Chapter 8Intro Macro Models

Introduction

Chapter 7 gave us the tools to measure the macroeconomy: GDP, unemployment, inflation, and the business cycle. We can now describe what happened (GDP fell by 3 percent, unemployment rose to 10 percent, inflation accelerated), but we cannot yet explain why it happened or what policymakers should do about it. This chapter builds the canonical models that fill that gap.

We begin with the simplest possible story of short-run output determination: the Keynesian cross, where aggregate demand alone drives production. From this foundation we construct the IS-LM model, which shows how the goods market and the money market jointly determine output and interest rates. We then use IS-LM as an engine for policy analysis, tracing the effects of government spending, tax changes, and central bank actions, before confronting the critical limitation that IS-LM holds prices fixed. The second half of the chapter lifts that restriction. We derive the aggregate demand curve from IS-LM, introduce aggregate supply in both the short run and the long run, and assemble the full AD-AS model. By the end, you will have a complete toolkit for diagnosing recessions, inflationary booms, and stagflation, and for evaluating the tradeoffs inherent in fiscal and monetary policy responses.

Everything in this chapter uses algebra: linear equations, substitution, and graphical reasoning. No calculus. No dynamic optimization. The models here are deliberately simple: they sacrifice some realism for clarity and tractability. Chapters 14 and 15 will rebuild these ideas with micro-foundations and forward-looking expectations. But the intuition developed here is the intuition that central bankers and treasury officials reach for first, and it is indispensable.

By the end of this chapter, you will be able to:
  1. Solve the Keynesian cross for equilibrium output and derive the spending, tax, and balanced-budget multipliers
  2. Derive the IS and LM curves and explain their slopes
  3. Solve the IS-LM system for equilibrium output and interest rates
  4. Analyze fiscal and monetary policy in IS-LM, including crowding out
  5. Derive the aggregate demand curve from IS-LM
  6. Distinguish short-run from long-run aggregate supply
  7. Use the AD-AS model to analyze demand shocks, supply shocks, and the self-correcting mechanism

Prerequisites: Chapter 7 (GDP, national income identities, business cycle facts).

Walkthroughs in This Chapter

8.1 The Keynesian Cross

The Keynesian cross is the simplest model of short-run output determination. It rests on a powerful and, in the 1930s, revolutionary idea attributed to John Maynard Keynes: in the short run, aggregate demand determines output. If households and firms want to spend more, businesses produce more to meet that demand. If spending falls, businesses cut production. Prices are held fixed; we relax that assumption in Sections 8.6 through 8.8.

The idea that spending circulates through the economy as one agent's outlay becomes another's income has a long pedigree: the physiocrats' Tableau économique was the first attempt to map that circular flow, and Hume's monetary thought worked out how money moves through it — see mercantilism, physiocracy, and Hume in the history of economic thought.

The Consumption Function

The model begins with a behavioral assumption about how households decide what to spend.

Autonomous consumption ($C_0$). The level of consumption spending that occurs regardless of current income, financed by savings, wealth, credit, or transfers. Even a household with zero disposable income must eat, pay rent, and keep the lights on.
Marginal propensity to consume (MPC, $c$). The fraction of each additional dollar of disposable income that a household spends on consumption, where \$0 < c < 1$. If $c = 0.8$, then for every extra dollar of disposable income, the household spends 80 cents and saves 20 cents.
Marginal propensity to save (MPS, \$1 - c$). The fraction of each additional dollar of disposable income that a household saves. Since every dollar is either spent or saved, MPC and MPS always sum to 1.

The consumption function is:

$$C = C_0 + c(Y - T)$$ (Eq. 8.1)

where $Y$ is total output (which equals total income in the circular flow), $T$ is net taxes, and $Y - T$ is disposable income. This is a linear relationship: consumption rises by $c$ for every dollar increase in disposable income, starting from the autonomous base $C_0$.

This function is Keynesian, not micro-founded. It assumes a mechanical link between current income and current spending. Later chapters will derive consumption from household optimization, incorporating expectations about future income and interest rates. But the simple Keynesian form captures the essential short-run mechanism: when income rises, spending rises. That spending becomes someone else's income.

Planned Expenditure

Planned expenditure (PE). The total amount that households, firms, and the government plan to spend on goods and services.

In a closed economy (no exports or imports):

$$PE = C + I + G = C_0 + c(Y - T) + I + G$$ (Eq. 8.2)

For now, investment $I$ and government spending $G$ are exogenous (determined outside the model, by animal spirits and political decisions respectively). Taxes $T$ are also exogenous. Only consumption responds to income.

Notice that planned expenditure is a function of income $Y$. This is the engine of the Keynesian cross: spending depends on income, and income depends on spending.

Equilibrium

Keynesian cross equilibrium. The level of output at which actual output equals planned expenditure: $Y = PE$. At this point, firms are producing exactly what people want to buy, with no unplanned accumulation or depletion of inventories.

If output exceeds planned expenditure ($Y > PE$), firms find unsold goods piling up on their shelves. Inventories accumulate beyond what was planned. They respond by cutting production. If output falls short of planned expenditure ($Y < PE$), firms see their inventories shrinking and ramp up production. Only when $Y = PE$ is the economy at rest.

Setting $Y = PE$:

$$Y = C_0 + c(Y - T) + I + G$$

$$Y = C_0 + cY - cT + I + G$$

$$Y - cY = C_0 - cT + I + G$$

$$Y(1 - c) = C_0 - cT + I + G$$

$$Y^* = \frac{1}{1 - c}(C_0 - cT + I + G)$$ (Eq. 8.3)
Intuition

What this says: Equilibrium output equals autonomous spending (the spending that doesn't depend on income) multiplied by the multiplier. The economy settles where total spending matches total output.

Why it matters: This is the core Keynesian insight: the economy can get stuck at an output level below full employment if autonomous spending is too low. Government spending or tax cuts can raise autonomous spending and lift output by more than the initial impulse.

