The IS-LM Model: Where Fiscal and Monetary Policy Meet

Two markets, one interest rate

The IS-LM model, built by John Hicks in 1937 to formalise Keynes's General Theory, finds the interest rate and output level where two markets clear at once: the goods market and the money market. Each market traces out a curve in (output, interest rate) space, and the economy sits wherever the two curves cross.

The IS curve (Investment = Saving) plots combinations of output Y and interest rate r for which planned spending equals output. Investment falls as the interest rate rises, because borrowing gets more expensive, so higher r means lower equilibrium Y: the IS curve slopes downward. The LM curve (Liquidity = Money) plots combinations for which money demand equals the fixed money supply. Money demand rises with income (people hold more cash to transact) and falls with the interest rate (holding cash means forgoing interest), so a higher Y needs a higher r to keep money demand in check: the LM curve slopes upward.

The algebra behind the curves

IS:   Y = C(Y-T) + I(r) + G          → r falls as Y rises → downward slope
LM:   M/P = L(Y, r)                   → r rises as Y rises → upward slope

Equilibrium: the (Y, r) pair where both hold simultaneously

C(Y-T) is consumption out of disposable income, I(r) is interest-sensitive investment, G is government spending, M/P is the real money supply, and L(Y,r) is real money demand. Solving the two equations together pins down both Y and r — you cannot ask what happens to one without the other; that coupling is the entire point of the model.

Fiscal policy and crowding out

An increase in government spending G shifts the IS curve right: at any interest rate, planned spending is now higher. Output rises, but so does the interest rate, because higher income raises money demand along the unchanged LM curve. The rise in r discourages some private investment — this offsetting effect is crowding out. The size of the output gain the model predicts is the government-spending multiplier 1/(1-MPC) tempered by how much crowding out the LM curve permits: a flat LM curve (interest-insensitive money demand, or a liquidity trap) means almost no crowding out and a big output effect; a steep LM curve means the interest rate jumps and much of the fiscal boost is absorbed by falling investment.

Monetary policy

An increase in the money supply shifts the LM curve right: at any income level, the interest rate needed to clear the money market is now lower. The lower rate stimulates interest-sensitive investment, and output rises along the unchanged IS curve. This channel weakens if investment barely responds to r (a steep IS curve) or if the economy is stuck in a liquidity trap where money demand becomes essentially horizontal at very low interest rates — the textbook explanation for why monetary policy struggled to boost output near the zero lower bound in Japan in the 1990s and much of the world after 2008.

Why the model still matters, and where it stops

IS-LM's power is pedagogical: it makes the fiscal-versus-monetary policy debate a geometry problem, and it is still the fastest way to see why the two policies interact through the interest rate rather than acting independently. Its well-known limits are that prices are fixed in the short run (there is no supply side or inflation dynamics — the AD-AS or New Keynesian frameworks add those), expectations are static rather than forward-looking, and it says nothing about the exchange rate unless extended to the open-economy Mundell-Fleming version. It is a snapshot of short-run demand-side equilibrium, not a full macro model, but it remains the fastest sketch of why an interest-rate-setting central bank and a spending-setting treasury are always negotiating with the same lever.

Frequently asked questions

Try it live

Everything above runs in your browser — open IS-LM Model and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.