1. Money Supply Money Demand & Money Market Equilibrium Lecture 17
Jennifer P. Wissink
©2019 Jennifer P. Wissink, all rights reserved.
March 25, 2019 1 1

2. The Money Multiplier
So: The money multiplier is the multiple by which demand deposits can increase for every dollar increase in reserves.
In our examples the required reserve ratio is 20%.
Each dollar increase in reserves caused an increase in deposits of $5.
An additional $100 of reserves resulted in additional demand deposits of $500.
Note: We assumed there were no leakages out of the system.
What if there were leakages?
So:
Remember:
Demand deposits increased by $500.
But in this example, M1 only increased by $400.

3. How the Fed Controls the Money Supply
Via actions that change banks’ reserves – particularly excess reserves - which in turn change demand deposits, which in turn change the money supply.
Three tools are available to the Fed for changing the money supply:
changing the required reserve ratio(rrr)
See hidden slides for details
changing the discount rate(dr)
engaging in open market operations(OMO)
Open market operations are when the Fed purchases(buys) or sells government securities in the open market from or to the public.
Open market operations are by far and away the most significant tool of the Fed for controlling the supply of money.
The Fed monitors and impacts the Federal Funds Rate via its OMO.

4. The Federal Funds Rate & OMO
The Federal Reserve Act specifies that the Federal Open Market Committee (FOMC) should seek "to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates."
At each meeting, the FOMC closely examines a number of indicators of current and prospective economic developments. Then, cognizant that its actions affect economic activity with a lag, it must decide whether to alter the federal funds rate.
By trading government securities at the direction of the FOMC, the New York Fed affects the money supply and federal funds rate, which is the interest rate at which depository institutions lend balances to each other overnight.
The FOMC establishes a target rate for trading in the federal funds market.
A decrease in the federal funds interest rate stimulates economic growth.
An increase in the federal funds interest rate will curb economic growth.

5. source: https://research.stlouisfed.org/fred2/

6. Open Market Operations
An open market purchase(buy) by the Fed of securities from the public results in an increase in reserves and an increase in the money supply by an amount equal to the money multiplier times the change in reserves.
An open market sale by the Fed of securities to the public results in a decrease in reserves and a decrease in the money supply by an amount equal to the money multiplier times the change in reserves.
Open market operations are the Fed’s preferred means of controlling the money supply because
they can be used with some precision
are extremely flexible
are fairly predictable.

7. An OMO: The Fed Sells Government Securities to the Public to Ms
Suppose the rrr = 20%
Suppose the Fed sells $5 in securities to the public, namely to Jane Smith.
a loss of Reserves of $5 (since Jane pays for them w/DDJane)
so Reserves = -$5
Note: with rrr = 20% the K$ = 5
An OMO sale of $5 in securities to Jane Smith leads to a decrease in the money supply of $25.
In this case, M1 = DDP = (K$)(Reserves)
Plugging in you get: -$25 = (5)( -$5)

8. An OMO Sale to Ms , with rrr=20%
The Numbers in Parentheses in Panels 2 and 3 Show the Differences Between Those Panels and Panel 1. All Figures in Billions of Dollars
PANEL 1: the initial situation
Federal Reserve
All Commercial Banks
Jane Q. Public
Assets
Liabilities
Securities
$100
$20
Reserves
Deposits
DDJane $5 $0
Debts
$80
Currency
Loans
SecuritiesJane
Net Worth
Note: Money supply (M1) = Currency + Deposits = $180.
PANEL 2: right after The Fed sells $5 of securities to Jane
Federal Reserve
All Commercial Banks
Jane Q. Public
Assets
Liabilities
Securities (- $5)
$95
$15
Reserves (- $5)
Deposits (- $5)
DDJane (- $5) $0
Debts
$80
Currency
Loans
Securities (+ $5) $5
Net Worth
Note: Money supply (M1) = Currency + Deposits = $175.
PANEL 3: after the Commercial Banks get “right” again
Federal Reserve
All Commercial Banks
Jane Q. Public
Assets
Liabilities
Securities (- $5)
$95
$15
Reserves (- $5)
$75
Deposits (- $25)
DDJane (- $5) $0
Debts
$80
Currency
Loans (- $20)
$60
Securities (+ $5) $5
Net Worth
Note: Money supply (M1) = Currency + Deposits = $155.

9. An OMO Purchase by The Fed to Ms
Suppose rrr=20%  K$ = 5
Suppose the Fed buys $70 in securities from Fred McCash.
The money supply will increase by $350.
Note: M1=DDP=(K$)(Reserves)
The $70 purchase increases reserves by $70
Plugging into M1  $350 = (5)($70)

10. Can You Do An OMO Purchase To Ms?
PANEL 1
Federal Reserve
All Commercial Banks
Fred McCash
Assets
Liabilities
Securities
$100
$20
Reserves
Deposits
DDFred $5
$70
Debts
$80
Currency
Loans
$75
$10
Net Worth
PANEL 2
Fred Z. Public
PANEL 3

11. The Money Market Money Supply (MS) Money Demand (MD)
Totally determined by The Fed.
So… a vertical line in our graphs.
What we were calling M1.
Now it’s MS.
Money Demand (MD)
Will make more interesting.
Determined by households’ desires to hold assets as money rather than interest bearing bonds.
Look at motives for holding money, rather than bonds.

12. The Demand Function for Money
Simple model that asks: What determines how much of a person’s assets/wealth will be held as non-interest earning balances, i.e., money?
Note, a households assets include:
money balances
0 interest and perfectly liquid
bonds/securities
+ interest and imperfectly liquid
claims on real capital (physical assets)
most of the time we will ignore this 3rd category

13. Bond Price and Interest Rate
Suppose I, Jennifer P. Wissink, offer to sell you a bond/security/promissory note where I promise to give you $1,000 in exactly two years from today assuming…
No inflation.
No risk!
What would you be willing to pay me (ok, loan me) for this promise?
What “price” would you pay?

14. Bond Prices and the Interest Rate
What is $1,000 in T=2 years from today worth today if r = 4% = .04?
Ask yourself…, how much would you have to put in the bank today ($PV) to have a balance or future value ($FV) of $1,000 two years from today given r = 4%?
After one year you would have ($PV + $PV∙r)
After two years you would have $FV = ($PV + $PV∙r) + ($PV + $PV∙r)∙r
$FV = $PV + $PV∙r + $PV∙r + $PV∙r2
$FV = $PV(1+2r+r2) = $PV(1+r)2
Solving for the present value ($PV) you get:
So the present value ($PV) of $1,000 in 2 years at r = 4% is: ($1,000)/(1.04)2 = $924.56
The General Formula for the $PV of $X in T periods at interest rate r is
$PV = $𝑋 (1+𝑟) 𝑇

15. i>clicker questions
So…
Suppose the interest rate r increases, holding everything else the same. The $PV of the promise to get $X = $1,000 in two years would now
increase.
decrease.
stay the same.
Suppose the interest rate stays at 4% = .04 but now you have to wait until 4 years to get the $1,000 - holding everything else the same.
The $PV of the promise would
increase.
decrease.
stay the same.

16. Bond Prices and the Interest Rate
So there is an inverse relationship between bond prices ($PB) and the market interest rate (r).
If r , then $PB 
If r , then $PB 