See Full Mode for the derivation.

The term $A = C_0 - cT + I + G$ is autonomous spending: the component of expenditure that does not depend on income. Equilibrium output is autonomous spending multiplied by $\frac{1}{1-c}$.

Interactive: Keynesian Cross

Drag the sliders to change the MPC, government spending, and taxes. Watch the planned expenditure line pivot and shift, and see how equilibrium output responds.

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Equilibrium: Y* = 2,000 | Multiplier = 5.00 | Autonomous spending A = 400

Figure 8.1. Keynesian cross. Equilibrium occurs where planned expenditure equals actual output. The slope of the PE line is the MPC.

The Spending Multiplier

Spending multiplier. The ratio of the change in equilibrium output to the change in autonomous spending. With MPC $= c$, the multiplier is $1/(1-c)$.
$$\frac{\Delta Y}{\Delta G} = \frac{1}{1 - c}$$ (Eq. 8.4)
Intuition

What this says: Every dollar the government spends creates more than a dollar of output. If households spend 80 cents of each extra dollar they earn, the multiplier is 5: a \$1 spending increase raises GDP by \$5.

Why it matters: The multiplier is the chain reaction of spending. My spending is your income, your spending is someone else's income. Each round is smaller, but they add up to far more than the original impulse.

See Full Mode for the derivation.

With $c = 0.8$, the multiplier is $\frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$. A \$1 increase in government spending raises equilibrium output by \$5.

Why does the multiplier exceed 1? Because of a feedback loop. A chain reaction of spending and income runs as follows:

  1. Government spends an extra \$1 on goods and services. GDP rises by \$1.
  2. That \$1 becomes income for the workers and firms who produced the goods. They spend $c$ of it (80 cents if $c = 0.8$). GDP rises by another $c$.
  3. That $c$ becomes income for yet another set of workers and firms. They spend $c^2$ of it. GDP rises by $c^2$.
  4. And so on, round after round.

The total effect is the infinite geometric series:

$\$1 + c + c^2 + c^3 + \ldots = \frac{1}{1 - c}$$

Each round is smaller than the last (because $c < 1$), so the series converges. But the cumulative effect far exceeds the initial impulse.

The Tax Multiplier

Tax multiplier. The change in equilibrium output per unit change in taxes: $-c/(1-c)$.
$$\frac{\Delta Y}{\Delta T} = \frac{-c}{1 - c}$$ (Eq. 8.5)
Intuition

What this says: Tax cuts boost output, but less than equivalent spending increases. A \$1 tax cut with MPC = 0.8 raises GDP by \$4, versus \$5 from a \$1 spending increase.

Why it matters: When the government spends \$1 directly, the full dollar enters the spending stream immediately. When it cuts taxes by \$1, households save part of the windfall, so the first-round boost is smaller.

See Full Mode for the derivation.

With \$c = 0.8\$, the tax multiplier is \$\frac{-0.8}{0.2} = -4\$. A \\$1 tax cut raises output by \\$4, less than the \\$5 from a \\$1 spending increase.

Why is the tax multiplier smaller in absolute value? When the government spends \\$1 directly, the full dollar enters the spending stream in round one. When the government cuts taxes by \\$1, the household receives \\$1 of extra disposable income but spends only \$c\$ of it (saving \\$1 - c\$). The first round is smaller (only \$c\$ instead of 1), so the total multiplied effect is smaller.

The Balanced-Budget Multiplier

Balanced-budget multiplier. The change in equilibrium output when government spending and taxes both increase by the same amount. It equals exactly 1, regardless of the MPC.

From Eqs. 8.4 and 8.5:

$$\Delta Y = \frac{1}{1-c} \Delta G + \frac{-c}{1-c} \Delta T = \frac{1-c}{1-c} \Delta G = \Delta G$$

$$\frac{\Delta Y}{\Delta G}\bigg|_{\Delta G = \Delta T} = 1$$ (Eq. 8.6)
Intuition

What this says: If the government raises spending by \$100 and pays for it with a \$100 tax increase, GDP still rises by exactly \$100, regardless of the MPC.

Why it matters: Even a fully financed spending increase is stimulative. The government spends the full \$100, but the tax only removes part of households' spending (they absorb some of the tax hit by saving less). The net effect is always a one-for-one increase in output.

See Full Mode for the derivation.

The balanced-budget multiplier is exactly 1, regardless of the value of \$c\$. A \\$100 increase in government spending, financed entirely by a \\$100 tax increase, raises output by exactly \\$100. The intuition: the spending increase adds \\$100 directly to demand, while the tax increase removes only \$c \times \\$100\$ from demand (because households absorb part of the tax hit by reducing saving). The net first-round effect is \$(1 - c) \times \\$100\$, which after multiplying by \$\frac{1}{1-c}\$ gives exactly \\$100.

Example 8.1: The Keynesian Cross with Numbers

Given: $C_0 = 100$, $c = 0.8$, $I = 200$, $G = 300$, $T = 250$.

Step 1: Autonomous spending:

$$A = C_0 - cT + I + G = 100 - 0.8(250) + 200 + 300 = 100 - 200 + 200 + 300 = 400$$

Step 2: Equilibrium output:

$$Y^* = \frac{1}{1 - 0.8} \times 400 = 5 \times 400 = 2{,}000$$

Step 3: Verify $Y = PE$:

$$C = 100 + 0.8(2{,}000 - 250) = 100 + 1{,}400 = 1{,}500$$

$$PE = C + I + G = 1{,}500 + 200 + 300 = 2{,}000 = Y^* \checkmark$$

Step 4: Multiplier: $\frac{1}{1 - 0.8} = 5$.

Step 5: What happens when $G$ rises by 50?

$$\Delta Y = 5 \times 50 = 250$$

New equilibrium: $Y^* = 2{,}000 + 250 = 2{,}250$.

