You just received a bonus at your job of $4,000 which you decide to put in a che

Question

You just received a bonus at your job of $4,000 which you decide to put in a checking account at the local bank. Assume that banks lend out all excess reserves and there are no leaks in the banking system. That is, all money lent by banks gets deposited in the banking system. Round your answers to the nearest dollar.

If the reserve requirement is 18%, how much the total value of checkable deposits in the whole banking system will increase, including your original deposit?

If the reserve requirement is 7%, how much the total value of checkable deposits in the whole banking system will increase, including your original deposit?

Explanation / Answer

Resultant change in the money supply = 1/m x initial change in excess reserves.

The value of m, the required reserve ratio, is 18% or 0.18.
    The deposit of $4,000 cash adds $4,000 to the bank's reserves.
    The bank's required reserves = m x demand deposits = 0.18 x $4,000 = $720.
    To solve for excess reserves in the formula on the first line, we use Excess Reserves = Reserves - Required Reserves.
    Excess Reserves = $4,000 = $720 = $3280. Substituting the values for m and excess reserves yields:
    Resultant change in the money supply = (1/0.18) x $3280 = $18222.22

(B) The value of m, the required reserve ratio, is 7% or 0.07
    The deposit of $4,000 cash adds $4,000 to the bank's reserves.
    The bank's required reserves = m x demand deposits = 0.07 x $4,000 = $280.
    To solve for excess reserves in the formula on the first line, we use Excess Reserves = Reserves - Required Reserves.
    Excess Reserves = $4,000 = $280 = $3720. Substituting the values for m and excess reserves yields:
    Resultant change in the money supply = (1/0.07) x $3720 = $53142.86  

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