Define liquidity trap. Show that fiscal policy is fully effective in the horizontal part while the monetary policy is fully effective in the vertical part of the LM curve. Illustrate your answer graphically with economic reasons.

Understanding the LM Curve and its Extreme Sections

The LM (Liquidity Preference-Money Supply) curve represents the equilibrium in the money market, showing combinations of interest rates (r) and national income (Y) where the demand for money equals the supply of money. The general equation for the LM curve is M/P = L(Y, r), where M is the nominal money supply, P is the price level, and L(Y, r) is the demand for real money balances, which is positively related to income (transaction and precautionary demand) and negatively related to the interest rate (speculative demand).

The LM curve typically slopes upward, indicating that as income rises, the demand for money for transactions increases, requiring a higher interest rate to maintain money market equilibrium (by reducing speculative demand and encouraging bond-holding). However, the LM curve has two extreme segments that are critical for policy analysis:

• Horizontal Part (Liquidity Trap): This occurs at very low interest rates, often approaching zero. In this zone, the speculative demand for money becomes perfectly elastic, meaning people are willing to hold any amount of money supplied without a further fall in the interest rate. They prefer cash over bonds, expecting bond prices to fall and interest rates to rise in the future.
• Vertical Part (Classical Range): This occurs at very high interest rates. Here, the speculative demand for money is zero or perfectly inelastic. People do not wish to hold idle cash balances, and any additional money is immediately used for transactions or to buy bonds, making the demand for money primarily dependent on income, not the interest rate.

Fiscal Policy Effectiveness in the Horizontal Part of the LM Curve (Liquidity Trap)

In the horizontal segment of the LM curve, the economy is in a liquidity trap. Here, the interest rate is at its minimum possible level and cannot be reduced further by monetary policy. In this situation, fiscal policy becomes highly effective.

Economic Reasons:

• No Crowding Out: Normally, an expansionary fiscal policy (e.g., increased government spending or tax cuts) shifts the IS curve to the right, increasing aggregate demand and income. This increased income usually leads to a higher demand for money, pushing up interest rates, which then "crowds out" some private investment. However, in a liquidity trap, the interest rate is fixed at its low level (r₀). Any increase in income and the resulting higher transaction demand for money can be met by the perfectly elastic speculative demand for money without raising the interest rate.
• Full Multiplier Effect: Since there is no increase in interest rates to dampen private investment, the fiscal stimulus has its full multiplier effect on national income. Government spending directly boosts aggregate demand, leading to a significant increase in output and employment.

Graphical Illustration:

In the diagram:

• The LM curve is horizontal in the range from Y₁ to Y₂, representing the liquidity trap. The interest rate is fixed at r₀.
• Initially, the economy is in equilibrium at E₁, with income Y₁.
• An expansionary fiscal policy shifts the IS curve from IS₁ to IS₂.
• The new equilibrium is at E₂, where income increases significantly from Y₁ to Y₂, while the interest rate remains unchanged at r₀. This demonstrates the full effectiveness of fiscal policy with no crowding out.

Monetary Policy Effectiveness in the Vertical Part of the LM Curve (Classical Range)

In the vertical segment of the LM curve, which represents the classical range, the demand for money is perfectly interest inelastic. This implies that the speculative demand for money is zero, and people hold money primarily for transaction purposes. In this scenario, monetary policy is fully effective, while fiscal policy tends to be ineffective due to complete crowding out.

Economic Reasons:

• Direct Impact on Interest Rates and Investment: When the LM curve is vertical, any change in the money supply directly and significantly impacts the interest rate. An increase in the money supply (e.g., through open market operations) shifts the vertical LM curve to the right. To restore money market equilibrium, the interest rate must fall sharply.
• High Interest Sensitivity of Investment: This sharp fall in interest rates strongly stimulates investment, leading to a substantial increase in aggregate demand and national income. The demand for money is insensitive to interest rate changes, making the central bank's control over interest rates and, consequently, investment very potent.

Graphical Illustration:

In the diagram:

• The LM curve is vertical in the range from Y₁ to Y₂, indicating that the demand for money is perfectly interest inelastic.
• Initially, the economy is in equilibrium at E₁, with income Y₁ and interest rate r₁.
• An expansionary monetary policy (increase in money supply) shifts the LM curve from LM₁ to LM₂.
• The new equilibrium is at E₂, where the interest rate falls sharply from r₁ to r₂, and income increases significantly from Y₁ to Y₂. This illustrates the full effectiveness of monetary policy.
• Conversely, if an expansionary fiscal policy were applied (shifting the IS curve to the right), it would only raise the interest rate, leading to complete crowding out of private investment, with no change in the equilibrium income.