Open Market Operations and Money Multiplier

Open Market Operations and Money Supply

Scenario: Central Bank Bond Purchase

  • Initial Action: The central bank buys 100 worth of bonds on the open market.
  • Assumptions:
    • Required reserve ratio is 10% (0.10).
    • Banks hold no excess reserves.
    • There are no cash leakages (i.e., all money is redeposited in banks).

Money Multiplier Effect

  • Money Multiplier Formula: The money multiplier (m) is calculated as the reciprocal of the required reserve ratio (rr):
    m = \frac{1}{rr}
  • Calculation: In this case, with a 10% reserve ratio:
    m = \frac{1}{0.10} = 10

Impact on Reserves, Demand Deposits, and Loans

  • Reserves: The initial purchase of 100 worth of bonds directly increases the reserves of the banking system by 100.
  • Demand Deposits: With a money multiplier of 10, the 100 increase in reserves leads to a 1,000 increase in demand deposits.
    \Delta Deposits = m \times \Delta Reserves = 10 \times $100 = $1,000
  • Loans: The increase in loans is the difference between the increase in demand deposits and the increase in reserves. In other words, it is the amount of new money created through lending.
    \Delta Loans = \Delta Deposits - \Delta Reserves = $1,000 - $100 = $900

Summary of Changes

  • Reserves increase by 100.
  • Demand deposits increase by 1,000.
  • Loans increase by 900.

Simultaneous Shifts in Supply and Demand

Market Dynamics

  • Consider a market where both the demand for and the supply of a good increase simultaneously.