Question

Assume the banking system has $200 billion in reserves, that required reserves are 5% of checking deposits, that banks hold no excess reserves, and that households hold no currency.

1) What is the money multiplier?

2) What is the money supply?

3) Assume the Fed increases the required reserves to 10% of deposits. What are the changes in reserves and in the money supply?

Answer 1

1.

Money multiplier = MM

Required reserve ratio = rrr

MM = 1/rrr

        = 1/5%

        = 1/0.05

        = 20 (Answer)

2.

Checking deposit = Reserves / rrr

                              = 200 / 5%

                              = 200 / 0.05

                              = 4,000

Money supply = M

M = Checking deposit × MM

    = 4,000 × 20

    = $80,000 billion (Answer)

3.

Increase in rrr = 10% - 5% = 5%

Increase in reserve = Checking deposit × Increase in rrr

                                = 4,000 × 5%

                                = $200 billion (Answer)

New total reserve = Checking deposit × New rrr

                              = 4,000 × 10%

                              = 400

New MM = 1/new rrr

                  = 1/10%

                  = 1/0.10

                  = 10

New money supply = Checking deposit × New MM

                                    = 4,000 × 10

                                    = $40,000 billion

Decrease in money supply = M – New money supply

                                                = 80,000 – 40,000

                                                = $40,000 billion (Answer)