To understand why an increase in the money supply leads to a fall in the interest rate when the LM curve is vertical, we need to delve into the basics of the IS-LM model in economics.

Understanding the LM Curve

The LM curve represents the relationship between the real interest rate and the level of real income (or output) that equates the money market. It is derived from the liquidity preference and the money supply.

In the money market, the interest rate balances the demand for money (liquidity preference) with the supply of money:

• The liquidity preference relates to people’s demand for cash or liquid assets.
• A higher interest rate increases the opportunity cost of holding money, thereby reducing the liquidity preference.
• The money supply is usually controlled by the central or federal bank.

Vertical LM Curve

The LM curve is vertical when the demand for money is completely inelastic to changes in the interest rate. This situation typically arises at very high levels of interest rates where further increases do not reduce the demand for money any further.

Effect of Increased Money Supply

If the central bank increases the money supply while the LM curve is vertical:

• The additional money supply will not affect the level of income as it is determined by fiscal policy in the IS curve.
• Instead, the excess supply of money causes the interest rate to fall as economic agents adjust their portfolios from excess cash balances to bonds or other interest-bearing assets.

Conclusion

Therefore, when the LM curve is vertical, an increase in the money supply leads to a fall in the interest rate, making the first option ("Fall in interest rate") correct. This is because excess money supply lowers interest rates until people are willing to hold any excess liquidity.