being depleted. When $AE<Y$, actual investment exceeds desired ($I_a>I$) because inventory is accumulating.

Textbook table typo: Row 6 in the textbook table (Figure 6-6) shows $Y=600$ with $AE=825$. This is incorrect — it should be $AE=585$ (since $510+75=585$). You can verify with the formula: $105+0.8(600)=585$.

Reading the equilibrium graph

The graph has two lines:

The 45° line ($AE=Y$) — this is the equilibrium condition, not an economic relationship. Every point on it represents a situation where desired spending equals actual income. It’s a ruler for checking whether the economy is in equilibrium.

The AE line ($AE=105+0.8Y$) — this is the economic relationship. It shows how much people want to spend at each level of income. Starts at 105 (total autonomous expenditure) and rises with slope 0.8 ($z=MPC$).

Equilibrium occurs where the AE line crosses the 45° line — at that point, $AE=Y$. In this model, that’s at $E_0=(525,525)$.

The vertical distance between the two lines tells you the size of the imbalance:

Where you are	Vertical gap means
Below equilibrium (AE line above 45° line)	Excess demand — people want to spend more than is being produced
Above equilibrium (AE line below 45° line)	Excess supply — firms are producing more than people want to buy
At equilibrium (lines cross)	No gap — spending plans match output

The 45° line plays a completely different role here than in the consumption function graph. In the consumption graph, the 45° line was $C=Y_D$ (a reference for where spending equals income). Here, it's $AE=Y$ (the equilibrium condition). Same visual line, different meaning, different axes.

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6. What Changes Equilibrium

Now that we know how equilibrium works (§5), we can examine what moves it — and how big those movements are.

Shifts of the AE function

The AE function shifts when one of its components shifts — a change in the consumption function or the investment function. These shifts change equilibrium national income.

Upward shifts in AE increase equilibrium income. Downward shifts decrease equilibrium income. The mechanism is the same as the disequilibrium adjustment: shift up → $AE>Y$ → inventories deplete → firms increase production → Y rises to new equilibrium where AE crosses 45° line again.

There are two ways the AE function can shift upward:

Type of shift	What causes it	What changes on the graph
Parallel shift (up or down)	Change in autonomous expenditure ($A$) — wealth, confidence, interest rates	Intercept changes, slope stays the same
Rotation (steeper or flatter)	Change in marginal propensity to spend ($z$)	Slope changes, intercept stays the same

left=0; right=1000; bottom=0; top=1000;
---
y=x|black|dashed
y=105+0.8x|blue
y=125+0.8x|green
(100,185)|blue|label:AE_0
(100,205)|green|label:AE_1 (ΔA = +20)
(525,525)|blue|label:E_0
(625,625)|green|label:E_1

What does prime notation mean on the AE shift diagram?

Prime (') is a label meaning "a modified version of the same thing." It solves the problem of needing two labels for two different points on the same curve.

In the textbook’s Figure 6-8, the subscript number identifies which curve you’re on. You need two different labels for two points on curve $A{E}_1$: one before income adjusts, one after. The prime marks the “just shifted, income hasn’t adjusted yet” point.

Label	What it means
$a{e}_0$	Spending level on curve $A{E}_0$ at income $Y_0$ (original)
$a{e}_1^{\prime }$	Spending level on curve $A{E}_1$ at income $Y_0$ (shifted, but income hasn’t adjusted yet)
$a{e}_1$	Spending level on curve $A{E}_1$ at income $Y_1$ (shifted AND income has adjusted)

The movement from $a{e}_0$ to $a{e}_1^{\prime }$ is the autonomous shift — the line moved up. The movement from $a{e}_1^{\prime }$ to $a{e}_1$ is the induced response — moving along the new AE line as income adjusts. You can’t call the first point $a{e}_1$ and the second $a{e}_2$ because the subscript 2 is already reserved for curve $A{E}_2$ (the rotation case in part (ii) of the same diagram).

