The IS–LM model (Investment–Saving and Liquidity preference–Money supply) is a standard Keynesian framework that shows how the goods market (IS) and the money market (LM) interact to determine short‑run equilibrium output (Y) and the interest rate (r). Introduced by John Hicks as a formal graphical interpretation of John Maynard Keynes’ General Theory, IS–LM is primarily a pedagogical device for thinking about fiscal and monetary policy interactions and short‑run macroeconomic fluctuations (Keynes 1936; Hicks 1937; Investopedia).
Key takeaways
– IS–LM represents simultaneous equilibrium in the goods market (IS) and the money market (LM).
– IS is downward sloping in (Y, r) space: lower r → more investment → higher Y.
– LM is upward sloping: higher Y → higher money demand → higher r for a fixed money supply.
– Fiscal expansion shifts IS right; monetary expansion shifts LM right. The size of output and interest‑rate responses depends on the slopes of the curves.
– The model is simple and useful for intuition/teaching but has important limitations (fixed prices, no expectations, closed‑economy baseline, money‑supply focus).
Origins and development
– John Maynard Keynes set out the underlying theory in The General Theory of Employment, Interest and Money (1936).
– John Hicks published “Mr. Keynes and the ‘Classics’” (Econometrica, 1937), presenting the IS–LM diagram as a compact way to capture Keynes’s insights. Hicks later described the model as a useful classroom device but not a final representation of macroeconomics. Modern macroeconomics has extended and replaced many of its assumptions (Hicks 1937; Keynes 1936; Investopedia).
Structure and dynamics of the IS–LM graph
– Axes: horizontal = real output/income (Y); vertical = nominal interest rate (r).
– IS curve: combinations of (Y, r) where planned spending = output (goods market equilibrium). Downward sloping: a lower r stimulates investment and thus equilibrium Y rises.
– LM curve: combinations of (Y, r) where real money supply (M/P) = money demand (liquidity preference). Upward sloping: higher Y raises transactions demand for money, so r must rise to restore money‑market equilibrium at a fixed real money supply.
Deriving and interpreting the IS curve (investment–saving)
– Core equation (simplified): Y = C(Y − T) + I(r) + G, where C = consumption, T = taxes, I = investment (falling in r), G = government spending.
– Intuition for slope: a higher r raises the cost of borrowing and lowers investment I(r); lower investment reduces aggregate demand and Y → negative relationship between r and Y.
– What shifts IS: changes in autonomous spending—fiscal policy (ΔG, ΔT), autonomous consumption, autonomous investment, expected returns on capital, business confidence. A rightward shift = higher demand at each r (expansionary fiscal policy).
Deriving and interpreting the LM curve (liquidity–money supply)
– Core money‑market condition: M/P = L(Y, r), where L is real money demand, increasing in Y (more transactions) and decreasing in r (higher r raises opportunity cost of holding money).
– Intuition for slope: at higher Y people want more money balances; for a fixed M/P, the interest rate must rise to reduce speculative money demand and restore equilibrium → LM slopes up.
– What shifts LM: changes in real money supply (M/P)—monetary expansion shifts LM right; changes in liquidity preference (money demand) shift LM left/right; changes in price level P also move the curve (higher P reduces M/P, shifting LM left).
IS–LM equilibrium: how the two markets interact
– Equilibrium = intersection of IS and LM: simultaneous goods and money market balance at (Y*, r*).
– Comparative statics (common cases):
• Expansionary fiscal policy (↑G or ↓T): IS shifts right → higher Y and higher r (crowding out of private investment through higher r). Magnitude depends on LM slope: if LM steep, r rises a lot, crowding out is stronger; if LM flat, output rises more and crowding out is limited.
• Expansionary monetary policy (↑M or ↓P): LM shifts right → lower r and higher Y. If IS is very steep (insensitive to r), monetary policy will mainly lower r but produce small Y changes; if IS is flat, monetary policy raises Y substantially.
– Special cases:
• Liquidity trap: LM is horizontal at low r (money demand infinitely elastic to r). Monetary policy is ineffective at raising Y; fiscal policy is powerful.
• Classical case: LM nearly vertical (money demand insensitive to r) and prices flexible—monetary changes mainly affect prices, not real Y.
Practical steps: how to use IS–LM to analyze policy and shocks
1. Set up baseline:
• Draw IS and LM for current economy (label Y0, r0).
• Note the underlying assumptions (fixed price level, closed economy, short run).
2. Identify a shock or policy:
• Fiscal shock (ΔG/ΔT) → shift IS right/left.
• Monetary shock (ΔM or ΔP) → shift LM right/left.