Example 8.2: The Multiplier Round by Round

Continuing from Example 8.1: government spending rises by $\Delta G = 50$ with $c = 0.8$.

RoundNew spending this roundCumulative total
150.050.0
240.090.0
332.0122.0
425.6147.6
520.5168.1
616.4184.5
713.1197.6
810.5208.1
98.4216.5
106.7223.2

After 10 rounds, the cumulative effect is \$10 \times \frac{1 - 0.8^{10}}{1 - 0.8} = 223.2$.

The theoretical total (infinite sum) is $\frac{50}{1 - 0.8} = 250$.

After 10 rounds, we have captured \$123.2 / 250 = 89.3\%$ of the total multiplier effect. The remaining 10.7% trickles in over subsequent rounds in ever-smaller increments.

Interactive: The Multiplier in Action

Set the MPC and initial spending impulse, then press Play to watch the multiplier unfold round by round.

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Round 0: Cumulative = 0 | Theoretical total = 250 | Captured = 0%

Figure 8.2. The multiplier round by round. Each round of spending is smaller than the last, but the cumulative total converges to $\Delta G / (1-c)$.

8.2 The IS Curve

The Keynesian cross holds investment fixed. But investment decisions depend heavily on the cost of borrowing. When interest rates are low, more projects are profitable. A factory that earns a 5% return is worth building when the interest rate is 3%, but not when it is 8%. This section makes investment respond to the interest rate, which transforms the Keynesian cross from a single-output solution into a curve: one that maps each interest rate to its corresponding equilibrium output.

Investment and the Interest Rate

Investment demand ($I = I_0 - br$). Total planned investment as a function of the real interest rate $r$. $I_0$ is autonomous investment; $b > 0$ is the interest sensitivity of investment.
$$I = I_0 - br$$ (Eq. 8.7)
Interest sensitivity of investment ($b$). How much investment falls for each percentage-point increase in the interest rate.

When $r$ rises, the cost of financing new capital goods increases. Firms shelve marginal projects. The ones whose expected return barely exceeds the interest rate get cut first. So investment falls. When $r$ falls, previously unprofitable projects become worthwhile, and investment rises.

Deriving the IS Curve

Substitute the investment function (Eq. 8.7) into the Keynesian cross equilibrium (Eq. 8.3):

$$Y = \frac{1}{1-c}(C_0 - cT + I_0 + G) - \frac{b}{1-c}r$$ (Eq. 8.8)
Intuition

What this says: The IS curve maps each interest rate to the level of output where the goods market clears. Higher interest rates discourage investment, which through the multiplier lowers equilibrium output. So the IS curve slopes downward.

Why it matters: This connects the financial side of the economy (interest rates) to the real side (output). Anything that raises autonomous spending shifts the IS curve right; anything that raises interest rates moves you along the curve to lower output.

See Full Mode for the derivation.
IS curve. The set of all combinations of output $Y$ and the real interest rate $r$ at which the goods market is in equilibrium. It slopes downward: higher interest rates reduce investment, which through the multiplier reduces equilibrium output.

The name "IS" comes from the equilibrium condition that planned investment equals planned saving. The goods market clears when what firms want to invest matches what the rest of the economy wants to save.

Why IS slopes downward: Start at any point on the IS curve, where the goods market is in equilibrium. Now raise $r$. Higher $r$ reduces investment by $b \times \Delta r$. Lower investment means lower planned expenditure, which triggers the multiplier. Output falls by $\frac{b}{1-c} \times \Delta r$. Higher $r$, lower $Y$: the IS curve slopes downward.

What shifts the IS curve? Anything that changes autonomous spending at a given interest rate:

The magnitude of each shift is governed by the respective multiplier. An increase in $G$ by $\Delta G$ shifts IS right by $\frac{1}{1-c} \Delta G$.

8.3 The LM Curve

The IS curve tells us how the goods market responds to interest rates, but it does not tell us what sets the interest rate. For that, we need the money market. The LM curve describes combinations of output and interest rates at which the demand for money equals the supply of money.

Money Demand: Liquidity Preference

Why do people hold money, an asset that (unlike bonds) typically earns no interest? Keynes identified three motives.

Transaction motive. The demand for money arising from the need to conduct everyday purchases. Higher income means more transactions and greater money demand.
Precautionary motive. The demand for money held as a buffer against unexpected expenses or income shortfalls. Like the transaction motive, it rises with income.
Speculative motive. The demand for money arising from the choice between holding money (safe, no interest) and holding bonds (interest-bearing but volatile). Higher interest rates raise the opportunity cost of money, reducing money demand.
Liquidity preference (money demand). The total demand for real money balances as a function of income and the interest rate: $L = eY - fr$.
$$L(r, Y) = eY - fr$$ (Eq. 8.9)

where $e > 0$ captures the income sensitivity of money demand (the transaction motive) and $f > 0$ captures the interest sensitivity (the speculative motive). Higher income raises money demand; higher interest rates reduce it.

Money Market Equilibrium

The central bank controls the nominal money supply $M$. The price level $P$ is fixed in the short run. The real money supply is $M/P$.

Equilibrium requires that real money demand equals real money supply:

$$\frac{M}{P} = eY - fr$$ (Eq. 8.10)

Solving for $r$:

$$r = \frac{e}{f}Y - \frac{1}{f}\frac{M}{P}$$ (Eq. 8.11)
Intuition

What this says: The LM curve maps each output level to the interest rate where the money market clears. When output rises, people need more money for transactions. With a fixed money supply, the interest rate must rise to convince people to hold fewer idle cash balances.

Why it matters: The LM curve slopes upward: booms push interest rates up, recessions push them down. The central bank can shift the entire curve by changing the money supply: more money means lower interest rates at every output level.

See Full Mode for the derivation.
LM curve. The set of all combinations of output $Y$ and interest rate $r$ at which the money market is in equilibrium. It slopes upward: higher output increases money demand, which at a fixed money supply pushes interest rates up.