Prime notation shows up elsewhere in economics. It always means the same thing — "same family, slightly different version." If you see $Y^{\prime }$, it means a modified version of $Y$, not a new variable.

The multiplier

The multiplier says that a change in autonomous expenditure changes equilibrium national income by more than the initial change. One dollar of new autonomous spending creates more than one dollar of new income.

$\text{Simple multiplier}=\frac{\Delta Y}{\Delta A}$

Where $\Delta A$ is the change in autonomous expenditure and $\Delta Y$ is the resulting change in equilibrium national income.

Memory hook: A is the Axis Anchor.

$A$ looks like it should be short for $AE$ (Aggregate Expenditure) — it’s not. They’re different things.

In the AE function $AE=A+zY$:

Symbol	What it is	On the graph
$AE$	The whole function — autonomous + induced together	The entire line
$A$	Just the autonomous piece — the axis anchor	The y-intercept (where the line meets the axis)

The multiplier measures what happens when the axis anchor shifts — not what happens to the whole line. The formula reads: “for every dollar the axis anchor shifts, equilibrium income moves by $\frac{1}{1-z}$ dollars.”

Check question: “What moved — the anchor or the line?”

• Anchor moved (wealth, confidence, interest rates changed) → that’s $\Delta A$ → use the multiplier
• You slid along the line (Y changed) → that’s induced → you’re already inside the chain reaction

Why is the multiplier greater than 1?

Because spending creates income, which creates more spending. Each dollar of autonomous spending ripples through the economy in successively smaller rounds, and the total of all rounds exceeds the initial dollar.

Walk through it concretely. A firm spends $1B building a paper mill:

• A factory actually gets built — real bricks, real machines, real construction
• Construction workers earn $1B in income
• Workers spend $0.8B of that on groceries, clothing, entertainment (MPC = 0.8)
• Grocery stores, clothing shops actually sell real goods — real food, real products
• Those businesses and their workers earn $0.8B,spend$0.64B of it
• Each round, real goods are produced and real needs are met
• Each round, 20% leaks out into saving (MPS = 0.2), so the rounds get smaller

This is not money just changing hands. At every step, real goods and services are produced. The money is moving in a circle, but what matters is what happens each time it changes hands — someone produces something, someone else consumes it. The chain dies out because saving pulls money out of circulation at every step.

The multiplier round by round

Starting with $\Delta A=1$ (one dollar of new autonomous spending), with $MPC=0.8$:

Round	New spending this round	New saving this round	Cumulative new income
Initial	$1.000	—	$1.000
1	$0.800	$0.200	$1.800
2	$0.640	$0.160	$2.440
3	$0.512	$0.128	$2.952
4	$0.410	$0.102	$3.362
…	keeps shrinking	keeps shrinking	approaches $5.00

Each round is MPC times the previous round. The total converges to:

$\text{Simple multiplier}=\frac{1}{1-z}$

Since $z=MPC=0.8$ in this model:

$\begin{array}{rl}\text{Simple multiplier}& =\frac{1}{1-0.8}\\ & =\frac{1}{0.2}\\ & =5\end{array}$

One dollar of autonomous spending creates five dollars of total income.

The denominator $1-z$ equals MPS in this simple model. So the multiplier is also $\frac{1}{MPS}$. A higher MPC means a higher multiplier (more gets re-spent each round). A higher MPS means a lower multiplier (more leaks out each round).

Applying the multiplier: the three-step method

Any time autonomous expenditure changes, three steps give you the new equilibrium:

Step 1 — Find the multiplier. Take $z$ (the slope of AE) and plug into $\frac{1}{1-z}$.

Step 2 — Find the change in income. Multiply: $\Delta Y=\text{multiplier}\times \Delta A$.

Step 3 — Find the new equilibrium. Add: $Y_{new}=Y_{old}+\Delta Y$.

