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# How Banks Create Money

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1. How Banks Create Money Chapter 14

2. Chapter 14 Table 14.1

3. Chapter 14 Figure 14.1 How checks clear

4. Chapter 14 Table 14.2 Bank Lending and Deposit Expansion

5. 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.

6. 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 + …

7. 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

8. Deposit Expansion and the Multiplier • Given the required reserve ratio R • Assume zero excess reserves • And all funds loaned are redeposited in the banking system • None are held as idle cash • All banks make the maximum amount of loans permitted by law • M = 1/R • Represents an upper limit which the financial system cannot exceed

9. Deposit Expansion in Reality • Numerous leakages exist • Not all borrowers spend or deposit all loaned funds • Banks hold excess reserves • Given the effective reserve ratio • RE > R • Define the Effective Money Multiplier • ME = 1/RE < M

10. Chapter 14 Figure 14.2