A liquidity trap arises when nominal interest rates are extremely low or at zero, rendering monetary policy ineffective. In this situation, individuals and firms hoard additional money as cash instead of investing or buying bonds, anticipating that future interest rate increases will lower bond prices. The demand for money thus becomes perfectly elastic, making the LM curve horizontal.

Fiscal Policy in the Liquidity Trap (Horizontal LM):
When the LM curve is horizontal, any increase in the money supply is absorbed into idle balances, leaving interest rates unchanged. Hence, monetary policy fails to stimulate demand. However, fiscal policy is fully effective. An expansionary fiscal policy—through higher government spending or tax cuts—shifts the IS curve rightward. The new intersection with the flat LM curve occurs at a higher level of income without changing interest rates. Since there is no crowding out of private investment, the fiscal multiplier operates at full strength, making fiscal expansion highly potent.

Monetary Policy in the Classical Range (Vertical LM):
At the other extreme, when the LM curve is vertical, money demand is perfectly inelastic to interest rates, usually at very high interest levels. Here, monetary policy is fully effective. An increase in money supply shifts the LM curve rightward, lowering interest rates and stimulating investment. Through the multiplier effect, national income rises significantly. By contrast, fiscal policy in this range is ineffective: an IS shift rightward raises interest rates, fully crowding out private investment, leaving output largely unchanged.

Graphical Illustration:

• In the liquidity trap, fiscal expansion shifts IS rightward along a flat LM, raising output without affecting interest rates.
   
• In the classical range, monetary expansion shifts LM rightward, reducing interest rates and increasing output, while fiscal expansion only raises interest rates.