Worked example

Given $AE=500+0.8Y$ and $\Delta A=20$ (autonomous expenditure rises by $20B):

$\begin{array}{rl}\text{Step 1: Multiplier}& =\frac{1}{1-0.8}=\frac{1}{0.2}=5\\ \text{Step 2: }\Delta Y& =5\times 20=100\\ \text{Step 3: }{Y}_{old}& =\frac{500}{0.2}=2,500\\ Y_{new}& =2,500+100=2,600\end{array}$

The same logic works in reverse — if autonomous expenditure falls by $20B,$\Delta Y = -100$and$Y_{new} = 2{,}400$.

The multiplier is effect over cause — $\frac{\Delta Y}{\Delta A}$, not $\frac{\Delta A}{\Delta Y}$. The change in income (the bigger number) goes on top. The change in autonomous expenditure (the smaller number, the thing that triggered the change) goes on the bottom.

The Trap

The initial spending is autonomous, the chain reaction is induced. The $20B investment decision is autonomous (it doesn’t depend on current national income). But the spending that follows — workers buying groceries, grocery stores paying suppliers — is induced by the new income those workers received. Don’t confuse the trigger (autonomous) with the ripple (induced).

The multiplier applies to any change in autonomous expenditure — not just investment. An increase in autonomous consumption (wealth goes up, optimism increases) triggers the same chain. The textbook uses $\Delta A$ rather than $\Delta I$ to emphasize that it's a general result.

What determines the size of the multiplier?

The marginal propensity to spend ( $z$) determines the multiplier's size. A higher $z$ means more gets re-spent each round, so the multiplier is larger. A lower $z$ means more leaks out, so the multiplier is smaller.

If $z$ (= MPC in this model) is…	Multiplier is…	Because…
0.9	$\frac{1}{0.1}=10$	Only 10% leaks out each round — chain dies slowly
0.8	$\frac{1}{0.2}=5$	20% leaks out each round
0.5	$\frac{1}{0.5}=2$	50% leaks out each round — chain dies quickly

In later chapters, additional leakages (taxes, imports) will shrink $z$ below MPC, producing a smaller multiplier. See the Zpender hook in §4 for why.

Why does a steeper AE line mean a bigger multiplier? (graphical intuition)

A steep AE line (high $z$) crosses the 45° line at a sharp angle. Shifting it up by $\Delta A$ slides the intersection point far to the right. A flat AE line (low $z$) crosses the 45° line at a shallow angle — almost parallel — so the same shift barely moves the intersection.

Think of it geometrically. Two lines that are nearly parallel to each other will cross far apart when one shifts. Two lines that meet at a sharp angle will cross close together. The 45° line has slope 1. The AE line has slope $z$. When $z$ is close to 1, the lines are nearly parallel and the multiplier is huge. When $z$ is close to 0, the lines meet sharply and the multiplier is small.

The three cases:

AE slope ($z$)	AE shape	Multiplier	Why
$z=0$	Horizontal (flat)	1	No induced spending at all — $\Delta Y=\Delta A$ exactly
$z$ is low	Shallow slope	Slightly above 1	Small induced spending each round, chain dies fast
$z$ is high (close to 1)	Steep	Very large	Most of each dollar gets re-spent, chain dies slowly

left=0; right=1200; bottom=0; top=1200;
---
y=x|black|dashed
y=105+0.5x|orange
y=105+0.9x|purple
(600,405)|orange|label:Flat AE (z = 0.5)
(600,645)|purple|label:Steep AE (z = 0.9)
(210,210)|orange|label:Multiplier = 2
(1050,1050)|purple|label:Multiplier = 10

The multiplier's minimum value is 1 (when $z=0$). It can never be less than 1 in this model because even with zero induced spending, the initial autonomous expenditure still creates that much income. There is no maximum — as $z$ approaches 1, the multiplier approaches infinity (though $z=1$ would mean no saving at all, which is unrealistic).