Why LM slopes upward: Start at a point on the LM curve. Increase $Y$. Higher output raises money demand. With a fixed money supply, the interest rate must rise to discourage speculative holdings and restore equilibrium. Higher $Y$, higher $r$.

What shifts the LM curve?

8.4 IS-LM Equilibrium

The IS curve gives all $(Y, r)$ pairs where the goods market clears. The LM curve gives all $(Y, r)$ pairs where the money market clears. The economy must be on both curves simultaneously. This pins down a unique output-interest rate pair.

IS-LM equilibrium. The unique combination of output $Y^*$ and interest rate $r^*$ at which the goods market and the money market are simultaneously in equilibrium. Graphically, it is the intersection of the IS and LM curves.

Solving the System

We have two equations in two unknowns ($Y$ and $r$):

IS: $Y = \frac{1}{1-c}(C_0 - cT + I_0 + G) - \frac{b}{1-c}r$

LM: $r = \frac{e}{f}Y - \frac{1}{f}\frac{M}{P}$

Substituting LM into IS and solving:

$$Y^* = \frac{f(C_0 - cT + I_0 + G) + b \cdot \frac{M}{P}}{f(1-c) + be}$$ (Eq. 8.12)
$$r^* = \frac{e(C_0 - cT + I_0 + G) - (1-c)\frac{M}{P}}{f(1-c) + be}$$ (Eq. 8.13)
Intuition

What this says: IS-LM equilibrium pins down a unique output level and interest rate where both the goods market and the money market clear simultaneously. Output depends on both fiscal variables (G, T) and monetary variables (M/P).

Why it matters: This is the central result of Keynesian macroeconomics. Neither the goods market nor the money market can be analyzed in isolation. They interact. Fiscal policy shifts IS, monetary policy shifts LM, and the equilibrium adjusts in both output and interest rates.

See Full Mode for the derivation.

Let $D = f(1-c) + be$ for convenience. This denominator appears in every IS-LM multiplier and captures the interaction between goods and money markets. The larger $D$ is, the smaller the effect of any single policy change.

Example 8.3: IS-LM Algebraic Solution

Given: $C_0 = 100$, $c = 0.8$, $T = 200$, $G = 300$, $I_0 = 300$, $b = 20$, $M/P = 500$, $e = 0.5$, $f = 50$.

Step 1: IS curve:

$$Y = 5(100 - 160 + 300 + 300) - 100r = 2{,}700 - 100r$$

Step 2: LM curve:

$$r = 0.01Y - 10$$

Step 3: Solve:

$$Y = 2{,}700 - 100(0.01Y - 10) = 2{,}700 - Y + 1{,}000$$

$$1Y = 3{,}700 \implies Y^* = 1{,}850$$

$$r^* = 0.01(1{,}850) - 10 = 8.5\%$$

Step 4: Investment at equilibrium:

$$I = 300 - 20(8.5) = 130$$

Step 5: Verify:

$C = 100 + 0.8(1{,}850 - 200) = 1{,}420$. $PE = 1{,}420 + 130 + 300 = 1{,}850 = Y^* \checkmark$

$L = 0.5(1{,}850) - 50(8.5) = 925 - 425 = 500 = M/P \checkmark$

Interactive: IS-LM Model

Adjust government spending, taxes, the money supply, and autonomous investment to see how the IS and LM curves shift and how the equilibrium changes.

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Equilibrium: Y* = 1,850 | r* = 8.50% | I = 130 | C = 1,420

Figure 8.3. IS-LM equilibrium. The intersection of the IS and LM curves determines the unique output and interest rate at which both the goods market and the money market clear.

8.5 Fiscal and Monetary Policy in IS-LM

IS-LM is, above all, a policy analysis machine. It tells us how government spending, taxes, and the money supply affect output and interest rates. It also reveals a crucial complication that the simple Keynesian cross misses: crowding out.

Fiscal Expansion

Suppose the government increases spending by $\Delta G$, keeping taxes and the money supply unchanged. In the Keynesian cross, the multiplier would give $\Delta Y = \frac{1}{1-c} \Delta G$. But this ignores the money market.

In IS-LM:

  1. Higher $G$ shifts IS rightward by $\frac{1}{1-c} \Delta G$.
  2. As output rises, money demand increases.
  3. With a fixed money supply, excess money demand pushes the interest rate up.
  4. Higher interest rates reduce investment, partially offsetting the output gain.
Crowding out. The reduction in private investment that occurs when fiscal expansion raises the interest rate. Government spending crowds out some private spending, partially undoing the stimulus.

The IS-LM fiscal multiplier:

$$\frac{\Delta Y^*}{\Delta G} = \frac{f}{f(1-c) + be}$$ (Eq. 8.14)

Since $be > 0$, we have $\frac{f}{f(1-c) + be} < \frac{1}{1-c}$. The IS-LM multiplier is strictly smaller than the Keynesian multiplier. The difference is crowding out.

The amount of investment crowded out:

$$\frac{\Delta I}{\Delta G} = \frac{-be}{f(1-c) + be}$$ (Eq. 8.15)
Intuition

What this says: Fiscal expansion raises output, but by less than the simple Keynesian multiplier predicts. The missing output is crowding out: government spending pushes up interest rates, which discourages private investment.

Why it matters: Crowding out is the key complication IS-LM adds to the Keynesian cross. Government stimulus does work, but part of the boost is offset by reduced private investment. The more sensitive investment is to interest rates, the more crowding out occurs.

See Full Mode for the derivation.
Example 8.4: Fiscal Expansion with Crowding Out

Baseline: $Y^* = 1{,}850$, $r^* = 8.5\%$, $I = 130$.

Policy: $G$ increases by 100 (from 300 to 400).

New IS: $Y = 3{,}200 - 100r$

Solve: $1Y = 4{,}200 \implies Y^* = 2{,}100$, $r^* = 11\%$

Investment: $I = 300 - 20(11) = 80$. $\Delta I = 80 - 130 = -50$.

