Difficulty: Intermediate-Advanced | Prerequisites: Ch. 1–3 notes (national income model), Ch. 4–5 notes (money, interest rates). Understanding the loanable funds market is essential.
Source: Mankiw, Macroeconomics, 9th Edition, Chapters 10–12
Tags: IS-LM model, aggregate demand, aggregate supply, Keynesian cross, multiplier, fiscal policy, monetary policy, liquidity preference, interest rate, short-run fluctuations, EC305
This is the heart of the course. The previous chapters described the long run, where prices are flexible and output is pinned down by supply. Now prices are sticky, and demand matters. The IS-LM model is the main framework for understanding short-run fluctuations: how changes in fiscal policy, monetary policy, and confidence affect output and interest rates before prices have time to adjust. The aggregate demand curve is derived from IS-LM. If there is one model you need to master for the exam, this is it.
The IS curve shows combinations of the interest rate and income where the goods market is in equilibrium. The LM curve shows combinations where the money market is in equilibrium. Their intersection determines short-run output and the interest rate. Fiscal policy shifts IS; monetary policy shifts LM. The AD curve traces out how the price level affects equilibrium income through IS-LM.
Aggregate Demand (AD) Curve
The relationship between the price level and the quantity of output demanded. It slopes downward: a lower price level raises real money balances, lowers the interest rate, and stimulates spending.
Aggregate Supply (AS) Curve
In the short run, it is horizontal or upward-sloping (sticky prices mean firms supply whatever is demanded at the prevailing price level). In the long run, it is vertical at the natural level of output.
Keynesian Cross
A simple model where planned expenditure (PE = C + I + G) is plotted against income. Equilibrium is where PE = Y. It is the building block for the IS curve. Think of it as the engine that produces the multiplier.
Government Purchases Multiplier
The amount by which equilibrium income rises when government spending increases by one unit. In the simple Keynesian cross, the multiplier = 1 / (1 - MPC). A higher marginal propensity to consume means a larger multiplier.
Tax Multiplier
The change in equilibrium income from a one-unit increase in taxes. It equals -MPC / (1 - MPC). Smaller in absolute value than the government purchases multiplier because a fraction of the tax cut is saved.
IS Curve (Investment-Saving)
The set of (r, Y) combinations where the goods market clears. It slopes downward: a lower interest rate increases investment, which raises income through the multiplier.
LM Curve (Liquidity-Money)
The set of (r, Y) combinations where the money market clears. It slopes upward: higher income increases money demand, pushing the interest rate up to keep money demand equal to the fixed money supply.
Liquidity Preference
Keynes's theory of money demand: people hold money for transactions (which rise with income) and as a store of wealth (which falls as the interest rate rises). The interest rate adjusts to equate money demand with the fixed money supply.
Crowding Out
When expansionary fiscal policy raises the interest rate, which discourages private investment. This partially offsets the initial increase in demand. Think of it as the government borrowing from the same pool of funds that businesses use.
Monetary Transmission Mechanism
The process by which monetary policy affects output: the central bank increases M, the interest rate falls (LM shifts right), investment rises, and output increases through the multiplier.
Liquidity Trap
A situation where the nominal interest rate is at or near zero, so the central bank cannot lower it further. Monetary policy becomes ineffective because the LM curve is flat at zero. Fiscal policy is especially powerful in this case because there is no crowding out.
In the long run, prices adjust and the classical model holds. In the short run, many prices are sticky (contracts, menu costs, coordination failures).
With sticky prices, actual output can deviate from the natural level. The economy can be in a recession (Y < natural Y) or a boom (Y > natural Y).
The AD-AS framework: aggregate demand slopes down, short-run aggregate supply is flat (or upward-sloping), long-run aggregate supply is vertical at the natural level.
Short-run fluctuations are driven by shifts in AD (demand shocks) or AS (supply shocks).
Planned expenditure: PE = C(Y - T) + I + G
The 45-degree line: points where PE = Y (actual spending equals income)
Equilibrium: where the PE line crosses the 45-degree line
If PE > Y, inventories fall, firms produce more, Y rises. If PE < Y, inventories accumulate, firms cut production, Y falls.
