Worked example 1
A central bank cuts its policy rate from 5% to 3% during a recession (Y < Yf, unemployment 9%).
(a) Trace the transmission mechanism to AD. (b) Show the effect on P and Y using AD–AS. (c) Give two reasons why the cut might be ineffective.
Show solution outline
(a) Transmission mechanism Rate 5% → 3% → mortgage and loan costs fall → C rises; firms' borrowing costs fall → I rises; lower r attracts less foreign capital → currency depreciates → (X−M) rises → AD shifts right.
(b) AD–AS effect Draw AD₁ → AD₂ (rightward shift). New equilibrium: Y rises (toward Yf), P rises slightly. Recessionary gap narrows; unemployment falls.
(c) Ineffectiveness
- Liquidity trap / confidence: firms won't invest despite low r if demand expectations are pessimistic (I inelastic).
- Time lags: 18–24 months before full impact — recession may deepen before policy bites.