IS-LM multiplier: \$150 / 100 = 2.5$ vs. simple Keynesian: \$1$.

Crowding-out gap: Keynesian cross predicts $\Delta Y = 500$, IS-LM delivers \$150$. Crowding-out ratio = \$150/500 = 50\%$.

Half the potential stimulus was neutralized by higher interest rates crowding out private investment.

Monetary Expansion

The IS-LM monetary multiplier:

$$\frac{\Delta Y^*}{\Delta(M/P)} = \frac{b}{f(1-c) + be}$$ (Eq. 8.16)
Intuition

What this says: Increasing the money supply raises output by lowering interest rates, which stimulates investment. Unlike fiscal expansion, monetary expansion reduces interest rates rather than raising them, so there is no crowding out.

Why it matters: Fiscal and monetary policy work through different channels. Fiscal policy directly boosts demand but crowds out investment. Monetary policy works indirectly (through interest rates to investment to output), but actually encourages private investment rather than displacing it.

See Full Mode for the derivation.

Monetary expansion shifts LM rightward. The interest rate falls. Lower interest rates stimulate investment, which through the multiplier raises output. Unlike fiscal expansion, monetary expansion reduces interest rates, so investment rises rather than falls. There is no crowding out.

Example 8.5: Monetary Expansion

Baseline: $Y^* = 1{,}850$, $r^* = 8.5\%$, $I = 130$.

Policy: $M/P$ increases by 100 (from 500 to 600).

New LM: $r = 0.01Y - 12$

Solve: $1Y = 3{,}900 \implies Y^* = 1{,}950$, $r^* = 7.5\%$

Investment: $I = 300 - 20(7.5) = 150$. $\Delta I = +20$.

Comparison:

Fiscal ($\Delta G = 100$)Monetary ($\Delta(M/P) = 100$)
$\Delta Y$+250+100
$\Delta r$+2.5 pp-1.0 pp
$\Delta I$-50+20

Fiscal expansion is more powerful for output but crowds out investment. Monetary expansion stimulates investment but has a smaller output effect.

Policy Mix

Policy mix. A combination of fiscal and monetary policy designed to achieve a specific target, such as raising output without changing the interest rate.

If the government wants to stimulate the economy without crowding out investment, it can combine fiscal expansion (IS shifts right) with monetary expansion (LM shifts right). The monetary expansion holds the interest rate down, preventing the crowding out that would otherwise accompany the fiscal expansion.

The Liquidity Trap

Liquidity trap. A situation in which the interest rate has fallen to zero and monetary expansion can no longer reduce it. People are indifferent between money and bonds, so additional money is held as idle cash.

In a liquidity trap, the LM curve becomes horizontal at $r = 0$. Monetary expansion shifts LM rightward but has no effect on the interest rate or output. Fiscal policy, by contrast, remains fully effective: shifting IS rightward along the flat LM raises output without any crowding out.

The liquidity trap was a theoretical curiosity for decades. It became policy reality in Japan in the 1990s and across much of the developed world after the 2008 financial crisis, when central banks cut rates to near zero and found that further monetary expansion had diminishing effect.

Interactive: Fiscal vs Monetary Policy Comparison

Adjust the policy size to compare the effects of equal-sized fiscal and monetary expansions side by side.

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Fiscal: ΔY = 250, Δr = +2.50 pp, ΔI = -50  |  Monetary: ΔY = 100, Δr = -1.00 pp, ΔI = +20

Figure 8.4. Fiscal expansion raises both output and the interest rate (crowding out investment). Monetary expansion raises output while lowering the interest rate (stimulating investment).

Interactive: Crowding Out Visualizer

See how much of the fiscal stimulus is lost to crowding out. Adjust the fiscal expansion size and the interest sensitivity of investment.

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Crowding out: Y₀ = 1,850 | Y₁ = 2,100 | Y_KC = 2,350 | Gap = 250 | Ratio = 50% | ΔI = -50

Figure 8.5. The crowding-out gap measures how much output is lost because fiscal expansion raises interest rates and displaces private investment.

8.6 From IS-LM to Aggregate Demand

IS-LM takes the price level $P$ as given. But prices do change. The key insight is that the price level enters IS-LM through the real money supply $M/P$. A change in $P$ shifts the LM curve and therefore changes equilibrium output. By tracing how equilibrium output varies with the price level, we derive the aggregate demand curve.

Deriving the AD Curve

Step 1: Start at an IS-LM equilibrium with price level $P_0$, real money supply $M/P_0$, output $Y_0$, and interest rate $r_0$.

Step 2: Increase the price level to $P_1 > P_0$. The real money supply falls: $M/P_1 < M/P_0$. LM shifts leftward.

Step 3: With LM shifted left, the new IS-LM equilibrium has higher $r$ and lower $Y$.

Step 4: Plot $(Y_0, P_0)$ and $(Y_1, P_1)$ in $(Y, P)$ space. Higher $P$, lower $Y$. The curve slopes downward.

Aggregate demand (AD). The set of all combinations of output $Y$ and price level $P$ at which goods and money markets are simultaneously in equilibrium. AD slopes downward: higher $P$ reduces $M/P$, raises $r$, and lowers $Y$.

From Eq. 8.12, we can express equilibrium output as a function of the price level:

$$Y = A_0 + A_1 \cdot \frac{M}{P}$$ (Eq. 8.18)
Intuition

What this says: The AD curve slopes downward because a higher price level shrinks the real money supply, which raises interest rates, which reduces investment and output. Lower prices do the reverse.

Why it matters: AD connects IS-LM (which holds prices fixed) to the price level. Fiscal and monetary expansions shift AD right, meaning the economy demands more output at every price level. This sets up the AD-AS framework for analyzing inflation alongside output.

