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 e = the desired excess reserve ratio ERu = Undesired excess reserves [=TR-RR-ER*] 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* 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.”

Who Determines changes in the Money Supply? We can also write this as: M1 = [(1+c)/(c+rrD+e)] • MB The Fed can change TR. The Fed could change C. The Fed can change rrD. Banks determine e. The public determines c.

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 = ER* = ERu = Loans Demand Deposits rrD=20% e = 0 M1

Money Creation: Getting to Equilibrium Assets Liabilities & Equity Reserves RR = ERu = Loans Demand Deposits rrD=20% e = 0 M1

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+ 𝑟𝑟 𝐷 +𝑒 M1 = [m*] • ERu D = [1/(1+c)] • M1 C = c • D TR = -C Loans = M1 = D + C

Money Creation Problem

Money Creation Problem .10 m* = 1/.10 = 10 8,000 What happened to C? What happened to MB? 7,000 +70,000 10*7,000 +70,000 1*70,000 0*70,000 -(0) +70,000 C+D MS changed from $80,000 to $150,000 15,000 150,000 15,000 +135,000

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

Appendix – Deriving m* MB = C + TR = C + RR + ER* in equilibrium MB = c •D + rrD•D + e •D = (c+rrD+e) •D Rearrange and solve for D = [1/ (c+rrD+e)]*MB M1 = C + D = c •D + D = (1+c) •D Substitute in formula for D into M1 to get: M1 = [(1+c)/(c+rrD+e)] • MB