The IS–LM Model

Fiscal Policy in the IS–LM Model

coreExam · highTA · PS3-Q1, PS3-Q2Mock · Q1, Q2

A fiscal expansion (↑G or ↓T) shifts the IS curve rightward, raising output Y* without changing the interest rate under a flat (interest-targeting) LM. The multiplier is 1/(1−c₁), but with lump-sum taxes the tax multiplier is −c₁/(1−c₁).

Derivation

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IS–LM Shock Lab

Flat LM (interest-rate targeting). Drag sliders to shock the model.

IS curve: Y = a − b·i. LM: i = iᵀ (central bank target). Equilibrium Y* = a − b·iᵀ.

Fiscal policy

G (govt spending)200

T (taxes)200

Monetary policy

iᵀ (rate target)4.0%

c₀ (autonomous C)100

Structure

c₁ (MPC)0.60

d₁ (invest. sensitivity)500

Intuition

Fiscal policy in the IS–LM model works through the goods market. When the government raises spending by $\Delta G$ , it directly increases demand for output. Firms produce more, households earn more income, and spend a fraction $c_1$ of it — triggering a multiplier chain.

The government-spending multiplier $\frac{1}{1-c_1}$ captures this chain: every unit of government spending ultimately raises income by more than one unit as it circulates through the economy.

Under modern (flat) LM — where the central bank targets an interest rate $i^T$ — the interest rate does not rise in response to a fiscal expansion. This is the key difference from the upward-sloping LM of older textbooks: there is no crowding-out of private investment.

The IS Diagram

The IS curve plots all $(Y, i)$ combinations at which the goods market clears. Fiscal expansion shifts the IS curve rightward by $\frac{\Delta G}{1-c_1}$ (the full multiplier shift). The new equilibrium is at the intersection of the shifted IS curve and the unchanged flat LM.

Tax Cut vs Spending Increase

A tax cut of $\Delta T$ raises disposable income by $\Delta T$ , but households save $(1-c_1)\Delta T$ immediately. The multiplier chain only starts in round 2. Hence:

\text{Tax multiplier} = \frac{-c_1}{1-c_1} = \frac{-0.6}{0.4} = -1.5

To achieve the same $\Delta Y^*$ , a tax cut must be larger than a spending increase by a factor of $1/c_1$ .

Worked Example

Baseline: c₀=100, c₁=0.6, T=200, I₀=150, G=200, d₁=500, iᵀ=4%. The government increases G by 50. Compute the new equilibrium output and the change.

Baseline Y*: A₀ = 100 − 0.6×200 + 150 + 200 = 330. Y₀* = 330/0.4 − (500/0.4)×0.04 = 825 − 50 = 775.
Multiplier: 1/(1−0.6) = 1/0.4 = 2.5.
ΔY* = 50 × 2.5 = 125. New Y* = 775 + 125 = 900.
Check: A₁ = 100 − 120 + 150 + 250 = 380. Y₁* = 380/0.4 − 50 = 950 − 50 = 900. ✓

Y* rises from 775 to 900, an increase of 125. The government-spending multiplier is 2.5.

Common Mistakes

—Using the tax multiplier formula for a spending shock (they differ by a factor of c₁).
—Forgetting to apply the multiplier — quoting ΔY = ΔG instead of ΔY = ΔG/(1−c₁).
—Assuming the interest rate rises (it doesn't under flat LM / interest-rate targeting).
—Confusing lump-sum taxes (T) with proportional income taxes (affects c₁ effectively).

Exam Cues

→If the question says 'central bank keeps i constant' → flat LM, full multiplier applies.
→Mock Q1 uses exactly this setup with interest-sensitive consumption; same algebra, just c₁ replaces (c₁ + c₂) effectively.
→Mock Q2 asks: what ΔiᵀT restores Y₀ after a fiscal shock? Solve ΔiᵀT = ΔG/d₁ × (1−c₁).
→Balanced-budget multiplier: ΔG = ΔT → ΔY* = ΔG. Multiplier = 1.