• Other shocks: changes in confidence, investment sensitivity to r, liquidity preference changes.
3. Shift the appropriate curve on the graph and locate the new intersection (Y1, r1).
4. Assess magnitude and direction:
• Consider curve slopes: steep vs flat determines extent of output vs interest‑rate change and degree of crowding out.
• If analyzing extreme regimes (liquidity trap or classical), adjust expectations about policy potency.
5. Add realism where needed:
• If analyzing over longer horizons, allow the price level to change and incorporate AD–AS dynamics.
• For open economies, extend to IS–LM–BP (Mundell–Fleming): include exchange rate and balance‑of‑payments effects.
6. Check robustness:
• Consider expectations, time lags, and supply‑side constraints—IS–LM won’t capture all these, so treat results as indicative rather than definitive.
Practical classroom or empirical exercise (step‑by‑step)
1. Specify a simple macro model: consumption function, investment function I(r), money demand L(Y, r), and a fixed M and P.
2. Calibrate parameters (marginal propensity to consume, sensitivity of I to r, sensitivity of money demand to Y and r).
3. Compute equilibrium numerically for baseline (solve simultaneously).
4. Simulate policy shocks (e.g., ΔG = +100, ΔM = +5%) and compute new equilibria.
5. Graph results and interpret: show how output and r move and how slopes change policy effectiveness.
Criticisms and limitations
– Fixed price level and short‑run focus: IS–LM typically assumes P is constant, so it cannot trace medium/long‑run price adjustments.
– Expectations and forward‑looking behavior are absent: modern macro models emphasize expectations (rational or adaptive), which can change behavior immediately.
– Money‑supply targeting assumption: IS–LM treats M as policy instrument; many central banks now target interest rates directly, complicating the money‑supply view.
– Closed‑economy baseline: basic IS–LM ignores trade and capital flows (Mundell–Fleming extends it).
– Poor at explaining stagflation: simultaneous high inflation and unemployment called into question Keynesian models in the 1970s.
– Aggregation and microfoundations: it is a reduced‑form partial equilibrium device lacking microfoundations later provided by DSGE/New Keynesian frameworks.
Because of these limitations, many economists use IS–LM mainly as an instructional tool or as a first approximation; more advanced policy analysis relies on models with price adjustment, expectations, and microfoundations (Investopedia; Hicks comment on its usefulness as a “classroom gadget”).
Is the IS–LM model actually used?
– Teaching and intuition: widely used in undergraduate macro to illustrate interactions between fiscal and monetary policy and the concept of crowding out.
– Policy and research: less used directly by modern central banks or research departments; instead, they rely on richer DSGE, structural macro, and forecasting models. However, IS–LM intuition (how fiscal and monetary policy interact, role of liquidity traps, etc.) remains influential in policy discussions.
Why does the LM curve slope upward?
– Mechanism: an increase in real income (Y) raises transactions demand for real money balances. With a fixed real money supply (M/P), the increased demand for money exerts upward pressure on the interest rate; a higher r reduces speculative money demand until money supply equals money demand again. Algebraically: M/P = L(Y, r) with ∂L/∂Y > 0 and ∂L/∂r 0 along LM. In words: higher output → more money needed for transactions → higher r for money‑market equilibrium.
Who developed the IS–LM model?
– John Maynard Keynes formulated the core ideas in The General Theory (1936). John Hicks published the IS–LM diagrammatic representation in “Mr. Keynes and the ‘Classics’” (Econometrica, 1937), which popularized the model and made it a standard teaching tool (Keynes 1936; Hicks 1937; Investopedia).
The bottom line
IS–LM is a compact, intuitive framework for thinking about short‑run interactions between the goods market and the money market and for illustrating how fiscal and monetary policy affect output and the interest rate. It remains valuable pedagogically and for quick comparative statics, but its simplifying assumptions (fixed prices, no expectations, closed economy, emphasis on money supply) limit its use as a detailed policy tool. For operational policy analysis, modern macroeconomists typically use models that incorporate expectations, price dynamics, microfoundations, and open‑economy channels.
Selected sources and further reading
– Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. Harcourt, Brace & Co.
– Hicks, J. R. (1937). “Mr. Keynes and the ‘Classics’; A Suggested Interpretation.” Econometrica, 5(2), 147–159.
– Investopedia. “IS–LM Model.”
– For extensions (open economy): Mundell–Fleming model literature; for modern replacements: standard DSGE/New Keynesian textbook chapters.
– Walk through a numerical IS–LM example (with simple functional forms) and plot the shifts; or
– Extend the analysis to an open economy (Mundell–Fleming), or show how price adjustments link IS–LM to AD–AS in the medium run. Which would you prefer?