The algebra of the simple multiplier (formal derivation)

The AE curve and the equilibrium condition are two equations with two unknowns ($AE$ and $Y$):

$\begin{array}{rl}\text{[1] AE curve: }AE& =A+zY\\ \text{[2] Equilibrium: }AE& =Y\end{array}$

Substitute [1] into [2]:

$\begin{array}{rl}Y& =A+zY\\ Y-zY& =A\\ Y(1-z)& =A\\ Y& =\frac{A}{1-z}\end{array}$

This gives equilibrium $Y$ in terms of autonomous expenditure and the marginal propensity to spend. If $A$ changes by $\Delta A$:

$\Delta Y=\frac{\Delta A}{1-z}$

Divide both sides by $\Delta A$:

$\frac{\Delta Y}{\Delta A}=\frac{1}{1-z}$

$\boxed{\text{Simple multiplier}=\frac{1}{1-z}}$

The step $Y-zY=Y(1-z)$ is called "factoring out." You're pulling the common $Y$ out of both terms. Think of it as: "I have $Y$ and I'm taking away $z$ copies of $Y$, so I have $(1-z)$ copies of $Y$ left." With numbers: $100-0.8(100)=100(1-0.8)=100(0.2)=20$.

Self-fulfilling prophecies and the multiplier

Because expectations drive spending and spending drives national income through the multiplier, widespread optimism can create a strong economy and widespread pessimism can create a weak one. The expectation becomes self-fulfilling.

The causal chain:

Optimism → firms invest more → AE shifts up → multiplier amplifies → Y rises → economy is strong → “see, we were right to be optimistic”

Pessimism → firms cut investment → AE shifts down → multiplier amplifies → Y falls → economy is weak → “see, we were right to be pessimistic”

In both cases, the firms believe they predicted the outcome. In reality, they caused it. Enough actors believing the same thing and acting on it will make it true.

The 2008-2009 financial crisis is a textbook example. Confidence collapsed → consumption and investment fell → the multiplier amplified those drops → deep global recession. Governments responded by increasing $G$ (government spending) to replace the lost private-sector demand — which is the fiscal policy application of this model.

Beyond the Textbook

Connection to communication as power: This is the theoretical foundation for why narrative matters in economics. Politicians managing economic messaging isn’t just spin — it has real macroeconomic consequences. If the public believes the economy is strong, they spend and invest, which makes it strong. If they believe it’s collapsing, they pull back, which makes it collapse. Controlling the narrative is controlling expectations, which is controlling aggregate expenditure, which is controlling national income. This also connects to Vroom’s expectancy theory from OB — when people expect the payoff is worth the effort, they act.

Connection to consulting: When diagnosing an organization’s problems, the same dynamic plays out at a smaller scale. If leadership projects confidence and acts on it, teams follow. If leadership signals fear, teams freeze. The multiplier isn’t just a macro concept — it’s a model for how confidence propagates through any system.

Beyond the Textbook

Connection to government policy: Government stimulus spending is the multiplier in action. Spend money building infrastructure → construction workers earn income → they spend it at local businesses → those businesses hire more people. The policy question becomes: how large is the multiplier in reality? If it’s large, government spending is a powerful tool for boosting GDP. If it’s small (lots of leakages), the ripple effect is weak. This is one of the most debated questions in macroeconomics and connects directly to the fiscal policy chapters later in the course.

