44 addional factors aecng the money supply recall

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Unformatted text preview: (r × D) + ER + C becomes MB = C. •  Thus, a $1 increase in MB that is held as currency (e.g. open market sale with cash payment) does not get mul<plied: currency does not par<cipate in the process of mul<ple deposit crea<on, since it is not deposited. 30 Deriving the Money Mul<plier •  Conclusion: While an increase in MB that flows into deposits is mul<plied, excess reserves and currency do not par<cipate in the process of mul<ple deposit crea<on. 31 Deriving the Money Mul<plier •  Recall that Currency ra<o: c = C / D ⇒ C = c × D Excess reserve ra<o: e = ER / D ⇒ ER = e × D •  MB = (r × D) + ER + C becomes MB = (r × D) + (e × D) + (c × D) = (r + e + c) × D •  Dividing both sides by (r + e + c), we get = (+ +) 32 Deriving the Money Mul<plier •  Define the money supply as currency plus checkable deposits, M = C + D (same as M1). •  We know C = c × D and = (+ +) •  Thus, M = c × D + D = (1 + c) D = + (+ +) = + (+ +) Money Mul<plier 33 Numerical Example of the Money Mul<plier •  Suppose we have the following informa<on: r = required reserve ra<o = 0.10 C = currency in circula<on = $400 D = checkable deposits = $800 ER = excess reserves = $0.8 M = money supply (M1) = C + D = $1,200 •  We want to calculate the money mul<plier m. •  Currency ra<o? c = C / D = $400 / $800 = 0.5 •  Excess reserve ra<o e? e = ER / D = $0.8 / $800 = 0.001 34 Numerical Example of the Money Mul<plier •  Given r = 0.1, c = 0.5 and e = 0.001, the resul<ng value of the money mul<plier is + +. = ++ = .+. +. . •  Recall the simple deposit mul<plier 1/r. –  Money mul<plier, m = 2.5 –  Simple deposit mul<plier, 1/r = 10 •  No<ce that the money mul<plier is much smaller than the simple deposit mul<plier. 35 Intui<on Behind the Money Mul<plier •  If some por<on of the increase in the monetary base finds its way into currency, this por<on does not undergo mul<ple deposit expansion. •  In the simple model of deposit crea<on, however, we do not allow for excess reserves...
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