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The BaumolTobin Model


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

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)

Money holdings over the year
  • N 1

Average Y/ 2
Money holdings over the year
N 2
Y/ 2
Average Y/ 4
Money holdings over the year
N 3
Average Y/ 6
Y/ 3
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

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

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)

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 .

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
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.

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.

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

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 abroad
  • Currency held by illegal entities

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.

  • 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

  • With no banks, D 0 and M CU 1000.

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

reserves 1000
deposits 1000
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
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
SCENARIO 3 Fractional-Reserve Banking
  • Suppose the borrower deposits the 800 in
  • 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
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
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
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

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.
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

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

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

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

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

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

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

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

mm money multiplier or stock of money to the
stock of high-powered money
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

The money multiplier summarizes the total
expansion of money created from a dollar increase
in the monetary base.
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

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?

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

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

  • 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

  • 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

  •  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

  • 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
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