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Lesson M15.L04: IS-LM and the Aggregate Demand Curve

Module: The IS-LM Model Part II Level: intermediate Duration: 30 minutes Learning Objective: Derive the aggregate demand curve from the IS-LM model by varying the price level. Data as of: 2024 Provenance: OpenStax Macroeconomics 3e | MIT OCW 14.02 Principles of Macroeconomics

Explanation

The IS-LM model assumes a fixed price level P in the short run. The aggregate demand (AD) curve relaxes this assumption by asking: what happens to equilibrium output Y as P varies? Tracing IS-LM equilibria across different values of P traces out the AD curve.

The mechanism: The LM curve depends on real money balances M/P. For a given nominal money supply M:

  • If P rises → M/P falls → LM shifts left → r rises → investment falls → equilibrium Y falls.
  • If P falls → M/P rises → LM shifts right → r falls → investment rises → equilibrium Y rises.

This inverse relationship between P and equilibrium Y — holding M, G, and all other autonomous components constant — defines the downward-sloping AD curve in (Y, P) space. Each point on the AD curve corresponds to a specific IS-LM equilibrium.

AD shifts (non-price shifts): The AD curve shifts when anything other than P changes the IS or LM:

Shift factor AD effect
↑ Government spending G IS shifts right → AD shifts right
↑ Nominal money supply M LM shifts right → AD shifts right
↑ Autonomous investment Ī IS shifts right → AD shifts right
↑ Consumer confidence (↑ c₀) IS shifts right → AD shifts right

Connection to AD-AS: The AD curve derived here feeds directly into the AD-AS model. Short-run equilibrium occurs at the intersection of AD and the Short-Run Aggregate Supply (SRAS) curve; long-run equilibrium involves SRAS adjusting to the LRAS. Understanding that the AD curve is grounded in IS-LM is essential for understanding why policy shifts AD and by how much.

Notation: P = price level; M = nominal money supply; M/P = real money balances; r = interest rate; Y = real output; IS: Y = a − b_r × r; LM: M/P = kY − hr → Y = (M/P)/k + (h/k)r.

Worked Example

Setup:

  • IS curve: Y = 1200 − 200r (r in %)
  • LM curve derived from money market: M/P = 0.5Y − 100r → Y = 2(M/P) + 200r
  • Nominal money supply: M = 500 (fixed)

Step 1 — Solve for equilibrium Y as a function of P:

Substitute LM into IS to eliminate r:

From LM: r = [Y − 2(M/P)] / 200

Substitute into IS: 

Y = 1200 − 200 × [Y − 2(M/P)] / 200
Y = 1200 − [Y − 2(M/P)]
Y = 1200 − Y + 2(M/P)
2Y = 1200 + 2(M/P)
Y = 600 + M/P

With M = 500: Y = 600 + 500/P

This is the AD equation: output falls as P rises (downward sloping).

Step 2 — Compute two points on the AD curve:

Price Level P M/P = 500/P Equilibrium Y = 600 + 500/P Interest rate r
P₁ = 1.0 500 1100 See Step 3
P₂ = 2.0 250 850 See Step 3

Step 3 — Find r at each price level:

At P₁ = 1 (M/P = 500): 

LM: Y = 1000 + 200r
IS = LM: 1200 − 200r = 1000 + 200r
200 = 400r → r₁ = 0.5%

At P₂ = 2 (M/P = 250): 

LM: Y = 500 + 200r
IS = LM: 1200 − 200r = 500 + 200r
700 = 400r → r₂ = 1.75%

Step 4 — Interpret:

When P doubles from 1 to 2, real money balances halve, the LM shifts left, r rises from 0.5% to 1.75%, and equilibrium Y falls from 1100 to 850. The AD curve slopes downward.

Step 5 — AD shift example (fiscal expansion):

If G rises so that autonomous spending increases by 100 (IS shifts right to Y = 1400 − 200r):

New AD: Y = 700 + 500/P

At P = 1: new Y = 1200 (up from 1100). AD curve shifts rightward.

Common Misconception

Misconception: The aggregate demand curve slopes downward for the same reason as a microeconomic demand curve — because goods become cheaper when the price level falls.

Correction: The AD curve does not slope down because of the substitution or income effects that apply to individual goods markets. It slopes down through a macroeconomic mechanism: a lower price level raises real money balances M/P, which shifts the LM curve right, reducing the interest rate and stimulating investment and output. This is the Keynes interest rate effect (and, to a lesser extent, the wealth effect via real balances). Knowing the correct mechanism matters for policy: it means AD can be shifted by monetary or fiscal policy, not just by price changes.

Practice Prompts

  1. Conceptual: Using the IS-LM model, explain step-by-step why the AD curve slopes downward. → Answer: A rise in P → reduces real money balances M/P → LM curve shifts left → at any given Y, money market clears at a higher r → higher r reduces investment → lower Y. So higher P is associated with lower equilibrium Y, giving a downward-sloping AD curve.

  2. Numerical: Using the model above (M = 500, IS: Y = 1200 − 200r), suppose P = 1.25. Calculate the equilibrium Y and r. → Answer: 

    M/P = 500/1.25 = 400
LM: Y = 2(400) + 200r = 800 + 200r
IS = LM: 1200 − 200r = 800 + 200r
400 = 400r → r = 1%
Y = 1200 − 200(1) = 1000
    At P = 1.25: Y = 1000, r = 1%.

  3. Application: The RBA's 2022–23 rate hikes raised the cash rate from 0.10% to 4.35%. In the IS-LM/AD framework, how do rising interest rates affect the AD curve, and what was the intended macroeconomic goal? → Answer: Higher interest rates effectively shift the LM curve leftward (or, in a model where the RBA targets r directly, can be thought of as shifting the AD curve leftward). For each price level, equilibrium Y is lower. This shifts the AD curve left, reducing aggregate demand and, with an upward-sloping SRAS, reducing inflationary pressure. The RBA's intent was to cool demand to bring CPI inflation (which peaked at 7.8% in Q4 2022) back toward its 2–3% target band.

Visual — Deriving the Aggregate Demand Curve from IS-LM

Price level P₁ Output, Y Interest rate, r IS LM(P₁) E₁ Y₁ r₁ Higher price level P₂ > P₁ Output, Y Interest rate, r IS LM(P₁) LM(P₂) E₂ Y₂ r₂ Aggregate demand in (Y, P) space Output, Y Price level, P AD (Y₁, P₁) (Y₂, P₂) Y₁ Y₂ P₁ P₂ IS-LM equilibrium at P₁ maps to point (Y₁, P₁) on AD. Higher P shifts LM left, giving lower Y and a point lower-left on AD.

Figure: Changing the price level changes real money balances and therefore the LM curve. A higher price level shifts LM left, raises the interest rate, lowers output, and traces out a downward-sloping aggregate demand curve in (Y, P) space.

Further Resources