Using the simple money multiplier {excess of reserves x (1/r)}, calculate the total change in the money supply resulting from a $1,000 initial deposit with a 10% reserve requirement.
To calculate the total change in the money supply using the simple money multiplier, you'll need to follow these steps:
Step 1: Determine the excess reserves.
Excess reserves are calculated as the difference between the total reserves and the required reserves. Required reserves are derived from the reserve requirement ratio.
Given that the initial deposit is $1,000, and the reserve requirement is 10%, the required reserves can be calculated as:
Required reserves = Initial deposit x Reserve requirement ratio
Required reserves = $1,000 x 0.10 = $100
Excess reserves = Initial deposit - Required reserves
Excess reserves = $1,000 - $100 = $900
Step 2: Determine the money multiplier.
The money multiplier is calculated as the inverse of the reserve requirement ratio. In this case, the reserve requirement ratio is 0.10, so the money multiplier becomes:
Money multiplier = 1 / Reserve requirement ratio
Money multiplier = 1 / 0.10 = 10
Step 3: Calculate the total change in the money supply.
The total change in the money supply is given by the formula:
Total change in money supply = Excess reserves x Money multiplier
Total change in money supply = $900 x 10 = $9,000
Therefore, the total change in the money supply resulting from a $1,000 initial deposit with a 10% reserve requirement is $9,000.