The multiplier effect: an increase in G by ΔG raises Y by ΔG / (1 - MPC). The initial spending creates income, which creates more spending, and so on.
A tax cut of ΔT raises Y by (MPC × ΔT) / (1 - MPC). Smaller than the spending multiplier because some of the tax cut is saved.
Derived from the Keynesian cross by varying the interest rate
A lower interest rate raises planned investment, which raises equilibrium Y in the Keynesian cross. Plot this: lower r, higher Y. That is the IS curve.
IS slopes downward in (r, Y) space
Fiscal policy shifts IS: an increase in G or a decrease in T shifts IS right
Changes in consumer or business confidence also shift IS
Money demand: L(r, Y). It rises with Y (more transactions) and falls with r (opportunity cost of holding money)
Money supply: M/P, set by the central bank (M) and the price level (P)
Equilibrium: M/P = L(r, Y). For a given Y, this pins down r.
The LM curve: higher Y raises money demand, which raises r (for fixed M/P). So LM slopes upward in (r, Y) space.
An increase in the money supply shifts LM right (more money at each price level means lower r for each Y)
The intersection of IS and LM gives the equilibrium (r*, Y*)
Fiscal expansion (increase G): IS shifts right. Y rises and r rises. The rise in r crowds out some investment, so the net increase in Y is less than the Keynesian cross multiplier suggests.
Monetary expansion (increase M): LM shifts right. Y rises and r falls. No crowding out; investment is stimulated.
Combined policy: fiscal and monetary policy can be used together. For example, fiscal expansion with monetary accommodation (shift both IS and LM right) raises Y without raising r.
In a liquidity trap (r = 0), LM is flat. Monetary expansion has no effect (LM shift does not change r or Y). Fiscal policy is fully effective because there is no crowding out.
Start with IS-LM. Now ask: what happens when the price level changes?
A higher P reduces real money balances (M/P falls), shifting LM left, raising r, reducing Y.
A lower P raises M/P, shifting LM right, lowering r, raising Y.
Plotting P against the resulting Y traces out the downward-sloping AD curve.
Anything that shifts IS or LM (other than P) shifts the AD curve: fiscal expansion shifts AD right, monetary expansion shifts AD right, a loss of confidence shifts AD left.
Planned Expenditure
PE = C(Y - T) + I(r) + GGovernment Purchases Multiplier (Keynesian cross)
\Delta Y = \frac{1}{1 - MPC} \times \Delta GTax Multiplier
\Delta Y = \frac{-MPC}{1 - MPC} \times \Delta TIS Curve (goods market equilibrium)
Derived from setting Y = C(Y - T) + I(r) + G and solving for the (r, Y) relationship. Slopes downward.
LM Curve (money market equilibrium)
\frac{M}{P} = L(r, Y)Solving for r as a function of Y gives the upward-sloping LM curve.
Aggregate Demand
Derived by tracing the IS-LM equilibrium Y as P varies. Every P gives a different M/P, a different LM position, and a different Y. The result is a downward-sloping curve in (P, Y) space.
Key Diagrams
The Keynesian cross: 45-degree line, PE line with slope MPC. Show how an increase in G shifts PE up and raises equilibrium Y by a multiple.
IS-LM diagram: r on vertical axis, Y on horizontal. IS slopes down, LM slopes up. Show fiscal expansion (IS shifts right, r and Y rise) and monetary expansion (LM shifts right, r falls, Y rises).
AD-AS diagram: P on vertical axis, Y on horizontal. AD slopes down, SRAS is flat or upward-sloping, LRAS is vertical.
The IS-LM model is the analytical backbone behind policy debates about fiscal stimulus. The 2008-09 financial crisis and subsequent discussions about government spending packages (ARRA in the US) were argued in IS-LM terms: with interest rates near zero (a liquidity trap), fiscal policy was expected to be especially powerful because there would be minimal crowding out.
The monetary transmission mechanism describes what central banks do in practice: the Fed lowers interest rates by increasing the money supply, which stimulates investment and consumption. The model explains why "quantitative easing" (buying bonds to increase M) was used when conventional rate cuts hit the zero lower bound.
