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Lesson M15.L01: Monetary Policy in the IS-LM Model

Module: The IS-LM Model Part II Level: intermediate Duration: 30 minutes Learning Objective: Trace the short-run effect of an RBA cash rate cut on equilibrium output in the IS-LM model. Data as of: 2024 Provenance: Reserve Bank of Australia | OpenStax Macroeconomics 3e

Explanation

The IS-LM model describes short-run equilibrium in the goods and money markets simultaneously. The IS curve (Investment-Saving) gives combinations of the interest rate r and output Y where the goods market clears. The LM curve (Liquidity-Money) gives combinations where the money market clears: real money demand L(r, Y) = kY โˆ’ hr equals the real money supply M/P.

Monetary policy in this framework operates through the LM curve. When the RBA cuts the cash rate โ€” its operational target for the overnight interbank rate โ€” it increases the money supply M or targets a lower r directly. An increase in M raises M/P (given a fixed price level P in the short run), shifting the LM curve rightward (downward in r-Y space).

The transmission follows two sequential effects:

  1. Liquidity effect: On impact, the increase in money supply makes money more abundant relative to bonds. Individuals sell bonds, bond prices rise, and r falls immediately.
  2. Income effect: Lower r stimulates investment spending (I = ฤช โˆ’ b_r ร— r), raising Y. As Y rises, money demand kY increases, partially offsetting the fall in r โ€” the new equilibrium has a somewhat higher r than the initial liquidity-effect low.

In Australia, the RBA made three consecutive cash rate cuts in 2019 (June, July, October), lowering the target from 1.50% to 0.75%. The aim was to lift output and employment toward capacity. By 2020, the cash rate hit its effective lower bound (ZLB) of 0.10% (November 2020), limiting further conventional monetary stimulus โ€” a topic explored in M15.L03.

Notation summary: - Y = real GDP; r = real interest rate; M = nominal money supply; P = price level; M/P = real money balances - k = income sensitivity of money demand; h = interest sensitivity of money demand - b_r = interest sensitivity of investment; ฤช = autonomous investment

Worked Example

Setup: The economy is described by:

  • IS curve: Y = 1000 โˆ’ 100r
  • LM curve: Y = 2(M/P) + 200r

Initial money supply gives M/P = 300, so LM: Y = 600 + 200r.

Step 1 โ€” Initial equilibrium:

Set IS = LM:

1000 โˆ’ 100r = 600 + 200r
400 = 300r
r* = 4/3 โ‰ˆ 1.33%

Substitute back into IS:

Y* = 1000 โˆ’ 100(1.33) = 1000 โˆ’ 133 = 867

Initial equilibrium: rโ‚ = 1.33%, Yโ‚ = 867.

Step 2 โ€” RBA expands money supply: M/P rises from 300 to 350.

New LM: Y = 2(350) + 200r = 700 + 200r

Step 3 โ€” New equilibrium:

Set IS = new LM:

1000 โˆ’ 100r = 700 + 200r
300 = 300r
r* = 1.00%

Y* = 1000 โˆ’ 100(1.00) = 900

New equilibrium: rโ‚‚ = 1.00%, Yโ‚‚ = 900.

Step 4 โ€” Interpret:

r (%) Y
Before monetary expansion 1.33 867
After monetary expansion 1.00 900
Change โˆ’0.33 pp +33

The LM shift lowers r by 0.33 percentage points and raises output by 33 units. Note that r falls by less than the full liquidity-effect amount because the income effect (Y rising โ†’ money demand rising) partially pushes r back up.

Common Misconception

Misconception: A cash rate cut directly and fully lowers all interest rates in the economy by the same amount as the RBA's announced cut.

Correction: The cash rate is the overnight rate at which banks lend to each other. Its pass-through to lending rates (mortgages, business loans) is partial and varies with bank margins, credit risk premiums, and competitive dynamics. In the IS-LM model, the income effect of rising Y partially offsets the fall in r, so the equilibrium interest rate falls by less than the initial liquidity-effect shift. Australian banks passed through RBA cuts by only 0.19โ€“0.25 percentage points in some 2019 cycles.

Practice Prompts

  1. Conceptual: In the IS-LM diagram, which curve shifts when the RBA cuts the cash rate, and in which direction? โ†’ Answer: The LM curve shifts rightward (or downward). A cut in the cash rate is implemented by expanding the money supply, raising M/P and shifting LM right, which reduces r and raises Y.

  2. Numerical: Using the model above, suppose M/P rises from 300 to 400 instead of 350. Calculate the new equilibrium r and Y. โ†’ Answer: 

    New LM: Y = 2(400) + 200r = 800 + 200r
Set IS = LM: 1000 โˆ’ 100r = 800 + 200r
200 = 300r โ†’ r* = 2/3 โ‰ˆ 0.67%
Y* = 1000 โˆ’ 100(0.67) = 933
    rโ‚‚ = 0.67%, Yโ‚‚ = 933. The larger expansion in money supply produces a bigger fall in r and a larger rise in Y.

  3. Application: In Juneโ€“October 2019, the RBA cut the cash rate three times from 1.50% to 0.75%. Using the IS-LM framework, explain why the resulting stimulus to output may have been limited. โ†’ Answer: Even though the LM shifted right, several factors dampened the income effect: (a) imperfect pass-through from the cash rate to lending rates reduced the IS-curve response; (b) weak consumer and business confidence meant the IS curve itself was relatively flat (inelastic investment); (c) with rates already low, the liquidity effect was compressed. The RBA's own assessment noted that monetary policy alone was insufficient and called for fiscal support.

Visual โ€” Monetary Expansion in the IS-LM Model

1. Initial IS-LM equilibrium Output, Y Real interest rate, r IS LMโ‚ Eโ‚ Yโ‚ rโ‚ 2. RBA expands money supply: LM shifts right Output, Y Real interest rate, r IS LMโ‚ LMโ‚‚ Eโ‚ Eโ‚‚ Yโ‚ Yโ‚‚ rโ‚ rโ‚‚ rL Liquidity effect: r falls on impact Income effect: Y rises, r partly recovers

Figure: Monetary expansion shifts LM right. The immediate liquidity effect pushes the interest rate down; then stronger output raises money demand, so the interest rate partially recovers as the economy moves to the new equilibrium with higher Y and lower r than initially.

Further Resources