IS–LM Model

IS–LM Model (standing for Investment–Saving / Liquidity Preference–Money Supply) is a foundational macroeconomic framework that represents the simultaneous short-run equilibrium of the real goods market and the financial money market in a coordinate plane defined by real output (Y) on the horizontal axis and the interest rate (r) on the vertical axis. Introduced by Sir John Hicks in 1937 as a mathematical formalization of John Maynard Keynes's General Theory (1936) and popularized by Alvin Hansen (the Hicks–Hansen synthesis), the model serves as a centerpiece of Business & Economics Theory for analyzing how Fiscal Policy and Monetary Policy interact to determine short-run Gross Domestic Product when the aggregate price level (P) is fixed or slow to adjust.

The IS curve (Investment–Saving) traces the locus of all combinations of the real interest rate (r) and real aggregate income (Y) for which planned aggregate expenditure equals actual output in the goods market. In a closed economy, planned expenditure (E) is the sum of household consumption C(Y − T), planned private investment I(r), and autonomous government purchases G. Equilibrium in the goods market requires:

Equivalently, subtracting consumption and taxes from both sides shows that total national saving S = (Y − T − C) + (T − G) must equal planned investment I(r), which gives the curve its Investment–Saving name. In standard linear specification, consumption is C = C₀ + c(Y − T) and planned investment is I(r) = I₀ − b × r, where c ∈ (0, 1) is the marginal propensity to consume and b > 0 measures the interest sensitivity of investment projects evaluated via Net Present Value. Solving for Y yields the algebraic equation of the IS schedule:

Because a higher interest rate r increases the user cost of capital and reduces planned investment (∂I ÷ ∂r = −b < 0), lower investment contracts income via the Keynesian multiplier 1 ÷ (1 − c). Therefore, the IS curve slopes downward in (Y, r) space with slope:

The IS curve is steep when investment is relatively insensitive to interest rates (small b) or when the multiplier is small (low c); it is flat when investment is elastic with respect to borrowing costs (large b). Any autonomous fiscal expansion—such as an increase in government spending ΔG > 0 or a reduction in taxes ΔT < 0—shifts the IS curve horizontally to the right by ΔY = [1 ÷ (1 − c)]ΔG.

The LM curve (Liquidity Preference–Money Supply) traces all combinations of the interest rate (r) and income (Y) for which the supply of real money balances equals the demand for liquidity. Following Keynes's liquidity preference theory, agents hold money for transactions and precautionary motives (which rise with real income Y) and speculative portfolio motives (which decline with the interest rate r, because r represents the Opportunity Cost of holding non-interest-bearing money rather than bonds). Letting M denote the nominal money stock controlled by the central bank and P denote the fixed short-run price level, money market equilibrium is:

where k > 0 measures the income sensitivity of money demand and h > 0 measures the interest sensitivity of money demand. Rearranging for the interest rate r yields the linear LM equation:

Because an increase in real income Y raises transaction demand for money (kΔY), and the real money supply M ÷ P is fixed along a given LM schedule, the interest rate r must rise to reduce speculative money balances and restore equilibrium. Consequently, the LM curve slopes upward in (Y, r) space with slope:

An expansionary monetary policy (an increase in M with P fixed) increases real balances M ÷ P, shifting the LM curve downward and to the right. By Walras's Law in a two-asset financial system (money and bonds), whenever the money market is in equilibrium along the LM curve, the bond market is simultaneously in equilibrium.

Simultaneous macroeconomic equilibrium (Y^*, r^*) occurs at the unique intersection of the IS and LM schedules. Substituting the LM equation for r into the IS equation yields the explicit reduced-form solution for equilibrium output:

From this reduced form, the general-equilibrium fiscal policy multiplier (dY^* ÷ dG) and monetary policy multiplier (dY^* ÷ d(M ÷ P)) are:

Notice that because b × k ÷ h > 0 in standard regimes, the general-equilibrium IS–LM fiscal multiplier is smaller than the simple Keynesian cross multiplier 1 ÷ (1 − c). This difference captures interest-rate crowding out: a rightward shift of the IS curve raises income and money demand, driving up the equilibrium interest rate r^* along the upward-sloping LM curve and reducing private investment by bΔr^*.