Students often think the multiplier from the Keynesian cross is the final answer for fiscal policy. It is not. IS-LM shows that the interest rate rises too, crowding out investment, so the actual output increase is smaller than the Keynesian cross multiplier implies.
Students confuse movements along a curve with shifts of the curve. A change in the price level moves you along the AD curve. A change in G, T, or M shifts the AD curve.
Students sometimes think monetary policy works by "giving people money." The mechanism is indirect: the central bank buys bonds, increasing bank reserves and the money supply, which lowers the interest rate, which raises investment.
Students often forget that IS-LM holds the price level fixed. It is a model of the short run at a given price level. To see what happens when prices adjust, you need the full AD-AS model.
⚠️ Be able to draw the IS-LM diagram and show the effects of fiscal and monetary policy on r and Y. This is the most-tested skill in the course.
⚠️ Know the difference between the Keynesian cross multiplier and the IS-LM outcome. The exam may ask you to explain why the actual change in Y is smaller than the multiplier predicts (crowding out).
⚠️ Be able to derive the AD curve from IS-LM by varying P and tracing the resulting Y.
⚠️ Understand the liquidity trap: when r = 0, monetary policy is ineffective and fiscal policy has its maximum impact.
⚠️ Know both the government purchases multiplier and the tax multiplier formulas, and be able to explain why the tax multiplier is smaller in absolute value.
True or False: The IS curve slopes upward. (False; it slopes downward.)
Fill in the blank: In the Keynesian cross, the government purchases multiplier equals 1 / (1 - ______). (MPC)
True or False: An increase in the money supply shifts the IS curve to the right. (False; it shifts LM to the right.)
Fill in the blank: In a liquidity trap, ______ policy is ineffective because the interest rate cannot fall further. (Monetary)
True or False: The AD curve slopes downward because a lower price level increases real money balances. (True)
Q: The MPC is 0.8. The government increases spending by $100 billion. What is the change in equilibrium output in the Keynesian cross? Why will the actual change in output in the IS-LM model be smaller?
A: In the Keynesian cross, ΔY = ΔG / (1 - MPC) = 100 / (1 - 0.8) = 100 / 0.2 = $500 billion. In IS-LM, the increase in Y raises money demand, pushing up the interest rate. The higher r reduces investment (crowding out), so the final increase in Y is less than $500 billion.
Q: Using the IS-LM model, show graphically and explain what happens when the central bank increases the money supply.
A: The LM curve shifts to the right (at each Y, there is now more real money, so the interest rate that clears the money market is lower). At the new IS-LM intersection, Y is higher and r is lower. The mechanism: lower r stimulates investment, and the multiplier raises Y. There is no crowding out because the interest rate has fallen.
Q: Explain how the aggregate demand curve is derived from the IS-LM model.
A: Hold IS fixed. Vary the price level P. A higher P reduces real money balances M/P, shifting LM left. The new IS-LM equilibrium has higher r and lower Y. A lower P raises M/P, shifts LM right, and gives higher Y. Plotting each (P, Y) pair traces out the downward-sloping AD curve.
Q: In a liquidity trap, the central bank doubles the money supply. What happens to output?
A: Nothing. When the interest rate is already at zero, the LM curve is horizontal. Shifting it further right does not change the intersection with IS, so r stays at zero and Y is unchanged. People are willing to hold any amount of money at a zero interest rate, so the extra money sits idle.
Q: The government simultaneously increases spending and the central bank increases the money supply to keep the interest rate constant. What happens to Y compared with fiscal expansion alone?
A: Y rises by more than it would with fiscal expansion alone. In fiscal expansion alone, r rises, crowding out investment. Here the central bank prevents r from rising (by shifting LM right to match), so there is no crowding out. The full Keynesian cross multiplier is realised. This is called monetary accommodation of fiscal policy.
The IS-LM model is the closed-economy version of what Chapter 13 (Mundell-Fleming) extends to an open economy with exchange rates. The aggregate demand curve derived here is one half of the AD-AS model completed in Chapter 14, where aggregate supply and the Phillips curve are introduced. The long-run classical model (Ch. 3) is the case where prices have fully adjusted: LRAS is vertical and output is at its natural level.
Related Terms / Search Tags
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