Notes on Determining the Interest Rate and Money Supply

Overview of Money Supply and Interest Rate Determination

• Financial markets depend on the equilibrium between money supply and money demand.
• There are two types of money in the economy:
  • Currency - supplied by the central bank
  • Checkable deposits - supplied by banks (not considered in simple initial models).

Key Concepts

• Money Demand and Supply

  • Demand for money is affected by:
  • Level of transactions in the economy
  • Interest rate (higher rates reduce demand for money).
  • Supply of money is usually determined by the central bank (Ms = M).

• Equilibrium Condition:

  • The LM Relation:
  • M = Y imes L(i)
  • Where:
    • Y is the nominal income
    • L(i) shows the demand for liquidity which depends on interest rate.

Graphical Representation

• Demand for money (Md) is downward sloping (higher interest rate leads to lower demand).
• Supply of money (M) is a vertical line, independent of the interest rate.
• Equilibrium is established where demand meets supply (intersects at point A).

Effects of Changes in Nominal Income and Money Supply

• Increase in Nominal Income:

  • Demand for money increases.
  • Md shifts right (from Md to Md').
  • Equilibrium moves from A to A', interest rate rises from i to i'.

• Increase in Money Supply:

  • Money supply shifts from M to M'.
  • Equilibrium moves down from A to A', interest rate decreases from i to i'.

Open Market Operations

• Expansionary Operations:

  • Central bank buys bonds, injecting money into the economy -> increases money supply.
  • Price of bonds goes up, interest rates go down.

• Contractionary Operations:

  • Central bank sells bonds, reduces money supply leading to higher interest rates.

Balance Sheets and Central Bank Operations

• Balance Sheet of Central Bank:
  • Assets: Bonds held
  • Liabilities: Total money issued in the economy.

Interest Rates in the Context of Bonds

• Bond price inversely relates to interest rate:
  • i = \frac{100 - PB}{PB}
  • Higher bond prices -> lower interest rates.

Interaction Between Money Supply, Demand, and Interest Rates

• The Federal Reserve controls money supply to maintain desired interest rates.
  • Changes to money supply impact interest rates directly.

Money Multiplier Concept

• Overall money supply increases with central bank money by a multiplier effect.
  • \text{Overall Money Supply} = \text{Central Bank Money} \times \text{Multiplier}
  • A change in central bank money can lead to greater changes in overall money supply due to the banking system.

Conclusion

• Interest rates are dictated by the balancing act of money supply and demand. The interplay of bank reserves, currency demand, and central bank actions shape economic stability. Understanding this relationship is crucial for grasping monetary policies and economic fluctuations.