See Full Mode for the derivation.

where $A_0 = \frac{f(C_0 - cT + I_0 + G)}{f(1-c) + be}$ and $A_1 = \frac{b}{f(1-c) + be}$.

What shifts AD? Anything that shifts IS or LM at a given price level:

8.7 Aggregate Supply: Short Run and Long Run

The AD curve tells us how much output buyers want to purchase at each price level. But it does not tell us how much firms are willing to produce. For that we need aggregate supply.

Long-Run Aggregate Supply

Potential output ($Y_n$). The level of output the economy produces when all resources are fully employed at their normal utilization rates. Determined by labor, capital, and technology, not by demand.
Long-run aggregate supply (LRAS). A vertical line at potential output $Y_n$. In the long run, output is determined by supply-side factors and is independent of the price level.

Why is LRAS vertical? In the long run, all prices and wages are fully flexible. If the price level doubles, wages and input costs eventually double too, leaving firms' real costs unchanged. Output stays at $Y_n$.

Short-Run Aggregate Supply

Short-run aggregate supply (SRAS). The relationship between the price level and the quantity of output firms produce in the short run, when some wages and prices are sticky. SRAS slopes upward: $Y = Y_n + \alpha(P - P^e)$.

Three stories explain why SRAS slopes upward:

  1. Sticky wages: Wages are set by contracts based on the expected price level $P^e$. If $P > P^e$, real wages fall, making hiring cheaper, so firms produce more.
  2. Sticky prices: Some firms set prices in advance. If the overall price level rises but their prices are fixed, their goods become relatively cheap, and demand for their products rises.
  3. Misperceptions: Firms may confuse a general price increase with a relative price increase for their product, and produce more.
$$Y = Y_n + \alpha(P - P^e)$$ (Eq. 8.17)
Intuition

What this says: In the short run, output can deviate from potential when actual prices differ from expected prices. If prices rise unexpectedly, firms produce more (their costs haven't caught up yet). If prices are lower than expected, firms cut back.

Why it matters: This is why demand stimulus works in the short run but not the long run. A demand boost raises prices above expectations, temporarily increasing output. But once workers and firms adjust their expectations, wages catch up, and output returns to potential. Only surprise inflation moves real output.

See Full Mode for the derivation.

where $\alpha > 0$ is the responsiveness of output to surprise inflation. When $P = P^e$, output equals potential: $Y = Y_n$.

Expected price level ($P^e$). The price level that firms and workers anticipated when setting wages and contracts. When actual prices deviate from expectations, output deviates from potential.

What shifts SRAS?

8.8 The AD-AS Model

With aggregate demand and aggregate supply in hand, we can analyze the full macroeconomy, with output and the price level determined simultaneously.

Short-Run Equilibrium

The economy's short-run equilibrium is the intersection of AD and SRAS. Output may be above, below, or equal to potential. The economy need not be at full employment in the short run.

Demand Shocks

Demand shock. A shift in the AD curve caused by changes in fiscal policy, monetary policy, consumer confidence, or investment sentiment.

Positive demand shock (AD shifts right): Output rises above potential and the price level rises. The economy is in a boom.

Negative demand shock (AD shifts left): Output falls below potential and the price level falls. The economy is in a recession.

Supply Shocks

Supply shock. A shift in the SRAS curve caused by changes in input costs, productivity, or expectations about the price level.
Stagflation. The combination of stagnant output (or falling output) and rising prices, typically caused by a negative supply shock.

Negative supply shock (SRAS shifts up/left): Output falls below potential while the price level rises. This is stagflation. The worst of both worlds.

Stagflation poses a cruel dilemma for policymakers. If they fight the recession with expansionary policy, they make inflation worse. If they fight inflation with contractionary policy, they deepen the recession.

The supply-shock half of this model was forced into existence by a real episode: the 1970s, when the oil shocks delivered stagnation and inflation together and broke the policy menu the postwar synthesis had relied on — see stagflation as a regime crisis in the economic-history book.

The Self-Correcting Mechanism

Self-correcting mechanism. The process by which the economy returns to potential output in the long run through adjustments in the expected price level and wages.

From recession back to potential: With output below $Y_n$, unemployment is high. Over time, workers accept lower wages. $P^e$ adjusts downward. SRAS shifts right. Output gradually rises back toward $Y_n$ at a lower price level.

From boom back to potential: With output above $Y_n$, workers demand higher wages. $P^e$ adjusts upward. SRAS shifts left. Output falls back toward $Y_n$ at a higher price level.

Long-run neutrality: In the long run, demand shocks affect only the price level, not output. Only supply-side changes can permanently raise output.

The self-correcting mechanism is real, but the question that has divided economists for nearly a century is: How long does it take? As Keynes quipped: "In the long run we are all dead." The right policy depends on how long the long run is.

Example 8.6: Supply Shock and Stagflation

Setup: $Y_n = 1{,}000$, $P_0 = 100$, $P^e = 100$, $\alpha = 5$.

SRAS: $Y = 1{,}000 + 5(P - 100)$. AD: $Y = 1{,}500 - 5P$.

Initial equilibrium: \$1{,}500 - 5P = 500 + 5P \implies P = 100$, $Y = 1{,}000 = Y_n \checkmark$

Shock: Oil crisis raises $P^e$ to 120. New SRAS: $Y = 1{,}000 + 5(P - 120) = 400 + 5P$.

New equilibrium: \$1{,}500 - 5P = 400 + 5P \implies P = 110$, $Y = 950$.

Diagnosis: Stagflation. Output fell from 1,000 to 950 (recession). Price level rose from 100 to 110 (inflation). The economy simultaneously stagnates and inflates.

Output gap: \$150 - 1{,}000 = -50$ (recessionary gap).

Self-correction: With $Y < Y_n$, unemployment is high. Over time $P^e$ falls, SRAS shifts right, output recovers toward $Y_n$ at a new price level.

Interactive: AD-AS Model

Shift aggregate demand and aggregate supply to explore recessions, booms, stagflation, and disinflation.

