Question

Suppose that the Fed increased the base money to $30,000. a. If half of the base money is held in currency and the other half in deposits, calculate the money multiplier as well as the total money supply if 80% of the deposits are used as loans and 20% are kept as reserves. b. Given the money multiplier in part (a), how much should the base money change for the money supply to rise by $10,000? Should the Fed purchase or sell bonds to achieve this change?

Answer 1

(a)

Currency (C) = Deposits (D) = $30,000 x 50% = $15,000

Currency-deposit ratio (c) = C/D = $15,000/$15,000 = 1

Reserves (R) = D x 20% = $15,000 x 20% = $3,000

Reserve-deposit ratio (r) = R/D = $3,000 / $15,000 = 0.2

So,

Money multiplier (MM) = (1 + c) / (c + r) = (1 + 1) / (1 + 0.2) = 2 / 1.2 = 1.67

Money supply (MS) = C + D = $15,000 + $15,000 = $30,000

(b)

To increase MS, Fed has to purchase bonds.

Required increase in base money = Increase in MS / MM = $10,000 / 1.67 = $6,000