IS-LM Model
Goods market and money market in one diagram. The clearest way to think about fiscal vs monetary policy.
Built and reviewed by Stephen Omukoko Okoth
Mathematical Economist · ex-Morgan Stanley FI · Equilar
Theory
What the model says, and why
IS-LM combines two equilibrium conditions on the same plane (output Y on the horizontal axis, interest rate r on the vertical). The IS curve traces output-rate combinations where the goods market clears (investment equals savings); the LM curve traces output-rate combinations where the money market clears (money demand equals money supply).
The linearized IS curve:
Goods-market equilibrium says output equals the multiplier times autonomous demand. Investment falls with interest rates (bᵢ > 0), so the IS curve slopes downward — higher r, lower Y.
The linearized LM curve, derived from money market equilibrium M/P = k·Y − h·r:
Money demand rises with income (transactions motive — coefficient k) and falls with the interest rate (opportunity cost — coefficient h). The LM curve slopes upward — higher Y, higher r.
Where they intersect is the simultaneous equilibrium of goods and money markets — the unique (Y*, r*) consistent with both.
What the model is for. It tells you, qualitatively, what fiscal and monetary policy do. Expansionary fiscal policy (G ↑) shifts IS right — higher output, higher rates. Expansionary monetary policy (M/P ↑) shifts LM right — higher output, lower rates. The relative effectiveness depends on the slopes — the steeper the LM curve, the more crowding-out from fiscal policy.
Interactive playground
Move the parameters, watch the equilibrium move
Parameters
Goods market (IS)
Money market (LM)
Equilibrium
Y* = 410.2, r* = 6.35%
Output Y*
410.2
Interest rate r*
6.35%
Multiplier
2.27
1 / (1 − c(1−t))
Autonomous demand A
190
C₀ + I₀ + G
In the classroom
How to teach it well
Classic teaching exercises. (1) Increase G — show IS shifting right, both Y and r rising. (2) Increase M/P — LM shifts right, Y rises and r falls. (3) Compare a steep LM (low h) vs a flat LM (high h): fiscal multiplier is small in the first, large in the second. This is where the “crowding-out” intuition comes from.
Limits of the model. IS-LM assumes prices are fixed in the short run — that’s why it’s a short-run model. It also assumes one country in isolation. The Mundell-Fleming extension adds an open economy. Pair both with AD-AS for the full Keynesian synthesis story.
Why students struggle. Two markets, two curves, simultaneous equilibrium — students often want to think sequentially (“first the goods market, then the money market”). Force them to sit with the simultaneous logic. Both equilibrium conditions must hold at once.
The liquidity trap, on the playground. Set h very high — LM becomes nearly flat. Now bumping G delivers full multiplier effect with almost no rate increase. That’s the liquidity-trap intuition: when monetary policy can’t move rates, fiscal policy is unusually powerful.