-300+300
-300+300
Equilibrium: Y* = 1,000 | P* = 100 | Output gap = 0 | Long-run equilibrium

Figure 8.6. The AD-AS model. Demand and supply shocks shift AD and SRAS, producing recessions, booms, stagflation, or disinflation.

Interactive: Self-Correcting Economy

Watch the economy recover from a demand shock through the self-correcting mechanism. SRAS shifts as wage expectations adjust.

-300-100
0.100.50
Frame 0: Y = 1,000 | P = 100 | Output gap = 0 | Long-run equilibrium

Figure 8.7. The self-correcting mechanism gradually restores potential output through wage and price adjustment, but the process may take years.

The Kaelani Republic: Diagnosing a Recession

Continues from Chapter 7. The Kaelani Republic's GDP has fallen from 10.0 billion KD to 9.0 billion KD. Unemployment has climbed from 10% to 14%. The central bank's policy committee is meeting to decide how to respond. From Chapter 7, we know the national accounts: $C = 6$B, $I = 2$B, $G = 2.5$B, $NX = -0.5$B.

Part 1: Building the Kaelani IS-LM Model

The central bank's economists estimate the structural parameters:

Deriving IS:

$$Y = 5(1.0 - 1.6 + 1.5 + 2.5) - 50r = 17.0 - 50r$$

Deriving LM:

$$r = 0.025Y - 0.2$$

Solving: $Y^* = 12.0$B KD, $r^* = 10\%$.

But the economy is at 9.0B, not 12.0B. Diagnosis: A collapse in business confidence reduced autonomous investment from $I_0 = 1.5$ to $I_0 = 0.9$ (a fall of 0.6B KD).

New IS: $Y = 14.0 - 50r$. New equilibrium: $Y^* = 10.67$B, $r^* = 6.7\%$.

The model correctly identifies the direction: a collapse in investment shifted IS leftward, reducing both output and the interest rate.

Part 2: Policy Options

Option A. Fiscal response: Increase $G$ by 0.5B KD. Result: $Y^* = 11.78$B, $r^* = 9.4\%$. Investment is crowded out heavily.

Option B. Monetary response: Increase $M/P$ from 4.0 to 5.5. Result: $Y^* = 12.33$B, $r^* = 3.3\%$. Investment partially recovers to $I = 0.57$B. Output rises while the interest rate falls.

Option C. Policy mix: Moderate fiscal ($\Delta G = 0.5$B) plus moderate monetary ($\Delta(M/P) = 0.75$). Result: $Y^* = 12.61$B, $r^* = 7.8\%$, $I = 0.12$B. Strong output recovery with limited crowding out.

Part 3: AD-AS Implications

In AD-AS terms, the Kaelani recession is a negative demand shock: AD shifted leftward. Without policy action, the self-correcting mechanism would eventually restore $Y_n$: wages fall, SRAS shifts right, the economy recovers at a lower price level. But this could take years. Kaelani's workers cannot wait.

If the central bank overshoots with monetary expansion, AD shifts too far right: output temporarily exceeds potential, and inflation accelerates. The 14% unemployment problem becomes a 4% inflation problem.

Connection to Chapter 7: The GDP gap, the unemployment rate of 14%, and the national accounts data all come directly from Chapter 7. Students now see the same economy through two lenses: measurement (Ch 7) and models (Ch 8).

Historical Lens: Keynes and the General Theory (1936)

In 1936, seven years into the Great Depression, John Maynard Keynes published The General Theory of Employment, Interest, and Money. Classical economics held that flexible wages and prices would restore full employment automatically. Yet by 1936, unemployment had been in double digits for half a decade. The classical prediction had failed spectacularly.

Keynes's revolutionary claim was that aggregate demand could be persistently deficient. Even with flexible wages, the economy could settle at an equilibrium far below full employment, trapped in a vicious circle that market forces alone could not break.

The solution, Keynes argued, was government intervention. If private spending was insufficient, the government should fill the gap with public spending, deficit-financed if necessary. The multiplier would amplify the impact.

In 1937, John Hicks distilled Keynes's ideas into the IS-LM diagram. What Keynes expressed in 400 dense pages, Hicks captured in two equations and a graph. IS-LM became the workhorse of macroeconomic policy analysis for the next forty years.

The AD-AS framework extended IS-LM by allowing the price level to vary. With AD-AS, economists could analyze not just recessions but also inflation and the devastating combination of both: stagflation.

Modern macroeconomics has moved beyond IS-LM to dynamic, micro-founded models (Chapters 14 and 15). But IS-LM remains the starting point for policy intuition: the model you learn first, the model that shapes how policymakers think, the model that captures the essential insight Keynes bequeathed to economics. Demand matters, and when it fails, governments must act.

The apparatus in this chapter was built to explain the Great Depression — see how the slump actually unfolded in the economic-history book. The lineage of the demand-deficiency idea, and Hicks's 1937 distillation of it into IS-LM, is traced in the history of economic thought: the Keynesian revolution.

The Phillips-curve and adaptive-expectations material this chapter touches is the opening of a longer thread on how economics models expectations — traced in full in the walkthrough Expectations: Keynes to prospect theory.

