The Mechanics of Money: ECO 473 - Money & Banking - Dr. D. Foster

The Banking System Reserves (Cash in vault) Assets Liabilities & Equity +$10,000 +$2,000 Reserves (Cash in vault) T-Bills (Liquidity & income) Loans (Banks’ earnings) Demand Deposits (Checking; Transaction) Equity +$10,000 +$8,000 Accounting Identity: A  L + E M1 +$8,000

The Federal Reserve determines rrD. Grinding it out: Terms TR = Total Reserves = RR + ER RR = Required Reserves rrD = required reserve ratio ER = Excess Reserves = ER* + ERu ER* = Desired excess reserves ERu = Undesired excess reserves e = the desired excess reserve ratio The Federal Reserve determines rrD. Banks determine e.

The public determines c. Grinding it out: Terms D = (Demand) Deposits C = Currency in circulation c = desired currency ratio MB = Monetary Base = C + TR M1 = Money Supply = C + D Δ = “Change In …” The public determines c.

Deriving RR, ER* and C RR = Required Reserves = rrD•D ER* = Desired Excess Reserves = e •D C = Desired Currency Holdings = c •D Can the ratio (rr) be greater than one? Can required reserves be negative? Why would a bank desire to hold excess reserves? How is it that undesired excess reserves can be negative? Explain what it means if “c” is 0.5 versus if it is 10. What would such a difference tell you about the financial system?

where m* is the “money multiplier.” From Reserves to Money Referring to M1 and MB, with some substitution and rearrangement, we can derive this equilibrium condition: 𝑀1= 1+𝑐 𝑐+ 𝑟𝑟 𝐷 +𝑒 ∙𝑀𝐵= 𝑚 ∗ ∙𝑀𝐵 where m* is the “money multiplier.” When the banking system is not in equilibrium, we can write this out as: ∆𝑀1= 1+𝑐 𝑐+ 𝑟𝑟 𝐷 +𝑒 ∙ 𝐸𝑅 𝑢

Money Creation: Getting to Equilibrium Assets Liabilities & Equity Reserves RR = ERu = Loans Demand Deposits +$10,000 +$2,000 rrD=20% e = 0 +$2,000 +$10,000 +$8,000 +$8,000 +$8,000 M1 -$10,000

Money Creation: Getting to Equilibrium Assets Liabilities & Equity Reserves RR = ERu = Loans Demand Deposits +$2,000 +$10,000 +$8,000 +$1,600 rrD=20% e = 0 +$1,600 +$2,000 +$8,000 +$10,000 +$8,000 +$6,400 +$8,000 +$6,400 +$8,000 M1 +$6,400 -$10,000

Money Creation: Getting to Equilibrium Assets Liabilities & Equity Reserves RR = ERu = Loans Demand Deposits +$1,600 +$2,000 +$1,280 +$6,400 +$8,000 +$10,000 rrD=20% e = 0 +$2,000 +$1,600 +$1,280 +$10,000 +$6,400 +$8,000 +$5,120 +$8,000 +$6,400 +$8,000 +$5,120 +$6,400 +$8,000 This process will continue until there are no more undesired excess reserves. M1 +$6,400 +$5,120 -$10,000 +$19,520

Arriving at Equilibrium Insure Assets = Liabilities Identify whether there are +/- ERu M1 = Loans = [m*] • ERu D = [1/(1+c)] • M1 C = c • D TR = -C Final values = Beginning values + changes

Money Creation Formulas RR = rrD*D ER* = e*D ERu = TR-RR-ER* C = c*D Money = M1 = C + D Monetary Base = MB = TR + C m* = 1+𝑐 𝑐+𝑟𝑟𝐷+𝑒 M1 = [m*] • ERu D = [1/(1+c)] • M1 C = c • D TR = -C Loans = M1 = D + C

The Mechanics of Money: ECO 473 - Money & Banking - Dr. D. Foster