Question

Consider two countries: North and South. In South, banks are required to hold 100% of their deposits as reserves. In North, the required reserve ratio is 50%. Banks do not hold excess reserves in North or in South. No cash is held by the public in South, while in North, citizens hold $500,000 in cash. Each country has $1 million in bank reserves. Residents buy goods and services and do their banking only in their own country. Neither country has any traveler’s checks.

a. What is M1 in each country? What is the money multiplier in each country?Explain, and show your work.

b. If Conrad makes a cash deposit of $1,500 in his bank in North, what will be the total change in North’s money supply, assuming no other changes in cash held by the public in North? Also assume banks in North still hold no excess reserves.Show your work.

Answer 1

(a) Since no bank keeps requires reserves, the reserve held by banks in each case are required reserves.

(1) M1 = Currency with public + Deposits at bank

(i) North: Reserve ratio = 50%

Bank deposits = Reserves / Reserve ratio = $1,000,000 / 0.5 = $2,000,000

M1 ($) = 500,000 + 2,000,000 = 2,500,000

(ii) South: Reserve ratio = 50%

Bank deposits = Reserves / Reserve ratio = $1,000,000 / 1 = $1,000,000

M1 ($) = 0 + 1,000,000 = 1,000,000

(2) Money multiplier (MM) = (1 + Currency deposit ratio) / (Currency deposit ratio + Required reserve ratio)

(i) North: Reserve ratio = 50%, Currency deposit ratio = Currency / Deposits = $500,000 / $2,000,000 = 0.25

MM = (1 + 0.25) / (0.25 + 0.5) = 1.25 / 0.75 = 1.67

(ii) South: Reserve ratio = 100%, Currency deposit ratio = Currency / Deposits = $0 / $1,000,000 = 0

MM = (1 + 0) / (0 + 1) = 1 / 1 = 1

(b)

In North,

Change in money supply = Change in deposit x MM_North = $1,500 x 1.67 = $2,500 (increase by $2,500)