Summary

Key Equations

LabelEquationDescription
Eq. 8.1$C = C_0 + c(Y - T)$, \$0 < c < 1$Consumption function
Eq. 8.2$PE = C_0 + c(Y - T) + I + G$Planned expenditure
Eq. 8.3$Y^* = \frac{1}{1-c}(C_0 - cT + I + G)$Keynesian cross equilibrium
Eq. 8.4$\frac{\Delta Y}{\Delta G} = \frac{1}{1-c}$Spending multiplier
Eq. 8.5$\frac{\Delta Y}{\Delta T} = \frac{-c}{1-c}$Tax multiplier
Eq. 8.6$\frac{\Delta Y}{\Delta G}\big|_{\Delta G = \Delta T} = 1$Balanced-budget multiplier
Eq. 8.7$I = I_0 - br$, $b > 0$Investment function
Eq. 8.8$Y = \frac{1}{1-c}(C_0 - cT + I_0 + G) - \frac{b}{1-c}r$IS curve
Eq. 8.9$L(r, Y) = eY - fr$Money demand
Eq. 8.10$\frac{M}{P} = eY - fr$Money market equilibrium
Eq. 8.11$r = \frac{e}{f}Y - \frac{1}{f}\frac{M}{P}$LM curve
Eq. 8.12$Y^* = \frac{f(C_0 - cT + I_0 + G) + b(M/P)}{f(1-c) + be}$IS-LM equilibrium output
Eq. 8.13$r^* = \frac{e(C_0 - cT + I_0 + G) - (1-c)(M/P)}{f(1-c) + be}$IS-LM equilibrium interest rate
Eq. 8.14$\frac{\Delta Y^*}{\Delta G} = \frac{f}{f(1-c) + be}$IS-LM fiscal multiplier
Eq. 8.15$\frac{\Delta I}{\Delta G} = \frac{-be}{f(1-c) + be}$Crowding-out of investment
Eq. 8.16$\frac{\Delta Y^*}{\Delta(M/P)} = \frac{b}{f(1-c) + be}$IS-LM monetary multiplier
Eq. 8.17$Y = Y_n + \alpha(P - P^e)$Short-run aggregate supply
Eq. 8.18$Y = A_0 + A_1 \cdot \frac{M}{P}$AD curve (from IS-LM)

Exercises

Practice

  1. P1. Given $C_0 = 80$, $c = 0.75$, $I = 150$, $G = 200$, $T = 180$: (a) Compute autonomous spending $A$ and equilibrium output $Y^*$. (b) What is the spending multiplier? (c) If $T$ rises by 40 (from 180 to 220), what is the new $Y^*$? By how much did output change, and is this consistent with the tax multiplier formula?
  2. P2. Given $C = 50 + 0.6(Y - T)$, $I = 100 - 15r$, $G = 200$, $T = 100$: (a) Derive the IS equation by expressing $Y$ as a function of $r$. (b) At what interest rate does IS cross the horizontal axis ($Y = 0$)? At what output level does IS cross the vertical axis ($r = 0$)? (c) Plot the IS curve with $Y$ on the horizontal axis and $r$ on the vertical axis.
  3. P3. Given $M/P = 180$, $L = 0.4Y - 40r$: (a) Derive the LM equation by expressing $r$ as a function of $Y$. (b) At what output level does the LM curve cross the horizontal axis ($r = 0$)? (c) Plot the LM curve. What is the slope of LM?
  4. P4. Using the IS curve from P2 and the LM curve from P3: (a) Solve for the IS-LM equilibrium $Y^*$ and $r^*$. (b) Compute consumption, investment, and planned expenditure at equilibrium. Verify that $Y^* = C + I + G$. (c) Verify that money demand equals money supply at equilibrium.
  5. P5. From the equilibrium in P4, government spending increases by 50 (from 200 to 250): (a) Derive the new IS curve. (b) Solve for the new $Y^*$ and $r^*$. (c) Compute the IS-LM fiscal multiplier $\Delta Y^* / \Delta G$. Compare to the simple Keynesian multiplier $1/(1-c)$. (d) How much investment was crowded out?

Apply

  1. A1. The 2008 crisis in IS-LM. The 2008 financial crisis caused a sharp decline in autonomous investment. (a) Show how the fall in $I_0$ affects the IS curve and equilibrium. (b) Explain why central banks responded by cutting interest rates. Show this as a shift in LM. (c) What happens when interest rates reach zero but the economy is still in recession? Describe the liquidity trap. Which policy is more effective in this situation, and why?
  2. A2. Policy mix design. A government wants to raise output by 200 without changing the interest rate. Using the parameters from Example 8.3: (a) Explain conceptually why fiscal + monetary expansion can achieve this. (b) Set up the system: $\Delta Y = 200$ and $\Delta r = 0$. Solve for the required $\Delta G$ and $\Delta(M/P)$. (c) Verify your answer.
  3. A3. Stagflation diagnosis. In the 1970s, OPEC quadrupled oil prices. Using an AD-AS diagram: (a) Show the initial equilibrium and the oil shock on SRAS. (b) Identify the new equilibrium and explain why it is stagflation. (c) If policymakers respond with expansionary demand policy, what happens? (d) If they do nothing, describe the self-correcting path.
  4. A4. Twin deficits and crowding out. The national saving identity from Ch 7 is $S - I = NX$. (a) In IS-LM, fiscal expansion raises $r$ and reduces $I$. What happens to $NX$? (b) Explain the "twin deficits" hypothesis. (c) Under what conditions might this link break down?

Challenge

  1. C1. Derive the balanced-budget multiplier algebraically. From Eq. 8.3: (a) Compute $\partial Y / \partial G$ and $\partial Y / \partial T$. (b) Set $\Delta G = \Delta T$ and compute $\Delta Y$. (c) Show that $\Delta Y = \Delta G$ regardless of $c$. (d) Provide economic intuition: why does the balanced-budget multiplier equal exactly 1?
  2. C2. IS-LM comparative statics: sensitivity analysis. From Eq. 8.12: (a) Show the fiscal multiplier is larger when $b$ is small. Explain. (b) Show the fiscal multiplier is larger when $f$ is large. Explain. (c) What happens when $f \to \infty$ (liquidity trap)? When $f \to 0$? (d) Analyze the monetary multiplier under what conditions it is most/least effective.
  3. C3. Self-correcting economy: speed and cost. From a negative demand shock: (a) Describe the adjustment path back to $Y_n$. (b) Under what conditions is self-correction fast? (c) When is it slow, and what are the costs? (d) Make the case for and against active policy. (e) Connect to the Keynesian vs. classical debate.
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