# Chapter 14 Determinants of the Money Supply The

Chapter 14 Determinants of the Money Supply The Money Supply Model Define money as currency plus checkable deposits: M1 The Fed can control the monetary base better than it can control reserves Link the money supply (M) to the monetary base (MB) and let m be the money multiplier

M =m MB Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-2 Deriving the Money Multiplier I Assume the desired level of currency C and excess reserves ER grows proportionally with checkable deposits D Then c = {C / D} = currency ratio e = {ER / D} = excess reserves ratio

Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-3 Deriving the Money Multiplier II The total amount of reserves (R) equals the sum of required reserves (RR) and excess reserves (ER). R = RR + ER The total amount of required reserves equals the required reserve ratio times the amount of checkable deposits RR = r ? D

Subsituting for RR in the first equation R = (r ? D) + ER The Fed sets r to less than 1 Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-4 Deriving the Money Multiplier III The monetary base MB equals currency (C) plus reserves ( R) MB = R + C = (r D)+ ER + C R evealsthe am ount of the m onetary base needed to support

the existing am ountsof checkable deposits, currency, and excessreserves. An increase in the m onetary base that goesinto currency is not m ultiplied, whereasan increase that goesinto supporting depositsism ultiplied. An additionaldollarof MB that goesinto excessreservesER doesnot support any additionaldepositsorcurrency Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-5 Deriving the Money Multiplier IV

c = {C / D} C = c D and e ={ ER / D } ER =e D Substituting in the previousequation MB =(r D )+ (e D )+ (c D ) =(r + e + c) D Divide both sidesby the term in parentheses 1 D= MB r+ e + c M = D + C and C =c D M = D + (c D ) =(1+ c) D Substituting again

1+ c M= MB r+ e + c The m oney m ultiplieristhen 1+ c m= r+ e + c Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-6

Intuition Behind the Money Multiplier r =required reserve ratio =0.10 C =currency in circulation =\$400B D =checkable deposits=\$800B ER =excessreserves=\$0.8B M =m oney supply (M1) =C + D =\$1,200B \$400 B =0.5 \$800 B \$0.8 B e= =0.001

\$800 B 1+ 0.5 1.5 m= = =2.5 0.1+ 0.001+ 0.5 0.601 Thisislessthan the sim ple deposit m ultiplier Although there ism ultiple expansion of deposits, there isno such expansion forcurrency c=

Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-7 Factors that Determine the Money Multiplier Changes in the required reserve ratio r The money multiplier and the money supply are negatively related to r

Changes in the currency ratio c The money multiplier and the money supply are negatively related to c Changes in the excess reserves ratio e The money multiplier and the money supply are negatively related to the excess reserves ratio e

Copyright 2007 Pearson Addison-Wesley. All rights reserved. 14-8 Factors that Determine the Money Multiplier (contd) The excess reserves ratio e is negatively related to the market interest rate The excess reserves ratio e is positively related to expected deposit outflows

borrowing by banks from the Fed Split the monetary base into two components MBn= MB - BR M = m(MBn + BR) The money supply is positively related to both the non-borrowed monetary base MBn and to the level of borrowed reserves, BR, from the Fed Copyright 2007 Pearson Addison-Wesley. All rights reserved.