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The Mechanics of Money:
ECO 285 – Macroeconomics – Dr. D. Foster
The Banking System
Reserves(Cash in vault)
T-Bills(Liquidity & income)
Loans(Banks’ earnings)
Demand Deposits (Checking; Transaction)
Equity
Assets
Liabilities & Equity
Accounting Identity: A L + E
M1
+$10,000
+$10,000
+$8,000
+$8,000
+$2,000
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.
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).
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:
where m* is the “money multiplier.”
From Reserves to Money
When the banking system is not in equilibrium, we can write this out as:
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.
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.
Money Creation:Getting to Equilibrium
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.
ReservesRR =
ERu =
Loans
Demand Deposits
Assets
Liabilities & Equity
M1
+$10,000
+$8,000
rrD=20%
-$10,000
+$10,000
+$8,000
+$2,000
+$8,000
+$2,000
Money Creation:Getting to Equilibrium
ReservesRR =
ERu =
Loans
Demand Deposits
Assets
Liabilities & Equity
M1
+$10,000
+$8,000
rrD=20%
-$10,000
+$10,000
+$8,000
+$2,000
+$8,000
+$2,000+$8,000
+$8,000
+$6,400
+$6,400
+$1,600
+$1,600
+$6,400
Money Creation:Getting to Equilibrium
ReservesRR =
ERu =
Loans
Demand Deposits
Assets
Liabilities & Equity
M1
+$10,000
+$8,000
rrD=20%
-$10,000
+$10,000
+$8,000
This process will continue until
there are no more undesired excess
reserves.
+$2,000
+$8,000
+$2,000+$8,000
+$8,000
+$6,400
+$6,400
+$1,600
+$1,600
+$6,400
+$5,120
+$6,400
+$6,400
+$5,120
+$1,280
+$5,120
+$1,280
+$19,520
Money Creation: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
Getting to Equilibrium
Money Creation Problem
rr =
e =
c =
$15,000 Deposits $80,000RRDes. ERUndes. ER
$65,000
DepositsRRDes. ERUndes. ER
Money Creation Spreadsheet Form
Loans
Change in L =
Assets LiabilitiesReserves
Change in M1 = Change in D = Change in C =
Change in TR =
Assets LiabilitiesReserves
Loans
Money Creation Problem
rr =
e =
c =
$15,000 Deposits $80,000RRDes. ERUndes. ER
$65,000
DepositsRRDes. ERUndes. ER
Money Creation Spreadsheet Form
Loans
Change in L =
Assets LiabilitiesReserves
Change in M1 = Change in D = Change in C =
Change in TR =
Assets LiabilitiesReserves
Loans
.05
0
0
4,0000
11,000
+220,000
0
0
MS changed
from $80,000
to $300,000
20*11,000
m* = 1/.05 =
20
1*220,0000*220,000
-(0)C+D
+220,00000
+220,000
300,00015,000
+285,000
15,000
Money Creation Problem
rr =
e =
c =
$15,000 Deposits $80,000RRDes. ERUndes. ER
$65,000
DepositsRRDes. ERUndes. ER
Money Creation Spreadsheet Form
Loans
Change in L =
Assets LiabilitiesReserves
Change in M1 = Change in D = Change in C =
Change in TR =
Assets LiabilitiesReserves
Loans
.10
.03
.15
8,0002,400
4,600
+18,893
2,893
0
MS changed
from $92,000
to $110,893
4.107*4,600
m* =1.15/.28 = 4.1071428
.8695*18,893.15*16,429
-(2,464)C+D
+16,4292,464
-2,464+18,893
96,42912,536
83,893
9,643
C changed
from $12,000
to $14,464
The Mechanics of Money:
ECO 285 – Macroeconomics – Dr. D. Foster
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
Appendix – Deriving m*