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Vocabulary Reference

Term	Definition
Desired (planned) expenditure	What agents want to spend — not necessarily what they actually spend
Actual expenditure	What gets spent in reality — may differ from desired due to inventory surprises
$I$ (desired investment)	The planned change in inventory — how much the firm expected shelves to change
$I_a$ (actual investment)	The actual change in inventory — how much shelves really changed. The ${}_a$ means “actually happened”
$I_a>I$	Shelves grew more than planned (sold less than expected)
$I_a<I$	Shelves shrunk more than planned (sold more than expected)
Autonomous expenditure ($A$)	Spending that doesn’t depend on national income — the y-intercept of AE. Memory: A is the Axis Anchor. Not short for AE.
Induced expenditure	Spending that changes in response to national income changes (slope × Y)
Consumption function	$C=a+b{Y}_D$ — the assumed linear relationship between consumption and disposable income
MPC (marginal propensity to consume)	Fraction of each additional dollar of disposable income consumed — slope of C function
MPS (marginal propensity to save)	Fraction of each additional dollar of disposable income saved — slope of S function
APC (average propensity to consume)	Total consumption divided by total disposable income — a ratio, not a slope
APS (average propensity to save)	Total saving divided by total disposable income — a ratio, not a slope
Break-even income	Level where $C=Y_D$ and $S=0$ — consumption function crosses 45° line
Dissaving	Negative saving — spending more than income by drawing on wealth or borrowing
Durable goods	Goods that deliver benefits over years (cars, appliances) — often bought on credit
Non-durable goods	Goods with short-term benefits (groceries, meals)
Animal spirits	Keynes’s term for business confidence/sentiment driving investment
Marginal propensity to spend ($z$)	Fraction of each additional dollar of national income spent on domestic output — slope of AE function. Memory: z is for Zpender (economy-wide spending). Not part of the MP_ family.
Level of sales	How much a firm is selling right now — a snapshot. Does not directly trigger investment.
Change in sales ($\Delta$Sales)	Difference between current and previous sales level. This is what triggers inventory investment — the transition, not the destination.
Demand-determined output	Assumption that firms produce whatever is demanded without changing prices
Equilibrium national income	Level where $AE=Y$ — no unintended inventory changes, no pressure to adjust
Simple multiplier	$\frac{1}{1-z}$ — how much equilibrium Y changes per dollar of autonomous expenditure change
Self-fulfilling prophecy	When expectations cause the outcomes that validate them
Prime notation (‘)	Label for “modified version of the same thing” — used to mark intermediate points on a curve
≡ (identically equal)	“Equal by definition” — stronger than = — used for accounting identities that always hold

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Appendix: Chapter 5 Prerequisites to Review

The following concepts from Chapter 5 are assumed knowledge in Chapter 6. Gaps in understanding these caused confusion during the study session. Review ECON-1221 Chapter 5 - Notes from the Textbook and tighten up these specific areas.

1. Production ≡ Income (the circular flow) Chapter 6 assumes you understand that total output produced equals national income by definition. Every dollar spent producing output becomes factor income (wages, rent, profit). This identity underpins the entire equilibrium model — the question “does what people want to spend match what firms produce?” only makes sense if you know that what firms produce is income.

2. GDP expenditure categories don’t overlap Chapter 6 depends on knowing that $C$, $I$, $G$, and $(X-IM)$ are mutually exclusive categories. The confusion about “buying capital goods sounds like consumption” comes from not having the Chapter 5 definitions locked in. Households buy goods for use (C). Firms buy goods for production (I). They don’t overlap.

3. Inventory as investment Chapter 5 establishes that changes in inventory count as investment in national income accounting. Chapter 6 uses this repeatedly — it’s the entire adjustment mechanism for equilibrium. If this definition isn’t automatic, every inventory question will feel unintuitive. Critical: inventory investment means the change in shelves, not the level of shelves and not the level of sales. Sales and shelves move in opposite directions — worse sales means fuller shelves. The $I_a$ and $I$ notation tracks shelves, not sales.

4. The expenditure approach to GDP The formula $GDP=C+I+G+(X-IM)$ from Chapter 5 becomes $AE=C+I+G+(X-IM)$ in Chapter 6 with the desired/actual distinction layered on top. Understanding what each component measures from Chapter 5 is prerequisite to understanding how they behave in Chapter 6.