How Banks Create Money

Chapter 14

Chapter 14 Table 14.1

Chapter 14 Figure 14.1

How checks clear

Chapter 14 Table 14.2

Bank Lending and Deposit Expansion

The Money Multiplier Formula

Initial Deposit, increases both required and excess reserves = D0 = D0(R) + D0(1- R)

The excess reserves are loaned out by the first bank and become deposits in the second bank.

L1 = D0(1- R)The loaned amount is deposited and then

part is loaned again, and again, and again.L2 = L1(1- R)L3 = L2(1- R), etc.

Derivation of the Money Multiplier∆M = L1 + L2 + L3 + … + Ln + … ∆M = (1-R)D0 + (1-R)L1 + (1-R)L2 + …

+ Ln + … ∆M = (1-R)D0 + (1-R)2D0 + (1-R)3D0 +

… + (1-R)nD0 + … ∆M = (1-R)0L0 + (1-R)1L0 + (1-R)2L0 +

(1-R)3L0 + … + (1-R)nL0 + …

Derivation of the Money Multiplier∆M = (1-R)0L0 + (1-R)1L0 + (1-R)2L0 + (1-

R)3L0 + … + (1-R)nL0 + … ∆M = ∑i=0,∞(1-R)nL0 = L0∑i=0,∞(1-R)n

for infinite convergent sums,m = ∆M/L0 = 1/R

R < 1 necessary for infinite sum to converge

m becomes bigger as R becomes smaller

Deposit Expansion and the Multiplier

Given the required reserve ratio RAssume zero excess reserves And all funds loaned are redeposited in

the banking systemNone are held as idle cashAll banks make the maximum amount of

loans permitted by lawM = 1/RRepresents an upper limit which the

financial system cannot exceed

Deposit Expansion in Reality

Numerous leakages existNot all borrowers spend or deposit

all loaned fundsBanks hold excess reservesGiven the effective reserve ratioRE > RDefine the Effective Money MultiplierME = 1/RE < M

Chapter 14 Figure 14.2