What Is the IS-LM Model? IS and LM Curves Explained

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The IS-LM model is a short-run Keynesian macroeconomic model that finds the combination of output (real GDP) and the interest rate at which two markets clear at the same time: the goods market, summarized by the IS curve, and the money market, summarized by the LM curve. IS stands for “investment-saving,” and LM stands for “liquidity preference-money supply.”

The price level is held fixed in the basic model, so the model answers one question: given current prices, where do output and interest rates settle, and how do fiscal or monetary changes move them?

The two curves on the IS-LM graph

The graph puts real output or income (Y, essentially GDP) on the horizontal axis and the interest rate (r) on the vertical axis.

The IS curve: goods-market equilibrium

In a closed economy, output equals planned spending: Y = C + I + G, where consumption depends on disposable income and investment falls as the interest rate rises. A lower interest rate makes borrowing for plant, equipment and housing cheaper, so investment rises. Higher spending raises income through the multiplier, and the goods market clears at a higher Y. That inverse link between r and Y is why the IS curve slopes downward.

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

• Higher government purchases, lower taxes, or a rise in autonomous consumption shift IS right.
• Weaker business confidence or lower autonomous investment shift IS left.
• In an open economy, spending includes net exports (X − M), so a rise in imports at every income level shifts IS left.

A change in the interest rate alone moves the economy along IS; it does not shift it.

The LM curve: money-market equilibrium

The LM relation is usually written as M/P = L(Y, r): the real money supply, set by the central bank in the basic model, equals real money demand. People hold more money when income is higher, because more transactions need financing. They hold less when interest rates are higher, because cash and checking balances earn little or nothing while bonds pay r, raising the opportunity cost of holding money.

Why the LM curve slopes upward: suppose income rises while the money supply stays fixed. Money demand now exceeds supply. People try to rebuild cash balances by selling bonds, bond prices fall and yields rise. The interest rate climbs until the higher opportunity cost of holding money brings money demand back down to the fixed supply. Higher Y therefore pairs with higher r.

The LM curve shifts when:

• The central bank raises the nominal money supply (LM shifts right/down) or cuts it (LM shifts left/up).
• The price level rises, which shrinks M/P and shifts LM left/up.
• Money demand rises at every income and rate, for example from a preference for liquidity in uncertain times, which shifts LM left/up.

LM describes only the money market, though it can also be read as a bond-market condition, since excess money demand mirrors excess bond supply.

Equilibrium

At the IS-LM intersection, planned spending equals output and money demand equals money supply, the model’s short-run resting point. Comparing equilibria before and after a shift shows how a policy or shock changes output and the interest rate.

Two special shapes matter for policy debates. A nearly flat LM curve, associated with a liquidity trap at very low rates, means monetary expansion barely lowers r, while fiscal expansion raises output with little crowding out. A nearly vertical LM curve, the classical case, means fiscal expansion mostly raises interest rates and crowds out private investment.

Worked example (hypothetical)

Goods market: C = 100 + 0.8(Y − T), I = 300 − 20r, G = 200, T = 200. Substituting into Y = C + I + G gives 0.2Y = 440 − 20r, so IS: Y = 2,200 − 100r.

Money market: money demand L = 0.5Y − 50r, real money supply M/P = 900. Setting 0.5Y − 50r = 900 gives LM: Y = 1,800 + 100r.

Equilibrium: 2,200 − 100r = 1,800 + 100r, so r = 2% and Y = 2,000.

Fiscal expansion: raise G by 40. IS becomes Y = 2,400 − 100r. The new equilibrium is r = 3%, Y = 2,100. With interest rates held constant, the multiplier (1 / 0.2 = 5) would have raised output by 200. Instead output rises by 100, because the higher rate cuts investment by 20. That gap is crowding out.

Monetary expansion: return G to 200 and raise M/P to 950. LM becomes Y = 1,900 + 100r. The new equilibrium is r = 1.5%, Y = 2,050. Lower rates raise investment, which raises output.

How the model is used

The model sorts policy effects into channels. Fiscal policy works through IS and tends to raise rates as it raises output. Monetary policy works through LM and moves rates and output in opposite directions. Combined, a government can expand output without higher rates if the central bank accommodates. Letting the price level vary across IS-LM equilibria traces out the aggregate demand curve, which links the model to AD-AS analysis.

Origins

British economist John Hicks presented the framework in 1937 in “Mr. Keynes and the ‘Classics’; A Suggested Interpretation,” a graphical reading of John Maynard Keynes’s The General Theory of Employment, Interest and Money (1936). Keynes never drew IS-LM himself. Alvin Hansen popularized it in the United States, hence the name Hicks-Hansen model.

Limitations

• Fixed prices. The basic model has no inflation mechanism, so it cannot explain stagflation, the combination of high unemployment and high inflation. Adding a Phillips curve (the IS-LM-PC version) addresses this.
• Money-supply targeting. Modern central banks set a short-term interest rate rather than a money stock. Many textbooks now replace the LM curve with a horizontal policy-rate line or a monetary policy rule (IS-MP), often linked to the Taylor rule.
• No expectations. Spending and money demand respond to current variables only, ignoring forward-looking behavior.
• Closed economy. Capital flows and exchange rates are absent.
• Short run only. Capital formation and labor productivity, which drive long-run growth, are outside the model.
• Single interest rate. It ignores the gap between policy rates and the rates borrowers actually pay, and between nominal and real rates.

Hicks himself later called the model a “classroom gadget.” Today it is mainly a teaching tool. Policymakers rely on richer dynamic models that carry its logic forward.

IS-LM vs. related models

• IS-LM vs. AD-AS: IS-LM holds the price level constant and determines output and the interest rate. AD-AS determines output and the price level, with aggregate demand derived from IS-LM.
• IS-LM vs. Mundell-Fleming: Mundell-Fleming extends IS-LM to open economies by adding a balance-of-payments condition, so results depend on whether exchange rates are fixed or floating.

The Bottom Line

Economics students and anyone following fiscal and monetary policy debates can use IS-LM to see how government spending and central bank actions move output and interest rates in the short run. The model works best as a teaching tool. Its fixed prices, lack of expectations, and money-supply targeting leave modern policymakers relying on richer dynamic models that build on its logic.