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## The BaumolTobin Model

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### Money supply (M) is linked to H via the money multiplier, mm Figure shows this relationship: ... mm = money multiplier or stock of money to the stock of high ... – PowerPoint PPT presentation

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Title: The BaumolTobin Model

1
The Baumol-Tobin Model
• A transactions theory of money demand.
• Notation
• Y total spending, done gradually over the year
• i interest rate on savings account
• N number of trips consumer makes to the bank
to withdraw money from savings account
• F cost of a trip to the bank(e.g., if a trip
takes 15 minutes and consumers wage 12/hour,
then F 3)

2
Money holdings over the year
• N 1

Average Y/ 2
3
Money holdings over the year
N 2
Y
Y/ 2
Average Y/ 4
4
Money holdings over the year
N 3
Y
Average Y/ 6
Y/ 3
5
Cost of Holding Money
• In general, average money holdings Y/2N
• Foregone interest i ?(Y/2N )
• Cost of N trips to bank F ?N
• Thus,
• Given Y, i, and F, consumer chooses N to
minimize total cost

6
Finding the cost-minimizing N
7
Cost of Holding Money
• Set holding and transaction costs equal to each
other
• i ?(Y/2N ) F ?N
• Thus,

8
Transaction Demand
• In general
• Starting income of Y
• n trips to the bank
• ? The average cash balance is
• Each trips costs tc
• ? The combined cost of trips plus forgone
interest is
• Choose n to minimize costs and compute the
average money holdings ? Baumol-Tobin formula for
the demand for money

• (1)

9
The Money Demand Function
• The cost-minimizing value of N
• To obtain the money demand function, substitute
N into the expression for average money
holdings (Y/2N)
• Money demand depends positively on Y and F, and
negatively on i .

10
Cost of Holding Money
• If the interest rate is 5 and the cost of a trip
to the bank/ATM is Sk100, what is the number of
trips to the bank/ATM that minimizes the cost of
holding money if your total yearly spending is
Sk1.000.000? What is the average money holding?

N 15.8
Sk31.623
11
Financial Innovation, Near Money, and the Demise
of the Monetary Aggregates
• Examples of financial innovation
• many checking accounts now pay interest
• very easy to buy and sell assets
• mutual funds are baskets of stocks that are easy
to redeem - just write a check
• Non-monetary assets having some of the liquidity
of money are called near money.
• Money near money are close substitutes, and
switching from one to the other is easy.

12
Financial Innovation, Near Money, and the Demise
of the Monetary Aggregates
• The rise of near money makes money demand less
stable and complicates monetary policy.
• 1993 the Fed switched from targeting monetary
aggregates to targeting the Federal Funds rate.
• This change may help explain why the U.S. economy
was so stable during the rest of the 1990s.

13
Money in the Economy
• Currency is the paper bills and coins in the
hands of the public.
• Demand deposits are balances in bank accounts
that depositors can access on demand by writing a
check.

14
CASE STUDY Where Is All The Currency?
• In 2005 there was about 4,596 in currency per
adult, half of which is in 100 notes.
• Who is holding all this currency?
• Currency held by illegal entities

15
Banks role in the money supply
• The money supply equals currency plus demand
(checking account) deposits
• M CU D
• Since the money supply includes demand deposits,
the banking system plays an important role.

16
Preliminaries
• Reserves (R ) the portion of deposits that
banks have not lent.
• To a bank, liabilities include deposits,
• assets include reserves and outstanding loans
• 100-percent-reserve banking a system in which
banks hold all deposits as reserves.
• Fractional-reserve banking a system in which
banks hold a fraction of their deposits as
reserves.

17
SCENARIO 1 No Banks
• With no banks, D 0 and M CU 1000.

18
SCENARIO 2 100 Percent Reserve Banking
• Initially CU 1000, D 0, M 1000.
• Now suppose households deposit the 1000 at
Firstbank.
• After the deposit, CU 0, D 1000,
M 1000.
• 100 Reserve Banking has no impact on size of
money supply.

reserves 1000
deposits 1000
19
SCENARIO 3 Fractional-Reserve Banking
• Suppose banks hold 20 of deposits in reserve,
making loans with the rest.
• Firstbank will make 800 in loans.
• The money supply now equals 1800
• The depositor still has 1000 in demand deposits,
• but now the borrower holds 800 in currency.

deposits 1000
reserves 1000
reserves 200 loans 800
20
SCENARIO 3 Fractional-Reserve Banking
Thus, in a fractional-reserve banking system,
banks create money.
• The money supply now equals 1800
• The depositor still has 1000 in demand deposits,
• but now the borrower holds 800 in currency.

deposits 1000
reserves 200 loans 800
21
SCENARIO 3 Fractional-Reserve Banking
• Suppose the borrower deposits the 800 in
Secondbank.
• Initially, Secondbanks balance sheet is
• But then Secondbank will loan 80 of this deposit
• and its balance sheet will look like this

deposits 800
reserves 800 loans 0
reserves 160 loans 640
22
SCENARIO 3 Fractional-Reserve Banking
• If this 640 is eventually deposited in Thirdbank,
• then Thirdbank will keep 20 of it in reserve,
and loan the rest out

deposits 640
reserves 640 loans 0
reserves 128 loans 512
23
Finding the total amount of money
• Original deposit 1000
• Firstbank lending 800
• Secondbank lending 640
• Thirdbank lending 512
• other lending