The IS–LM framework serves as the building block for three broader macroeconomic models:

1. Derivation of the Aggregate Demand (AD) Curve: If the price level P is allowed to vary, an increase in P reduces real money balances (M ÷ P), shifting the LM curve upward and leftward, which raises r and contracts equilibrium output Y. Plotting the resulting (Y, P) pairs traces the downward-sloping Aggregate Demand schedule. When paired with a short-run Aggregate Supply schedule (or Phillips Curve) and long-run potential output determined by the Solow–Swan Model, the model bridges short-run demand shocks and long-run classical neutrality.
2. The Open-Economy Mundell–Fleming (IS–LM–BP) Model: Developed independently by Robert Mundell (1963) and Marcus Fleming (1962), the open-economy extension incorporates net exports NX(e, Y) into the IS curve and adds a Balance of Payments (BP) schedule representing international capital mobility. Under perfect capital mobility (r = r^*_world), the Mundell–Fleming model formalizes the Impossible Trinity: under fixed exchange rates, fiscal policy is potent while monetary policy is powerless; under floating exchange rates, monetary policy is potent while fiscal expansion is offset by currency appreciation.
3. The New Keynesian Three-Equation (IS–MP–PC) Synthesis: As noted by David Romer (2000), modern central banks do not target a fixed nominal money stock M; instead, they adjust money and reserves endogenously to set the real interest rate r via a Taylor-type reaction function. Replacing the LM curve with a Monetary Policy (MP) schedule and adding forward-looking microfoundations from intertemporal utility maximization yields the modern New Keynesian dynamic general equilibrium system.

What is the liquidity trap in the IS–LM model?

A liquidity trap occurs when the nominal interest rate falls to its effective lower bound (near 0%), making bonds and money close substitutes because neither pays meaningful interest and bond prices can only fall if rates rise in the future. In this region, the interest sensitivity of money demand approaches infinity (h → ∞), rendering the LM curve horizontal. Injections of base money by the central bank are absorbed passively into idle cash balances without lowering interest rates further, whereas fiscal expansion shifts the IS curve along the flat LM segment with zero interest-rate crowding out.

Why does the IS–LM model distinguish between nominal and real interest rates in extended versions?

In the baseline Hicks (1937) formulation with a fixed price level P and zero expected inflation (π^e = 0), the nominal interest rate (i) and the real interest rate (r = i − π^e) are identical. In extended versions incorporating expected inflation, investment I(r) on the IS curve depends on the real interest rate r, whereas money demand L(Y, i) on the LM curve depends on the nominal interest rate i = r + π^e. Consequently, a rise in expected inflation shifts the IS curve upward in (Y, i) space (or shifts the LM curve downward in (Y, r) space), stimulating output via the Mundell–Tobin effect.

Why did John Hicks later critique his own IS–LM diagram?

In a 1980 retrospective article ("IS–LM: An Explanation"), Hicks noted that the model compresses a flow equilibrium (goods production Y and investment I measured over a period of time) and a stock equilibrium (asset portfolio allocation between money M and bonds at a point in time) into a single static diagram, setting aside the role of uncertainty and shifting long-term entrepreneurial expectations (animal spirits) emphasized by Keynes.

1. Hicks, J. R. (1937). Mr. Keynes and the "Classics"; A suggested interpretation. Econometrica, 5(2), 147–159. https://doi.org/10.2307/1907242
2. Hansen, A. H. (1953). A Guide to Keynes. McGraw-Hill Book Company. https://archive.org/details/guidetokeynes0000hans
3. Mundell, R. A. (1963). Capital mobility and stabilization policy under fixed and flexible exchange rates. Canadian Journal of Economics and Political Science, 29(4), 475–485. https://doi.org/10.2307/139336
4. Romer, D. (2000). Keynesian macroeconomics without the LM curve. Journal of Economic Perspectives, 14(2), 149–169. https://doi.org/10.1257/jep.14.2.149
5. Blanchard, O. (2021). Macroeconomics (8th ed.). Pearson Education. https://www.pearson.com/en-us/subject-catalog/p/macroeconomics/P200000005926