Question

Suppose that currency in circulation is $ 500 billion, the amount of checkable deposits is $ 800 billion, and excess reserves are $ 20 billion. Required reserve ratio is also 15% (rr=0.15). Suppose the central bank conducts an unusually large open market purchase of bonds (from the banks) of $ 1400 billion. Banks choose to hold all of these proceeds as excess reserves rather than loan them out, due to fear of a financial crisis. Calculate the money supply, money multiplier and the base money after the open market operation.

Answer 1

Initial money supply (MS) ($B) = Currency + Checkable deposits = 500 + 800 = 1300

rr = 0.15

cr = Currency / Deposit = 500/800 = 0.625

er = Excess reserves / Deposit = 20/800 = 0.025

Money multiplier (MM) = (1 + cr) / (cr + rr + er) = (1 + 0.625) / (0.625 + 0.15 + 0.025) = 1.625 / 0.8 = 2.03

Initial base money (MB) ($B) = Currency + Total reserves = 500 + (800 x 0.15) + 20 = 520 + 120 = 640

After bond purchase,

New MB ($B) = 640 + 1400 = 2040

MM = 2.03

Increase in MS ($B) = Open market purchase x MM = 1400 x 2.03 = 2842

New MS ($B) = 1300 + 2842 = 4142