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.
Prerequisites: Chapter 7 (GDP, national income identities, business cycle facts).
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 — an assumption we will relax in Sections 8.6 through 8.8.
The model begins with a behavioral assumption about how households decide what to spend.
The consumption function is:
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 — and that spending becomes someone else's income.
In a closed economy (no exports or imports):
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.
If output exceeds planned expenditure ($Y > PE$), firms find unsold goods piling up on their shelves — unplanned inventory accumulation. 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 $Y = PE$:
$$Y = C_0 + c(Y - T) + I + G$$
$$Y = C_0 + cY - cT + I + G$$
$$Y - cY = C_0 - cT + I + G$$
$$Y(1 - c) = C_0 - cT + I + G$$
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 $\frac{1}{1-c}$.
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.
Figure 8.1. Keynesian cross. Equilibrium occurs where planned expenditure equals actual output. The slope of the PE line is the MPC.
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:
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.
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.
From Eqs. 8.4 and 8.5:
$$\Delta Y = \frac{1}{1-c} \Delta G + \frac{-c}{1-c} \Delta T = \frac{1-c}{1-c} \Delta G = \Delta G$$
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.
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: $Y^* = 2{,}000 + 250 = 2{,}250$.
Continuing from Example 8.1: government spending rises by $\Delta G = 50$ with $c = 0.8$.
| Round | New spending this round | Cumulative total |
|---|---|---|
| 1 | 50.0 | 50.0 |
| 2 | 40.0 | 90.0 |
| 3 | 32.0 | 122.0 |
| 4 | 25.6 | 147.6 |
| 5 | 20.5 | 168.1 |
| 6 | 16.4 | 184.5 |
| 7 | 13.1 | 197.6 |
| 8 | 10.5 | 208.1 |
| 9 | 8.4 | 216.5 |
| 10 | 6.7 | 223.2 |
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.
Set the MPC and initial spending impulse, then press Play to watch the multiplier unfold round by round.
Figure 8.2. The multiplier round by round. Each round of spending is smaller than the last, but the cumulative total converges to $\Delta G / (1-c)$.
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.
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. So investment falls. When $r$ falls, previously unprofitable projects become worthwhile, and investment rises.
Substitute the investment function (Eq. 8.7) into the Keynesian cross equilibrium (Eq. 8.3):
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.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 — 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 $\frac{1}{1-c} \Delta G$.
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.
Why do people hold money — an asset that, unlike bonds, typically earns no interest? Keynes identified three motives.
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.
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:
Solving for $r$:
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.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?
You just saw money as a quantity M in the LM curve. But what IS money? The model treats it as a given — it never asks why people accept green pieces of paper as payment.
In IS-LM, money is a stock (M) that people hold because they need it for transactions and because bonds are risky. The interest rate is the opportunity cost of holding money. Increase M, excess money supply pushes the interest rate down, investment rises, output rises. Money is a policy lever — the central bank controls M, and the model treats money's nature as irrelevant. All that matters is the quantity and its effect on interest rates.
IS-LM treats money supply as exogenous — the central bank sets M. But modern central banks target interest rates, not the money supply. The LM curve is arguably better described as a horizontal line at the target rate (the IS-MP framework). More fundamentally, IS-LM doesn't ask why people accept money at all. The model assumes money exists and works — it doesn't explain why. The commodity view says money must have intrinsic value (gold). Chartalists say money is a creature of the state — taxes create demand for government tokens. Credit theorists say all money is debt. IS-LM sidesteps all of this.
The mainstream moved from money-stock targeting (Friedman's k-percent rule) to interest-rate targeting (Taylor rule). The LM curve became a footnote in many graduate textbooks, replaced by a monetary policy rule. But the question 'what is money?' became more urgent, not less, as digital payments, cryptocurrencies, and central bank digital currencies emerged. If money is just a social convention, can a decentralized algorithm sustain one?
IS-LM gives you the macroeconomics of money — how changes in money supply or demand affect output and interest rates. It is a powerful tool for policy analysis. But it gives you no insight into what money fundamentally is. For that, you need the deeper theories: cash-in-advance, money-in-utility, the fiscal theory of the price level, and the credit theory of money. The nature of money may seem philosophical until a crisis forces the question — every hyperinflation is a failure of the social convention that money depends on.
If money's nature doesn't matter for IS-LM, does it matter at all? Come back at Chapter 16 (§16.1, §16.5–16.6), where the monetary theory gets serious — CIA, MIU, the Friedman rule, and the fiscal theory of the price level all depend on what you think money is. And the answer has real policy implications: if money is a government liability backed by future surpluses (FTPL), then fiscal policy determines the price level, not the central bank.
Peter Schiff told Joe Rogan's audience that Bitcoin fails every test of money. No intrinsic value, no government backing, wild price swings. Yet millions hold it. Does it satisfy the definition — or does it need a new one?
IntroIncreasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
IntroThe 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.
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:
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.
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:
$$Y = 2{,}700 - 100(0.01Y - 10) = 2{,}700 - Y + 1{,}000$$
$$2Y = 3{,}700 \implies Y^* = 1{,}850$$
$$r^* = 0.01(1{,}850) - 10 = 8.5\%$$
Step 4 — Investment at equilibrium:
$$I = 300 - 20(8.5) = 130$$
Step 5 — Verify:
$C = 100 + 0.8(1{,}850 - 200) = 1{,}420$. $PE = 1{,}420 + 130 + 300 = 1{,}850 = Y^* \checkmark$
$L = 0.5(1{,}850) - 50(8.5) = 925 - 425 = 500 = M/P \checkmark$
Adjust government spending, taxes, the money supply, and autonomous investment to see how the IS and LM curves shift and how the equilibrium changes.
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.
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 — and reveals a crucial complication that the simple Keynesian cross misses: crowding out.
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:
The IS-LM fiscal multiplier:
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:
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.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.
The IS-LM monetary multiplier:
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 — 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 — investment rises rather than falls. There is no crowding out.
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.
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.
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.
Adjust the policy size to compare the effects of equal-sized fiscal and monetary expansions side by side.
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).
See how much of the fiscal stimulus is lost to crowding out. Adjust the fiscal expansion size and the interest sensitivity of investment.
Figure 8.5. The crowding-out gap measures how much output is lost because fiscal expansion raises interest rates and displaces private investment.
You now have the multiplier and IS-LM. Here's what they say about this question — and what they can't answer yet.
The Keynesian cross gives a multiplier of $\frac{1}{1-MPC}$. A \$100 billion increase in $G$ raises GDP by $\frac{\$100B}{1-MPC}$. In IS-LM, the effect is smaller because higher $Y$ raises money demand, which raises interest rates, which crowds out private investment. The multiplier is still positive, but less than $\frac{1}{1-MPC}$. Monetary policy looks more powerful — an increase in $M$ shifts LM right without the crowding-out problem that limits fiscal policy.
The classical and Austrian critique: government spending must come from somewhere. If financed by taxes, it directly reduces private spending. If financed by borrowing, it competes with private borrowers for loanable funds, driving up interest rates. The government doesn't create resources — it reallocates them. In the extreme, the multiplier is exactly 1 (pure crowding out) or even less than 1 if government spends less efficiently than the private sector. The IS-LM model builds in the Keynesian answer by assumption — the consumption function assumes people spend a fixed fraction of income, rather than optimizing intertemporally.
The mainstream absorbed crowding out into IS-LM — that's exactly what the LM curve does. The debate shifted from "does fiscal policy work?" to "how big is the multiplier?" The answer depends on the slope of LM. A steep LM curve (the monetarist position) implies a small multiplier — most of the fiscal expansion is offset by rising interest rates. A flat LM curve implies a large multiplier. The slopes are empirical questions, not theoretical ones.
At this level, fiscal policy works but imperfectly. The multiplier is positive but less than the naive Keynesian cross suggests. Be skeptical of anyone claiming a specific multiplier number without specifying the model and conditions. And note what IS-LM hides: it assumes backward-looking consumers who spend a fixed fraction of current income. Forward-looking consumers might save a tax cut entirely, anticipating future taxes to repay the debt. That possibility — Ricardian equivalence — needs micro-foundations you don't have yet.
IS-LM is static and ad hoc — the IS and LM curves aren't derived from optimization. Forward-looking consumers might behave very differently from the MPC story. Come back in Chapter 9 (§9.1–9.2), where consumption is micro-founded via the Euler equation. And then in Chapter 15 (§15.7), the zero lower bound changes everything — when interest rates hit zero, crowding out disappears and the fiscal multiplier may exceed the textbook value.
The multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
IntermediateIncreasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
IntroIS-LM shows monetary policy shifting LM and changing output. The central bank looks powerful. But how much control does it really have?
In IS-LM, the central bank controls M. An increase in M shifts LM right, lowering the interest rate and raising output. The advantage over fiscal policy: no crowding out — the interest rate falls rather than rises, so investment is stimulated rather than displaced. At the extreme, if LM is flat (liquidity trap), monetary policy is impotent. But outside that special case, the central bank appears to be the most effective macroeconomic policymaker in the model.
The Monetarist critique (Friedman): IS-LM focuses on interest rates, but what matters is the money supply itself. The transmission mechanism is broader than the interest rate channel — money affects spending through wealth effects, portfolio balance, and credit availability. Central banks should target money supply growth, not interest rates. The Austrian critique: central banks can lower interest rates temporarily but only by distorting the price signal that coordinates saving and investment. Artificially low rates cause malinvestment — overbuilding, speculative booms, misallocation of capital — that leads to inevitable busts. The central bank doesn't control the economy; it destabilizes it.
