The Mechanics of Money: ECO 285 – Macroeconomics – 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 where rrD is the required reserve ratio (0 to 1), and it is fixed to the level of demand deposits (D). ER* = Desired Excess Reserves = e •D where “e” is the excess reserve ratio and is presumed to be fixed to the level of deposits (D). Note that ERu = TR – RR – ER* and may be +, 0, -. C = Desired Currency Holdings = c •D where “c” is the currency ratio and is presumed to be fixed to the level of deposits (D).

where m* is the “money multiplier.” From Reserves to Money We know that: M1 = C + D MB = C + TR = C + RR + ER* + ERu In “equilibrium” (no more money creation/destruction): ERu = 0 With some substitution and rearrangement, we get: 𝑀1= 1+𝑐 𝑐+ 𝑟𝑟 𝐷 +𝑒 ∙𝑀𝐵= 𝑚 ∗ ∙𝑀𝐵 where m* is the “money multiplier.”

From Reserves to Money When the banking system is not in equilibrium, we can write this out as: ∆𝑀1= 1+𝑐 𝑐+ 𝑟𝑟 𝐷 +𝑒 ∙ 𝐸𝑅 𝑢 When ERu is positive, banks will create more money. When ERu is negative, banks will destroy money. When ERu is zero, the banking system is in equilibrium.

Money Creation: Getting to Equilibrium With a bank holding positive ERu, they will lend these funds out, raising M1. Those funds become part of another bank’s reserves – they will keep some and lend out the rest. This will continue until ERu are zero. With a bank holding negative ERu, they will reduce their loans, lowering M1. [As loans are paid off, deposits fall.] This contraction of the money supply will continue until ERu are zero.

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

Getting to 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 Problem

Money Creation Problem .05 m* = 1/.05 = 20 4,000 11,000 MS changed from $80,000 to $300,000 +220,000 20*11,000 +220,000 1*220,000 0*220,000 -(0) +220,000 C+D 15,000 300,000 15,000 +285,000

Money Creation Problem .10 .03 .15 m* =1.15/.28 = 4.1071428 8,000 2,400 4,600 MS changed from $92,000 to $110,893 +18,893 4.107*4,600 +16,429 .8695*18,893 2,464 .15*16,429 -2,464 -(2,464) +18,893 C+D C changed from $12,000 to $14,464 12,536 96,429 9,643 2,893 83,893

The Mechanics of Money: ECO 285 – Macroeconomics – Dr. D. Foster

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