Total money supply (1/re ) ? 1000 where re
ratio of reserves to deposits In our example,
re 0.2, so M 5000
24
Money Multiplier and Bank Loans
• Provide an alternative way of describing the
working of the multiplier by showing how
adjustments by banks and the public following an
increase in H produce a multiple expansion of M
• A Fed open market purchase increases H, and
increases bank reserves
• The bank in which the original check was
deposited has a reserve ratio that is too high
(has excess reserves) ? increase lending
• When bank makes loan, person receiving a loan
gets a bank deposit of the amount of the loan ?
money supply has increased by more than the
amount of the open market operation
• The expansion of loans (and money) continues
until the reserve-deposit ratio has fallen to the
desired level and the public has achieved its
desired currency deposit ratio

25
Money creation in the banking system
A fractional reserve banking system creates
money, but it does not create wealth bank loans
give borrowers some new money and an equal
amount of new debt.
26
Money Stock Determination
• The Fed has direct control over high powered
money (H)
• Money supply (M) is linked to H via the money
multiplier, mm ? Figure shows this relationship
• Top of figure is the money stock
• Bottom of figure is the stock of high-powered
money monetary base
• Money multiplier (mm) is the ratio of the stock
of money to the stock of high powered money ? mm
gt 1
• The larger deposits are, as a fraction of M, the
larger the multiplier

27
The Money Multiplier
• How much money is eventually created in this
economy?
• The money multiplier is the amount of money the
banking system generates with each dollar of
reserves.

28
A model of the money supply
exogenous variables
• money supply, M CU D
• the monetary base, H CU reserves
• controlled by the central bank
• the reserve-deposit ratio, re reserves/D
• depends on regulations bank policies
• the currency-deposit ratio, cu CU/D
• depends on households preferences

29
Money Stock Determination
• Money supply consists of currency, CU, plus
deposits

• (1)
• High powered money consists of currency plus
reserves

• (2)
• Summarize the behavior of the public, the banks,
and the Fed in the money supply process by three
variables
• Currency-deposit ratio
• Reserve ratio

30
Money Stock Determination
• We can rewrite equations (1) and (2) as
• and
• This allows us to express the money supply in
terms of its principal determinants, re, cu, and
H

• (3)
• where mm is the money multiplier, given by

mm money multiplier or stock of money to the
stock of high-powered money
31
Money Stock Determination
• Some observations of the money multiplier
• The money multiplier is larger the smaller the
reserve ratio, re
• The money multiplier is larger the smaller the
currency-deposit ratio, cu
• ? The smaller is cu, the smaller the proportion
of H that is being used as currency AND the
larger the proportion that is available to be
reserves

The money multiplier summarizes the total
expansion of money created from a dollar increase
in the monetary base.
32
The Reserve Ratio
• The central bank sets the required reserve ratio
the portion of each deposit commercial banks must
keep on hand
• Looking at the money multiplier shown in equation
(3), it is easy to see that the central bank can
increase the money supply by reducing the
required reserve ratio (RRR)
• The RRR is not a policy tool of choice as
reserves pay no interest, and thus are an
interest free loan from banks to the central bank
• Changes in the RRR have undesirable effects on
bank profits

33
Discussion Question
• What happens to the money supply if you take
Sk100 that you keep under your pillow and deposit
it in a bank with a reserve requirement of 10?

34
Exercise
where
• Suppose households decide to hold more of their
money as currency and less in the form of demand
deposits.
• Determine impact on money supply.
• Explain the intuition for your result.

35
Solution to exercise
• Impact of an increase in the currency-deposit
ratio ?cu gt 0.
• An increase in cu increases the denominator of
mm proportionally more than the numerator. So mm
falls, causing M to fall too.
• If households deposit less of their money, then
banks cannot make as many loans, so the banking
system will not be able to create as much
money.

36
• If the currency-deposit ratio is 23 and the
reserve ratio is 7, the size of the money
multiplier is a. 0.3b. 2.0c. 3.0d. 3.3e. 4.1

37
• If the currency-deposit ratio is 20, the reserve
ratio is 10 and the stock of high-powered money
is H 400, money supply is a. 1,000b. 1,200c.
1,600d. 2,000e. 4,000

38
•  If money supply is M 1,200, bank deposits are
D 800 and the monetary base (high-powered
money) is H 480,  a. The reserve ratio is 40
and the money multiplier is 4 b. The reserve
ratio is 40 and the money multiplier is
2.5 c. The reserve ratio is 10 and the money
multiplier is 4 d. the reserve ratio is 10 and
the money-multiplier is 2.5 e. the reserve ratio
is 10 and the money multiplier is 1.5

39
• 1. Other things remaining the same, the smaller
the currency-deposit ratio,  a. The larger the
reserve ratio b. The smaller the reserve
ratio C. The larger the money multiplier d. The
smaller the money multiplier e. The larger the
monetary base

Quiz 6 Tuesday Seminar
2. If the Fed were to abolish reserve
requirements,  a. it could no longer exert any
influence over money supply b. the size of the
money multiplier would become infinite c. The
size of the money multiplier would become
1 d. Both A and B E. None of the above
3. Which of the following functions does money
NOT serve?  a. As a unit of account b. As a
standard of deferred payment C. As a protection
against inflation d. As a store of value e. As
a medium of exchange
40
Quiz 6 Wednesday Seminar
• 1. The size of the money multiplier  a. Cannot
be influenced by actions of the Fed b. Declines
with a decrease in high-powered
money c. Decreases as the currency-deposit ratio
decreases D. Increases as the reserve ratio
decreases e. Increases as the reserve
requirement is increased

2. Over which of the following does the central
bank have the most control? a. The stock of
moneyB. The stock of bank reservesc. The amount
of excess reserves held by banksd. The size of
the money multipliere. The currency-deposit ratio
3. According to the Baumol-Tobin transaction
demand model, the amount of money balances held
should increase as a. The interest rate
increasesb. The level of income decreasesC. The
cost of money transactions increasesd. The cost
of illiquidity increasese. None of the above