The mainstream moved away from money supply targeting after Goodhart's Law (money demand is unstable when targeted) and toward interest rate targeting. But Friedman's deeper point — that monetary policy operates with long and variable lags — survived and influenced Taylor rule thinking. The question shifted from 'can the central bank control M?' to 'can the central bank control r effectively, and does controlling r control the economy?'
At this level, central banks can control the economy through interest rates. The IS-LM framework is clean and powerful — shift LM, change output. But note two things the model hides: expectations (people may anticipate and offset policy) and the zero lower bound (interest rates cannot go below zero, which turns a theoretical curiosity into a practical constraint). IS-LM gives you the mechanics but not the limitations.
IS-LM is static and backward-looking — agents don't anticipate policy changes. Come back at Chapter 9 (§9.5–9.6) for expectations and the Mundell-Fleming constraint (the impossible trinity), Chapter 15 (§15.5–15.7) for the Taylor rule, the NK framework, and the zero lower bound, and Chapter 16 (§16.2, §16.5) for time inconsistency and the fiscal theory's challenge to central bank power.
Ron Paul and Peter Schiff have warned for decades that the Fed is debasing the currency. The clips have millions of views. But long and variable lags, the zero lower bound, and fiscal dominance all complicate the story. How much control does the Fed really have?
AdvancedIncreasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
IntroIS-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.
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.
From Eq. 8.12, we can express equilibrium output as a function of the price level:
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:
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.
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 $Y_n$.
Three stories explain why SRAS slopes upward:
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: $Y = Y_n$.
What shifts SRAS?
With aggregate demand and aggregate supply in hand, we can analyze the full macroeconomy — output and the price level determined simultaneously.
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.
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.
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.
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.
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.
Shift aggregate demand and aggregate supply to explore recessions, booms, stagflation, and disinflation.
Figure 8.6. The AD-AS model. Demand and supply shocks shift AD and SRAS, producing recessions, booms, stagflation, or disinflation.
Watch the economy recover from a demand shock through the self-correcting mechanism. SRAS shifts as wage expectations adjust.
Figure 8.7. The self-correcting mechanism gradually restores potential output through wage and price adjustment, but the process may take years.
You now have AD-AS — the first model that gives a causal story for recessions. But the story has conspicuous gaps.
In the Keynesian cross and AD-AS, recessions happen when aggregate demand shifts left. A fall in confidence, investment, or exports reduces planned expenditure, and the multiplier amplifies the initial shock. If prices are sticky (SRAS slopes upward), the adjustment falls on output and employment rather than prices. The economy can remain below full employment for extended periods — the self-correcting mechanism works, but slowly. Keynes's insight: demand deficiency is real, persistent, and painful.
The classical and RBC response: why would demand fall? Rational agents optimize intertemporally — they don't suddenly stop spending without reason. The Keynesian story requires either irrationality (animal spirits) or some real shock that reduces optimal spending. If it's a real shock, the recession may be an efficient response, not a market failure. Say's Law, updated: supply creates its own demand — income from production is spent or saved and invested. Persistent demand deficiency requires a coordination failure that the price system should resolve. The Keynesian model asserts sticky prices but doesn't explain why prices are sticky or how long they stay that way.
Keynes's insight that coordination failures can persist was revolutionary — the Great Depression proved that markets don't always self-correct quickly. The mainstream absorbed the idea but wanted microfoundations: why exactly are prices sticky? How do rational agents generate demand shortfalls? The answer came decades later with the New Keynesian synthesis (Chapter 15), which derives sticky prices from monopolistic competition and staggered price-setting.
Demand shortfalls are a real cause of recessions — the evidence from the Great Depression, the 2008 financial crisis, and COVID is overwhelming. Output fell, unemployment soared, and the pattern matches the AD-AS story. But the Keynesian model at this level needs two things it doesn't have: a trigger (what causes AD to shift left in the first place?) and a mechanism for persistence (why don't wages and prices adjust faster?). 'Animal spirits' and 'sticky prices' are labels for the phenomena, not explanations of them.
What are the microfoundations? Why are prices sticky? Is the demand story the whole story, or are supply shocks equally important? Come back at Chapter 14 (§14.1–14.6) for the RBC alternative — recessions as efficient responses to technology shocks — and then at Chapter 15 (§15.1–15.8) for the New Keynesian synthesis that nests both demand and supply explanations in a single framework.
Yield curve inversions, consumer confidence drops, and leading indicators flash warnings. But predicting recessions is notoriously unreliable — the models that explain them after the fact can't reliably predict them in advance.
IntermediateThe multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
IntermediateContinues 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.
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.
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.
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).
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, and the model that captures the essential insight Keynes bequeathed to economics: demand matters, and when it fails, governments must act.
| Label | Equation | Description |
|---|---|---|
| Eq. 8.1 | $C = C_0 + c(Y - T)$, \$1 < 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) |