The IS–LM model is the workhorse of intermediate macroeconomics. It puts the goods market and the money market on a single diagram and asks them to agree — and out of that agreement comes the interest rate, the level of output, and a clean answer to what fiscal and monetary policy actually do. If you are taking intermediate macro at a New York university, this is the model your midterm is built around. Work through it once, carefully, and half the course falls into place.
1 · Two markets, one diagram
An economy has to clear two markets at the same time: the market for goods and services, and the market for money. Each market links two variables — output Y and the interest rate r. One equation cannot pin down two unknowns, so you need both.
That is the whole idea of IS–LM. The IS curve collects every (Y, r) pair for which the goods market is in equilibrium. The LM curve collects every pair for which the money market is in equilibrium. Only where they cross are both markets clearing at once. That crossing is the economy’s short-run equilibrium, with prices held fixed — the assumption that defines the short run in this model.
Draw the diagram with output Y on the horizontal axis and the interest rate r on the vertical. Everything that follows lives on this one picture.
2 · The IS curve — the goods market
The IS curve slopes downward. To see why, follow a rise in the interest rate through the goods market.
A higher interest rate makes borrowing dearer, so firms invest less. Write investment as falling in r: I = I₀ − br, where b measures how sensitive investment is to the rate. Lower investment means lower aggregate demand, and lower demand means lower equilibrium output. So higher r goes with lower Y — a downward-sloping curve.
The size of the drop depends on the multiplier. When demand falls, income falls, which cuts consumption, which cuts income again. With a marginal propensity to consume of c, the multiplier is 1/(1 − c). A given change in the interest rate moves output by the change in investment times that multiplier. The steeper investment responds to rates, and the larger the multiplier, the flatter the IS curve.
Fiscal policy shifts the IS curve. A rise in government spending G or a tax cut raises demand at every interest rate, moving IS to the right. The horizontal shift is not the change in spending itself — it is the change magnified by the multiplier. That detail is where the crowding-out story begins.
3 · The LM curve — the money market
The LM curve slopes upward, and again it pays to trace the logic.
The central bank fixes the money supply. Money demand rises with output — more transactions need more money — and falls with the interest rate, which is the opportunity cost of holding cash rather than bonds. For the money market to clear at a fixed supply, a rise in output (which pushes money demand up) must be met by a rise in the interest rate (which pulls it back down). So higher Y goes with higher r — an upward-sloping curve.
The slope of LM reflects how sensitive money demand is to the interest rate. If money demand barely responds to rates, the LM curve is steep, and clearing the money market takes a big rate move. That sensitivity turns out to control how much fiscal policy gets crowded out.
Monetary policy shifts the LM curve. An increase in the money supply moves LM down and to the right: at every level of output, the rate that clears the money market is now lower.
4 · Equilibrium, and what moves it
Equilibrium is the single (Y, r) pair where IS and LM intersect. Both markets clear. Nothing pushes output or the rate away from that point until a curve moves.
Two policy levers move the curves, and keeping them straight is half the battle:
- Fiscal policy — government spending and taxes — shifts IS.
- Monetary policy — the money supply — shifts LM.
A fiscal expansion shifts IS right, raising both output and the interest rate. A monetary expansion shifts LM right, raising output but lowering the interest rate. The opposite signs on the interest rate are the model’s sharpest prediction, and the reason the two policies interact.
5 · Crowding out — the central lesson
Here is the result the whole model is built to deliver. When the government spends more, output does not rise by the full multiplier amount. The interest rate gets in the way.
A fiscal expansion shifts IS right. If the interest rate could stay put, output would rise by the full multiplier effect. But the rightward shift raises money demand, which pushes the interest rate up along the LM curve. The higher rate chokes off some private investment, and that lost investment — magnified by the same multiplier — cancels part of the stimulus. The output that is lost this way is crowding out.
How much gets crowded out depends on the slope of the LM curve. A steep LM — money demand insensitive to rates — means the rate rises sharply and crowding out is severe. A flat LM means the rate barely moves and fiscal policy is powerful. In the vertical-LM extreme, crowding out is complete: fiscal policy raises the interest rate and nothing else.
Worked example — a fiscal expansion and its crowding out
Take an economy described by two equations. The goods market gives the IS curve r = 10 − 0.1Y, and the money market gives the LM curve r = 0.1Y. Behind the IS curve, consumers spend half of each extra dollar of income (c = 0.5, so the multiplier is 1/(1 − 0.5) = 2), and investment falls by 5 for every one-point rise in the interest rate (I = I₀ − 5r).
Step 1 — Find the initial equilibrium. Set IS equal to LM: 10 − 0.1Y = 0.1Y. Then 10 = 0.2Y, so Y = 50 and r = 0.1 × 50 = 5%. Call this point E₁ = (50, 5).
Step 2 — Apply a fiscal expansion. The government raises spending by ΔG = 10. With a multiplier of 2, demand rises at every interest rate, shifting IS right by the multiplier times the spending change: 2 × 10 = 20. The new curve, IS′, has the same slope and sits 20 units to the right: r = 12 − 0.1Y.
Step 3 — Find the new equilibrium. Set IS′ equal to LM: 12 − 0.1Y = 0.1Y. Then 12 = 0.2Y, so Y = 60 and r = 6%. Call this E₂ = (60, 6). Output rose, and so did the interest rate.
