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Intermediate Macroeconomics Unit 7: IS-LM Model

The IS-LM model explains how output and the interest rate are determined in the short run when prices are fixed, and how fiscal and monetary policy affect them.

Covers: The Keynesian cross and multipliers, The IS curve, Liquidity preference and the LM curve, Fiscal and monetary policy in IS-LM, Shocks and policy choice, The Great Depression and the liquidity trap

Study guide

In the short run, prices are sticky, so output is determined by demand. The Keynesian cross starts with planned expenditure PE = C(Y − T) + I + G. Equilibrium is where actual output equals planned expenditure; if output is higher, unplanned inventories build and firms cut production. Because extra income is partly spent, any change in spending has a multiplied effect. The government-purchases multiplier is 1/(1 − MPC), the tax multiplier is −MPC/(1 − MPC), and a balanced-budget change in G and T has a multiplier of 1.

The IS curve brings in the interest rate. Investment falls as r rises, so a higher interest rate lowers planned expenditure and equilibrium income. The IS curve plots the combinations of r and Y where the goods market clears; it slopes down. Fiscal expansion shifts IS right by the multiplier times the change in G (or the tax multiplier times the tax cut). Shocks to consumer or business confidence also shift IS. IS is flatter when investment is more interest-sensitive or the multiplier is larger.

The LM curve describes the money market. Keynes's theory of liquidity preference says the interest rate adjusts to balance the supply of real balances M/P, set by the central bank with P fixed, against money demand L(r, Y), which falls with r and rises with Y. When income rises, money demand rises, and r must rise to restore equilibrium, so LM slopes up. An increase in M or a fall in P shifts LM down. Higher money demand at every r and Y shifts LM up. The intersection of IS and LM gives the short-run equilibrium r and Y.

Fiscal expansion shifts IS right: income and the interest rate both rise, and the higher r crowds out some investment, so the IS-LM multiplier is smaller than the Keynesian cross multiplier. Monetary expansion shifts LM down: r falls, investment rises and income rises. Policies interact. If the central bank holds r constant, fiscal policy has its full Keynesian effect; if it holds income constant, a tax increase lowers r and raises investment. When IS shocks dominate, targeting the money supply stabilizes output better; when money-demand shocks dominate, targeting the interest rate is better.

IS-LM is used to interpret history. The spending hypothesis says the Great Depression began with a leftward IS shift from collapsing consumption and investment. The money hypothesis of Friedman and Schwartz emphasizes the 25% fall in the money supply, a leftward LM shift, and the contractionary effect of expected deflation, which raised real interest rates. The Pigou effect suggested falling prices would help by raising real wealth, while debt-deflation theory argued they would hurt. When nominal rates hit zero, the economy is in a liquidity trap: LM is flat, more money does little, and fiscal policy is unusually powerful.

Key ideas

• In the Keynesian cross, equilibrium output equals planned expenditure, and spending changes have multiplied effects.
• The IS curve slopes down because higher interest rates lower investment and income.
• The LM curve slopes up because higher income raises money demand and the interest rate.
• Fiscal expansion raises Y and r; the higher r crowds out some investment.
• Monetary expansion lowers r and raises Y.
• Money-supply targets stabilize IS shocks better; interest-rate targets stabilize LM shocks better.
• At the zero lower bound, monetary policy loses power and fiscal policy gains it.

Formulas and rules

Common mistakes

• Using the Keynesian cross multiplier in IS-LM without accounting for crowding out.
• Shifting the IS curve for monetary policy or the LM curve for fiscal policy.
• Forgetting that a lower price level shifts LM down and is a movement along AD.
• Claiming that holding income constant leaves investment unchanged after a tax change.
• Assuming monetary expansion always lowers interest rates, even at the zero lower bound.

Before the test, make sure you can

• Calculate equilibrium income and multipliers in the Keynesian cross.
• Explain why IS slopes down and LM slopes up, and what shifts each curve.
• Solve a linear IS-LM model for equilibrium r and Y.
• Analyze fiscal and monetary policy and their interaction in IS-LM.
• Find the money supply change needed to hold r or Y constant.
• Compare interest-rate and money-supply targets for different kinds of shocks.
• Explain the spending and money hypotheses of the Great Depression and the liquidity trap.

Words to know

Planned expenditure

The amount households, firms and government plan to spend: C + I + G.

Keynesian cross

A model of income determination where output equals planned expenditure.

Government-purchases multiplier

The change in income per dollar of extra government purchases, 1/(1 − MPC).

Tax multiplier

The change in income per dollar of tax change, −MPC/(1 − MPC).

Balanced-budget multiplier

The effect on income of equal changes in G and T; equals 1 in the Keynesian cross.

IS curve

Combinations of r and Y where the goods market is in equilibrium.

LM curve

Combinations of r and Y where the money market is in equilibrium.

Liquidity preference

Keynes's theory that the interest rate adjusts to balance money supply and money demand.

Crowding out (IS-LM)

The fall in investment when fiscal expansion raises the interest rate.

Monetary accommodation

The central bank increasing the money supply to keep the interest rate from rising.

Spending hypothesis

The view that the Great Depression began with a fall in spending (IS shift).

Money hypothesis

The view that the Great Depression was caused largely by the fall in the money supply (LM shift).

Pigou effect

Falling prices raise real wealth and consumption, shifting IS right.

Debt-deflation theory

Unexpected deflation redistributes wealth from debtors to creditors; debtors cut spending more than creditors raise it, shifting IS left.

Liquidity trap

When the interest rate is at zero and more money cannot lower it.

Zero lower bound

The floor near zero below which nominal interest rates cannot easily fall.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.