Step 4 — Ask what the multiplier alone would have predicted. If the interest rate had stayed at its original 5%, the new IS′ would deliver 5 = 12 − 0.1Y, giving Y = 70. That is the full multiplier effect: ΔG = 10 times the multiplier of 2 is +20, taking output from 50 to 70. Mark this reference point C = (70, 5).
Step 5 — Measure the crowding out. Output actually reached only 60, not 70. The difference, 70 − 60 = 10, is crowded out. Trace it: the interest rate rose by one point (5 to 6), which cut investment by 5 × 1 = 5, and through the multiplier that removed 2 × 5 = 10 of output. Exactly the gap. Half of the fiscal stimulus was crowded out.
Step 6 — Interpret. Fiscal policy still worked — output rose from 50 to 60 — but the interest-rate response halved its punch. Had the LM curve been flatter (money demand more sensitive to the rate), the rate would have risen less and crowding out would have been smaller. This is why the effectiveness of fiscal policy is really a question about the money market.
Not sure why a fiscal expansion pushes the interest rate up? That crowding-out mechanism is the single most tested idea in the IS–LM model, and exactly what a one-on-one intermediate macroeconomics tutor works through with you until it is automatic. Book a trial session.
Practice
Q1. An economy has IS curve r = 15 − 0.1Y and LM curve r = 0.05Y. Find the equilibrium output and interest rate.
Q2. From the Q1 economy, a fiscal expansion shifts the IS curve right by 30, to r = 18 − 0.1Y. Find the new equilibrium. What output would occur if the interest rate stayed at its original level, and how much output is crowded out?
Q3. From the Q1 economy instead, a monetary expansion shifts the LM curve down to r = 0.05Y − 1.5, with the IS curve unchanged. Find the new equilibrium. What happens to the interest rate and to investment?
Answers: Q1: set 15 − 0.1Y = 0.05Y, so 15 = 0.15Y, Y = 100 and r = 0.05 × 100 = 5%. Q2: set 18 − 0.1Y = 0.05Y, so Y = 120 and r = 6%. At the old rate of 5%, the new IS gives 5 = 18 − 0.1Y, so Y = 130. Crowding out = 130 − 120 = 10 (output rose 100 → 120, a gain of 20 out of a potential 30). Q3: set 15 − 0.1Y = 0.05Y − 1.5, so 16.5 = 0.15Y, Y = 110 and r = 0.05 × 110 − 1.5 = 4%. The interest rate falls from 5% to 4%, so investment rises — a monetary expansion crowds investment in, the mirror image of fiscal crowding out.
Key takeaways
- The IS–LM model finds the output and interest rate at which both the goods market (IS) and the money market (LM) clear, with the price level held fixed.
- The IS curve slopes down because a higher interest rate cuts investment and, through the multiplier, output. The LM curve slopes up because higher output raises money demand, which raises the rate.
- Fiscal policy shifts IS; monetary policy shifts LM. A fiscal expansion raises the interest rate; a monetary expansion lowers it.
- Crowding out is the output lost when a fiscal expansion drives the interest rate up and chokes off private investment. Measure it as the gap between the full-multiplier output and the actual equilibrium.
- The steeper the LM curve, the more fiscal policy is crowded out — so the power of fiscal policy is decided in the money market.
Why New York students choose our intermediate macroeconomics tutoring
- Course-matched tutors: whether your intermediate macro course sits at NYU, Columbia, Yale or Princeton, our tutors teach IS–LM in the notation and emphasis your professor uses, from your lecture slides to your problem sets.
- Model specialists: sessions are led by tutors who teach the short-run models as a connected system — IS–LM, AD–AS, and the open-economy Mundell–Fleming extension — so you see how the pieces fit rather than memorising each in isolation.
- Exam-first preparation: we work past midterms with the mark scheme in view, because crowding out, curve shifts and the fiscal-versus-monetary comparison are exactly where intermediate-macro marks are won and lost.
FAQ
Q: What does the IS–LM model actually show?
A: It shows the short-run equilibrium of an economy — the level of output and the interest rate at which both the goods market and the money market clear simultaneously, holding the price level fixed. It is the standard framework for analysing fiscal and monetary policy at intermediate level.
Q: Why does the IS curve slope downward?
A: A higher interest rate reduces investment, which lowers aggregate demand and, through the spending multiplier, lowers equilibrium output. So higher interest rates go with lower output, giving a downward-sloping curve.
Q: Why does the LM curve slope upward?
A: With the money supply fixed, higher output raises the demand for money for transactions. To keep the money market in balance, the interest rate must rise to reduce money demand back to the fixed supply. Higher output therefore requires a higher interest rate.
Q: What is crowding out in IS–LM?
A: Crowding out is the private investment lost when a fiscal expansion raises the interest rate. The higher rate reduces investment, cancelling part of the fiscal stimulus, so output rises by less than the simple multiplier would predict.
Q: What is the difference between fiscal and monetary policy in the model?
A: Fiscal policy (spending and taxes) shifts the IS curve; monetary policy (the money supply) shifts the LM curve. A fiscal expansion raises both output and the interest rate; a monetary expansion raises output but lowers the interest rate.
Q: Is IS–LM still worth learning if it assumes fixed prices?
A: Yes. It is the foundation for the AD–AS model, which relaxes the fixed-price assumption, and it remains the clearest way to see how the goods and money markets interact in the short run. Almost every intermediate macro course builds on it.
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